tag:blogger.com,1999:blog-79715957689280707252024-03-06T19:34:24.555-08:00The Normal GeniusDr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.comBlogger112125tag:blogger.com,1999:blog-7971595768928070725.post-1542373360299347382021-02-16T10:23:00.005-08:002021-02-23T09:55:00.819-08:00SHOULD I BOTHER TO TAKE THE ACT OR SAT?<p>FIRST CHOICE COLLEGE: "Applications do not require an ACT or SAT exam."</p><p>MOM & DAD: "So do we bother with either exam?"</p><p>TUTORING RESOURCES: "That depends...</p><p><br /></p><h2 style="text-align: center;"><span style="font-family: verdana;"> SHOULD I BOTHER TO TAKE THE ACT OR SAT?<br /></span></h2><p><span style="font-family: verdana;">More and more colleges and universities are rescinding a previous requirement to include a college entrance exam score with the admissions application. This may be a bright spot in your student's path toward moving on to the next step in education. Some students shouldn't worry about the tests and move instead on filling in other areas of their <i>curriculum vitae</i>, like leadership, grades, and non-academic talents. Here's how to decide which, if any, exam to prepare for.</span></p><p><span style="font-family: verdana;"> </span></p><h3 style="text-align: left;"><span style="font-family: verdana;">WILL THIS TEST HELP MY APPLICATION?</span></h3><p style="text-align: left;"><span style="font-family: verdana;"><span><b>EMERGING STUDENT:</b> If your student had a considerable change in grades since Freshman year, adequate ACT or SAT study could help to bolster a lackluster former performance. An exam score higher than the GPA, substantiated with an essay describing a viable reason for the positive trend and a preplanned discussion point for admissions interviews, would demonstrate the student's current intellectual commitment and status.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><b>ADVICE:</b> Begin studying for the test with at least 4 months of assessment, practice, original learning, and creating resources to use in college. The goal score for the ACT should be above 24 and for the SAT, above 1250.<br /></span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span> </span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><b>AVERAGE STUDENT:</b> If your student happily brings in C's and B's, GPA between 2.0 and 3.0, and is applying to a school that only requires an ACT of 21, it may be more constructive to invest time and resources on an activity in which the student excels. The goal of every college application is to help the student stand out from the thousands of other hopefuls. For many of us, academic work is only a fraction of our skills and talents and is frequently not what counts as success in life.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><b>ADVICE:</b> Consider a cost-benefit analysis to analyze your options, including whether the test results will be productive. If the entrance exam score would simply fall within the average range of 21 to 24 (ACT) or 1070 to 1210 (SAT) List your student's extracurricular activities and evaluate how these could contribute to the well-rounded applicant most colleges are looking for.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><br /></span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><b>HIGH ABILITY STUDENT:</b> If you are the lucky parent of a student who consistently achieves high academic grades without excessive prompting, a merely above-average score on a college entrance exam might survive only the first cut. High ability students (and their parents) quickly learn there are a lot of good students out there, each one of them representing the competition for admission. For the high-ability student, especially those with, for example, a 4.3 GPA on a 4.0 system, achieving a "nearly perfect" score can be crucial.</span></span></p><p style="text-align: left;"><b><span style="font-family: verdana;"><span>ADVICE:</span></span></b><span style="font-family: verdana;"><span><span style="font-family: verdana;"><span><b> </b> It is more difficult to raise an ACT score from 31 to 36 than it is to elevate a 21 to a 26. Same 5 points, but with an entirely different approach. High ability students study differently and need more focused preparation from a knowledgeable mentor. <br /></span></span></span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><span style="font-family: verdana;"><span>The self-motivated student should be encouraged to find their own errors, correct them, and highlight a plan to avoid similar mistakes in the future.</span></span> It is well worthwhile to engage a private tutor to guide the student through material that is new or presented in unique ways, someone who knows the test and can predict the concepts covered in the test and the ways in which understanding of the concept are tested, who has experience with retired tests and training in tailoring information to the student's learning style. For this academic approach, the homework goals should be stringent, with a maximum target of no more than 2 errors in any section of either test.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span> </span></span></p><h3 style="text-align: left;"><span style="font-family: verdana;"><span><b>OVERARCHING CONSIDERATIONS </b><br /></span></span></h3><p style="text-align: left;"><span style="font-family: verdana;"><span>1. Check out the guidance provided by your considered schools.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><span> </span>a. If no test is required, seriously examine whether the time, effort, and cost of studying for and taking the ACT or SAT is worthwhile for your student and family.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><span> </span>b. Some schools with not even LOOK AT test scores, so don't bother to send one.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><span> </span>c. If a "good" score will enhance your student's application, weigh the benefit of the school's tuition reductions and scholarships based on test score.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span>2. Assess your student's academic history and commitment to set, strive toward, and achieve a realistic goal.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span>3. Start now to work smarter, not just harder or longer. For high ability and emerging students, studying with an experienced tutor can expedite progress to achieve a realistic goal score.</span></span></p><p style="text-align: left;"><span style="font-family: verdana;"><span><br /></span></span></p><div style="text-align: left;"><span style="font-family: verdana;"><span><i>Dr. Sandi Ferguson is owner and lead tutor at TUTORING RESOURCES in Barrington, IL. TR has been guiding students through the college entrance exam experience since 1989.<a href="http://tutoring-resources.com" target="_blank">www.tutoring-resources.com</a></i><br /></span></span></div><span style="font-family: verdana;"> </span><br />Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-35435217344445399202020-08-16T14:55:00.002-07:002020-08-18T11:07:19.846-07:00HOW TO SUCCEED AS AN ONLINE STUDENT, part 2: Learning from online lecture and text<h2 style="text-align: left;">HOW TO SUCCEED AS AN ONLINE STUDENT Part 2: HOW TO LEARN FROM LECTURE AND TEXT </h2><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><span>Substituting online learning for the customary in-school lessons presents some unique challenges. Materials presented online are less personal and lack the face-to-face connection that allows teachers to assess the comprehension level of class members and provides a student the immediate gratification of asking a question and getting an instantaneous response. </span></span></span></p><p style="text-align: left;"><span style="font-family: arial;"><span style="font-size: medium;"> </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuFhirrjDtYxpfGAwiQK4Jr0aRNQChQ876iABaQ_xG__8Nr4tSPHPv7kS0J8kIsXv_fhOnbfLFPOQYZkW_mFwrbUpQBDyK55wFjTTyCl1sxbIk-3-UU3xxE5UrHJcvLcyxzXWjEUclTbFK/s550/boy-working-on-laptop-classroom-school-clipart.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="550" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuFhirrjDtYxpfGAwiQK4Jr0aRNQChQ876iABaQ_xG__8Nr4tSPHPv7kS0J8kIsXv_fhOnbfLFPOQYZkW_mFwrbUpQBDyK55wFjTTyCl1sxbIk-3-UU3xxE5UrHJcvLcyxzXWjEUclTbFK/s0/boy-working-on-laptop-classroom-school-clipart.jpg" width="245" /></a><span style="font-size: medium;">The new online role casts the student as an <span style="color: #2b00fe;">independent learner</span>, requiring techniques that are rarely innate for a college student, much less those in middle school or high school. But there are steps for navigating autonomous online learning which can be equally beneficial when school resumes and later in higher level education. While compliance with every suggestion that follows is an unreasonable expectation, each action that is applied increases the probability of success for the elearning student.</span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><br /><br /><b>STEP ONE:</b> As usual, the first step is to <span style="color: #2b00fe;">PREPARE</span>, and that starts with an effective and efficient <span style="color: #2b00fe;">work area</span>. In addition to the suggestions given in Part 1 of this series, an efficient independent study space includes a few amenities not possible in the regular classroom. An oral learner, for example, can have chewing gum or noshies at the desk, and every student should have water or similar fluid to help maintain hydration which is vital for productive brain function.<br /><br />If the teacher provides a syllabus or similar <span style="color: #2b00fe;">course content index</span>, a printed copy will serve as a ready reference throughout the semester and a casual reminder if posted at the work station on a white board or bulletin board. Similarly, a <span style="color: #2b00fe;">calendar</span> or assignment planner can formalize a study routine, and if the calendar is digital, <span style="color: #2b00fe;">notifications</span> can ensure timely follow-through on assignments. The purpose of each of these tips is to maintain assignments and due dates. If the student is required to log on at specific times to engage in an in-person format, the calendar and notifications will ensure timely entrance in the video conference.<br /><br /> <br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;">The study schedule should fit into the student’s <span style="color: #2b00fe;">daily routine</span>. Beginning the “school day” in the morning will make transition to the regular classroom easier whenever school resumes, but the flexibility of online learning offers options to accommodate the student’s preferred activity schedule. While the timetable is more pliable than an in-school agenda, variability should be kept to a minimum in order to establish a true routine. Envisioning an “ideal day” can form a template for arranging course work to include “every class/every day,” breaks, and other activities. <br /><br />To establish an appropriate environment for study, the student should <span style="color: #2b00fe;">get dressed</span> as if going to school and establish an <span style="color: #2b00fe;">end to the study day</span> to avoid becoming either obsessive or negligent.<br /></span></span></p><h4 style="text-align: left;"><span style="color: #ffa400;"><span style="font-size: medium;"><span style="font-family: arial;">IN-PERSON LECTURE VERSUS PRERECORDED FORMATS</span></span></span><br /><span style="font-size: medium;"><span style="font-family: arial;"></span></span></h4><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><b>PREPARATION:</b> The classroom teacher may set up lectures either as in-person video conferences or as prerecorded presentations. In either case, preparation beforehand should include <span style="color: #2b00fe;">review of the previous lesson</span>. This approach is common in Math classes where the instructor inspects homework and answers questions before moving on to the next issue. For courses in social studies or English, it may be necessary for the student to independently survey previous discussions in order to establish context.<br /><br /><b>NOTE TAKING:</b> For <b>in-person lectures</b>, a strong procedure for contemporaneous <span style="color: #2b00fe;">note taking</span> is required because of the one shot approach to information dissemination. <br /> — Notes should be <span style="color: #2b00fe;">brief</span>, highlighting the major concepts that can be expanded later in review. Most people are unable to listen, retain, and write in full sentences simultaneously. <span style="color: #2b00fe;">Key words and phrases</span> are preferable for synchronous notes. (Words highlighted in orange in this essay are examples of key items that would be the initial outline.)<br /> — The note taking template should leave a <span style="color: #2b00fe;">wide margin</span> to the side so that additional notes to summarize or expand can be added during review.<br /> — If the instructor is mentioning categories first and then returning to fill in details, the outline should leave plenty of <span style="color: #2b00fe;">room in the body</span> to add information as the lecture progresses.<br /> — The student should develop a <span style="color: #ffa400;"><span style="color: #2b00fe;">coding system</span> </span>for frequently used terms. For example, a psi sign (<img alt="" src="data:image/png;base64,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" />) could be used to represent psychology, psychologist, psychiatric, psychedelic, psychosomatic — depending on the course and context.<br /><br />Since material presented in <b>recorded lectures</b> can be reviewed several times if necessary, note taking can be more loosely structured and altered as needed. Still, a consistent note taking format can improve the efficiency and effectiveness of study and should follow the same guidelines as recommended for in-person lectures.<br /><br /><b>PARTICIPATION:</b> A video conference lecturer might allow communication with other students or an opportunity to ask questions during a lecture. <br /> — The student should understand how to <span style="color: #2b00fe;">join</span> in the conversation without causing a disruption and be prepared to <span style="color: #2b00fe;">participate</span> constructively.<br /> — <span style="color: #2b00fe;">Questions</span> should NEVER be left dangling. If participation is allowed, the question should be posed immediately. As an alternative, the issue should be written down and either asked or researched as soon as possible.<br /><br />LECTURE RESOURCES: Some lectures will be a “talking head” while others may include PowerPoint or similar slides. <br /> — Lecture notes offered by the instructor as <span style="color: #2b00fe;">printable worksheets</span> should be saved, possibly in printed form, and used as reference for review. The effort that goes into this resource is a direct indication of what is valued by the instructor and should inform the student for written projects and test review. <br /></span></span></p><h3 style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><b>LEARNING FROM TEXT</b></span></span></h3><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><b>PREPARATION:</b> As with learning from lecture, gaining information from the printed page involves <span style="color: #2b00fe;">review of previous material </span>to set the stage for supplementing previous knowledge. Effective learning creates several mental pathways to knowledge, connecting ideas through chronology as in history, through theme as in literature, through hypothesis in science, and through sequencing in math. The goal of most learning is to add to existing intelligence, and efficient learning avoids recreating the wheel.<br /><br />With printed text, preparation steps should include <span style="color: #2b00fe;"><u>Survey</u></span> of the new material.<br /> — An outline of key concepts begins with <span style="color: #2b00fe;">titles and headings</span>.<br /> — <span style="color: #2b00fe;">Highlighted words</span> offer a preview of important vocabulary.<br /> — <span style="color: #2b00fe;">Captions</span> add detail and interest to key concepts.<br /> — <span style="color: #2b00fe;">Charts, graphs, and diagrams</span> present vital statistics in visual form.<br /><br />Establishing a purpose for reading revolves around the <span style="color: #2b00fe;"><u>Question</u></span> tactic. When the social studies teacher assigns 8th graders a chapter to read and instructs them to answer the 3 questions at the end, most students will read the questions before delving into the written pages. They are employing a Question tactic by identifying beforehand the information to search for. Without this predetermined purpose, the student should formulate distinctive questions to motivate investigation of the text.<br /><br />Actual <span style="color: #2b00fe;"><u>Reading</u></span> of the text is an active process. The student should be prepared to <span style="color: #2b00fe;">highlight</span> with pen or markers and also to jot <span style="color: #2b00fe;">notes</span> either in margins or on separate paper. Note taking techniques used when learning from lectures apply equally to documenting data points from text, but the latter can be less intense since it does not rely on a lecturer’s pace. <br /></span></span></p><h3 style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><b>FOLLOW UP</b></span></span></h3><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;">Once essential concepts have been gathered from either lecture or text, learning continues through the steps of Recite and Review.<br /><br />The <span style="color: #2b00fe;"><u>Recite</u></span> maneuver can take several tracks, dependent on a student’s natural preferences and experience.<br /> — An inspection of notes can be a <span style="color: #2b00fe;">verbal recitation</span> as if the student is giving a lecture on the topic, a recap of information through construction of a<span style="color: #ffa400;"> <span style="color: #2b00fe;">mind map</span></span>, or revisions of notes through <span style="color: #2b00fe;">highlighting</span> or <span style="color: #ffa400;"><span style="color: #2b00fe;">addition of details</span>.</span> <br /> — Attempts to answer the initial questions spotlight missing data points and establish an objective for the final step…<br /><br /><u><span style="color: #2b00fe;">Review</span>,</u> during which the student returns to the printed material to augment notes with relevant information.<br /><br />This process is dubbed SQRRR (Survey, Question, Read, Recite, Review) but could as easily be related to lectures as SQLRR (Survey, Question, Listen, Recite, Review). It encourages the planning and thinking that orbits around actual reading or sitting through a lecture, which are, in reality, a small portion of the overall strategy. It enhances the theory that “learning” is more than just listening to an expert or reading about an issue. It requires moving information from working memory to short-term memory from which long-term memory is developed. Classroom teachers can guide unsuspecting students through the method with periodic, subtle comments and review. With elearning, it is up to the student to design and administer a study program to attain understanding, retrieve knowledge, and demonstrate comprehension through homework and exams.<br /></span></span></p><p style="text-align: left;"><span style="font-size: medium;"><span style="font-family: arial;"><br />Although our American style teaching is heavily dependent on students being in a group classroom environment, the online learning situation we find ourselves in today can provide the opportunity for our students to learn a system for higher level learning that could have impressive benefits after high school. College, trade school, on-the-job training, or just pursuing a hobby or special interest all require continuing education. Unlike the fatalistic prognostication that elearning will put our kids behind, figuring out how to learn independently now can put them ahead of the game for a lifetime.</span></span></p>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-77622155251872436012020-08-03T09:12:00.007-07:002020-08-05T21:46:20.429-07:00HOW TO SUCCEED AS AN ONLINE STUDENT Part 1: Preparing for online learning.<font size="5"><font size="2">High school and college teachers experienced in distance learning have found that planning, consistency, and use of the vast array of outside resources increase the success rate of online students. <div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT1XuCspZdq-BcD2HyuelGJ0p2DSK3pQ7wP6WbDZ2OHUXNrUDiFhrIq74_BJ7RRW-_TJ-nci7NixCa4tq_A97PKsyfgs2ILOIbdk7LWWqb8QFEzPsk-UG5fCezVLkScU1YIgKMdDhwgvJU/s550/boy-working-on-laptop-classroom-school-clipart.jpg" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="400" data-original-width="550" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT1XuCspZdq-BcD2HyuelGJ0p2DSK3pQ7wP6WbDZ2OHUXNrUDiFhrIq74_BJ7RRW-_TJ-nci7NixCa4tq_A97PKsyfgs2ILOIbdk7LWWqb8QFEzPsk-UG5fCezVLkScU1YIgKMdDhwgvJU/s0/boy-working-on-laptop-classroom-school-clipart.jpg" /></a></div></font></font><br /><div><font size="5"><font size="2"><br />While elearning is relatively new to high school curricula, colleges and some states have been exploring the distance model for decades and have gathered data on skills and practices needed for success. A recent survey of online courses shows that the expected completion rate ranges around only 40%. For our high school students, the requirement to complete every class suggests that as many as 60% will have difficulty just finishing a course, much less achieving the knowledge level desired. <br /><br />Today, students who are required to or choose to continue with digital learning need specialized skills if they are to excel in their studies. The potential for our students’ success as they earnestly enter the realm of online learning can be accelerated by following the suggestions of experienced elearning practitioners.<br /><br /><br /><font size="3">CHARACTERISTICS OF SUCCESSFUL VIRTUAL LEARNING STUDENTS</font><br /><br />Years of experience have revealed specific characteristics of highly successful virtual learning students. They are skilled in managing their time and can communicate effectively in both speech and writing. They are self motivated, academically ready for the next level of study, and have a strong background in the use of technology.<br /><br />While most 13 to 18 year olds are not in this elite category of exceptional students, there are practices that can level the playing field and contribute to success in this rookie year of virtual education.<br /><br /><span> </span>1. Establish a work space environment.<br /><span> </span>2. Maintain a calendar to keep up with homework.<br /><span> </span>3. Log on to “school” every day, checking in with each class.<br /><span> </span>4. Engage a variety of resources.<br /><br /><br /><br /><font size="3">PREPARATIONS FOR SUCCESSFUL VIRTUAL LEARNING</font><br /></font></font><p style="text-align: left;"><font size="5"><font size="2"><u>WORK SPACE ENVIRONMENT</u>: Controlling routine tasks and deadlines requires a robust organization system, starting with the work space. As parents have heard since the kids were in kindergarten, students should have a dedicated study space in the house. But today, for distance learners, this requirement is even more crucial. A corner of the kitchen table between meals is insufficient when the student is working on course material for 5 or more hours a day. </font></font></p><font size="5"><font size="2"><br />Even if the appointed desk is a series of TV trays, the <span style="color: #2b00fe;">surface area</span> should be adequate to accommodate auxiliary computer components like multiple screens and other equipment that is ergonomically functional for the student. The <span style="color: #2b00fe;">location</span> should be away from household traffic and devoted to only one thing: school. Think of this as the student’s “home office.” Students should avoid the temptation to “study in bed” or on the sofa. <span style="color: #2b00fe;">Seating</span> should be in a comfortable, structured chair.<br /><br />The space should include the requisite <span style="color: #2b00fe;">physical tools</span>: large screen computer, pens and pencils, calculator, paper, reference materials, and miscellaneous supplies of the student’s preference. Access to a printer is advisable, but it does not have to be in the study space.<br /><br /><span style="color: #2b00fe;">Digital tools</span> to acquire might include a cell phone as an auxiliary source of internet research, an online calculator or cell phone app, and online resources such as the Quizlet app. Newer computers might support HDMI for displaying the screen on an appropriate television.<br /><br /><u>MATERIALS</u>: The useful materials for any class go beyond a textbook and #2 pencil. For the distance learner, a computer and access to internet are obviously requisite. Suggestions from experienced on-line teachers include using the <span style="color: #2b00fe;">largest screen available</span> and exploiting a wide variety of internet resources. Opening multiple screens during lectures and presentations could provide greater flexibility by using one for accepting input and another for notetaking or additional research. Students should eschew using a cell phone for coursework because of the potential to lose details on a small screen, reserving this device for quick tasks like basic arithmetic.<br /><br />Teachers should be publishing a <span style="color: #2b00fe;">course syllabus</span> that lists expectations, due dates, and grading criteria. The most helpful outline will also include the order in which topics will be assigned on the calendar. If an inventory of topics is not announced, the school’s course catalog can provide a list of subjects that will be covered.<br /><br />A <span style="color: #2b00fe;">printout</span> of worksheets and added research materials, as well as notes recorded on the computer screen, can be a permanent resource, easily organized, and a way to record and update notes for review before tests and quizzes.<br /><br />Online schooling is not anonymous education, but distance learning removes the <span style="color: #2b00fe;">student’s voice</span> from the educational environment. Teachers cannot see the confused look on a student’s face or the raised hand of inquiry. The successful online learner will develop a cadre of resources with which to <span style="color: #2b00fe;">participate</span> in the learning process and interject immediately when a question arises. The syllabus should include how to contact the course instructor: internet consultation, email, phone, or text. Having a study group of other students provides an opportunity to compare notes, exchange homework, and share ideas. Engaging a private tutor who can explain complex ideas in ways that match the student’s learning style and unique foundational knowledge can offer a personal connection to the virtual material.<br /><br /><br /><u>TIME MANAGEMENT</u>: Once the work space is organized, the student should consider how to keep up with the daily, weekly, and periodic expectations. An <span style="color: #2b00fe;">assignment planner</span> should be used regularly. Since the student will not be in the classroom where the teacher can remind everyone that the test is on Friday, a structured calendar will help to stay up-to-date. Suitable examples include a white board, cell phone reminder app , Google calendar, or Apple watch. The planner should include a notification signal to remind the student of upcoming due dates several days beforehand. <br /><br />The student should <span style="color: #2b00fe;">log on to “school” every day</span> and survey each course. Assignments should be entered into the Planner and grades checked and recorded.<br /><br />Organizing the <span style="color: #2b00fe;">class schedule</span> could take a fixed or flexible track. Some students find it helpful to schedule individual “class” time, just like the in-school schedule, with order and time allotments predetermined. Or the student may establish the order in which classes will be opened, but let the duration of attention remain flexible to accommodate assignment difficulty. The most flexible approach might alter, even on a daily basis, the order in which classes are approached, but then must include a follow-up system to ensure “every subject, every day.” The most important point is to have a consistent plan to cover all classes. The workable scheme will depend on how the teacher organizes lectures and other resources, whether there are specific hours for student participation and homework submission. The <span style="color: #2b00fe;">schedule</span> is intended to set a cadence that encourages continuous momentum and closely follows the routines which will be reestablished once students return to the school building. <br /><br />A word of caution from experienced online teachers warns that students should avoid the temptation to work on a different subject each day, e.g. Math on Monday, English on Tuesday, etc. While an emersion tactic can be seductive for some learning styles, it diminishes long term learning and, when the school is requiring daily work in each class, presents the possibility of missing assignment dates and participation points. Students should strive to maintain the rhythm expected of the regular school term when in-class instruction returns.<br /><br />If the student is easily distracted, teachers recommend installing apps like OFFTIME for Apple or Android that block non-school interference.<br /><br />Although many in-school subjects are set in a 45-minute scaffold, on-line students have more freedom and may want to experiment with a Pomodoro-style format: 20 to 25 minutes of study, followed by 10 minutes of “relaxation” before another 25 minutes of study, and so forth. This approach supports consistent productivity while the frequent breaks keep motivation and creativity at their peek. <br /><br /><br /><u>ADDITIONAL RESOURCES</u>: Many questions remain regarding the framework of lectures, assignments, consultations, and other strategic procedures of online learning as schools, students, and teachers are thrust into digital education. Plans differ among local districts and individual classes and teachers. The syllabus provided for each class should include methods for <span style="color: #2b00fe;">contacting the teacher</span> which should be the first and immediate step to follow whenever questions arise. The student should be aware, however, that there may be a delay in response, so additional sources should be developed.<br /><br />The absence of a controlled classroom also means the absence of an assembly of like-minded classmates. If the online teacher does not establish <span style="color: #2b00fe;">work groups</span>, students should assume the responsibility to form associations with other students taking the same class, not necessarily with the same teacher. These informal groups can serve both an academic and social purpose. On the academic front, input from other students adds depth to the virtual learning environment and can provide direction when the online teacher is not available.<br /><br />There are also many <span style="color: #2b00fe;">online resources</span> to find alternative explanations of complex issues, develop deeper foundational knowledge, or learn background information to enhance understanding. A few worth exploring include <a href="http://www.grammarly.com">www.grammarly.com</a> for free online writing help, <a href="http://www.sparknotes.com">www.sparknotes.com</a> for summaries of novels, and <a href="http://www.cliffsnotes.com">www.cliffsnotes.com</a> for novel summaries and general academic topics. In addition, an internet search can be initiated by entering either a general topic (e.g. complete the square) or a specific question (like a word problem from the math text). A few searches will pinpoint specific sites that the student finds useful.<br /><br />To skirt the complication that might arise from the need for skills and knowledge which differ from those in a more traditional classroom setting, the State of Michigan’s elearning program (established in 2014) assigns a <span style="color: #2b00fe;">tutor</span> to each student for the purpose of ensuring homework completion and adequate knowledge development. Tutors provide critical support to online learners by developing a face-to-face connection, keeping students on schedule, and providing support which make online courses less overwhelming and more manageable for students. This tutoring system is shown to increase student success by as much as 25%.<br /><br /><br />The path to successful online learning can be encapsulated into four steps:<br /><span> </span>1. Establish a work space environment.<br /><span> </span>2. Maintain a calendar to keep up with homework.<br /><span> </span>3. Log on to “school” every day, checking in with each class.<br /><span> </span>4. Engage a variety of resources.<br /><br />It is often said that today’s teens are the most technologically literate group in history. The time is right to apply that sophistication to the educational arena.<br /><br /><span style="color: #999999;">Dr. Ferguson leads a group of tutors who meet with individual students through Facetime, Skype, and Zoom for face-to-face distance learning.</span></font><br /></font></div>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-82956797426207777692020-03-14T21:54:00.002-07:002020-03-14T21:54:51.742-07:00GRAPHING RATIONAL FUNCTIONS<div style="margin-left: 1em; margin-right: 1em; text-align: center;">
<span style="color: blue;"><span style="font-size: medium;">QUICK TIPS FOR </span></span></div>
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<span style="color: blue;"><span style="font-size: medium;">GRAPHING RATIONAL EQUATIONS</span></span><br /><span style="color: blue;"><span style="font-size: medium;"><span style="font-size: x-small;">(A topic for the 2020 School Closing Series)</span></span></span></div>
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<span style="color: blue;"><span style="font-size: medium;"><span style="color: black;"><span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">The
‘artist’ in me loves graphing. I could watch my TI-84 (or any grapher) draw pictures
all day. I even like homework assignments that force me to graph by
hand. What I DON’T like are instructions that expect me to “calculate”
50 points before “sketching” a graph. When I just need to imagine what
the graph looks like, where it is positive or negative, what direction
the end points face, etc<span style="font-size: x-small;">,</span>
I’m in favor of estimating. I believe it’s a good practice even when a
more specific graph is eventually called for, because I can quickly
find silly errors.<br /><br />Here’s a quick and dirty review on finding a few specific points when graphing rational expressions.<br /><br /><b><br /><span style="font-size: small;">1.</span> <span style="font-size: small;"> FIND VERTICAL ASYMPTOTES by setting the denominator to 0.</span></b></span> </span></span></span></span></div>
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" /></span></span></span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b> </b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>2. FIND THE X-INTERCEPT by setting<span style="font-size: small;"> the numer</span>ator to 0.</b></span></div>
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" /></b></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"> </span></span></b></span></div>
<div style="text-align: left;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">Notice
that both of these tell you something about the X-axis and run left and
right in the original equation, like the X-axis does on the graph. </span></span><br />
<br />
<b><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></b></b></span></div>
<div style="text-align: left;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><b><span style="font-family: "arial" , "helvetica" , sans-serif;">3. FIND THE HORIZONTAL ASYMPTOTE by reducing the leading variable. </span></b></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><img alt="" 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" /> </span></b></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><b><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></b></b></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><b><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></b></b></span><b><span style="font-family: "arial" , "helvetica" , sans-serif;">4. FIND THE Y-INTERCEPT by reducing the constants.</span></b></div>
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" 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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">5. FILL IN THE GRAPH.</span></span></span></span></b></div>
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" /> <span style="color: blue;">Done. Sketched. </span></span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b> </b></span></span></span></span></span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b> </b></span></span></span></span></span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b><span style="color: blue;"><u>Other conditions</u></span> tell even more about the graph.</b></span><br /><br />-- Suppose in step 3, the exponent on the denominator’s variable is larger than the one on the numerator. <span style="color: blue;">Think of ‘end behavior,’ what happens way out there at infinity.</span>
If the leading coefficient of the demominator is LARGER than the one in
the numerator, the fraction gets very, very small at infinity -- almost
nothing. So the horizontal asymptote is 0.<br /><br />-- Suppose reducing
the leading coefficients leaves a variable in the numerator, like y = x
or y = x/3. This indicates a SLANT (or SKEW) ASYMPTOTE, which is not
considered “horizontal” even though it goes through the y-axis. <span style="color: blue;">Notice that it also goes through the x-axis. </span><br /><br />-- Suppose there is no constant in the numerator. <span style="color: blue;">Fill in a place holder, 0.</span> Then the fraction is zero divided by something and equals zero.<br /><br />-- Suppose there is no constant in the denominator. <span style="color: blue;">Again, fill in a place holder, 0.</span> The fraction becomes division by zero, which is undefined and the graph never crosses the y-axis.<br /><br />-- Look at a bunch of rational graphs. <span style="color: blue;">Notice that asymptotes are like the poles of a magnet. They repel the graph.</span>
The segments separated by the asymptotes act in a similar way. In MOST
(but not all) cases, if the graph is heading up on one side of the
asymptote, the other side will NOT follow the same pattern. Simple
rational expressions generally occupy only 2 quadrants formed by the
vertical and horizontal asymptotes: I and III, or II and IV.</span></span></span> </span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b> </b></span></span></span></span></span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b>FINDING THE <span style="color: blue;"><u>BLACK HOLES</u> </span>OF A RATIONAL EQUATION</b></span></span></span></span> </span></span></span></span></b></div>
<div style="text-align: left;">
<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><br />As problems become more complicated, factoring and reducing become necessary.</span></span></span></span></span></span></span></b></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span> <img alt="" 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" /></span></span></span></span></b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">
This reduced form gives a vertical asymptote at x = -1, but x can not
equal +3 either because it was part of the original equation. Although
there is no vertical barrier at x = 3, the graph will skip over that
point and create a hole.</span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><img alt="" 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" 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<span style="font-size: medium;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></b></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></b></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></b></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">WHAT DOES THE GRAPH LOOK LIKE WHEN THERE ARE 2 VERTICAL ASYMPTOTES?</span></span></span></b></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></b></span><br />
<span style="font-size: small;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span>The principle of <span style="color: blue;">repulsion</span>....</span></span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: small;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span> </span></span></span></span></span></span></span></span></span></div>
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" /></span></span></span></span></span></span></span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></span></span></span></span></span></span></span></span></div>
<div style="text-align: left;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: medium;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></span></span></span></span></span></span></span></span></div>
<div style="text-align: left;">
<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></span></span></span></span></span></span></span></span></span></div>
<div style="text-align: left;">
<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">And
some equations present wierdnesses like part of the graph crossing the horizontal
asymptote, looping around, and finally adopting the behavior we
expected. </span></span></span></span></span></span></span></span></span></span></span></span></div>
<div style="text-align: left;">
<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">WITNESS:</span></span></span></span></span></span></span></span></span></span></span></span></div>
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" /></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">Notice the x and y intersections and the repulsion principle. For this one, a couple of calculated -x values could be useful in verifying that they fall BELOW the horizontal asymptote.</span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">--- And another rule breaker....</span></span></span></div>
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" /> </span></span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">How does it get that squiggle? No vertical asymptote because it's an
imaginary number, but a horizontal asymptote at 0. For X between -sqrt 2
and (roughly) 2.4, the y value is increasing; for all other values it
is ever decreasing. While the numerator can turn negative, the
denominator will always be positive. </span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">--- Here's a cute one that defies the repelling principle.</span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"></span></span></span><img alt="" src="data:image/png;base64,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" /><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">Will this graph ever enter negative territory? Nope. The fraction will always be positive.</span></span></span> </span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">With
just a few morsels of data, the general shape of most rational equation
graphs can provide valuable information to check more intricate
drawings, as well as inform Calculus questions later in math study.</span></span></span> So let's get graphing!</span></span></span></div>
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Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-31393038375465542602019-02-08T14:00:00.000-08:002019-02-08T14:00:03.168-08:00LAST DAY TO CRAM BEFORE THE ACT - MATH TIPS<a href="https://www.blogger.com/blogger.g?blogID=7971595768928070725" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-family: "arial" , "helvetica" , sans-serif;">Last day to CRAM for the ACT! Let's look at Math. <br /><b><br />Math equations that you will need to use.</b><br /><br /> SOH-CAH-TOA<br /><br /> Pythagorean Theorem <br /> a^2 + b^2 = c^2<br /><br /> distance = Pythagorean Theorem<br /> = √ [(X1 - X2)^2 + (Y1 -Y2)^2]<br /><br /> slope = rise over run<br /> = ∆ y/ ∆ x<br /> = (Y1 - Y2) / (X1 - X2)<br /><br /> Mean = Average = Sum / Number<br /><br /> Median is the middlemost<br /><br /> Mode is the most frequent<br /><br /> Midpoint = (the average x, the average y)<br /> = [(X1 + X2)/2, (Y1 + Y2)/2]<br /><br /> All AREA formulas:<br /> Parallelogram....bh<br /> Triangle.....1/2 bh<br /> Trapezoid (often forgotten, frequently needed).....1/<span style="font-family: "arial" , "helvetica" , sans-serif;">2 (b<span style="font-family: "arial" , "helvetica" , sans-serif;">1 + b2)h</span></span><br /> Rhombus and Square (special ones using diagonals).....1/2 (d1)(d2)<br /> Circle.....π r^2<br /><br /> General VOLUME formula:<br /> Flat-top prisms and cylinders……area of the base times height<br /> Pointed-top cones and pyramids..(area of the base times height) / 3<br /><br /> Probability <br /> Successes / Total Possible<br /><br /><b>PROCESSES that will come in handy.</b><br /><br /> 1) Set up ratios and proportions<br /> for SIMILAR TRIANGLES<br /> for RATES</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> for CONGRUENT FRACTIONS<br /><br /> 2) Write out equations and substitute values <br /><br /> 3) Use all the data provided.<br /><br /> 4) Draw diagrams.<br /><br /> 5) Use the calculator to visualize by graphing and to check calculations.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> 6) Compare fractional values by finding a common denominator. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Don't
get hung up on a single question. Remember that the score is an
accumulation of points, so missing 1 is not as bad as not finishing all
60. Plan to spend the least amount of time on the first 30, an average
of 1 minute or less on 31 through 45, and invest the remaining time
efficiently on the final 15. This last group will probably contain the
most challenging problems, but be sure to recognize the 2 or 3 that are
super simple; they are your reward for getting that far within the
allotted time.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">GOOD LUCK!!! </span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-16064229559744175732019-02-07T12:00:00.000-08:002019-02-07T12:00:14.290-08:00ACT 2 DAYS TO EXAM - ENGLISH TIPS<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">Only
2 days left to CRAM for the ACT. Since you’re probably applying at an
American school, let’s make sure the English section demonstrates a
respectable level of knowledge.</span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b> </b></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>ENGLISH - REVIEW RULES OF GRAMMAR</b></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">Several standard rules are ALWAYS tested, some more than once on a single test.<br /><br /><b>ITS-IT’S</b><i> </i></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><i>its </i>is like <i>his</i> — it shows possession</span><br />
<a href="https://www.blogger.com/blogger.g?blogID=7971595768928070725" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><i>it’s</i> is an abbreviation for <i>it is</i><br /><br /><b>INTRODUCTORY PHRASES</b> must relate to the subject of the sentence<br />(good) Sitting on the balcony, we watched the parade.<br />(not good) Sitting on the balcony, the parade passed right by us.<br /><b><br />SUBJECT-VERB AGREEMENT</b><br />Single subjects do not usually end in ’s’ but single verbs do.<br />Plural subjects usually end in ’s’ but plural verbs do not.<br /><br /><b>VERB TENSE</b> does not change in the middle of a paragraph.<br /><br /><b>PRONOUN REFERENCE</b><br />The pronoun usually refers to the preceding noun.<br />If you can’t answer the question “who?” then use the noun.<br /><br /><b>SPECIAL NOTES ON PUNCTUATION:</b><br /> -- Two commas (or two dashes) means that the words in between are not needed.<br /> -- The subject and verb can NEVER be separated by a single comma.<br /> -- When adding an ‘-ing’ phrase after a full sentence separate it with a comma if it does NOT describe the preceding noun.<br /> -- A COMMA ALONE CAN NEVER, NEVER, NEVER SEPARATE TWO INDEPENDENT SENTENCES! (But comma-conjunction can.)<br />--
A period, colon, semicolon, and comma-conjunction are usually
interchangeable when there is a full sentence in front, so finding more
than one in the alternatives tells you to look for special
circumstances.<br /><br /><b>REMOVE REDUNDANCIES</b><br />If a shorter alternative gives enough information, pick it.<br /><br /><b>COULDAV-WOULDAV-SHOULDAV</b><br />Spell
it out, don’t just say it. These contractions replace ‘could HAVE,’
‘would HAVE,’ ‘should HAVE,’ so abbreviate them as could’ve, would’ve,
should’ve.<br /><br /><b>ADVERBS VERSUS ADJECTIVES</b><br />The difference may be in the -LY (which makes the word modify a verb, adjective, or another adverb).<br /><br /><b>OMIT, DELETE</b><br />If
‘omit’ is an alternative, there is a 50% chance that it’s the right
answer. Be sure information is VITAL before including it.<br /> </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>WHO-WHOM</b><br />“Who” is the subject doing the action.<br />“Whom” is the person the action is affecting (direct object, indirect object, object of a preposition).<br /><br /><b>REFLEXIVE PRONOUNS</b> (himself, herself, myself)<br />The person DOING and the person RECEIVING the action must be the same person.<br /><br /><b>CONNECTOR AND TRANSITION WORDS</b><br />Lump them into general categories:<br /> a) showing contrast (however, but, instead, although, nevertheless, yet)<br /> b) showing cause and effect (therefore, consequently, as a result)<br /> c) giving proof or more examples (likewise, besides, moreover, indeed)<br />
d) Since the English section is usually informal, when given a choice
between ‘however’ and ‘but’ or ‘therefore’ and ‘so,’ choose the informal
‘but’ and ‘so.’</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">ONLY 2 DAYS LEFT TO SATURDAY'S ACT, so if cramming is your style, you'd better get to it!</span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-33454809461465894522019-02-05T16:19:00.000-08:002019-02-05T16:19:39.549-08:003 DAYS BEFORE ACT TIPS<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">With
only 3 days left to CRAM for the ACT, the panic is starting to set in.
Here are 6 last minute activities to maximize your efforts.</span></span></span><br />
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<b><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">1. REVIEW PREVIOUS WORK</span></span></span></b><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Pull
out all the tests you used for practice and review the answers you got
wrong. Think about what you SHOULD HAVE DONE to get the right answer.</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>2. <span style="font-size: large;">ENGLISH - </span>REVIEW RULES OF GRAMMAR</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Since
about 2/3 of the English test involves grammar, you stand to gain the
most points in this area. Tomorrow's post will list several concepts
that will most likely be on Saturday's test.</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>3. <span style="font-size: large;">MATH - </span>REVIEW BASIC ALGEBRA AND GEOMETRY EQUATIONS</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Make a list of those that appear in your practice problems. There are quite a few, but they are always the same.</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>4. <span style="font-size: large;">READING - </span>PRACTICE FINDING SPECIFIC WORDS IN CONTEXT</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Take any magazine or newspaper article. (Magazines are better because the columns are generally <b> </b>wider and more like the layout of the test.<b>) </b>Have
someone list 5 or 6 words they find in the article. (Nouns are the best
sources since ACT questions usually refer to specific names or ideas.)
Peruse the article, circling the words listed. This practice will help
you to more quickly find specific information from the Reading passages
without the need to actually READ the whole article.<b> </b></span></span></span><br />
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<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>5. <span style="font-size: large;">SCIENCE - </span>PRACTICE READING CHARTS AND GRAPHS</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Search
"science graphs" in your browser. When I 'google' it, I get samples,
pictures under the heading 'images.' Click on one and answer the
following questions:</span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b> </b> a) what is the independent variable? (What does the x axis represent?)</span></span></span><b><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> </span></span></span></b><br />
<b><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> </span></span></span></b><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">b) what is the dependent variable? (What does the y axis represent?)</span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> c) pick a spot on the graph and identify the meaning.</span></span></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Here's an example:</span></span></span><br />
<a href="https://www.blogger.com/blogger.g?blogID=7971595768928070725" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpfjiAlgDaDVmVMzwUFT-mH165q3eW4S3Aar1UYTis5HP_zGgFF77MqNEzwZlEUFmUIf05Wk_Fu-iNGY682Mwu0n1Hb2N1QFVfsgjtD5MiMJOvKX4S1RFBIQcVBv3b0lkB7NOzb-L1iwtv/s1600/Screen+Shot+2016-09-07+at+12.43.51+AM.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="185" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpfjiAlgDaDVmVMzwUFT-mH165q3eW4S3Aar1UYTis5HP_zGgFF77MqNEzwZlEUFmUIf05Wk_Fu-iNGY682Mwu0n1Hb2N1QFVfsgjtD5MiMJOvKX4S1RFBIQcVBv3b0lkB7NOzb-L1iwtv/s320/Screen+Shot+2016-09-07+at+12.43.51+AM.png" width="320" /></a></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">a) hours elapsed </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> b) bacteria </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> c) after 5 hours had elapsed, approximately 23 bacteria were reproducing.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Don't
obsess over why we need to know this information. Just answer the
question and move on. The test task is to read the graph accurately and
work on the next question.</span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>6. <span style="font-size: large;">SCIENCE - <span style="font-size: small;">COMPARE RESULTS</span></span></b></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">Using
the same graphs, analyze results. In this example, an analysis
statement might be "as the hours increase, the number of bacteria
reproducing <span style="font-family: "arial" , "helvetica" , sans-serif;">in</span>creases." Personally, I use a shorthand system that looks
more like.... </span></span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigGRWt0dCHLBH5TOGBbeYuGvENFcbUdnMbLX1HmfNgEYPFqp82b_BgW1PWQhrc5pLi7LNhDt0YY3cADLSHdgrhqdHrMsDLNbnTtD-A3ierjPaw-Ufn1maOM7_1K-tefyDCkHNxc0kESm0f/s1600/Screen+shot+2019-02-05+at+6.15.11+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="135" data-original-width="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigGRWt0dCHLBH5TOGBbeYuGvENFcbUdnMbLX1HmfNgEYPFqp82b_BgW1PWQhrc5pLi7LNhDt0YY3cADLSHdgrhqdHrMsDLNbnTtD-A3ierjPaw-Ufn1maOM7_1K-tefyDCkHNxc0kESm0f/s1600/Screen+shot+2019-02-05+at+6.15.11+PM.png" /></a></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"> ....to take less time than full sentences.</span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><br /></span></span></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">Three days left.....keep working!!!</span></span></span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-25379903045562740122019-01-30T14:54:00.000-08:002020-01-16T10:39:54.995-08:00WHY SKIP THE "TRIAL ACT"<div class="separator" style="clear: both; text-align: center;">
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<h2 class="separator" style="clear: both; text-align: center;">
Don't let the first ACT obscure your true potential to succeed in college.</h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgsFHSURfSZ3RV-lqshS9xuWpKIPFTJz9S0IyYmOE21X63eMD4BJOYrbqzaJF20_tZSumbvI9hUhsgv7NAf8Cs243QdeauoenPdw61AxcjUXq441TRaVvo4RCLNdA06MvhmHpAMZkXdCHQ/s1600/FINALS+FEAR.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="605" height="158" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgsFHSURfSZ3RV-lqshS9xuWpKIPFTJz9S0IyYmOE21X63eMD4BJOYrbqzaJF20_tZSumbvI9hUhsgv7NAf8Cs243QdeauoenPdw61AxcjUXq441TRaVvo4RCLNdA06MvhmHpAMZkXdCHQ/s200/FINALS+FEAR.png" width="200" /></a></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">Taking a "trial" ACT just to see "how I might do on the real test" is putting the cart before the horse. The ACT and SAT are supposed to predict readiness for college, and although you might be intellectually prepared for everything a university curriculum might challenge you with, a "pop quiz" effort is not likely to present a realistic portrait of your talents.</span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> </span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Taking any test without knowing how to respond to the </span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> </span></span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">unique parameters (content, format, structure, allotted time) is like </span></span> trying to take a typing test on a manual typewriter without ever having seen a QWERTY keyboard. </span></span>You will be slow. </span></span>You
won't know how much pressure is needed to make those keys hit the
paper. Your fingers will accidentally hit wro<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">ng keys. Mistakes</span></span></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_MclSniNEylXWzqMEUxAqg4kAuu1sLPV8aEdbapB3_gJCvdrxtgcHvFrwcDzaxcikZae2VvyQCDpG1R4I-8yRGtSBW527o_VBd3RiqujsxB2freFwWNlHoCtoDUEC6mBep_J2suMtIy7K/s1600/APP+REJECTION.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="137" data-original-width="134" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_MclSniNEylXWzqMEUxAqg4kAuu1sLPV8aEdbapB3_gJCvdrxtgcHvFrwcDzaxcikZae2VvyQCDpG1R4I-8yRGtSBW527o_VBd3RiqujsxB2freFwWNlHoCtoDUEC6mBep_J2suMtIy7K/s200/APP+REJECTION.png" width="195" /></a><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">
generated by
lack of practice will obscure your true ability to type. Don't let your
first ACT obscure your true potential for success in college.</span></span><br />
<br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">According to the publishers of the ACT, the practice of retaking the exam has gained popularity over the years. In 2009, 41% of the tested students took more than one administration; by 2015, the number had increased to 45%. Although 57% of the multiple-testers improved the score, <b>27% went down!</b> Of the retesters, an average increase of only 2.9 points was earned and only by <b>sitting up to 10 times!!</b> Based on statistical analysis, ACT predicts that simply taking the test a second time will earn an average of only 1.1 composite points. </span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">To achieve a noticeable elevation in score requires identifying</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> -- a clear baseline of existing knowledge,</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> -- gaps in comprehension AND application, and</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> -- suggested alternative strategies.</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>The first ACT experience</b> should be untimed and given over a period of days so that each section receives "fresh eyes."</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>Analysis of the results</b> should differentiate between concepts the student already knows and can be exploited, as well as principles that require a revised approach or additional study.</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">The test, taken in a<b> stress-free environment</b>, should pinpoint the student's natural pace in order to predict the need for timing mitigations to be instituted after sufficient mastery of concepts has been proven.</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">And the <b>results</b> should be presented as input for the sole purpose of designing an efficient, effective study program, not an intimidating appraisal of the student's intelligence.</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Sitting for the ACT or SAT (in either a national administration or a "mock" setting) without sufficient preparation doesn't give a fair reading of the student's true potential on the exam. So skip those options and find a program that focuses on a workable analysis that will inform your personal study plan.</span></span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><br /></span></span>
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Work smarter, not just longer or harder.</span></span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-35800542703601112312018-10-17T15:51:00.002-07:002018-10-17T15:51:49.908-07:00TRANSLATING GPA TO COMPARIBLE ACT/SAT SCORES<span style="font-family: Arial,Helvetica,sans-serif;">The following chart suggests ACT and SAT goal scores to support and verify GPA on a college application.</span><br />
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<span style="font-family: Arial,Helvetica,sans-serif;">GPA COMPATIBLE SCORES </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">ACT SAT</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">+4.0 36 1570-1600</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">4.0 35 1530-1560</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.9 34 1490-1520</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.8 33 1450-1480</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.7 32 1420-1440 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.6 31 1390-1410</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.5 30 1360-1380</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.4 29 1330-1350</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.2-3.3 28 1300-1320</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3.0-3.1 27 1260-1290</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">2.8-2.9 26 1230-1250</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">2.6-2.7 25 1200-1220</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">2.4-2.5 24 1160-1190</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">2.2-2.3 23 1130-1150</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">2.0-2.1 22 1100-1120</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.8-1.9 21 1060-1090</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.6-1.7 20 1030-1050</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.5 19 990-1020</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.4 18 960-980</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.3 17 920-950</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.2 16 880-910</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.1 15 830-870</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">1.0 14 780-820</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">While every college will have its own desired GPA and entrance exam standards, these guidelines are based on a compilation of schools across the nation. If the student's GPA is significantly higher than the ACT or SAT would suggest, he or she should be prepared to introduce the disparity and provide a reasonable explanation on college application essays and interviews. For example, "I've always worked harder than the classroom teacher requires and taken advanced classes where I had to study longer and smarter than some other students. My grades are an indication of my commitment to challenging myself to achieve academic excellence."</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">If the entrance exam score is noticeably higher than the GPA, an explanation might include reference to an illness that was overcome or a "slow start Freshman year" that can be shown to have risen impressively over the next 2 years.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">The best outcome is the highest possible GPA supported fully by the ACT or SAT result. But if the situation requires, a college essay about a hurdle that was overcome can counter anomalies. </span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-90797189277034265962018-10-17T15:07:00.000-07:002018-10-17T15:07:10.120-07:00ACT SCORES CAN LOWER COLLEGE TUITION COSTS<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Over the years, my students have reported impressive scholarship awards <span style="font-family: "arial" , "helvetica" , sans-serif;">based on higher classroom grades and ACT scores. To motivate students to aim high and work hard, I mention that a scholarship or tuition reduction is a gift to give to the parents. For parents, an investment of a few hundred dollars in test preparation can <span style="font-family: "arial" , "helvetica" , sans-serif;">significantly lower the cost of tuition.</span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Here are some <span style="font-family: "arial" , "helvetica" , sans-serif;">examples of <span style="font-family: "arial" , "helvetica" , sans-serif;">Freshman</span> awards given to former students <span style="font-family: "arial" , "helvetica" , sans-serif;">and renewable annually</span>. Each of these were "automatic," based solely on <span style="font-family: "arial" , "helvetica" , sans-serif;">exam score and G<span style="font-family: "arial" , "helvetica" , sans-serif;">PA.</span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></span></span></span> </span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">School <span style="font-family: "arial" , "helvetica" , sans-serif;">Past Awards ACT GPA</span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">-------------------------------------------------------------------------------------------------</span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Hope College (Michigan) $3000 25 3.6</span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Hope College (Michigan) $6000 <span style="font-family: "arial" , "helvetica" , sans-serif;">28 3.75</span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Illinois Wesleyen <span style="font-family: "arial" , "helvetica" , sans-serif;">$10,500 28 Top 25%</span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Roosevelt $1500 24 3.2</span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Roosevelt $6000 28 3.5</span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Indiana University $8000 30 <span style="font-family: "arial" , "helvetica" , sans-serif;">3.8</span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Indiana University $5000 29 3.8</span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Carroll University $15,000 27 <span style="font-family: "arial" , "helvetica" , sans-serif;">3.75</span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Carroll University Full Ride 34 3.9</span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">U of <span style="font-family: "arial" , "helvetica" , sans-serif;">Colorado-Boulder $6250 29 3.85</span></span></span></span></span></span></span></span></span><br />
<a href="about:invalid#zClosurez" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/u/1/blogger.g?blogID=7971595768928070725" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">University of Iowa $7000 26 3.6 </span> </span> </span> </span> </span></span></span> </span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">From a strictly business standpoint, preparation for the ACT has visible return-on-investment benefits. Even a small improvement could have tremendous financial advantages across the 4 year college experience. To get the quest for scholarship money underway, follow a few easy steps.</span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">1. Have the student take a verifiably accurate test to determine the current level of competence. That means taking a test by the actual publisher, either a retired version from a previous student or from a study manual by ACT (ACT exam) or College Board (SAT exam). Do not rely on a manual published by any other source since the questions may be mere facsimiles and not truly representative of the type or format of the real exams. (Using authentic, published retired exams, Tutoring Resources-Barrington, IL offers a nationwide ACT/SAT Readiness Evaluation to help students analyze current strengths, knowledge gaps, and potential strategies for success. This narrative report can be used by any qualified tutor to design a personal study program for the individual student.) </span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">2. Identify weaknesses for the student to mitigate through</span></span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"> either</span></span></span> independent study or tutorial assistance. See "Getting Ready to Study for a College Entrance Exam" in Thenormalgenius@blogspot.com, Tuesday, June 5, 2018 -- or read suggestions for finding study help at tutoring-resources.com/test preparation/when, what, how to study.</span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">3. Establish
a goal score that supports the student's GPA** and aims toward a result
that will earn the highest potential scholarship or tuition reduction
amount based on guidance from the student's college choices.</span></span></span> </span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">4. Set interim benchmarks and don't forget to CELEBRATE incremental steps toward improvement. </span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-size: small;">**Check out the next blog for suggested ACT goals based on GPA. </span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><br /></span></span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-22563710392181370302018-06-05T10:20:00.001-07:002018-06-05T10:46:26.990-07:00GETTING READY TO STUDY FOR A COLLEGE ENTRANCE EXAM<br /><div style="text-align: left;">
<span style="font-family: "trebuchet ms" , sans-serif;">As tenth grade students wind down Sophomore year and begin to think about which college has the best academic reputation, sports opportunities, geographic location, and parties, they might also be thinking about when to take the ACT OR SAT college entrance exam. Now is an optimum time to collect information and create a study plan.<br /><br /><b>ACADEMICS:</b> Consider the academic load in eleventh grade. List the courses in which the student will be enrolled and estimate the time requirements for homework completion based on the student’s previous subject experiences. Try to be realistic when judging how quickly the student learns, especially when considering honors or AP courses, but lean toward over estimating rather than under estimating time commitments.<br /><br /><b>OUTSIDE OBLIGATIONS:</b> If the student will have a job or will be participating in extracurricular activities, estimate the calendar of events and the time commitments involved. Starring in the musical, for example, will undoubtedly occupy all available time a week before the performance. Again, it is useful to allot more time than to find out later that the student is over committed.<br /><br /><b>SOCIAL COMMITMENTS:</b> Look at the school calendar and the family’s vacation plans to identify blocks of time unavailable for study. Include birthdays and other social events that may disrupt a study plan.<br /><b><br />KNOW THE LIMITS:</b> Research a few possible schools to determine the academic and entrance exam expectations. Visiting schools in person or on internet can provide all needed information and also the motivation for the student to implement a study schedule.<br /><br /><b>KNOW THE LIMITATIONS:</b> Use results from the PLAN (a standardized test given in Sophomore year) or have the student take a practice ACT (OR SAT) to evaluate the level of existing knowledge. Every test has a basic structure and list of concepts to be included. The ACT, for example, incorporates fundamental Trigonometry, but the SAT goes only to Algebra II. Consider consulting an experienced testing coach who can match the student’s current skill set to the testing company’s expectations and recommend the level of study required to achieve a desired score.<br /><br /><b>CREATE A STRUCTURE FOR THE STUDY PLAN:</b> Use a 9-month or longer calendar to mark out large blocks of time that are already committed. For example, if the student is a football player or cross country runner, block out the Fall when focus will be on the sport and keeping up with school work. Don’t forget semester finals which may consume as much as 2 weeks for intense study. <br /><br />Based on previous experience, estimate the length of time the student will need for entrance exam preparation. For an average student, incremental improvements in any of the 4 ACT sections might require a week for each 2 point elevation in score. For example, if the entry score for English is 24 and the target score is 30, figure 3 weeks of concentrated study to accomplish the goal. This estimate should be adjusted according to the student’s academic history and current level of achievement. It will take longer to go from a score of 34 to a 35 than from 14 to 15. In the first case, the student will need to search for unknown concepts to study, while the latter might be accomplished by studying just one of many possible rules.<br /><br />Determine when the student will be taking the ACT. For public school students in Illinois, the SAT is given in mid April of the Junior year, is required for high school graduation, and may become part of the student’s permanent high school record. While the SAT score need not be the highest the student will ever achieve, a respectable score is necessary since every potential college may see it. Don’t rush into a national administration of the test, however. December of Junior year is a recommended ACT testing date only for students who have completed a course in Trigonometry and have adequate time in the Fall to prepare. February’s test results do not include actual answers to test questions and cannot be used for effective study. ACT offers an early April test, but many Juniors wait until June, or the new July date added in 2018. An incoming Senior can take the test in September or October and usually have results in time for early admission to the college of their choice. College Board runs a similar schedule for the SAT.<br /><br /><b>STUDY SMARTER:</b> The best results on any test come from a smart plan of action. Realistic evaluation of the knowledge expectations of the specific test, the student’s existing skill set, school and family obligations, and desire to excel are vital components for designing an effective program of study. </span></div>
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Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-72245144468297938122016-09-08T22:02:00.000-07:002016-09-08T22:03:17.088-07:00 ACT: LAST MINUTE HINTS FOR SUCCESS - MATH<span style="font-family: "arial" , "helvetica" , sans-serif;">Last day to CRAM for the ACT! Let's look at Math. <br /><b><br />Math equations that you will need to use.</b><br /><br /> SOH-CAH-TOA<br /><br /> Pythagorean Theorem <br /> a^2 + b^2 = c^2<br /><br /> distance = Pythagorean Theorem<br /> = √ [(X1 - X2)^2 + (Y1 -Y2)^2]<br /><br /> slope = rise over run<br /> = ∆ y/ ∆ x<br /> = (Y1 - Y2) / (X1 - X2)<br /><br /> Mean = Average = Sum / Number<br /><br /> Median is the middlemost<br /><br /> Mode is the most frequent<br /><br /> Midpoint = (the average x, the average y)<br /> = [(X1 + X2)/2, (Y1 + Y2)/2]<br /><br /> All AREA formulas:<br /> Parallelogram<br /> Triangle<br /> Trapezoid (often forgotten, frequently needed)<br /> Rhombus and Square (special ones using diagonals)<br /> Circle<br /><br /> General VOLUME formula:<br /> Flat-top prisms and cylinders……area of the base times height<br /> Pointed-top cones and pyramids..(area of the base times height) / 3<br /><br /> Probability <br /> Successes / Total Possible<br /><br /><b>PROCESSES that will come in handy.</b><br /><br /> 1) Set up ratios and proportions<br /> for SIMILAR TRIANGLES<br /> for RATES</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> for CONGRUENT FRACTIONS<br /><br /> 2) Write out equations and substitute values <br /><br /> 3) Use all the data provided.<br /><br /> 4) Draw diagrams.<br /><br /> 5) Use the calculator to visualize by graphing and to check calculations.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> 6) Compare fractional values by finding a common denominator. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Don't get hung up on a single question. Remember that the score is an accumulation of points, so missing 1 is not as bad as not finishing all 60. Plan to spend the least amount of time on the first 30, an average of 1 minute or less on 31 through 45, and invest the remaining time efficiently on the final 15. This last group will probably contain the most challenging problems, but be sure to recognize the 2 or 3 that are super simple; they are your reward for getting that far within the allotted time.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">GOOD LUCK!!! </span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-86231709611889401902016-09-08T00:41:00.000-07:002016-09-08T00:41:25.862-07:00ACT: LAST MINUTE HINTS FOR SUCCESS - GRAMMAR<span style="font-family: Arial,Helvetica,sans-serif;">Only 2 days left to CRAM for the ACT. Since you’re probably applying at an American school, let’s make sure the English section demonstrates a respectable level of knowledge.<br /></span><span style="font-family: Arial,Helvetica,sans-serif;"><b> </b></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><b>ENGLISH - REVIEW RULES OF GRAMMAR</b></span><br /><span style="font-family: Arial,Helvetica,sans-serif;"></span><span style="font-family: Arial,Helvetica,sans-serif;">Several standard rules are ALWAYS tested, some more than once on a single test.<br /><br /><b>ITS-IT’S</b><i> </i></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><i>its </i>is like <i>his</i> — it shows possession</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><i>it’s</i> is an abbreviation for <i>it is</i><br /><br /><b>INTRODUCTORY PHRASES</b> must relate to the subject of the sentence<br />(good) Sitting on the balcony, we watched the parade.<br />(not good) Sitting on the balcony, the parade passed right by us.<br /><b><br />SUBJECT-VERB AGREEMENT</b><br />Single subjects do not usually end in ’s’ but single verbs do.<br />Plural subjects usually end in ’s’ but plural verbs do not.<br /><br /><b>VERB TENSE</b> does not change in the middle of a paragraph.<br /><br /><b>PRONOUN REFERENCE</b><br />The pronoun usually refers to the preceding noun.<br />If you can’t answer the question “who?” then use the noun.<br /><br /><b>SPECIAL NOTES ON PUNCTUATION:</b><br /> -- Two commas (or two dashes) means that the words in between are not needed.<br /> -- The subject and verb can NEVER be separated by a single comma.<br /> -- When adding an ‘-ing’ phrase after a full sentence separate it with a comma if it does NOT describe the preceding noun.<br /> -- A COMMA ALONE CAN NEVER, NEVER, NEVER SEPARATE TWO INDEPENDENT SENTENCES! (But comma-conjunction can.)<br />-- A period, colon, semicolon, and comma-conjunction are usually interchangable when there is a full sentences in front, so finding more than one in the alternatives tells you to look for special circumstances.<br /><br /><b>REMOVE REDUNDANCIES</b><br />If a shorter alternative gives enough information, pick it.<br /><br /><b>COULDAV-WOULDAV-SHOULDAV</b><br />Spell it out, don’t just say it. These contractions replace ‘could HAVE,’ ‘would HAVE,’ ‘should HAVE,’ so abbreviate them as could’ve, would’ve, should’ve.<br /><br /><b>ADVERBS VERSUS ADJECTIVES</b><br />The difference may be in the -LY (which makes the word modify a verb, adjective, or another adverb).<br /><br /><b>OMIT, DELETE</b><br />If ‘omit’ is an alternative, there is a 50% chance that it’s the right answer. Be sure the information is VITAL before including it.<br /> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><b>WHO-WHOM</b><br />“Who” is the subject doing the action.<br />“Whom” is the person the action is affecting (direct object, indirect object, object of a preposition).<br /><br /><b>REFLEXIVE PRONOUNS</b> (himself, herself, myself)<br />The person DOING and the person RECEIVING the action must be the same person.<br /><br /><b>CONNECTOR AND TRANSITION WORDS</b><br />Lump them into general categories:<br /> a) showing contrast (however, but, instead, although, nevertheless, yet)<br /> b) showing cause and effect (therefore, consequently, as a result)<br /> c) giving proof or more examples (likewise, besides, moreover, indeed)<br /> d) Since the English section is usually informal, when given a choice between ‘however’ and ‘but’ or ‘therefore’ and ‘so,’ choose the informal ‘but’ and ‘so.’</span><br />
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<span style="font-family: Arial,Helvetica,sans-serif;"></span><span style="font-family: Arial,Helvetica,sans-serif;">ONLY 2 DAYS LEFT TO SATURDAY'S ACT, so if cramming is your style, you'd better get to it!</span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-53717926176293040892016-09-06T23:25:00.000-07:002016-09-06T23:25:00.833-07:00ACT: LAST MINUTE HINTS FOR SUCCESS<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">With only 3 days left to CRAM for the ACT, the panic is starting to set in. Here are 6 last minute activities to maximize your efforts.</span></span></span><br />
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<b><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">1. REVIEW PREVIOUS WORK</span></span></span></b><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">Pull out all the tests you used for practice and review the answers you got wrong. Think about what you SHOULD HAVE DONE to get the right answer.</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"><b>2. <span style="font-size: large;">ENGLISH - </span>REVIEW RULES OF GRAMMAR</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">Since about 2/3 of the English test involves grammar, you stand to gain the most points in this area. Tomorrow's post will list several concepts that will most likely be on Saturday's test.</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"><b>3. <span style="font-size: large;">MATH - </span>REVIEW BASIC ALGEBRA AND GEOMETRY EQUATIONS</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">Make a list of those that appear in your practice problems. There are quite a few, but they are always the same.</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"><b>4. <span style="font-size: large;">READING - </span>PRACTICE FINDING SPECIFIC WORDS IN CONTEXT</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">Take any magazine or newspaper article. (Magazines are better because the columns are generally <b> </b>wider and more like the layout of the test.<b>) </b>Have someone list 5 or 6 words they find in the article. (Nouns are the best sources since ACT questions usually refer to specific names or ideas.) Peruse the article, circling the words listed. This practice will help you to more quickly find specific information from the Reading passages without the need to actually READ the whole article.<b> </b></span></span></span><br />
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<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"><b>5. <span style="font-size: large;">SCIENCE - </span>PRACTICE READING CHARTS AND GRAPHS</b></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">Search "science graphs" in your browser. When I 'google' it, I get samples, pictures under the heading 'images.' Click on one and answer the following questions:</span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"><b> </b> a) what is the independent variable? (What does the x axis represent?)</span></span></span><b><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> </span></span></span></b><br />
<b><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> </span></span></span></b><span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">b) what is the dependent variable? (What does the y axis represent?)</span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> c) pick a spot on the graph and identify the meaning.</span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;">Here's an example:</span></span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpfjiAlgDaDVmVMzwUFT-mH165q3eW4S3Aar1UYTis5HP_zGgFF77MqNEzwZlEUFmUIf05Wk_Fu-iNGY682Mwu0n1Hb2N1QFVfsgjtD5MiMJOvKX4S1RFBIQcVBv3b0lkB7NOzb-L1iwtv/s1600/Screen+Shot+2016-09-07+at+12.43.51+AM.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="185" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpfjiAlgDaDVmVMzwUFT-mH165q3eW4S3Aar1UYTis5HP_zGgFF77MqNEzwZlEUFmUIf05Wk_Fu-iNGY682Mwu0n1Hb2N1QFVfsgjtD5MiMJOvKX4S1RFBIQcVBv3b0lkB7NOzb-L1iwtv/s320/Screen+Shot+2016-09-07+at+12.43.51+AM.png" width="320" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">a) hours elapsed </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> b) bacteria </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> c) after 5 hours had elapsed, approximately 23 bacteria were reproducing.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Don't obsess over why we need to know this information. Just answer the question and move on. The test task is to read the graph accurately and work on the next question.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>6. <span style="font-size: large;">SCIENCE - <span style="font-size: small;">COMPARE RESULTS</span></span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: large;"><span style="font-size: small;">Using the same graphs, analyze results. In this example, an analysis statement might be "as the hours increase, the number of bacteria reproducing decreases." Personally, I use a shorthand system that looks more like....</span></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: large;"><span style="font-size: small;"><img alt="" src="data:image/png;base64,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" /> ....to take less time than full sentences.</span></span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: large;"><span style="font-size: small;">Three days left.....keep working!!!</span></span></span><br />
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<span style="font-size: large;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> </span></span> </span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-44389775481264316432016-04-27T18:45:00.000-07:002016-04-27T18:45:02.074-07:00The NEW ACT - SCIENCE SECTION HINTSWhile the SAT has undergone massive revisions in the past few months, the ACT is also responding with a few tweaks to the Science section. Nothing major is changing, but it's worth a look so June test takers are prepared.<br />
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In the old ACT version, you would rely on there being 3 raw data, 3 research summary, and one differing viewpoints data sets, with 5, 6, and 7 questions, respectively. In the updated version, there are still the three TYPES of information presentations, but the number of data sets and the number of questions in each can vary.<br />
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Don't worry. The strategies for finding, comparing, and extrapolating details won't change. The only real difference is that with possibly 6 questions based on raw data, you may have to dig a little deeper to analyze the information given. That could actually be a benefit to the test taker because there is less need to adjust to a new topic. Once you're "into" a data set, you can stick with it longer, albeit in greater detail.<br />
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So here's the plan for tackling the Science section.<br />
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1) Answer the questions in the order presented. More often than not, the easier ones come first and can give you an idea of what's being reported, without trying to understand nonessential minutiae.<br />
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2) Identify key words in the question stem and match them with labels from the data set. <br />
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<img alt="" 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" /><br />
<br />
3) <span style="color: #6aa84f;">Take personal notes.<span style="color: black;"> The example here uses "T" for temperature and "RT" for reaction time, but this code is temporary and refers only to this particular question set. The next group of questions may ask about Turtles, so "T" could stand for something entirely different. </span></span><br />
<br />
<span style="color: #6aa84f;"><span style="color: black;">4) Notice that I'm not concerned at this point with what is said about Experiment 1. My assumption is that "Reaction Time" is the time it takes for "the purple color to disappear" since that's the only thing reported in the chart. Strategy 4 is to NOT WASTE TIME with useless information like "a 3.2 mL sample of some chemical I don't recognize anyway is poured into a clean 4L cylinder by a graduate student at UWM on Tuesday before his mother's birthday..." Focus on the details of the question.</span></span><br />
<br />
<span style="color: #6aa84f;"><span style="color: black;">5) Use your personal note taking system to organize collected data. "T up -- RT dn" is an example. Another question type could give a comparison and ask for sentence completion. Be careful to identify the SUBJECT of the sentence you're finishing.</span></span><br />
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<span style="color: #6aa84f;"><span style="color: black;"> <img alt="" 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" /> </span></span><br />
<br />
<span style="color: #6aa84f;"><span style="color: black;">6) Don't be afraid to write all over the test booklet. Nobody will ever look at it, and nobody else will be reusing your booklet. </span></span><br />
<span style="color: #6aa84f;"><span style="color: black;"> <img alt="" 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" /> </span></span><br />
<span style="color: #6aa84f;"><span style="color: black;"> </span></span><br />
<br />
<span style="color: #6aa84f;"><span style="color: black;">Even without the ability to actually read the axes in this smudged graph, I can pick out "boiling point," match the chemical, find 80%, and estimate the direction of the curve. This is a lot of note taking, but with it, the answer pops out as a whole lot bigger than 115˚C. Watch for those "smaller than" and "greater than" options. Usually, if you are expected to extend a graph past it's domain or range, the answer will be one of those extremes.</span></span><br />
<br />
<span style="color: #6aa84f;"><span style="color: black;">7) Use a system of ELIMINATION to discard answers that are obviously wrong. A, C, and D in Tip 2 are easy examples. For this one...</span></span><br />
<span style="color: #6aa84f;"><span style="color: black;"> <img alt="" 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" /> </span></span><br />
<span style="color: #6aa84f;"><span style="color: black;">I'm looking at Experiments and 2, and if MnSO4 is not mentioned, I'm throwing F out.</span></span><br />
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<span style="color: #6aa84f;"><span style="color: black;">For more discussion of ACT in general or specific sections, return to top and go to the upper left corner of the first page. Enter the topic you are researching. Scroll past the index and see what tips will help you earn a top score on the ACT. </span></span><br />
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<br />Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-73626873212268776192016-04-08T22:02:00.000-07:002016-04-13T16:11:57.950-07:00DeMoivre's Theorem for Powers and Roots of Complex Numbers<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>DeMoi<span style="font-family: "arial" , "helvetica" , sans-serif;">vr</span>e’s Theorem</b> (pronounced də ‘mwavʁ)<br />is a handy way to find p<span style="font-size: small;">owers</span> and roots of complex numbers. Just think of the Draconian feat required to raise (3 + 4i ) to the 7th power this way…<br /><br /> (3 + 4i)(3 + 4i)(3 + 4i)(3 + 4i)(3 + 4i)(3 + 4i)(3 + 4i) = ? </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">I doubt that even a 100% grade on a homework assignment could inspire me to work this out longhand. Thanks to Abraham deMoivre (1667 - 1754), we can significantly cut down the required work.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;">POWERS OF COMPLEX NUMBERS</span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"> Raising a complex number to a higher power is a pretty straightforward process with few steps.</span></span></div>
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" /> </span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> (a + bi)^n </span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">1) Write the complex number </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> (a + bi) in polar form <br /><br /> z = r(cos theta + i sin theta) <br /> </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> by calculating r (modulus, </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> magnitude) <br /> r = √(a^2 + b^2)<br /> and<br /> theta (argument) <br /> theta = tan^(-1) b/a </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br />
<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"> (If the degree comes up negative, add 180˚ or 360˚ to get it into the range [0,360]. You’ll want to remember some inverse trig concepts here to ensure you’re maintaining the positive and negative natures of functions. I highly recommend graphing the complex number to provide a suitable location map.)</span></span></span><br />
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<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"> <span style="color: black;">2) from r(cos theta + i sin theta) <br /> a) raise r to the desired power n<br /> b) multiply theta by n<br /> r^n [cos n(theta) + i sin n(theta)]</span></span></span></span><br />
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<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><b>EXAMPLE: (7 - 24i)^5</b><br /><br /> r = 25<br /> theta => Tan^(-1) (-24/5) = -78.2˚ (180 - 78.2 = 101.8˚)<br /><br /> POLAR: z = 25 (cos 101.8 + sin 101.8)<br /><br /> z^5 = 25^5 [cos (5•101.8) + i sin (5•101.8)]<br /> = 9,765,625 (-.857 + i .515)<br /> = -8,369,140.63 + i 5,029,296.88 </span></span></span></span><br />
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<span style="clear: right; color: black; float: right; margin-bottom: 1em; margin-left: 1em;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="color: blue;"> </span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="color: blue;"><span style="font-size: small;">WOW! Those numbers got very big, very fast! I don't even want to check the arithmetic. The classroom is more likely to use a less intimidating example like -------></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"> </span></span></span></span><br />
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WN6nkzFbKo01DfYjqDSaeHZsl3o/LVTSjpNmiS5isbLZP+prfxi+Jk+nNGcvuy01KNZXK0NOVqDgNeYEx5SbVbEGalQY4zCI9UuhB/GDDYVCPkalOlC+bKE24poN5ct4vHJdVa5cFNDetECzkN111o8jpA0YNOCrWPFnllUKm8kqwf59VlinGNGLm2KjDHiHSM0iRDT2GC4+oCpfcxkQf3BNHa9Uu3ZvmTPsMGQ9UHfJ328dp4uZWbtVB2hnjniZBZfu4pcXEAtgirsaThz+RgtYTUe4S7bFBHW7P3dNmaFWbU1swwB45KCGTYCmHPP+sPVufYP+GA5wckLBxWDKpC1BI91PvWrUKgeq8gLCS8qT5aYaG3I0RoEvMac4kLeo5mSh2xcfcZO+pnHb9IsaXO7rBrl/7t6Ut2A2g299+QmnqExNnTipsRNi5sS9qcutQa7bMNMhj0nNtC0NZ+ptVs/rR6iZrO0dTawh0E1HNdto00S2njgTzPVxpoHNqyC2R6p05AcoNa9ULGXXZm44mtX2eOLzGly0vH/9hklmYrDbNo33TeqvGDY7UcXoiHtoihburymymuZoi8etKnJWpzREYbx+dsm0m/vgKk+mtUEE4ckDVuWhPhHwPNXnRdpL8s3ai5eijBl1adKJbnGasvPa7+gL9ngjeljVwGzLlB/pq/9nI2hd5XK9OOqj7mY8dQ63rBQSX5c+TGvg7pANYq3dNUEXWIpC8zE6Hf15kVlzB36W0eqwBJRu2oD6JV6X7DxepSaBUPl2tsd0hoCZgYnLvtAnWuzeerCzX/frxjEjDmaZ84uK2YIKcRR3TKD777oLYz3K8r+ZYYEqNCYKYvvAPVQY86x0YIZRJgAZm/4St0jmGgB/nipVXNiboitPkmzHgG/lJzAgAa1nMXTya3VlD7eaKmSpVUzVrChaKqSMzjS8Wrfj1rO4PJtaNH2KWzkvk/NnnqdH7Rjzooo1e7XjaPZ1tSe1cl0TvNpCXujN1L/qcYG49FdVrP9YoZiEsM7LlZFsJZmBc/YYTHipJ47CeoEjN0f8jIBvK1hi+v7/ES19ubV7yrT7LejtabcOkbw6vp2vKwCjBjS4JsNv6bC2Uvb1eEKX2SGBBK1ZbyiUTPO21XicAGGt5SN+fEZMJkRzepaoWz2/TWiCbO0PeoOU/Y+2Pwe8Iwqlj30fvZ/tkkUo3IS5zsEQnja3d4Q8rhtZxuT+9LBAabgj/33Dy8vuMIPWBlel2Jvf3EFE6aiMYuUI0MBypAqa6zZscyg6fBsNLrLKjtVMtZCFiTC+AspLG/mMKVeoM/neArflc3LsWlNFfrule3KCAxJDLOAmsrimB/XccVXXyfWZbXm9Vof8ac7ZfLX0Cf57BxrxIZHdaepvQ+YkrBBGCRM3GOwVcGYri0t8BnRQd6QMz6CbrviJX4pOWnjhXVCBbJGaJduH8HMivNyhdgC3rYIULnAAPUzfLGVsyoNUh5+WkCf3WVMWlntiH47Sktamv4YV3z1dcFQD1sd1KT4Yk5Y89Wl5mDTjAn0Q0rGN38S/A8Bv7Q5+RImfANY7+Nkahq51zPmP7fxJY2B0ham7CEF4mNaX4dHEx7XeEa3s6+blva8hIBfq3Ve6rNdtTA+Y+0UJLTYVCC7Qn54gX5gdXomnjUzM2ngrS5AvUNwteTB6vbjq12r+xFs9QWtWueLgcJMnZnZHV/QEpc20I+4qoNxaV8r62umFN/tau3L0XoEErxaZz2kUqMgIAhYgYAwJytQlDoEAUHAcgSEOVkOqVQoCAgCViAgzMkKFKUOQUAQsBwBYU6WQyoVCgKCgBUICHOyAkWpQxAQBCxHQJiT5ZBKhYKAIGAFAsKcrEBR6hAEBAHLERDmZDmkUqEgIAhYgYAwJytQlDoEAUHAcgSEOVkOqVQoCAgCViAgzMkKFKUOQUAQsBwBYU6WQyoVCgKCgBUICHOyAkWpQxAQBCxHQJiT5ZBKhYKAIGAFAsKcrEBR6hAEBAHLERDmZDmkUqEgIAhYgYAwJytQlDoEAUHAcgSEOVkOqVQoCAgCViAgzMkKFKUOQUAQsBwBYU6WQyoVCgKCgBUICHOyAkWpQxAQBCxHQJiTE0jhy+7e/btOUiVaEBAEvI2AMCcDhB8+fEjD/uhK8AUnQRAQBOIHAWFOBrjvPLaGIvI8HdAegA26JVGCQEAhIKKBwXAt3z2DnindifZFb6b52yYpCap+qQ4UlquiQW6JEgQEAW8gIJKTA6r3H9ynf09tpcxpc9GAqQ0pfcosVK5AbRo0qxVtP7rKIbdcCgKCgLcQCHjJCYxkzd7f6cbtK5Q5TS5qU7WvW1jdvHOd5m39jlpUfkOV2350JZXOV4N2MCOqVOQ56lJrsIrfF72FVv/zG6dVd6t+ySwICAKeIRDwzOnqzYs0fc3n1K3OEKpfuoMdCntPbqK90Zvs4nDRoExnSh6akh48fEBjF/ahQ2d2UJn8Nalw9tK0fNcMalKxJxXIGkHVw5ursrfu3qAN++dzG5/GqEsiBAFBwDsIBDxzAiyFmKm0fvrtGAiBqVy9eSFG/ENmSgiJQhLRO40n0J9/f08r98xihlSCjpzbzUyqjK3MlkNL6H8L3qDI8KZUoVB9W7ycCAKCgHcRCArmlCFVNkOUiuQoS7kyFoqRloylJn2oFtaUek+OpJJ5I6ks25e0MPOvL2nVntn0QfNpSqrS4uUoCAgC3kcgKJiTM5iW7pxGUVsmxEge3mExpUuZyRafOnk6ypG+AE1e/iH1azJJxW8+uJiW7fqZxnb9i2frEtvyyokgIAj4BoGgZk7PV3iF8DMTakW0pqmrhyrVDvmhzmGVeIsROW3Fa0e0odef/cp2LSeCgCDgPQRCeDX0Q6Pqaw0OMYqm5R8ZZjfMG0iRd+7dpgvXTlH29PkDiWyhVRDwawSc8REQ7YqXyDqnx0ObNEkyYUx+fZsLcQkNAWFOCW3Epb+CQIAgIMwpQAZKyBQEEhoCwpwS2ohLfwWBAEFAmFOADJSQKQgkNASEOcXziGNDuxnrRqjvA+OZFGleEPArBAJ+ndPtuzdp08GFVC3sBbU2aQkvvOz/eCGlK6T1ZV3l9SR91T+/0plLR6lllT6q+PS1w+j81VO2qlpUfpOu376s1lYd5O/7JAgCgsATBAJecrp265L69g1dunv/Dl2/dflJ71yc6cu6yOp28qmLh2n4H93p0NmdtrJRm8er7/bw7R5+KZKmokLZStEV/v6vfMG6tnxyIggIAkQBLzmNnPcqXbx+hkZE9aCqYU3o1t3r9AUzhd3H16nv5F5rMEp9frKedxXACvD7D+5Rw3Jd+deN9GXfbjyeFm7/keZvnajui5olWlHTp3p5dI+gDWzz26h8d6btrKoDDChj6uy8I0KnGHXWLdkuRpxECAIJHYGAZ06vNRjJH+1u4c9KRtPWw0uVijekbRR1rDFQbRa389hqllLK0qh5vej/Ws8m7Ejw+ZyXKFOanKQvC+bx+8ax9HGb33g7lVT0yrcVqTLv55QjQwHbPeJqCxYt4/crBlMkf0ycOnl6G3M6eeEAnecV6F2+juDdEBKrbVs0dU8rJ0dBQBB4gkDAM6fQxMkohP+wwhuhYNZSVKVoI3VePHdlOnnhIJ25fIzyZi5G0XyOUISZ1cYDf6qjVhblv+y0jO1Wi+nE+f281cpFOnvluB1zcrUFC+rGbpkHTm+joe3m0qLtUxClQpJEoWrr33bVBtAllqb6/dSAsGsC9pGSIAgIAjERCHjm5NilXBkL26KwmwAkJY0pQXJBKJqzPOXLHG7Lh5Nj/+2l/lOfYwbSke1ApZmZhdml48LMFizY+A5qZt8pzyhJCftJjVvUl3rW/0KVRz1Z0+UhfES8bl+UMCcAIkEQMEAg4JlTSEgI72h536BrT6KqF29Ofx9ZwTak19QGc5OXf0QwhuvLglFULtKQOtccxGmXadT8mPYmM1uw9H9hMt25d0s1vnbvHNrBamXrp99RWwFvObSUPmwxXdm9EN+qSswN8p5QLWeCQMJGIOCZEzaaS5ksLX32exeqWaKl4WhiRgzS0svjyyvGkD19PoJ6lTRJclvZDtXfV5LTe9Ofp7u8QwH2Cp/Fm83p9ww3swVLhlRZbTSkS5mZZ+RSsyE8G9Vj7y2Ld0ylPj/UVmojpDCZobNBJSeCQAwEgmLLFOz6glk6MILYwnV2gnDlxnk7O5K+LDyvnL8ardQu1HOZ8+o3pYutbrNpF66dUdJb+lRZzBaRfIJAwCIQly1TAl5ywqhBPXPFmJAvFUtY+OmDvixsVLAHacFqxoR6IUVJEAQEAdcIBPwiTNddlByCgCAQiAgIcwrEUROaBYEEgIAwpwQwyNJFQSAQERDmFIijJjQLAgkAAWFOCWCQpYuCQCAiIMwpEEdNaBYEEgACwpwSwCBLFwWBQERAmFMgjprQLAgkAASEOSWAQZYuCgKBiIAwp0AcNaFZEEgACAhzSgCDLF0UBAIRAWFOgThqQrMgkAAQEOaUAAZZuigIBCICwpwCcdSEZkEgASAgzCkBDLJ0URAIRASEOQXiqFlI89Fz/xC8DksQBPwNAWFO/jYiPqQHu4DCv17iREGx56APkZOmfIFAgmFOeBBv3rnmC0wDpo2dx9ZQRJ6n1U6iZoh+wJ5sgKMEzxHAVtASzCEQ8K/MG7evUqexxW29hYvvqsWaUJuqfXn/78yEfcPhFnzr4WUUmjgpJeEfvKFo3nzh7HLQrFb0bY+ttjr0Jyjf7ZsyynNLqypvqaQ77ACh/ejCtmzY3jdXxiLUovKb7DOvoS3e30+W756hfOnti95M87dNUhJUfXbEEJaroiHpQ37tQG82/JqdhaYzTLcqctU/v9KZS0dJczo6fe0w3tv9kVsvtAGc4aTCnYDxX8IOJvo1meiymDt59ZWZoXvzwUWUivGrxR6lJcSOQMBLTnib/3f1BP30+r80tfcBGtV5Jf17agv9vulr1fMBUxsqz7uz3jpOv7x9koa9uIB+WT9SPYzIAHsLnBo4Cyt2z6SUSdPQ3C3f6rI8VG1OfnWnavP7XnvYu0p7+uDnFwjMMhAC3uD/ntpKmdPmUp6R06fMQuUK1FaMGo5BHcOWQ0soGzMEbzOmUxcPq5fJobM7bSREbR7PXpvL2H54AbkbiuYoT+0j3zVVzJ28WoVm6a7PfhHh2xAOWiXEjkDAMyete6HssRdee+FAADfADn7Azl05QXtOrKfudYcqN1DIC2eZ8F+3mt/OZsKff3/Prs6/Ut5d4I5cH+BtGG0mD01JdUq2Y6ks1OZ+fMKSd2nnsbX67B6dL9k5jd78vqbtB9dSnoSbd64zU/7KVnT70ZXs9qqGwqkSu13vUmswVQt7gZnsi4zNb7Z82slPq4eoNO36j83f0EvjSjFdtWgN++fTwrytE1nSLEvvTKlPK/f8oqKhCk5cNpB6fluJRi/orVxjafn1x/sP7ikbWKPy3W3RcBOfMXV2dt/eyfaDRGwUIF1ByjIKx8/vY9dcP9klOaNLy4t7Z9LyD2nkvFfZjXxJdQSNjsEdunG/wMvz0p3THauRawcEAl6t0/oD+0mikERK/P9l/Sh6tkwX2rB/AZXKF0lpU2TUsqljZHgz+m7p+zbnl3aJugu4JT935aR6iCGG4+bWqzyQJsAU4UQTTjlL5K7C6l0hVUPuTEWUxKarzqPTp4s2Vr7z8CCNmNuDMqfJFaMeMM290faME5kalOmsGCeky7EL+9ChMzvUg1E4e2lavmsGNanYkwpkjaDq4c1VnXibb9g/n7rV+TRGGyibJ1NRFX/60hGavWE0S6krlKstSIxPFW5AF9ij8ox1w2lg82l078FdGjbnJSrIPgOBIzwqj+m6lt29L6VvFvejT9rEZIDfrxhMkWFNFW4X2WU7AtRueGru8nUEj29i1SdN3VMZdP+u3rpI6/+dR22r9tPFPjq9fOM/2n9qm138eu6rEV1a3rBcT6n+fN5+vqoTHqF3HF1NZQvUsqvHXbrzZSmucG5YrqtdPXJhj0DQSE6/bvifemA2HviTXq77Gb3wVC86e+U4ZUqdw77HfAUX5bfv3WAHm7EbJyE1hfMNuuv4OrZxFKClux5569UqhGSAh3zF7lls01pK+bOW0JLoubIv8YP/5NqW4OZJymRpKEva3LRs1890i6WfPmzzcQxgKnB77vhDPxHAtN9pPIHgFHTlnlnKseiRc7uVmoSZOkh8YLSvTKhIlYo8SxUK1bdr4szlY+xSK51tVm/N3t+pTkRbggPRfFnC6XNWldEWJK66LEHCYShwa1iuu5IQsqfPT5DUpq4eqsoYMSaokgdOb6NmlV63aztJolBlFxv/8hYa2m6u8pwM7836AJVq2+HltPfkRuXJGef43b1/R58txrkZuuBUFZIO8pbKG0nRFw/Z1eMJ3XkzF6Pj5/+1q0cuYiIQNJLTRy1nqIdQ30WocHPY9gQmBKO1FjaxUTJnhkLs6y6VFhXjCGlj4fYfqWTeagQVBgEG9Y0HFrKn3jrq+q1G31Cy0BTq/PDZXdR9fDl6pd4wmwqpEiz49xdLA1FbxtPX3dYrRuJYJZiBJrHp05KxuqkP1Vgq6T05kvsUyW//J+rhTPZsvGrPbPqAJR5IVY7hwrXTSkLU4vFg5c/yhPGCeYLJQcqBbUgfIFWCSY95aS0tZ/sdpD886INaztRnU3aYi9fPUN8pzyhJCYx23KK+1LP+F4rZITN8CtaOaKOkVDAMLcB2BjX9+u3LLL2dVgwMacAFY+YsmKEreeiTewR91Bi+VifsR+7SjXGBt2kJsSMQNMzJqJvVWX0bv7g/G8fHUvNKvVUWePEFw2pjIPrr64AkAfvVhy2e2Abw5l+8Y4qNOenzQz3CzXv15kXKlCaHesPCNuLoxFNfxsz5kXN7aETUy2zI/1PNPhqVWcp2qagtE2IkDe+w2M5jMYzZOVgCnMx2lH5NJqn8mw8uVlLZ2K5/2TFwfWVg5KdYYtCYPFRNMGyohWA+3dnGNP7lzfR0sedV/HOsrmCiASpixxoDFbOAy3i4fMeMZ6uReVU6JDYt9H9hsk3NXss2rB3HVqtZ1Xlbv1OqIMYBth3Et6rytlZMHWsUb074AauRc3syk51ql+7sAnUb0eUsv1G8J3RHXzhIhVjdlRA7AkHNnPB2wkP96a/taRZLBxlZxYu+eJBejHyPGpd/2YYM7BuNPktvu86QKhsVzVnezgCMxJpsd/px1cdqeYIts+4kbYpM9M/JDcqw/Mns9mrKu3ZEa10O908nLBmgJALYdbQwrvsGO0YFdQ0/M6EW0wMmq6mcYMJYJd5iRE5bcUgnmATQAjwf58lUjE5fOswSWmEqx5LjLJ7x7MxLODApABsQ1E/M9k1bM5Q6jQlXKhWksOJsh4NkNXBGM1qwDQzopsJFz5jQDlRELYCpw4MzXg71eGnDYl4CgIkA2K4gDZUvWFfLGqcj6nFFl6sGPKH7xIX9yhbnqu6Enh7ChlbDVXXOfJwv/8gwu9/jiJkcGEzxkOlVPL8n3GICsUYLhmuoVu6E3zaOUdPfemMzVKh0vARBjyduJxjM8WKABKkPp3ntEmbeMGPlbrhw7YxS29OnyuJuUZf540KXq8qN6H77R2aKzaeTN/riih5fpzvjI6DDFS8JGoO4K9DxoOTnWRL9g+SqTDCmgzG4y5iAQ+PyPZTRXG9kBqNxxDMkJIRyZCgQgzGhDiyc9IQxoSykKG89zHGhC7TFFhzphqG+fMF6XutLbLQEWlpQq3WBNhj+TC/UsP5sp7rLkldsRmZ/7oM/0JY1XV4qwZ8MSXCNgDAn1xhJjscIwHYkIW4IGM2qxq3G4C2dYNS64B1C6ZkgEJwICHMKznGVXgkCAY+AMKeAH0LpgCAQnAgIcwrOcZVeCQIBj4Awp4AfQumAIBCcCAhzCs5xlV4JAgGPgDCngB9C6YAgEJwICHMKznGVXgkCAY+AMKeAH0LpgCAQnAgIcwrOcZVeCQIBj4Awp4AfQumAIBCcCAhzCs5xlV4JAgGPgDCngB9C6YAgEJwICHMKznH1Sa+wgya245UgCHgDAWFO3kA1AdSJHS+H/dGVN5uTXXcSwHDHSxeFOcUL7IHRKDzQONnFmR2GrqEI3jQNO186Blcutxzzy7V/IeAv4yevPf+6L9ym5qv5r/GWuDmV0wYUhuuq5btnqL264SyzGDtq8DQM+bUDvcl+8oxckKONZ0p3on3Rm5Vrd0hQ9dkZAZyOLtg2iVKxpxc4ItUHd2mFS6xR7G0XHonfajROX5Wl5zfvXKNvl75HvZ8dbavXGY7wKIz96LXQovKbavth7drMcevhZbSEnTb0azLRZXZ38mqVxbU/m9l1mtH4afX76iiSk6+Q9kI7cNW958QG5dQTth94tP3ij24UlrOi8uQ7gD3U4kb1JMArSzbe89uIMeHNCl9xmdPmogFTG1J6dnIAzyuDZrVi55mrlDt4+HODs08teELrffYaDE/C3mRMcML6OXsm1runjw3HqM3jlW8++OfDLzbfh1rfHY9Fc5Sn9pHvOkYbXruTFxVY0Z/6pTsqP4L68TMkzsuRIjl5GeC4Vr+EfdLN1fmkC2HvvSM7LVPVLvz7B3bP3Yn+uxpN8MKLm6ldtf7KnxwyzFw3giWbLeyxtobbZPy0egi98dwYVe4mexqGj7cWld9Q1/DeWzpfDXbNvUpJNV1qDVbxaAtefzUvuUt3Tmevv49cbltBK3zl/c4+B+GCCxJLtbAmqt15WycSvMPAAQJcftUo3kKpo5PYPx+kgPDclajZU68TXMQ7BjDTlEnT2EUfZNfrRjgWzFZSSaTA3FWAdLWIfRzqvdVoZY6f36d8+nWuOUiLckqvlhdMGu7T4SodLtFL5YtUkp6jzc+q/sBpqX78bIT68ESYkw/B9qQpOLDEww7bD7zlZk6Ty1YNbn4wKjjyHB7VnUZ0XKLS/j6ykpnVb+ocdiF92HtyE+2N3qSPUucNynSm5DoPwYf4Ac2TqSjB7jR2YR/CNW5Y+KKDC3Y41IQjUaiOCGCMcKLZrc6n6jofe7rBtcacPKFVVfT4H9xNzd4wmkZ1XkFX2DEq/PjhgYWbqxnrhrOrpWl0jyWtYSwFFWSHlfBxd+y/vTSm61rllPObxf3IyA169zpD2FPxQdp0cKGtOY35OOK4n92ln+f2unwdwW6qEvOLobPy2WcrqDuBG7L1rJYaMScwGEhn+gDGY0SvljeM3bujn5+3n6/q7M9SMZhU2QK19NWQVf1xHD+7Rnx0IWqdj4D2tBk4q4RjgWW7fqZbLMH0YRsQAlyCV2UPu6mTp1eumHAzwZsxwm1mFFDnrt26xF5wd6s47R+YCFx9O/70brbPXD7GnorTqZm4RCypvdN4gnLauXLPLOV1F3VCpcFbG15ZoAK+MqEiS1HPUoVC9VVTeTMXUzTiwlNaNZpxhGRYJ6Ktcr6ZL0s4ff7iAmbYD5SkVrdkO+VsM5wf4Ibluqs3PtxfQcKDA1E4vjRiTPr6jc4dcUySKFTZ2ca/vIWGtpurpMm/j6ywK3rq4mGC+6e9Jzcq/HGOn96lll2Bxxdm6NUkUuQtxS7lo9kLszvBnf7ox8+dNqzMK5KTlWh6qS4YhqO2jKevu61XzADNQKrRqwUw5kKkh7txMAn8Ri/ozd5yf1KMRCMNHnONPIAk00lNcJYZ6uD4slpYU+o9OZJK8kNRlu1LWpjJnpRX7ZnNLsCnKalKi0d9cKyJ4CmtWl04gsHlz1LCFgWGDeZ48sIBu/4hA1ykw6PxmJfW8uTATCVx4oEe1HKmrXxsJ85w7Fl/uGKCKJs1XR6CZ+R1+6KURKnVB1sc7FfXb19mqe60YmBIA+6xudQyQ2/y0FRaM6rv+heKLcHgxJP+6MfPoEqfRInk5BOYPW/kyLk9NCLqZfq49W92LsiNasTM2cy/RigVEOlnLx9X7sD1eZeyDeu96c/H+EE11ELODIXoFL+V9VPKMIyD8U1mO06tEo9crG8+uFhJdF91WWXHmFBPNKtKhVi9chbM0KovC/UW9iOomZD+Xvq6pJIkn2bpESoR4uHNGKpklaINFVOAGtah+vv0VeeVSnoxu2DUGW2wu/3fL20VWfcf3KMdx1bbJEWN1hrFmzOjnko96g2jvJnD1DmuIeHGFlC3p/TGVi/SPOmPq/Fz1aYV6SI5WYGiF+uYsGSAegvDxqKFcd03GDIqqDfDmZEpm0iixMompBmNtbLPV3hFqWjatdExXcpMym376UuHWcoqbMtSK6K1UpPwlkeAOodV4i1G5LTlgTTx+rNf0YkL+5Xtx5bgcGKGVn2RcgXr0Kz1I6nz2OIsgSRTth6ovJglnLZmKHUaE65UJ9jEiueuolThgTOa8bKGycy0bioDOlRQM8EZbWDWi3kJQJ8faiubFqSh8gXrmqnSZR7U4ym9rir3pD+uxs9Vm1akh7Ch9aFRRc58nLvyb25Ul8T5FoFL18/xFHdqShaawuOGMfsFCUVv0IVkAgM0VCRX4e0f+WFrPt2l2+3YaIWdacP+BfR24/G25qAqpeOlC3o36LiFYTCHGgm38/pw+tJRNcPmiRt0Z7RduHaGDeKJXPZNT4fZ87jQ66oNd/pjdvxctemMj6CcK14iap0rdAMwHVPqcWFM6HLj8j2UZKQ35OIBN8OYYAAuX7CeqYfXFa0wOE9b85ltFDKmzm7HmJCAVeo5MhSIwZiQlp3XannCmFDWGW0ZU2cz1TfU4W6IC72u2jLbH3fGz1WbcUkXtS4u6AVxWahA/ZtMorssLcVmyDWCIGu6vFTCYQmDUT5XceUK1KGP2/zGSxyeGIJdlZH0uCNg1fjFlRKRnOKKYBCXx4wY7DrOgrNdCTAb6Km0om8LbefnJRKQJvTBWbv6PP54Hih0WzV+cR0DYU5xRTCBloedJz52JYivduM6zIFKd1z7HZfywpzigl4CLhvbrgRGsMS2w4Fj/tjyxtaufumDY52+uPYl3fHdV1/gKczJFygHUBtYEzOSdwLAAk586uIsYFcCrHcymx87HFy/fcVZdXbxseWNrV3shoBFl47hfwveUJ+GmKXVsbz+GrsEDJvz6HtBfTzOfUm3s7460hTI18KcAnn0LKYdHxAb7TLg2Aze2rHtSuCYP7YdDtzJ66pdo6/pUWbX8bVsO0trqm+O9DheO9slILY+eoNuo7460hro14kHcTDqxA8rH31p7pim/2TCMU2uAxuB9fvn8bR8Il5EOUqtbsa3evhCH5+szNk0jhc3VlYdxPT+A37o796/bZgfH+TqA7ZxaVdtgKnpd31e7IbgTrtYGY7PXLAOqWiOcoqE7fwR9G3+nOXBw/umaEUh7CgwZ/M47ndVfTfUOfBY9c9su09WkOBruo36GoNYP4hwxkdAmiteIpKTHwygL0iAiobtRhx/WGipBWw1go98ERCPT0EqFKqndiVYtms6HTi9XaVhV4LavFrcKP9ThZ9RefT/tB0O9HHOzrW8sN9gNwR329W+ptfqX827M0SGNzVNK8ppOwpodeiP2i4B+jicxwfdjn11pCnQr4U5BfoImqQfzMZxJwJc6z8eNdplAFKQJ7sSaGTpdzhA3Np9f9CYP/uoH1Ys64M+rxW7IWCGbNextSwBVVMfyjrbQUGjwdMdBeKLbn/YOUDDzhtHWYTpDVT9sE4zuxGAbGe7DLi7K4EGgeMOB2lTZFSruZHu+K2bY17kcbdd/df0/57aonYDAKNDcNY3lcj/PN1RIL7o1vdV60MwHYU5BdNoxtIX7EYQpdtRU8s6vMNi/lYtk7rUdhkY2/WvGJ+I6Hcl6McrxxFiy68y8D/9Dgf4Hg5SDH5GwTEv8rjbrv5r+lW8dUlkeDPVlBlasaMAftgJYuTcnmpHASM6HePii259Xx1pCoZrYU7BMIom+mBmN4LYdhlAE+7sSqCR5GyHAy1df3SW15129V/Tbz20lDrV+Eg14apvejrcPY8vuvV9dZfmQMgvuxIEwij5CY3u7EqgJ9lohwN9uv7cKK877Vr1Nb2eJjPn8UF3fPXVDB5aHtmVQENCjl5FwOyuBI5EGO1w4JhHuzbKa7bd+Pya3td0x2dftbHy9lHUOm8jLPUrw7fZHQ78YTcET4bM13T7y84BnmBltowwJ7NISb44IYAdDswGd/Lq6zTaG12f7u1zX9Id3331NpaoX9Y5+QJlaUMQEATcRkCYk9uQSQFBQBDwBQKi1vkC5QBuA1/yz+ev/bF6vH6pDhSWq6JHvTGqB1/4L2GHAf2aTPSoTikU3AiI5BTc4xun3pndpcBVI87qcfaFv6v6JD1hICCSU8IYZ496uYOddFYq8hx1qfVoh4p90VuUh114nnUM+JIfLsf13lq0PM7qgbcUfFzs6ut0rR45JiwEhDklkPHGrgR7o2NuHtegTGd2IJDSEAXsOlA9vLlK03Yp6FbnU8O82pf8RszJWT3OvvA3bEAiExwCwpwSyJBruxI4dle/KwF2DMDiPoQXI9+z7b+ETz+wmyS2HqlQqL5dFfiSHz7jzlw+StduXbKVj+C9kDSvLbBXITjWs/HAn3Z1yYUgoEdAmJMejSA+N7MrgdGOAVZ9ye+qniCGXrrmIQLCnDwELtCKmdmVwHHHAKu+5DdTT6DhKfR6HwFhTt7H2C9aMLMrgSOhVn3J76yeiga7ZjrSINcJFwGnuxIkXEik54KAIOAPCMg6J38YBaFBEBAEYiAgzCkGJBIhCAgC/oCAMCd/GAWhQRAQBGIgIMwpBiQSIQgIAv6AgDAnfxgFoUEQEARiICDMKQYkEiEICAL+gMD/A1DGcHT45HlCAAAAAElFTkSuQmCC" 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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;">ROOTS OF COMPLEX NUMBERS</span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;">Finding the n roots is much more arithmetically intensive and is well guided by a consistent structure that emphasizes the repetitious nature of the calculations.</span></span></span></span></span></span></div>
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" 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" /></a><span style="font-size: small; margin-left: 1em; margin-right: 1em;"> </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"> 1) Write the complex number (a + bi) in polar form.... <span style="font-size: large;"> <b><span style="font-size: small;">z = r(cos theta + i sin theta).</span></b></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"> r (modulus, magnitude) = </span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"> √(a^2 + b^2)<br /> and<br /> theta (argument) = </span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"> tan^(-1) b/a</span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;">Look at the number of roots you need and list Polar forms that represent that many coterminal angles by adding 360˚ or 2π, depending on whether you're working in degrees or radians.</span></span></span></span></span></span></span></span></div>
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" 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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;">2) Raise the modulus to the fractional exponent and multiply the argument by the same fraction. </span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"><br /></span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"><b>z^(1/n) = r^(1/n)[cos theta/n + i sin theta/n]</b></span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"><span style="color: blue;">NOTICE that to raise a complex number to a HIGHER POWER, the strategy is to RAISE the modulus to a power, N, and MULTIPLY theta by n. To find the ROOTS, the exponent on the modulus is a FRACTION, 1/n, and multiplying theta by a fraction with a numerator of 1 is the same as dividing by the denominator. The exponent tells everything you need to know about the steps to take. Keep in mind the rules of exponents. </span></span></span></span></span></span></span></span></span></div>
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" /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;"><span style="color: blue;"> </span></span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="font-size: small;">3) Calculate. Now the process turns into simple arithmetic (combined with a healthy knowledge of trig values of angles).</span></span></span></span></span></span></span></span></div>
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<span style="clear: right; float: right; font-size: small; margin-bottom: 1em; margin-left: 1em;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;">TIPS.......</span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="color: blue;"><span style="font-size: small;">NOTICE that once theta is reduced, the distance between the angles is directly proportional to the number of roots</span></span></span></span></span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: x-small;"><span style="color: blue;"><span style="color: black;"><span style="font-size: large;"><span style="font-size: small;"><span style="font-size: large;"><span style="color: blue;"><span style="font-size: small;"> <u>360</u> OR <u>2π</u><br /> n n<br /> Number of Roots<br /> 2 180˚………… π<br /> 3 120˚………… <u>2π</u><br /> 3<br /> 4 90˚………… <u>π</u><br /> 2<br /> 5 72˚………… <u>2π</u> Use this factoid to avoid<br /> 5 mistakes on the arithmetic.</span></span></span></span></span></span></span></span></span></div>
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" 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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">NOTICE also that the final roots are evenly distributed around the circle. So a visual display may be another tip for avoiding errors.</span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: small;">When the classroom curriculum turns to finding powers and roots of complex numbers, the process is well defined. It requires an established system to organize the process and strict attention to arithmetic and trig calculations. </span></span> </span></span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-31335138377288869622016-04-07T10:47:00.001-07:002016-04-07T10:47:26.720-07:00ACT - LAST MINUTE TIPS<span style="font-family: Arial, Helvetica, sans-serif;">With only a couple of days left before the next ACT administration, what can be done to boost that score?</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">If a previous score is already... </span><br />
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<b><span style="font-family: Arial, Helvetica, sans-serif;">IN THE 30s...</span></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;"> 1) avoid silly mistakes. Read questions carefully and highlight specific information to guide your decisions.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> 2) watch your timing. Don't let a single challenging question slow you down. Skip it and come back for a second look if time permits at the end of the section.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>...25 TO 29...</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b> </b>1) review previous preparation homework. You're probably falling for "typical" ACT red herrings. Identify your personal, common errors and evaluate ways to avoid them.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b> </b>2) conquer impending fatigue. Especially if you start out strong and peter out as the test moves on, try wiggling in your seat, stretch, take deep breaths, adjust your posture, have an appropriate snack during breaks, and stay hydrated with water or sports drinks - no soda pop or coffee, please. When<b> </b>weariness threatens, use a couple of the available seconds to refresh and dig back in with renewed energy. </span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>...20 to 24...</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"> 1) focus on accuracy. You don't need to answer every question in order to climb to the high 20s; you just need a few more CORRECT answers. There's no penalty for leaving an answer blank, so insure that any work you do is precise. Default questions that resist solution and mark them for reconsideration if time permits later in the section.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b> </b>2) stay focused on answering questions. Avoid cluttering your mind with unimportant information. Use your pencil to circle or underline vital data, but don't try to <u>remember</u> details from an article or statistics from a math or science problem. Take each question one step at a time and move on to the next challenge.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>...IN THE TEENS...</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"> 1) relax. You're probably undermining your best effort with worry or lack of self confidence. You can always take the test on a later date, so concentrate on doing what you can right now, at the moment, this time.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b> </b>2) keep moving. Adopt a "point collection" attitude. If a question is daunting, skip it, mark it ON THE TEST BOOKLET (not the answer sheet) and move on. If there's time remaining after you've addressed the last question, return to the skipped ones and either reconsider an answer or default it. </span></div>
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<b>...FOR EVERYONE...</b></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> Experts will tell you to get a good night's sleep, eat a healthy breakfast, have your photo id and entrance ticket laid out the night before, be on time, have several pencils (and a WHITE eraser), and fresh batteries in your calculator. Some of my friends recommend yoga or other relaxation exercises and 'envisioning success.' </span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> Personally, I favor a 'get in the groove' approach. Before the English section, I think about the routine grammar rules I expect to see, like <i>its-it's, subject-verb agreement, punctuation between sentences.</i> In Math, I anticipate <i>operations on fractions, mean-median-mode, properties of quadrilaterals </i>and similar basics in the first half of the section<i>.</i> For Reading, I'm prepared to identify relationships in the Fiction essay and will look for nouns to research in the Non-fiction articles. When Science Reasoning is the upcoming section, I plan to focus on the axes in graphs and the headings in charts.</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: small;"> Whatever your preferred strategy, keep in mind that this is just one test out of the hundreds you'll take in your lifetime. This one is not the most important, nor is this your 'last chance.' Prepare beforehand and CELEBRATE WHEN IT'S OVER. Good Luck!</span></span></div>
Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-47301530659636794272016-04-03T20:05:00.000-07:002016-04-03T20:10:57.893-07:00SIMILARITY OF RECTANGULAR, COMPLEX, TRIG, VECTOR, AND POLAR FORMS OF A SINGLE POINT<br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">During fourth quarter, the academic brain may begin to feel so full that not even one more concept could be stuffed in. This is the time to ORGANIZE existing knowledge, making comparisons and identifying similarities and differences. <br /><br />And so it is with the introduction of POLARS to the Precalculus or Advanced Algebra curriculum. There’s the rectangular way of noting a coordinate, (x,y), that we’ve known about since Algebra I. Then came the complex numbers, i, that appeared when the quadratic formula gave us square roots of negative numbers. After that came Trigonometry and the unit circle. Vectors may have been included in some courses. Now we have polar coordinates and graphs.<br /><br />At this point we have so many ways to identify a single point that similarities among the terms can create a perplexing cacophony. <br /><br /> (x, y)...................................RECTANGULAR<br /> (x + iy)................................COMPLEX<br /> (cos, sin)............................TRIG<br /> (r cos theta, r sin theta)......VECTOR<br /> (r, theta).............................POLAR I <br /> r (cos theta + i sin theta)....POLAR II<br /><br />Equations for converting from one configuration to another are standard instruments in the math toolkit, but visual representations can highlight the relationship between the forms and possibly reduce confusion.</span><br />
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" 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" /></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>(x,y) RECTANGULAR coordinates</b> are ubiquitous and should be well understood by now. They describe things like sales, speed, population, distance, and many more common real life situations. The x axis is what we control, the independent variable like time; the y axis reports results, outcomes.<br /><br /><br /><b>i = √-1 Imaginary numbers</b> were a convenience when we ran into the square root of a negative number, a frequent result from the quadratic formula. Mathematicians are uncomfortable with answers like ‘cannot be determine,’ so in the 1700s, Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855) popularized the use of i, √-1, elevating imaginary numbers from a derogatory classification to a useful tool.<br /><br /><b>(3 + 4i)</b> Combining a real number with an imaginary one creates a <b>COMPLEX NUMBER</b> that can be graphed on the ‘imaginary plane’ in the same way that (x,y) appear on the coordinate graph. Complex forms frequently appear in electronics and in descriptions of electromagnetic fields, but higher level computations with them can be tedious. </span></div>
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" 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" /></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>(COS, SIN)</b> The Unit Circle in TRIGONOMETRY is our first foray into what will become a template for the polar graphing system. But first, extend the trig information to express… </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>VECTORS</b> in <b>(r, theta)</b> form indicate magnitude and direction and <b>(r cos theta, r sin theta)</b> describe horizontal and vertical positions on the standard coordinate plane. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Trig class examples are made practical by asking about navigation, aviation, and cartography.</span><br />
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EyP5zKdau/KnrR10RGu/tq61MzPCXHZZayckjwklOWx58mg607aqZduA4E1vCUjf3HX4L9MVu6SDLzwrQExn84Z/+1etPff5HeC/GC92Tzr68wHt2363tQu+19q3zwi4vt7aHbcFCC9p7Zv5XQKE26YNHow3fMs7Wtvx6RnuQ4eA9gUB+T9e3Y0Wr4tRAHtfii58JYb0UKiCshBGc3EAffNN3TFq89XTA7znJa/U57yU6bZfxAhTh7MD+rvyG7i/9uUAO9SGgTw9BvBQyrT7jq298rWhZlH1ePRe+ZPWXpQ6APYOMbhXxOi3377b1sWwz/1ul+eEf9OqW5784he/aFdffXWo5u3trnDcx6uDVlNVebMHHug8734HdB1/+eUBQTqexwainfcMcF/e2mvf2Np7/lU82bcCgpe19ryA/g0B5k8CinVrA6QA/B8uDtCeu76GwLTvvvHo0X3E4a0dfEgMaLdw6OjdLYb0uRjMA/cnn2ui58ehAjd29+Lm3/tOa1/8XDxwwIwuXXD+er3KPRgustsphnHAPh3oH8xIcljyeThGJc2agPLEU1LWF7S2/7rWbk0ZCdDunXuA9uijuxFnu4D+jhjDNrnvS8n30ZThmgD9Z1d0RrhX0t+Sck8hWyTAt0nn8uA33XRTu+666zKfSoOtNuElv/WNeNRLWjv5lNaeGarCWz56ZzxlgLdzQH7fPa3deUdrV1+Zjg8g1wYoPCFg/vSyeMHdQz8Cjne9twPMB//DUC17YEQbLv1R8jksANs3wIvXRWduvytePuB8LMAkPDGjODxg3TPAOjw0Yb+kHyXo0XNe0tqbfzNU6NrWvvCJGGq8L9qxbUYQ1IhzeVp0biBJoGjk4Uda+9EPWzvymNRnz9ae/6KuXvekXAMHkPuV7YADu/QT/k0ptlzZNp21XYZqgF91AkgHPTMTzIDiS/GS+x3cge7bhwbE8XZHnxAw5vqf/cfW9tgr/DxeHF354mda++M/THVy/x/9+45jf/bj8dahNSe9dsNqGup33q07t2aP0J8zQm9+OwDfu9PHyPYNmK+9JmVJ/gS1OTzGtteaePYrQjFe3p33VzvuGsPbYcfu3I7Z/+A7oSW3h+YkrxedmGIF1LsnL7QHH98mx6jX9k9AjY6dd+7mAQwgt7WLzgyNipHsn7K88dRuAgzsjwX8RgmjzpFHd3lO+HebLXGp/uabb85E/7a2xx57tP32228A8gnbZdMlvz9e8JF4KBMsHX5JOPLZZ7b23n/ZHQsjPj382UZEPgz3qdsAROiAsN3j2e8Wj963ZddsA08aMPO4JomMq6Sfps7VngH00zrPIwNpOQ1zHdzepBgYB/qSRkEq3fA9RRmVC683cimX4xJ6pMPpPx+j/p3f6+pX18fbn7ZFe3BtsCq9d79zdGxfnn18uOdPA+SHO9AAcl94z7WhFiVAtOsTXrrO1b4A5hhNGJWun6buq/0wuAd6eiB0zOPz9iUDfT0Dcr4P3OHjmkjW/bWnhzwQ8L/0pM4BdGcm+jtU2onuXSSeVwtY1CivRuepGa4N/5MKr8fr2o8z76i0k+ZT6Rlhcfc619/Tv1I5Bh7/iXIPp2Vg68K9j39OPNUTUKVzWOgwkhgNhmSLBviq9d46BKDtrWCKaOCZg+N0oM4qr1edJ+Zc4veojr41w/m532uZXbf24f/Zpemnkyfdlc/3v9vFo+ntX6t8+nv39MWi1Pe/n8nuT/pnO8DTJd/rr+9Cl2Lbpd++RFnE+q/KiIWanR4q4r5+mZ8WTy4dsQJ70fnd6ObYeWlNRkWRvnNWzm0I8m3/JCLtapXhp3nvC4+8P4sQD8brLbVJ80isGcBtoij9tA+kQeg1CS3ZZMYw6PjruuV5HucXt3SAfPYJHfC+n0nb1el0kyy8VtTke2d3S9YmksIPF16YOPbPOk5a3FxFPv/J1j71kUxGX5KFloAPfbju2kwk9++4tFjzDy/I5C98Hij+87/LSBGKdPjRCQkmmiNGvn0mhqIzfVFmy+8iO2V4rgOucpo0Eos4F/0gob3o3isTY4JqPJYyq9MVifw8Gl0ojfN3BLAf+9+5lnLtnonvJT8aVG9wfr+U2cimvFdd2eV9ecr3N3+RyfcR3UT34ly76cauDOoqDi/kapLbyek5uzqlYtdi2QAKkM4B92Np8GHg92sBrE9LRwAysI+SHTLD3ykAkpbevdIhjt23UcGugz/0n9JBAcu7/yAx5ABizwAEmM/6RhdT3v/AdHyA+gd/1Nr/+mBi2Id2oTSTuT0Djv/35YTnXpAVvwD6n5/WgVIlgYbRGs6vOC+rizGac88JmO/vwn4fiVd33zn/IzToHd19bPynl2e5/ouhAkn/l7n2bz/QAYpOHteCzic/1tq/+P2OxwM573neuQHbwV283WT5jJT/oeR1c4zy5hjEAQe19pUvxRAz+bzy0qyKnpI0X2vt3/xxF8mhf2AwKffDue/ylPmQw7o2MWe4PXrksc++idbEYI89LmXePgaUvM7P+WuuyeQ7Bnl5dL/l7d1q6AXRcfAzaR7IqgI44AIb73vrrbdmnvVw2vHRAaCrwLwucALiUkKPTZodR3DZyuPudBxDAWgeXvqnxyOuWbNmEHnZXmPOW0Q7Wpr9DW9JRwQc3/pqF5c25F95dVY335aQ2FHxaj+Lp85wvFs85D97T0J2AeE3vt4tV1+fayeenEWgEzsvXWU8NgD9cbzgvvsEiAHF298ZAAU8114XwN0c8CffgwMgq4Uo0SFHJK9j4/UyMpz40qyU3ptrl3VUgLdOGw7KIf3lF+fZkHO6uPhRz0qOqYeIDqATHvTBGOBd0XF0dAr5WXk1UuyZOpyQslq1vTH58rpClUKJRz0796Yvd9srxnJ0a79xau6JjssC2ttuibdPXdYeEroTg8H5D07bHJV0t9/ZeXvrAbfFEERtdkmZgb0nKdXmFQADLoAEuHvuuWcAciAsATRABUTgBsDlwNcPE+6///4bUBE6jQhWO+VtK0rjGuNSBnntm5VA+TwjHTE3z/7LgGaPtV3H8bgPBwAtdQUU4TKey/6+e7qhfvsdu45VOOk9j/Le94f/np1VxhjAn/1FvNhOrnY68HNGdPCRnXcUC9/mCaBZrt82Oo4JqOj5TigS0JwTXSiNBZs1KVvaZCD2wPjTKwLc2zvDGIAyAB8kiS5lItKe9Jouzdf/rltEOulVT5QhQN5916QNkIUSGU7dY5K6TerMmaw9tNOnzo+mXCicyM8uGeGs0jKUqwLon9/cPQ7AqFAShiZ/OoC8J5sN4IAFaJbSAZu3BipAcg2odtttt4EndW7n8Dz7eQhjOfDAAweq5FVG5TfgMza/rYTay1t5yrPPXIb054C/UmTZWqwbRTkuwPvQfw3I4n113D99d/cg03/5k3ipAOzt7wpvvaO1L38+3i6eGE/luUp2DxhuuL6btFn+Ji5bxTz5lNb++i9DWb4d8OTkya/o8jznrG6FlGHg4Hiv1VXDPACdlHSeXbknHvM97+3i1aXX6FD5W5E0f7g13pR3Tt8NDI0B6Lfg71dSRsGYd4rRnRvj2jEGYJGISL/HmjxicGQmqV+Lt/5Fx7MPOyzluK+bg8j3jls7L4+G3nBdyh6ga5eebPKFHoCx3ZIJCT6NJ5Oa8AERMPGcNqCfVFby4MvpM5ooH4qkbH26g77sGS/C8Kq8y+kaec3IxCuaaAH1FZcHGN9t7Z+8rfNAJlU7BpzHHN8N4Z4VNwG0iGMZG6hEDHg3TyLuEwMp4Y09zurJPIC1tG8iZ3RYE9BdfVXoytUB76G594iU44ZukYYxXXlFN/nkMfH4Zx5SWjuP61kVS/hAT9JGg8dmeU2TUsc8qzxM8g49vDvnMdjByBHQOn9rwMrLokDuuTuGc0PKwdCJvXtMdneI7stTH8v2R4SWBBuDtoMJK6PX5T4LZEYVhnnhD/IA16tSztS7k9M2KcBr+Oe1K5KBclhO51VN9IBoVpkF4JU3imRUYYh+A775gLICN+qjrMtRpdK17F4nm8C98tWdR57CoJfVvzVcZNjXXttFpF6U0aaMsLVNA3AesXgvOkCARNQCqFGAaTz1Un03D4AP6y6Pjq8DvG2XeKK1WVVccaTBM/HEEquRJnwloWppgHiseK2FTN4C6YuBB9d+68FNz8ZdqgdsXvvOO+8ccG0esPh0Pyw3eY02/R17h1cCtZHHcy6AjmJdf/31g9Fn2WdefnB23tz5bwF1gHx/yv6+f90971wgz+i1kBlaAGdHU0ZIz42MuDrDKWA2xAO3jYc2vPPW86IiMxRvqlvLONEqE1D1A/iiW2W0TxqNbglX/OY3AvDMN+5N1m8+NRw5XidUdyEbtwU2CsCB+47M9i3SmKTpcBybFzRBe6oLSnJwYti8ODoE6KiXaJDQoonoBpPQ7TJZ2j0TpKcF4EBtArXg2psEBnMFuCEcoIGb1/abtwNq2zwmkJukVcbMxGh0QCIL5hc1Ga09kP/qWXQvBfzpfw+oE9kIHW8nPD9AX7jvMZt5pmRzAzhwi44ANo8G3DydjrbNK4Y9bm2fRBPGvXHCdEKaNvn9PJ9UUG8jF4/Om5uIbrPu4DwVl20hm7wFws5nF+AGbJEGEy8iQrJPYrQbE9wmsfIe3uTvGtCNuub6vMXLFSgYr0549RsS37033wlRloVsnhaYOQ6u83BP4NapuCc6YsKFd89beMiS/hJ7nbMHKtdQol2zENAfPXhU1IFswJMHZ2b/oz1MQLUJ45KHmLk22VSjyuy12GI0zB4mNBQXuAGHJwPuAtG8mgqwAUZeKBAxWjg3LIBkY3AiHCXAh04U4JXT8TzLKl+8nAC5cgO8PMq7V3kW+43fAjNxcJ0HQGLdOnD3LNnOE9wAWXy+ohTyIq7xjsV/+03lHsAHNlSpxL1AX0ZhddIkGJWii8cv8Nc90+zly2vbm5dUO9XjuNPonOs9abs0bJbQ5z/CzrWcc1A2NcB1Wn13BNgMwXN7GCkVox9QheEYEbDUZvIKjMCJ4zvuy1IrmTwq+gLgKIw9kPu0BMGh6WOs8ppFGEp5ciD3EBedRriNQY0mKqtPUXiw6uWvmOi2JRMzFostabfVJlOVqOLcwoG8Is9k+J3HUA/Y9DMeYKS/vCrwFbDtJwUhI7QVwBmmfHh1v61Qoj1GIXUaNpxpOo8uo496VZSFIVWdptG55D0x2gxp3cNRqFlGpcHTevU+oxtTjsErYt4I8vCWh7LSlk2sfilxj0cN6lHXAe3LKGAlFqgv+VH3WOthh3cPdq2ikWEqgOswwNBpvCivNA9+SR9Px7sCHQEyYKs8JgX1qD4DLpNPYiIsL+A2YjAqx/K1/D5rvbSPcGGBW/0YJ0ObqwDd6Z9r7Z2/m7d/LsrXqPJkXfqlvezkPFV4YPfknlEJWC+J9z72+Lzi9qkcB6je5PFi7ygPzAA8aXjJpXniMc+Le+3tnDPTMTGktXlc17da7s7zRfcyrkSQPPnoLXiGtgpk4jAhENTSNBCgJbj3rB4JuC2SCDeiDXSLeKxbt26wDeLJM9KGUe0N4MB2yCGHDDw34PPmynBjHhEFeMfTStES7YSa0EWn+s5VvG3jAzvowukBrjdqvDTx95/vznm3k8Q5Dd4DvSagveHa1g6J1/3E/41Xv3JwecM/qXcm9YOPE33/zM7be6/yoeRxzLO6r2ntuVf2eTz1qKO6FxN+kuvXXLOhms14NBHAgZunw2Wr44BjVk6ps9EdegGA1zO0A/eoSeTGaC/1Mdn0dCCvzWBrDlCx/VnyRUtqjqKujHkWw3lSWb4eIB93XAfm34wXf/FLs3IairJdJpKXxat++hPdE3eeJfeu5uHH5JNvp7X2rKO7lwvu85DMkHh52HcKd4hnXndo90KB9yHvuztGEoMxgce9vWLHoFATn6C76LwhRZvvcCKA89w1OeP55hFiA26hPxtujMePfJ5jE7VRUZOKl6MrwnzqPSsga0LMeIxUFRGauWoipXflxYFdQgsy6g1ezvXO5UUXhBMn6rRm744/n/fdvEAQD4uSeAUMrfirDweUAe+zQ1H6YoTxJVn05ORT8p5k0nrpea/o8s6laJYXo40IJShO6Njgnjq3mfdjA5w308n2gM0j2c8idPFkPBpwMxq816gwK+WZpVxGEBEQ5WBwymlV0txjFpAb6ehVT/VFgeZCVby/OHi3Md0pQuIb4j6s+a53x9PelreBwsVPfmU+x/yxvFSxX95tDK3wVvqn/qb77PIb3xSOHivxChiDICnf4JuFPPRZZ4SDX9i9ynbgwd1njl/4onjvTEx9rP5Xsk0mnknvK7arRMaeZOKkNp2EpxrGZ5nwAQ0vJoRW4GY0G4trT9re6omyqKMy8rYmikT9p607p6CORgZtwGkwpJkkBtn2iOf2epqvsP70J3nt65aOUvDMO8cRAbbX0dLGg1fBLvx+9uHY0nmB+djnxeOHx/uA55p9zO5be+tvdVGR66/LpDH8/jlJ892k5bV3CJj3jC6vx5Uk+pUoQehPKMsqkbEALmxnYoSi6IxZPbe6i8IAOI8oqgDcswBnY7Qn7w3kymh+AJBAzsMr87RiUg7YuL3Ri7OYdR7TXvuOeNhLQx/Cw990amhC3vX0gR8ARx2A+7T3dRRDSPBVrwsYQ2MeD1ClA2iUpT+fZjg2X7n1sX5GcsqvJ1ISmvPIAxkVjul4eDWErwHccnP3CYo6t5n3YwHc0KxDdLiO1cHTejBg4Q2NBn4brmcFNz22vlT5jA71exraA3jmBEQ7lNfF1acFpToDtTbgNGy8+kxi0eYLn+nCgOvixW19yUjUBt8zeeLks47PBDNbifZ7xRu6F4jrXO29NOwbLgS9eenLu9/Df33bxQvNaMwqkRUBrkN1AC/Ow9qm7Vh1Bm7em04GI7IwCy2hr4Z7IAdmx0TZ0QvABnQjjzwZ6CRSIKeDJxfLptOkcVpRbwYD5HSK9c/SroOIxpvf2sW7pykUAzjooGnuXH8P7n3iiYmmxCBWiawIcGAxlOpQ3pvnmlYAUIcaDfzmxYBuGs8K2DYApg+Yy4vTB+iMqB/iU37eUwhSPSapC/ABJZ3yKmoxqbFU2ymjcojQoGpGsZkATrFPtKVNV5TUIQ3RfZ7BpxyW69M4tsH3BJ+e9H0xCcXFBRrq/hloW1/1PH9nyru0AAzPba/xZxmW5UIXwAEmcOOiPOokIuoAZEYB4AA0+pSPTiNM6bQ3OtiUvTy6iAgvPOmCCx21qMXwaw4xSfkrLQMs4/ab4c8kPpP2rW92FAX40iZp8CertOp4biaKJqRf/2obfGcE4N1D0tcDQ3Gvcz+7MiujF3TnrWoyIteU9+ILu/+i1t25Kv8uiy7A4R3tAWcSjzdcW0YCYMDpN2+og3XuuALchvVaVndfTfiAGfgcCz0yAGUu/uwYxWBg9KAFNtfdN473lIanVQflKGOd1osXyKtODHGa0WzQft8JaD0roj3Fru8LEC2+CBf2xbWP/nlrf/iB7kP7PqlmAmpFE0W55uruK1G7h2vj3T7DdkPOHZe4ua9H3ZooiY8QHXFkGj+juXDj2tznY0WrUJYFOCDUJA0YbdNKgRM48E2AnAbcPK+RANgAgte27wO09No7b/P4KkFpeEt7ZaoVxXFHEzpFkoCb8dumBbj75Avg6mSbVlc748ut/f7747njZT/+kUwWMzF+/ZufDHD/cvBuWzz5HQl7/jiRF//d7LLLEhZ8R/d8yrYB670ZEfxvS7Hxe+7ovuh6zpnx6kkL8O9+XyaTh3TfNQR6y/WrUJakKLysTgRIYOwDaJp60EMfDwWUuPC4wsgAEhiBAMhM8CwKjet9Ky/peW2eWL3oZjT0+z2OePCLkSoHiqRM04p2VQ46UJ6pxANTdweEzxCJSR1Sn3bSyXle5Ngnq3vuC+OZc/458cjoyGtem08P/3bHx394fsB7bSaKL4uucHlflX3ei1s7NOn98ynfQjw+911/TTz9z7qICwPYYLHnyVluzjNLAlyhUBMNX55y2oIyFrpQFBM9AAeOcYXHLSAxEOC2TWt0ZSCAinYVyBnhuGKCSJTNSDCtGBUZizJon6nksfBtxskT2+99YMCYjdwV4ItPl7j+SI4fTF33DrXYY59ukrjjTvHU8drbZZT2Jdl9AmZL+P4DhS/g+jSaBaEYdNtlj5xLnoQhxEBXqywJcKDU6MBgm5obpuY6rkJ35bHGbZCaBzA0ng4o8Xe/ZxF14sUL5OqLKowLMvnb6JnliUPtWm2svW0Ti7DnrgFojQAiI4Mvv0bT976Vj1RevV4l3rzL7vHUNwTga7qHpTKKDDy0lcqDYhgmk/4Zq+dO9kgo1Ef70RBffN0pI6+v2DIGz7/sFUPwbw5XqSyJEsDinXTAtJ6y6gzcuKqOLP5d11baG7ZNKnU8QPKcs4K78iyQ28vDRJSgMCsZNK6Mi7vP6GJEoWcaMYq41wiizaea67z67d1KpmVyq46+XktSvrau58E9UvvOd3cT0te+vnsQy/Llq1/XLQ75SP1VWep/VmjJMcd03Nv3x4+IXu4QHXrb72W0yG9fyT14Xffd7hyuRlkS4AClsWsSt1KHL1U5egzhPCQdOnNcg3GPTrd3n7KMe+9S5Rk+D1goGENi1PJT5pXqqxyMlSgfI67j4TxWOma09SiEMkwlJ5/S/T9JRnbU0etVnBTgPkGnBid56+e+YP31+nXY4d2vw4/IsyTZSowOv/bS7mjNy+tsF448/7wYwbO75fz1V1bVryUpilLqfB2ps6f1TqhFhdMm1VH8FoBQCfx9Uh3jtLYJb0ViGOO4NIVubSM976+c04jRQL1qm0bH4HvbvxHPHePcQIT+YsBzF3Xl5Q8JT1/FsizAlXvaTqs6u790AKhtHOFFeVUgBwAgXMmrFtd3L7DY86y25TyjtEYH+dCBi48zcaxy9es4Tt02WprQpPC3DdWnbhtF5JOIVDplo6ifl9Kh1piX2ifrASJD+LjhQVSB5wdSQFrOewOYIZ4XBdACON7PQOSNt+PWyuB4WCwKMSjGgFMXNRtO1z+mq/hz//zi9+ppgU1qfuXJx6k+kPKiKNJy3JtOHtcbQQBdnrfyAmagZzDi3cXpR5WhlvnpcH/pGJV2ce6p0QKbFOCTNAlg2tCSpQDOCHhukQzAldZCTk32eH0hRefoMiIAOUMYBV48fCUaNEkdFmk3fwtsQFH6nd7/rZjDx5MUvX9v0YdJ7+/rqHt52uLpgClsJyKBYkiP2jgH8I4B21YREPu+MILNLauhDJu7DeaZ/wDggMIT4p/VwKIfxPAOMMNgGLcQdNcErzh15bGcjuLS0gDxqNg33Tx3CRB7gMo5ebjeXyBSDpzc3jZsNNLXubp3pbJKLw3DlddK6ausw/vSQ0e1vTSj6j187+J46RYYfF0WmHzuDJd9qg7RBZCqqmMevD+pBHx1LV4/DEb3MHTgRotMIFcSOjmG4bxWum/4unwBu5+v8giPOreQqVqg+7osUFs9s69O19g8rk4eJ0S3VPY8W4Xp6AGEymOpe5wHMvkTZRs1gtAtjbQV0eCZ5Uf8BuiSyld6D1eNEmls9ALYSlLph/Na6b7h66VnOF961e2p6niG67mpjwcUxTDIU/T5saGcdwJIvNZ+GtFBIhwMxiROPjpzJcGVC6iWwUfFz+m2AayJJP3uqUmnMvN+BQ7gUSf1FTGp81UWgEaH6MPdxwkBGvXkqXzyGqdulV9/L19tpFz9UKoyTauzr39r/f2rSeYw19PYGhcIXBtnuB7ViIyGjtI1rqHIU8e6X96j8u93vrRVzppMAoooSnl/NAzIpRv1TAtgA2wBjcGsBC7g5gyUz7MyK6Uf1UbOyddow7CAvC/T6uzr2Fp//wrgSzUAEM1LJu0oedsAiGEMe1zlqvLxgK73wSE/5+xREt67ygD0w/r69MC1unec+vfzGif9UmlKz1LXF+cna4Fl4+A6GAXgpXjSWaSA2ufE4+jjTWsCNpweSIufAy9qwnsX6KVXbpEVNEneALQUlWAEvLg0tpVEu2iffn4r3TPqOu+tnOPkOer+xbmlW2BJgBvGDfE1BE/biTqtPCUQ8sbjCI9dy/OACXjDAuD4Oa8tH7ot19v3j4EbEJ2T3lZlKp0MST6AxgBQDumXE/loH7qKBi2XfqlrDFD+6jtqrrHUfYvzK7fAsgDX2IA9i/fW8fQwGLrGNRQAL+8MnAW+4SoxQoCt1UoevADuHl4dCIFVGtx7FJ+vUUI6PHjcuYL6qFsZ2XD5xjnWvjZ1GTffcfQu0mQdYZxGKIAJV00qAA4A9qWHNx7H45nkGb5xY3udP6oMdY5OusuzypeRACFQM4RR4FYuXpRBMEb6VvLePK5yEfnKZxqRpzKPa/jT5LE137MkwHWwzgYq1MJWQJq0wXgmugCJNwWOcQBeHg1geVhe0rlheqE8yga8gOJ5E/c4V1GU5WiEuikXoWOUEQwu9v6oA6MjPP5KBtG7dYOfymmTJ4NeyHxbYEmKIpsCuM7kaeynEaAsr0hPgWkcXbxudTwuXROyUffy2IACzIAOdAXYpQyKPjSGF+WF6z+ujdJf5+gGSu3hd9Gjuj7uXp7awl6ZGcpC5tsCywIcOAATOAzHPN20UkM/gNM1Lq+XPwApAzAAeUU7pi1L3YeW+BRFgUwcWznHEUZBLFwxrGmEgXjOB7jHXQCbJp+t+Z5lAQ5UKIoO0BmzcMUCuMZGNwB9XAHyWnQpkNMxrpGMysf9FTqkx+SzRplR6fvngFv5jRBok/aZRrRpjQKzTFKnyXtruWfFnqkhHrh5Xjx6GgECIAUiOgzx4wKUh+RdK7wHFEDGkwMamjCuMBC0pDx3UYxRK5ujdCp7GRdKI6Q4rTAwgsItRaGm1b24r2uBFcdWnlcnAiSA23TGNB1iNChdAApceOc4uhiaCSNDMawrD4CgGYzGdV6wTxdq4icfK50Mqp5xYSTluYEbyFYSxiRPVE1+RZ1Wum/U9VpZVbZxjWuUnsW55VtgRYADFODoVOAAcCAdB5TDWdMFSMBBH084iS738eIMBbCVRZnoUp4yPueA23memvDawFSjBsMFUHWjdxzh/ZWZHmWoye849/bTuL/mEYzTSFDG2E+3+D17C6wIcFnoTJ0AQAUqk6JJRSfS415DPSACKtCOazDAyOsDKI/KmwOy37xyibycsxEUi3dnYDym+9WL0Y0jwC0vetyHMvVHi3F0VBqjiXZURgZO30I2TguMBXAg4K10Cg8GUDpmXM/XLzog85w8Kn2W1umfZLiXvgBqz0iUCfgK2MAuL+BxjvDWPKZtEgFuI4HyGgGAe1rvrYzF4RnbInoySU9MnnYsgFMLKLwv7gtQZFzuOkjc+wN4wFZeF6/V8fSN68mpA3TlMgLQV0Cmj5dU3lroQQsYpHsmEeD2j6eMNsAN2LOAu156VtaiW5OUZ5F2shYYG+CAUZM5nsymo8eZnI0qEo8NdDw4ulKenEebBOR0S9+/p0AMRAygf21UWZY6V567wM1gLARNS00YMefAUIpqlVEuVYbF+dlaYGyAywbAeR3A1PkmSjoKTZhUgA6Y6RJR0en2ZBqQD+dP7yyifuVtlQ24fUR/UnpTZTBaeeECyBndLBy+dC72K7fARADnGU3wdL4OwyUJGjBNxxfI6QXuim8D1KR0ZeWqjp+Cx1YeoxRAoj889zR1lGuBu/TRtViWH78/Zkk5GSFNTsBYkzVeEsgrNjxNQQz36ApA+w3kohUoC2BsSqmRSX2AHLiLx08LbvSrODx99KB2RaM2Zf22xrwm8uDVQDqJ18YfAdzEk1dHVabhlOXJee7i5CaJQAb48gP+aXRXmZfbAzZjqgUkntY54PZvUqYFtzy1C31Fc+ibhtItV/7FtaVbYCqAA5owIRDoOCE6kyd83PlpBMjxe7oBGyh4c97PRJaXp3vaCd5SZZIPA61lf3kCoHzqY51L3bvSee1SESLGQp/9QjZdC0wFcMUDREMtz8dLASVwmDxNyy+BiscGdMDjUUuvPXAwBB51lomo8hopGCe99oxVnQ444ICB/lmiL9qHwYidoyj0G/GmNX76FjJdC0wNcNkBBDADuQ6t50Nc68elHY8rxU0rBCmSUYs46JDrwF8RHAYBjH0BKGJfAHPsHjqcV+ZKV6OCKMk8+HE9zCVvhsNgF+DWA5teBp9umzVbYBF1wJt1qCEepQDyYfBNmpeJGZ1AY+t7XMAEeIbWF8C1Oc/jl9R5ezqNBMpq1JHONqyr7h1nb2Sw9T23kQbvLiMaR88izdxa4LS5AFxx+iB3DCgAJCQ2D95ZoARwnpHUqDE46P0pkAJxXxzzprU4xasywBo1+mkn/Q3YN95442AUcy/DZDjq3zeySfUu0s/UAvMDOPDg4EUfUAECRDoayAt4sxS5QGsPVIA0LPi1/OWJwvQBzOgcu79/fljHuMf0MO4Ct+PKdx50Z9xyLNKNbIHu45sjL014Enhr+ZlXdCyywuMCgM420ZqVspSR2APrKAFuQKuoTnlQ5/r3j7p3knNGlZtuumngtdWRsann2rVrB3lXXpPoXKSdbwvMNMkcVRSditcCM2AVpQB2AMPNXS/QjdKxsc7NE3DqU+FR9cKxzTmEAmc14o1V/61R79wBrhEBiXfFdVGWWumsxRs8uBaKnoqNLrJjUg3YBW5eW503h+E+FdtwU5V5owBc4YFcZxuyAZ3Hq1XKes4DP8ZX58GFN3aDmdgKgyp7cX/lrri5UWkhq68FNhrAq6qAbsgGZoDnxQEFdTHEi6MDuTQMYTWBnXdWTvsCdoUaTZ5REpRrNZW52n2x71pgowO8GhoIgAGYyxPaC/XZgN8Qj7rwhvPky1WGSfZWUdErAK8Qpb06FLjVaQHuSVp106fdZABXNWDgpXlrGw8OSIZ84EEDRCOkA3ZgEgkB9o0JpAo12uPX9sok7Ml7y1s5KqZvQrm5DXDTQ+WpmeMmBXg1EXDUJBRFMfwDO3Dz6sAOYFYuCWOwIlgrl4xkHIAtlQZo5UMYlfzlWccFeGWko+YKQL6Qp1YLzG0lc5ZqF6AAHC0AOrTFHnUpoNoDOYrg/FJS/J4hSDvs/XlmxgPUdAK837YyJvoZn+v9MiyV5+L8qmyB+a1kzqN6gGYjPDrgi7zw5nW+n2apPMsgXK/7htNKU+kAW+jS/IAB1Rxg2DCGdSyOV30LzG8lcx5V7YMO2AiaAICAal+AXy4/hsFLAyiPPCx08ez9CAj6IX2BfviexfFTswU2Cwcfp6kKaMO8d5x4s6f58GoxeE/yjaIzfWMapzyLNE/NFli1AF+qOSehDUAs/ST3LJXv4vxTswUmfun4qVnNRam31hZYAHxr7fmtpN4LgG8lHb21VnOLBHiFEpcKEW6tnb011nuLBLhYdj3AVdGYrbFzF3XOU63xchu+uLgFtEp58EUocAvozNmqsLoWemary/q7F8Be3xZb+68tkqJs7Z26qP/6Fvj/u0+kO7cNovsAAAAASUVORK5CYII=" 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" /></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>(r, theta) POLAR coordinates </b>and<b> r(cos theta + i sin theta)</b>, the<b> POLAR form of a complex number,</b> combine what we know about Imaginary numbers, Complex numbers, and the Circle. Real life uses include navigation, robotics, and electronics.</span></div>
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" 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" /></a><span style="font-family: "arial" , "helvetica" , sans-serif;">The visual aide graphs demonstrate that each of the forms uses the same related information.</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">RECTANGLE (5, 12)</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">COMPLEX (5 + 12i)</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">TRIG, VECTOR (5, 12) </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> (13 cos 67.4˚, 13 sin 67.4˚)</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> or</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> (13 cos 1.18 <span style="font-size: xx-small;">radians<span style="font-size: small;">, 13 sin 1.18<span style="font-size: xx-small;"> radians<span style="font-size: small;">)</span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: xx-small;"><span style="font-size: small;"><span style="font-size: xx-small;"><span style="font-size: small;">POLAR (13, 1.18 <span style="font-size: xx-small;">radians<span style="font-size: small;">)</span></span> </span></span></span></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> 13 (cos 1.18 + i sin 1.18)</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Any two pieces of data provide the basis for calculating the others and constructing the required form of a point.</span></div>
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<span style="clear: right; float: right; font-family: "arial" , "helvetica" , sans-serif; margin-bottom: 1em; margin-left: 1em;"> </span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-46305500782508112952016-04-01T15:52:00.001-07:002016-04-01T15:52:31.291-07:00THE NEW PSAT AND NATIONAL MERIT QUALIFICATION<span style="font-family: Arial,Helvetica,sans-serif;">The decennial revisions to the PSAT and SAT standardized tests necessitate a revision in the conjectures about and preparation for achieving success. The 2012 blog post about the PSAT needs updating to reflect the new format of the test. Here’s what to expect for the upcoming Fall administration of the PSAT/NMSQT.<br /><br />The new test has a few more questions and allots about 30 minutes more of testing time. The difficulty of questions is equivalent to previous administrations, but the format is significantly different. The vocabulary subsection has disappeared, and grammar questions are now presented in the context of a full article. Reading passages may contain graphics and visual aides similar to sidebars in magazines and newspapers. But the biggest change is in the scoring process; there is no longer a penalty for incorrect answers. The score is a reflection of only the number of questions answered correctly.<br /><br /><br /><b>WHY THINK ABOUT THE PSAT?</b><br /><br />There is no greater honor for a high school senior than to be nominated, selected, chosen, recognized as a National Merit Scholar. The only way to win the honor which represents the very pinnacle of student achievement is to get an outstanding score on the PSAT in October of Junior year of high school. The path to that accolade begins long before the actual distinction.<br /><br /><b>WHEN SHOULD STUDY FOR PSAT AND NATIONAL MERIT BEGIN IN EARNEST?</b><br /><br />The PSAT test serves as a qualifier for National Merit recognition only when taken in October of junior year. Some students begin preparation in Middle School, others after completing Algebra 2, and a few as they enter eleventh grade. All 2018 grads should be thinking about this opportunity right now. Many high schools offer a “practice” PSAT to sophomores. Those who demonstrate the potential to excel should double down on preparation immediately.<br /><br /><br /><b>HOW DO YOU KNOW IF IT IS WORTHWHILE TO STUDY FOR THE PSAT?</b><br /><br />Recent changes to the PSAT and SAT tests have created a significant parallel to the ACT. For this reason, results from the first 3 ACT sections are a good predictor of PSAT prospects. The best source of practice samples, of course, would be the College Board, but the newness of the exams limits the availability of previous tests. A few examples of questions and a sample test can be found at <a href="http://www.collegeboard.org/">www.collegeboard.org</a>. Other prototypes offered by a variety of publishers may or may not be reflective of the real standardized test.<br /><br />At Tutoring Resources, we suggest that students take one of the REAL ACT tests out of the study manual of the same name. Individual section scores over 30 on the English, Math, and Reading portions are good indicators of the necessary foundational knowledge. <br /><br /><b>WHAT STUDY GOALS SHOULD BE ESTABLISHED?</b><br /><br />Students identified at Tutoring Resources as potential National Merit scholars are invited to study for the PSAT beginning in the Spring of sophomore year. Each state has a unique cutoff for NM recognition, but in Illinois, we generally expect that a student cannot miss more than one question in each section in order to achieve a sufficient score for National Merit.<br /><br /><b>WHAT IF I DON’T GET PICKED TO CONTINUE THE NATIONAL MERIT QUALIFICATION PROCESS?</b><br /><br />As a certifiable academic, I will never be convinced that learning is not worthwhile. With that prejudice in mind, I would argue that recognizing a high scholastic aptitude is a reward in itself. Striving toward the coveted academic award has its own compensation in terms of personal satisfaction and ultimate success on national college entrance exams. Winning a National Merit Scholarship is the icing on the cake but only a small part of the whole experience.</span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-44131484988600407652016-03-30T18:35:00.001-07:002016-03-30T18:35:45.527-07:00DIAGRAMMING VECTOR FORCES<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">Once the basics of vectors (magnitude, direction, computations) have been covered, most courses introduce practical applications. At this point, the rather routine manipulations become more obscure. The first step in deciphering vector word problems is to design a visual representation — <br /><br /><span style="color: blue;"><span style="font-size: large;"><b>Step One: DRAW A PICTURE</b></span></span><br /><br />This step cannot be too heavily emphasized. A picture puts the problem in context, allows labeling of key parts, highlights what is missing, and puts the problem solver in control of how the relationships are depicted. Having a standard framework from which to operate is most important in controlling the problem. Here are several routine situations and common patterns for designing descriptive visual aides.</span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><b>GIVEN TWO OR MORE VECTORS, DETERMINE THE RESULTANT</b></span></span><br />
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<a href="https://www.blogger.com/blogger.g?blogID=7971595768928070725" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;">The most simple situation yields easily to a ‘Head to Tail’ approach and uncomplicated vector computations. The design simply puts the back end of the second vector at the arrowhead of the first. </span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><img alt="" 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" /> H<span style="font-family: "arial" , "helvetica" , sans-serif;">ead to Tail ---<span style="font-family: "arial" , "helvetica" , sans-serif;">> <span style="font-family: "arial" , "helvetica" , sans-serif;"></span><img alt="" src="data:image/png;base64,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" /> </span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Converting multiple vectors to Head to Tail...</span></span></span></span><br />
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" 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" /> <img alt="" 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" />---><img alt="" src="data:image/png;base64,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" /> </span></span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">Word problems often involve opposing forces: airplane encountering crosswinds, crossing a river with a current, 2 people pulling a cart in different directions....what is the resultant vector, speed (force), direction?</span></span></span></span></span><br />
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<span style="clear: right; color: blue; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" 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" /> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"> <span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>EXAMPLE: </b>Plane traveling N45E at 200 miles per hour; wind blowing N60E at 100 miles per hour.</span></span></span></span></span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> RESULTANT VECTOR</span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> <span style="font-family: "arial" , "helvetica" , sans-serif;">< 100<span style="font-family: "arial" , "helvetica" , sans-serif;">√</span>2 + 50<span style="font-family: "arial" , "helvetica" , sans-serif;">√3, 1<span style="font-family: "arial" , "helvetica" , sans-serif;">00<span style="font-family: "arial" , "helvetica" , sans-serif;">√</span>2 + 50 ></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> <span style="font-family: "arial" , "helvetica" , sans-serif;"></span>≈ < 228.0, 191.4 <span style="font-family: "arial" , "helvetica" , sans-serif;">></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span>SPEED</span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> √((228.0)^2 + (191.4)^2) ≈ 297.7mph </span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> D<span style="font-family: "arial" , "helvetica" , sans-serif;">IRECTION</span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> Arctan (191.4/228) ≈ 40.0˚</span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> 40˚ = N50E</span></span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">NOTICE that 40˚ is measured counterclockwise (anticlockwise) from the x-axis as in a trigonometric unit circle (since that's what my calculator does)...but the flight direction is a bearing measured from facing North and turning in an Easterly direction, so the correct answer would be in bearing form.</span></span></span></span></span></span></span></span></span><br />
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<span style="clear: right; color: blue; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" 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" /> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;">EXAMPLE: </span></b><span style="font-family: "arial" , "helvetica" , sans-serif;">Crossing river in motorboat going straight east at 20 mph; current flowing straight south at 5 mph. What is the actual speed and direction of the boat?</span></span></span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> RESULTANT VECTOR</span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> < 20,5 ></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> SPEED</span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> √<span style="font-family: "arial" , "helvetica" , sans-serif;">[</span>20^2 + (-5)^2 ]</span> </span>≈ 20.6 <span style="font-family: "arial" , "helvetica" , sans-serif;">mph</span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> DIRECTION</span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> bearing S76E = 104˚ from true North</span></span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>EXAMPL<span style="font-family: "arial" , "helvetica" , sans-serif;">E: </span></b><span style="font-family: "arial" , "helvetica" , sans-serif;">One child pulling a wagon on vector < 10,10 > while another pulls on vector < 5, 5√3 >. What direction will the wagon move?</span></span></span></span></span></span></span></span></span><br />
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/> </span></div>
<span style="clear: right; float: right; font-family: "arial" , "helvetica" , sans-serif; margin-bottom: 1em; margin-left: 1em;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">First, orient the forces <span style="font-family: "arial" , "helvetica" , sans-serif;">with the coordinate </span></span> <img alt="" src="data:image/png;base64,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" /> </span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">plane<span style="font-family: "arial" , "helvetica" , sans-serif;">.</span></span></span></span></span></span></span></span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Place vectors <span style="font-family: "arial" , "helvetica" , sans-serif;">head to tail. <img alt="" 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" /> </span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Recognize the task-at-h<span style="font-family: "arial" , "helvetica" , sans-serif;">and is vector addition.</span> </span></span></span></span></span></span></span></span></span></span><br />
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<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"> RESULTANT VECTOR</span></span></span></span></span></span></span></span></span></span></span><br />
<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"> < 15, 10+5√3 > ≈ < 15,<span style="font-family: "arial" , "helvetica" , sans-serif;"> 18.7 ></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> <span style="font-family: "arial" , "helvetica" , sans-serif;">DIRECTION</span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> Arctan <span style="font-family: "arial" , "helvetica" , sans-serif;">(18.7/15) ≈ 51.3˚ measure<span style="font-family: "arial" , "helvetica" , sans-serif;">d from <span style="font-family: "arial" , "helvetica" , sans-serif;">x-axis</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> <i>A v<span style="font-family: "arial" , "helvetica" , sans-serif;">ariation on the basic question might ask how much force is required to PREVENT movement of the wagon. Instead of the force applied in the pulling direction, the force would be in the OPPOSITE direction. In the wagon example, a third child would need to pull with the resultant force at 231.<span style="font-family: "arial" , "helvetica" , sans-serif;">3<span style="font-family: "arial" , "helvetica" , sans-serif;">˚.</span></span></span></i></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
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" /> </span></div>
<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><i><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"></span></span></i></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span></span></span> </span> </span> </span> </span></span></span></span></span></span></span></span></span></span><br />
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<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;">This variation introduces....<b><span style="font-size: large;">GIVEN OPPOSING FORCES</span></b></span></span> </span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">This "<span style="font-family: "arial" , "helvetica" , sans-serif;">weighty" problem frequently involves a weight hanging from ropes, guy wires holding up a pole against the wind, or people pulling in counterforce. This drawing requires the <span style="font-family: "arial" , "helvetica" , sans-serif;">tension</span>s exerted by the upward forces to equal the downward force of the object (wind, third person pulling).</span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="clear: right; float: right; font-family: "arial" , "helvetica" , sans-serif; margin-bottom: 1em; margin-left: 1em;"><img alt="" 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" /> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">EXAMPLE: A 40 pound weight is hung from ropes at 30˚ and 45˚ angles from the horizon.</span></span></span></span></span></span></span></span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> U = right side rope - 4<span style="font-family: "arial" , "helvetica" , sans-serif;">5˚ angle</span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> vector U = 3 cos 45˚ + 3 sin 45˚</span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> V = left side rope - 30˚ angle</span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> vector V = 7 cos 30˚ + 7 sin 30˚</span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> W = hanging <span style="font-family: "arial" , "helvetica" , sans-serif;">object</span></span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> U + V = W</span></span></span></span></span></span></span></span></span></span></span></span><br />
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<div style="text-align: left;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="background-color: blue;"><span><span style="background-color: white;"><span style="color: blue;">NOTICE that the smaller the angles, the greater the tension on the ropes.</span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></div>
<div style="text-align: left;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span> </span></span></span></span></span></span></span></span></span></span></span></div>
<br />
<div style="text-align: center;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span> <b><span style="font-size: large;">GIVEN A RA<span style="font-family: "arial" , "helvetica" , sans-serif;">MP</span></span></b></span></span></span></span></span></span></span></div>
<div style="text-align: center;">
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<span style="clear: right; float: right; font-family: "arial" , "helvetica" , sans-serif; margin-bottom: 1em; margin-left: 1em;"><img alt="" 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" /> </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">In researching this blog post, I ran into more "ramp" problems than any other kind, many of them in Physics examples. Because of the ubiquitous problem type, there are many diagrams, each with a special twist. For use as a data gathering structure, the ramp, load, and solution triangle should be controlled by the problem solver. If the problem offers a drawing with an unfamiliar layout, I tend to redraw it to my own lik<span style="font-family: "arial" , "helvetica" , sans-serif;">ing.</span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Ramp problems require more description of the forces applied. Gravity, of course, tries to pull the object down the ramp, but the force is actually <span style="font-family: "arial" , "helvetica" , sans-serif;">PERPENDICULAR</span> to flat ground and equal to the weight of the object. </span></span></span></span></span><br />
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<b><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">EXAMPLE: </span></span></b><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">What force is required to prevent a 100 pound block from sliding down a ramp set at 24 degrees from horizontal? </span></span><span style="clear: right; float: right; font-family: "arial" , "helvetica" , sans-serif; margin-bottom: 1em; margin-left: 1em;"></span><span style="clear: right; float: right; font-family: "arial" , "helvetica" , sans-serif; margin-bottom: 1em; margin-left: 1em;"><img alt="" src="data:image/png;base64,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" /></span></div>
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<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> SIN 24 = x/100</span></span><br />
<span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> x = 40.7 foot pounds </span></span><br />
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<a href="https://www.blogger.com/blogger.g?blogID=7971595768928070725" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;">My Physics friends use a more complicated version of the ramp diagram. It flips the triangle and places the force to push or pull the object or prevent it from slipping down the ramp on a line PARALLEL to the ramp, with the angle touching the inclined plane equaling the angle of elevation of the ramp.</span></span></span></span><br />
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5cuXp2XLlo3pkYhetGhRinRhev7559P999+ffvnLX445px1fOmcdtOPp2nwPHMngKm9RuVMAvWPHjrR79+5EvGvZMMufrR5qn6NbSOG33367ENm33HJLeuqppxLDDPBHHHFEOuWUU9K+ffvS008/3cIRvNd1H+j3aNHU/1577bV04403ppdffjlFmVYBMo4/44wz0saNG9P8+fPTbbfdFtU9w8XW1JtX6awPdBWiNLILlzLA7rrrrlEuBjAjjTt1wQUXFCC7B5Db1fpAN5HSQP7Zz36W6GNim6sF5DPPPLMA+MgjjyzEdhNvWXdXfaDrJtX4J77xxhuFiH7ssccKd4nBhVtXr15dRMXOP//8wiAbv4f6j+zZs6eQGIIvxxxzzKhRN1EPfaAnotAEx4HMT3744YcLPczg4j6dfPLJ6corr0zz5s0bExErd5cDLPWI8J07dxaBlwceeKCYVCtWrEgf+chH0lFHHVXuctz/+0CPS5raB4hmHCy+7RO4QLaxqC+55JIi2kV0j9dMBhNh8eLFNYMlLHOGGz/cpKAS+OWTaX2gJ0Otg+cC9d5770333HPPaMQLAIODg2nNmjXFp/h2LZB1deKJJxbncrnGa88880zinkmWmET6PO+889LKlSvT4YcfPt5lh+zvA30ISWrvIG6JTxGuN998c/RkhGdR+6wF3OgF8U+tYAlgH3/88UJivPDCCwUnO//ss88ugGbY1bq+fB//94GupMg43wEsMyW6RVwT3biYy8QvxsFcqMkQv9qtcK174GKGV+biOXPmFBNJFkzAZbKtD/QEFENoIEs+3HfffWn//v0FwLhWbPvSSy8tuLhRgA1DYIUuFmSR8XJfovrcc88tRDwDbCog63tGAY0DBTN8aohWS8wiNGtalmnv3r0FyPYxnojpo48+ukhiNAvkn/zkJ0VINHPx3Llzi1QmicFom0jnFw81zp8ZATRgX3/99QIs4jeLXWLw1FNPTfRduTG2cK74tPOFM/WB2NwZxpAccrmQoHz9ZP7nngm03H777WNAFiqlj6Uv3bfRNiOA5oMSiUQjAwpouIMeBDrAM9iObd++vfCNTQ5uDC6WatyyZYtVp8W5zeJiY2BZkzQmmH7Xr1+fLrroooSjG+Hi8uToaaAZM0Tu3XffPeqeSCbgRKADUUwauMKUOJdudP4rr7xSAKzyg6jG+VwnRlEzmnuZfMqPTCRjOP744wuDjlqoNxBS71h6Fuhdu3alW2+9tQBOgAEx6eTNmzcX3HnnnXcW1jNOAiwRirNMAJxlA/CFF15YiGnXNouLWe3UwhNPPFGMC1gmmlApgJs1mcqToOeA5nPaHnrooVH3BOEEJ/i4p59+egE40KQRcS6w+caMIBtii1PTw+q6mkV4el+ghfWe7+VTCRIubmXdWE8BLUSoCO/ZZ58tCEkcAumcc85JGzZsGGNlK7+97LLLCl1MxON4kSYTQbLAxPC9GVxMTAuTmoDbtm0r7gVgE8m9qIVWgoyzewJoepULlIMZQAPQpk2bEt8TQSv9T0bOYIQsTQQiPoOduT8bZ2XxN5X/qQ2WOwljXBq14N7i4QIttVy8qdyz2jXTHmgg5xwwAmYrlWuCk4nh8bjSfpEtBCcJcBwRbj9dXjk5qhGw1j7GXs5sAdnmfvQxNaKQMI+3Vj/NODZtgSYOt27dWoCDkzO38D9ZrwhaT5ABoZ3L6KKzuVR0qP0mylQ424TTB+OOUeg7NcI1M6nUcptM7QI5bj79RDcu4Qv/9Kc/LSxXANN3iJYrObhQ43FxNe5wLRDoSdY33zq7XcKP9YJNTAPVtYA2Vo1kEEW74oor2srF5WedVhyNcFwhWR1uUOZigYXB0Hnck6kWwgODcYars4QAFv0pBDkR2CYbCcPoIm2M1T7ieUsEWrhqgi6datMGaGFChGR04brMxeWqSvp4quLQdbju8ssvLwIZxC7ONrGARucDqlr/JIyYOE52jbEBlqGVU5eTkTCtmAxdDzTfE4fIHgE554AZMwhJtzaLU4BIf8pIscSBDWS+r0nERSv71MS0TJPoFpCJbiAbFzHNF3d+tcnRCjBr9dnVQOMO4vPBBx8sAEZIjY8LDACXCV/rQes9BhR5ZQZddrmy7i33AVBiWhgzx6kBz50jql3faS4uj7crgcZFgh42IpHYZrUiIvHKQAJGKzgFqKpHlAkZh5ZtAWPQJEkEZ5yT1YhJRxowCLsNZGPuOqCJZr6sDRFxCUIjHmNLJKlR/9aDV2u4FHhsAePwnfjlfrm/ZIiJJ07ODTMu4zP5ZJtE27pFVFc+X9cAjWgC/QL+mYvtQ0Suj+hW1nmVD9Hod4BKTarTMsGyHaCChC+dAXQOXczidw0/XSWnSUCdtCPCNdVn7SjQWRQiGj2MmzIRPRBCM7ZwFC5uhajO984FBpmQVAML3L13xMoLJbc+cXIGGRdLSAC4m/RxfobyZ0eBxiE2Rhedl8Uhq5WFS0zzQydT1lp+uIn+Z02LXJEi7AASxL3ZACQJmwC4qj9we56YJh01IhnRbGNwojFP9XhHgVYUIJtDVOIIgCK0ZMRgBEB8bwUXA1TQhY9MgmgCIgBkzbs3i/u6664rQqzOAXIGmNFlErRqAk4VzFrXdRRohMMRgPaJi61yIDabUY9V+eBELr+cGM4GFQBF04hhEoT1LDKWy20dt5kIJgFR3a0GV+Xzlr93FGhRLe4MESooIiBCLwO62Q3IO0IM83upiBzBAiwATTATjuskkyUQ4hoAM7rUcclVTxdRXUm/jgKNa8WRuVECI0Q5fWg/S7dZXE30sgEkQrIuFh/HyUKULHrAXn/99UXFSQ6QAFnFJ5BJn1aokUpAWvW9o0B7KLqZvsM1fFL5ZWIVp1W++GUqRGADCGeSGHQzLpWlAuC6desKDhWYIard2zkApqe5TkT1dNLF49Go40AbGOtVGJF7pYYL17GEcVwjROaXE9UkBT1rIjH2Msj229yX8WUSEM3Kf1nVjdx7PIJ3an9XAI2rEZc/KiBBjBLhwDEJJktwHJpDlDgZgES1oAYx7dN+KyOcqznHOBiEJsJk79kpAOu9b1cAbbBAJib51UDA2cpw7CdC6yU8vzgXxQMOgESxCBe3jbRgD7C8Wdcmk/MYhlRI1sf1EnC6nNc1QGewWbbEKQMK2IATnaoHaOfedNNNRXDDBGHMAZfbpPie0ec46xvAjCsgO0eQhJ3Qq63pQMvNCkbI/CAknSejI9KE8LUs18y9QMDNAMd5kvg4jfit1uhXXEpc5wiW+7KoqQQWs0nDKOM+aQBm8Yufmwi9DLLnbTrQ9KsVCAITQAUewwqxiUaEz+U+gHe83OxTNA9s1Z0AEsHSlwmTwXaccQVkBhddax+AbbhUVQgjDxezqFV5EuX6IjmIc2OZCa3pQAOqXNLDJ0VgIAAcxwOXGwOIapzquKAJUAU3BDJ+/vOfF5MluzsmAGMKgDknjEuV6QLRGNyD70zvmxSOmwQMPJEwRYQzpTUdaERm1QIWoYlU3AZwhhDg8jFcj8OqNREyopcIJ5JFsoCLQxlrold0MgDpb6JXdIvVrOFy7pVz3Q/ILG598qMZaDOpNR1oItqWmzpmgCO6QAjRTnQCqFbD1SaMicDlArbKD9/9nys1gSzwgZMBaCJxzZT5ZDshi+qLL764OKfWfXv1WNOBriQUUQkY8WzGlYabFPcRz5U6unw9gLhWAGNIkQj6yRIBl9LbxLBzqQYSBMgmkvOoEgYXkd/rBleZdpX/txRooha4ODL7rIgvzadKkjU9UQMgg4k+zckIk0cfuYQHmAoH3IeKIEFcly19Rhcxb2Jw1WpNronGM12PtwzonArMIhbAiD+VplRHcb3yW0AS1zmSxsK3n0vnmDYYcWrlR6x39V9EOlfKQjeiX8JkpoHddKC5O8CVcmRt4y7AEJ++M46m0nCiLTeiGYiscYaaZjKZFHQx1ZCBBy6xLfplXNpMA7upQAMS4bkzWXziHHqUYcWCJn4bbUCWiCCuc0kuMInzDDIxXdmoANwuo2VSiJbNFM5uCtAsadxFD9LLiI7QXJ0sRhlSiNtoY2wR01klmFAiW7nOS3qzlooQtOGfE+PGSALMBLAbBhrIOJWuzC4TwtGJNvoxt0aANnlypWh20QBKJdDfuLkaF+d7lz8ZdsS4SaPNBLCnDDT9R98COb9Zh/ULZEYQY6kMcpnQk/kfx9qsvWJVkxiavLISIC4a670WF1e7HzEuKmfyZN1u/L3apvRkAKaLWbv+BzoiiYrZVIbkmHQl4XAmwtbD3RlgYlaoUyhU07+aawZVvVxcOQ7fiXlgZzHey67XpIBm+AhbAllQgrULYBat8KKEPeJVawAhMnGfOHQtvWgSCHVy0RhcQLZPoIWU2HLwxW6NgJzHqD8xd4kTY+KWNaPf3H+3fNYNNMILLbJYgY2LESYDTITWEn0IetVVVxWAEbOCHtUaLs7hUsEWk4sUMIHEqVnvJtZkRXW1e+V9Jt6mjRvSVgX9+0Lvh3F37MJZ6bCpuf252676rAtonGs9FBHnfzPezBd5YlkDeSLCu4Y/PVGj700oeeUMMFEt4yQcWo6jT9RXPj4rAHs7Qus/jFT0M/tSunBlShtXpDTnoAd2066UVs1bkM7YeF76xi2706KX96bf2rwkzT/8UBct9zndPmsCTSeycCXrczGBB6TLJCsEJSYCuF6CiFO7V46JA7ngtMgrS1o0km2aEynvrz+U0vNvRSFipJ+viR+EvebClNZF+fijL6f0+dtT+vRZKV19yhHpA2euTNt3bE/P79qX5q7pnXBpAD1+FomFm61qHIn4UoGSCNKIzQKZLpa0EFWji4lvVjFRzbhrBOTQEumdeMTlUZzy8VNSOjqqhW7endJLAforsX1/R0rnxM9JzjtY/7DpuLnplIXHpUfCyh8eHnkfWC17ot6J3NHzggg1OToPDvEFGnKumWvTDIOF1Q5k4jqXANG/Mk38Y5KjEZCNP4aehGl+c21Kr8W69r+8O6XD46nXRj7lO0+kdOUxKd0XGmVuiRILFi6KZz2jUFX6GIxo2nQHu/R4HmlsYyGrbyY6GUNEdTMAdhcgKxXyaSLZGGhKgKpVnYwd2eS+zQ5ufShE9N8/mNJ5oZs/c3aI8TdS+t9dKT0cofcHXkhpaXD8CeEwnBoTgE4nUUy4HBuf7mDXBJovXE4kTI68h54NTOKfu6QIIdd5sdYFWBh47jeeD35ojxPvCamVhqOI5av3B5DxE1EnLUxp6574DEC/enFKbwa7fysmwDEh0o+O40DOzURnBLJPjL2Zr3HO92jXZ02gmz0ISQ/RLYaX5AZdTCTyY1tVbgu3N0NHs7J3RT7lv59Oyb7fCVCJby7UhwdTWhwcvbCKx8ejyBG0nIWbjmK8LUDzhRl23CY6OUfScC4iAppubkUbCo49IkT3H60LgEvcWr7XJavL3w7939hk4ExSnE3qTDewWw60ECkxDeD88hlEQrj169dFpGxpXf71oeSvfw9jrNEGbPaDRAiwp1sipKVAZ/dMNE2gBYEEPNaddmrafO6mtGBRyM5CkB4KwzvxxuN7nw+jKCziwTjtyIPuz6Fntm8PA40tIXikTSewWwK03LMlNYoDdsTyF6KaRb1s2dJ00uBgmr367PRXj81PT4fO/NXjU/rgCaEjo3CULv1GBDYuOjoMpwhs7N6f0t4oHjkmyq+7AWjgCuVSNypSNQZas+IJRYct+tN0oAEsQSCtKD7OymZVS11y1eYtWJy+ePdA2hhRqfcfm9K/PBocG5bw+QHuD56MMOX2+B7AnrU8AA8f98gY4bwqRlKL6FFXt8Q4l1OKE8iyaN0OdlOB5jaJpOWVEajGPcmFekQfkfzRk4MTgmNfjsjU7Agnzw4j6a4Q06JVGwPgbP2uOKouunfkJJxNjIv/K7iQbGlWjKEVD9QUoBlZyojoYqI6V5oIMkhdSn7kGX946NqzlqV0ayxL/reITJ0XCYb5wbHf3ZbS+8L6fT1E9VsxGd5thgXVCoqV+pR2FRIWVGFgdrMYbxho+pjb4Y17DK4MqHApkGWe8r5Mo28/PhKp4vJILNwbkandUVPwjUdSeuSllO5/ZURHnxHHygGMfH03ffKzc3UpY9PkrnzebhjvlIFmYHE1ZLby2ioPKD9tltNbZnzlQxPXP9wRSYYwvm6I4MUtwdm/tialv7koIlghwr96T/wGVHA8vd3tIGcAxf65i+jhebuRs6cEtACIKhNcrAiBbsoge6WjBEglwJkoDKs/3jiSMnw3QpNE+fxY7zbn4Eg+dnq4VHHO3CYYYHkM+TOPoRWfuVKFNc74lJRpx33rfZZJAQ1g+lfOmMWZa7jyjGZ0sUhZ2+O1YNq0EbcerDiiig8E4AfLwdLKGJFo1tshyhttebzGaWs14cUIiG46272bmQSaLC0q8wWTAppoYmVyobhNGm4W/QK+2Sx+3U2N3UC9tMsiZpSxWyRCxMbp7U40EqbcJgU0ThXtMlvL3IHLc+Sr3Hk3/I/w1Es7G9qUpZpJlhmjXeOAR7lNCmgWNEOLIVYGutxhN/2PmxQ0yKWLzHVizJhAiVQtu6UVNGuIo7kRtunSzGpvRrBipJqb147nYBsIBct4iY13YrJ5zt4pc6yCWqeIWh4KowhzKGG2dUpn9zTQnSJqGWj/80rk3JVNiRx2Ylw9DXQlwTv5nZ0AbK/56ARn94FuI/q54NCSX4mfdlrifaDbCLRbKThUXSrTp+qmXWK8D3SbgXY7iRD5bDpbMKcdYPeB7gDQbinhI58tvUtnt1qM94HuENBuK6hhFecLz8XPMz6zq6Wc3Qe6g0C79Zy589KsY9enrY8+lXa1UIz3ge4g0Ioh//DGqI37z4XpmaWb0o4nt6WdLTLQ+kB3EOjvRPnUt6OY9IQoZ754zfy0OYond8cqlla4Xj0FtDz2dGl3R/nUF++I97FEkeS3PxRVNVE2NTfEuEoVQZVmu16Tyl5NlYhPxq8CKguykE1FiZWNW+NBT1kShYIeMEZxV3x/OPafHVWgp8UMv2P3yP4z4/tRB0f5/eAABFKooALl42tjsVwUMOyJLOQ/xkK5PbFC0jro345atMEgYLe2VyOD+NEfpbR9b0pfuCSeuVQbxxrnZ1skwO1SltSMXHpLOVpp73VPxdsEbk7p+qdT2h86CcjfiiJAtWP/Ggse7o4y3x8/k9J/RMGgfd8MwAAO0IejSJAey81kODZqvn/j1JGC/3+O61+NNc9/e18AHKXBn44SpRXzRvqwFrpbmwrXF+NZ1cg9GMWQ+w6MHWle2OfFALJvImmN+totBZokXRRFgMcFOHmh+Z17Rmq3P3FazOQoAgT8DTtT2rI6pd8NTsT1216L9zAE16r5DlqMNq8UmRfcre57WfRrmavVkK8HqLhEMcenzogFdevDT42lPN3aLDP6/gfjTQuxgOF7MVmv/G6UPsdEJ6ly43rhbhW2RHlXA20V44WrUtoQgOYlNbgW+I4Bymz2iolF8fD2rQjRSxIAurK9FftMim8+EIvaHxrJsVIJf7Y5zo9r/vzOlD55Q0yeEIkKD7u1zYkJe3mA/F8B9pcuT+nxGO8nf5TS79+Y0hvxHCJm1157bbG0+Oqrry5e0tOo+G6LjmYk4W4NB+4PcM1eHGg1xs7QrW/EPuASMUujKvTZfSPnRlXOaDsqJsInQmxfeXyI9Dj/T24LPRf630T503NHVnzc/GxKXwtRriZ8ZUyebm6rQ9J9/pyRBQ1/vXXk3So7dsVvWT+3s8h04erKSpGpPk9bgAagDdhqtn+8K0RvgEkPvz9AOxCz+NYQ6UT1tgBuQxhgACbWFxDVAdjqEOm43z4rOx4LLjB40uEfgsMfDX3+oRNHJszKkAq4Zrq0D69J6bJl+9OLe19NTzzyQLog3CxpzWa2tgANOHqJaKaLGSL/syOl9QH6utjOXREuxhMhyp5M6dJjRl47sTf0rglxQxhqFPX7QtSxwBkv34trl0R/nw3ji/7/XHDFP4Uo/4s7wkIP4P8gdDTr+93oYzo0Rtf9B4v/N8cPrTUbZDQIoGFdMm1bQJktx43t9GNrU7KV26fWlb+l9Ctxja2etmZh+KQXjqiCsqgPQdH1zes+lAZvOvgbXPW8dG+yD0X7tYWjJzuwqZ5fBnmqfbTrOrXxONn7XKxT41K1ssatp4BuF0iN3kf5r/XjSpEtRGxHKXAf6EZRm+T1fGLLi63Nsk6tlVxcHlof6DI1Wvg/UW3ZkibEWV4z3sLbjnbdB3qUFK37xzImC+/UeBPT7QbZk/WBbh2+RXmQt0FYXmzduB95aZeornysPtCVFGnSd0tx/BCqBX5+Sa+TIHukPtBNArbcDZAtIR4cHCxCmJ1a91UeUx/oMjUa/J+YxsECIPTwiSd2z5uK+kA3CG6+PHOx8l2iGsid0sd5TOXPPtBlakzhf/XY3vjAN2ZRA7lTa7FrDb8PdC3qTHAMF1sd6ZXU3t3STaK6cujTKJlXOfTOfvfqClws0iXbZA10o8UBrXyiPkdPkrpexuPVHor3/N6H38XsZoDz4/WBzpSo4xPI3swkKcEv9iLb6QCyR+sDXQfATskgA5Z/7J0klb/cp7pTqZRKGmVS3fTmwz7QEwDtVVs2y1sVBTC4/PBaZVOJ+nBUv2w4OqUX4mV4r0XZ0+mLuwfsPtCViJW+08XyxgIguNgL2cerAFGj9u/boqLztViMsCelq9Yc/GmlUn+d/LcPdBXqq6Emqv2irs8rrriiqLEeD2RdeIH8Z85K6devTekDJ0SlapRBeQ95t7Q+0BVIeAGcX7lV/eF/BhcfeaJGL78c4tvCgrdDbL8TVa+5ln2ia9txvO9Hl6iMey1uk1YUt64XZF28GpWtf3d//Ljp+cHJUY78g+1jV16UbtORf/scHWQXxrSJcuHm4rc/6uDiMmIDIaY/u2HkRfNeNr8ngGeBd0ub8UADmEXNN2ZdW7Zaj6iuBNBCApvmdy5t3dRmNNBAtuicPmZoeeFb5XuuuwmsRsYyI4HOotrbgNRz0cWtrqtuBKRmXDvjgAay1YqK9byjE8gWsnVT7rgZwFb2MaOA5h/7UXJv7VOst2rVqiLK1esgA73ngQYigL27G8Cs6pNPPrnnRfWM42i+sZyx3wKRkPBqxl7Xx5Ug9zxHA1YVCKPLD5ErEPBLNjNBVFeC3fOi2080SUgsX758RgKcAe9poBXp4eTpUhyQQWnFZ8/Huvsgj0ybnge6FdwxHfusJrrjdTHJm0P6bXpTQOZ0tB0CdFikX4qjtn7rIQoUQA8MzPLTwMR4FyXWeojKHXyUSNYMHDjwZpo9PDwE3MURRDj+y1/+cmRR+62XKBCL/pYcdtjsWcHRA/si9b75wIGhr7WFn8dojpHS2DGErTg+5tiUvkRNT92tmTevJhwr+692Tt2DrevEKEkeiBDwtv8HeB8FlMaodv8AAAAASUVORK5CYII=" 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" /></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> <span style="font-size: small;"><span style="color: black;">I offer it here only as an alternative which<span style="font-family: "arial" , "helvetica" , sans-serif;"> may have <span style="font-family: "arial" , "helvetica" , sans-serif;">some benefit in Physics.</span></span></span></span></span></span></span></span></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: small;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Before publishing this post, I asked <span style="font-family: "arial" , "helvetica" , sans-serif;">the P<span style="font-family: "arial" , "helvetica" , sans-serif;">hysics tutors to review and edit the work for accuracy. Every one of them commented on the indisputable need to draw the pic<span style="font-family: "arial" , "helvetica" , sans-serif;">ture!! Before I added diagrams for each example, every Physics expert scribbled a drawing next to the problem, labeled it, and verified my calculations. I figure i<span style="font-family: "arial" , "helvetica" , sans-serif;">f these experts need the visual aides,<span style="font-family: "arial" , "helvetica" , sans-serif;"> </span>we <span style="font-family: "arial" , "helvetica" , sans-serif;">should all take a lesson from them</span>. </span></span></span></span></span></span></span></span> </span></span></span></span><br />
Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-80982016454698339222016-03-22T19:42:00.000-07:002020-03-14T20:57:07.328-07:00GRAPHING RATIONAL FUNCTIONS<div class="separator" style="clear: both; text-align: center;">
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<span style="color: blue;"><span style="font-size: large;">QUICK TIPS FOR </span></span></div>
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<span style="color: blue;"><span style="font-size: large;">GRAPHING RATIONAL EQUATIONS</span></span><br />
<span style="color: blue;"><span style="font-size: large;"><span style="font-size: small;">(A topic for the 2020 School Closing Series)</span> </span></span> </div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The ‘artist’ in me loves graphing. I could watch my TI-84 draw pictures all day. I even like homework assignments that force me to graph by hand. What I DON’T like are instructions that expect me to “calculate” 50 points before “sketching” a graph. When I just need to imagine what the graph looks like, where it is positive or negative, what direction the end points face, etc<span style="color: blue; font-size: small;">,</span> I’m in favor of estimating. I believe it’s a good practice even when a more specific graph is eventually called for, because I can quickly find silly errors.<br /><br />Here’s a quick and dirty on finding a few specific points when graphing rational expressions.<br /><br /><b><br />1. FIND VERTICAL ASYMPTOTES by setting the denominator to 0.</b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> <img alt="" src="data:image/png;base64,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" /> </span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>2. FIND THE X-INTERCEPT by setting the numerator to 0.</b><br /> </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARkAAACRCAYAAAD3hMwWAAAC0WlDQ1BJQ0MgUHJvZmlsZQAAKJGNlM9LFGEYx7+zjRgoQWBme4ihQ0ioTBZlROWuv9i0bVl/lBLE7Oy7u5Ozs9PM7JoiEV46ZtE9Kg8e+gM8eOiUl8LALALpblFEgpeS7Xlnxt0R7ccLM/N5nx/f53nf4X2BGlkxTT0kAXnDsZJ9Uen66JhU+xEhHEEdwqhTVNuMJBIDoMFjsWtsvofAvyute/v/OurStpoHhP1A6Eea2Sqw7xfZC1lqBBC5XsOEYzrE9zhbnv0x55TH8659KNlFvEh8QDUtHv+auEPNKWmgRiRuyQZiUgHO60XV7+cgPfXMGB6k73Hq6S6ze3wWZtJKdz9xG/HnNOvu4ZrE8xmtN0bcTM9axuod9lg4oTmxIY9DI4YeH/C5yUjFr/qaoulEk9v6dmmwZ9t+S7mcIA4TJ8cL/TymkXI7p3JD1zwW9KlcV9znd1Yxyeseo5g5U3f/F/UWeoVR6GDQYNDbgIQk+hBFK0xYKCBDHo0iNLIyN8YitjG+Z6SORIAl8q9TzrqbcxtFyuZZI4jGMdNSUZDkD/JXeVV+Ks/JX2bDxeaqZ8a6qanLD76TLq+8ret7/Z48fZXqRsirI0vWfGVNdqDTQHcZYzZcVeI12P34ZmCVLFCpFSlXadytVHJ9Nr0jgWp/2j2KXZpebKrWWhUXbqzUL03v2KvCrlWxyqp2zqtxwXwmHhVPijGxQzwHSbwkdooXxW6anRcHKhnDpKJhwlWyoVCWgUnymjv+mRcL76y5o6GPGczSVImf/4RVyGg6CxzRf7j/c/B7xaOxIvDCBg6frto2ku4dIjQuV23OFeDCN7oP3lZtzXQeDj0BFs6oRavkSwvCG4pmdxw+6SqYk5aWzTlSuyyflSJ0JTEpZqhtLZKi65LrsiWL2cwqsXQb7Mypdk+lnnal5lO5vEHnr/YRsPWwXP75rFzeek49rAEv9d/AvP1FThgxSQAAFDlJREFUeJzt3Xt0FFWeB/Dvr/OAhA6QNISoicRAkIbRBFzWhPhCWFDZs6wog0QYjzqMzx1dcY67DOPq7IwccR4cH4PHYV1nWGTc1Rnd0UERUcAA4vpmQEnAgDySkARCXpIHv/2jukN1pzvpSqq6E/L9nHMP3XVv377ddP1SdevWvaKqIKLIiYiqqthQlQKwo54+zRXrBhDR2Y1BhogcxSBDRI5ikCGKEZGzvjsGAIMMETmMQYaIHMUgQ0SOYpAhipGBMkaNQYaIHMUgQ0SOYpAhIkcxyBDFCMfJEBHZgEGGiBzFIENEjmKQIYoRjpMhIrIBgwwROYpBhogcxSBDFCMcJ0NEZAMGGSJyFIMMETmKQYYoRjhOhojIBgwyROQoBhkichSDDFGMcJwMEZEN4p1+g4yMjCEzZswoiouLK2xpaRnX1NSU2djYOKqhoWF4c3Pz4KampkENDQ3xzc3Nrra2NmltbUVraysAICEhAQkJCYiPj9ekpKTTbre7LTk5+VRSUtK3brf7xJAhQyqTk5MPJSYm7m1vb9++cePGkoqKikanPxMRRU7svIw2derUizIyMm5sbm6+rKqqavyhQ4dGVlVVxQOI1nGhpqent2VmZh5LT0//Mikp6f2KioqXt23b9kWU3p8GABFRVe31b9quevq6XgWZ3NzcMWPHjv3h8ePHZ5aVleXU1NQk2tg223g8npaxY8fuT01N3VBWVvZkaWnpvli3qSdEJB5Aoqo2xbotA5mNwUERvT/AMWM5yOTm5k4877zzHjlw4MDflZeXD3OoXY7Kzs6uGz169NuHDx9+pLS09K+xbk9XRCQBwKMArgIwCUACgN0APgCwTFUrY9e6gYlBxpqIgoyIJE6dOvVHlZWV/7Rv375RVt7A5XIhKysLOTk5yMnJQWZmJjIyMpCRkYERI0Zg2LBhGDp0KFJSUpCYmNjRDwMA/v6ZlpYW1NfX4+TJk6irq0N1dTUqKipQUVGBQ4cOYf/+/di/fz8OHjxoeRTlmDFjKkeNGvXUtm3bnlDVFksvdpiIDAbwMoDZYYp8BWCGqh6KXquIQcaaLoOMiCQXFBSs/PLLL7934sSJQd1VNnjwYEyePBmXXnop8vPzcdFFF8Hr9WLw4MG2NjqUffv24eabb8YHH3zQo9cPHz781Pjx43+/Y8eO+1S12ebm9YiI/ALAEtOmXQBOACgEEOfbVqKql0W7bQMZg4xFqhoyFRQULPN4PM0wvoiQKS4uTi+//HJ99NFHtaSkRFtaWjQWvvjiC3W73WHbCUAHDRqk+fn5GhcX12U5j8fTXFBQsCzc9xKtBGN4wRFT235pypsf1O6cWLd3ICVjt+k79fT11GlDdnZ2ttfrLQu3E4qITp8+XVevXq3Hjh3TvuCKK64IaGN+fr4+9NBDesMNNwRsnzJlilZVVenq1at1+vTpKiJhg43X6y3Lzs7O1tj9kGcEtSktKP9rU17Mg+JASgwyFj+n+UlRUdG1qampLaF2utTUVF26dKmWl5drX7J+/fqAdt52220B+StWrAjI37BhQ0deeXm5Ll26VFNTU0MGmtTU1JaioqJrNTY/5H8xtaU8RP6fTPmvxqKNAzUxyFj8nP4HM2fOvHnQoEGng3e0oUOH6vLly7W+vl53796t+fn5mpeXp3l5eZqfn6+7d+9Ws/vuu68jPy8vT1esWKFOeuyxxwLaW1ZWFpB/+PDhgCOWJUuWdKqjvr5ely9frkOHDg11mnV65syZN2vXP5ZRAH5nMd3UTZ2/NrVjc4j8J03527uqi8nmnYZBxtrnVFXMnj17qtvtbgvewebNm6dVVVVqdscddwSUmTVrVkfezp07A3bozMxMPXHihDpp0aJFHe+XkJCg7e3tncpMmjSpo8ykSZPC1lVVVaXz5s3rFGjcbnfb7Nmzp2r4H8vYcKddXaQnwtXnq3OtqexfQuQvN+Xv66ouJpt3GvuCg1319OkEAOL1eqvNO0BcXJyuWrVKQzl58qSef/75ATvM66+/rqqqRUVFAdvXr18fsg47LViwIOA9m5qaOpW5+OKLO/LT09O7rXPVqlWdOoh935Fo6C/RiSDzlqnsyyHyf2LKr+uqLibbdxq1qS676unTKb64uHjZiy++6IHJCy+8gIULFyKUlJQUrF69GjNnzuzY9sADD6Curg4lJSUd2xYvXoxrrrkmZB12mjhxYsDzrVu3BrTt8OHD2LNnT8fz2trabuu888474Xa7sWjRoo5te/bs8RQXFy8D8O8hXlIN4EGLTf+/bvIbTI9DjaQ2b2sIkU/UNxQVFR2E6S/sLbfcopFYvHhxwF/mhISEjsejR4/WkydPRlRPb23YsCGgHWPGjNHNmzdrQ0ODbt68WfPy8jodRdTX10dU9y233BLwuqKiooMavb+WvzG996YQ+eY+m4+j1S4mHslY/r7S0tIC+mI+/fRTjURdXZ1mZWV12oFFRN95552I6lBVXb16tSYlJYVM48aNi6iO4EvV3aXW1taI6v3kk08CXpeWltamoX90CQDGW0wjQ9VlqvMR03vvCpH/X6b8N7uqi8nmnYYdv9Y+p8vlCrii1NjYqJF66623Ou3Ad999d8SvV1V99tlnwwaDrKysiOqorq7Wyy67LGQdiYmJOn78+I7nKSkpEbetsbExoC6Xy3VaQ/9YnOiTWWQq2wpgcFD+56b8Z7qqi8nmnYZBxlJyDR8+/DRM9u7di0i1tbV12lZZGf379TweD7Zs2YLnn38es2fPRlZWFiZPnoz7778fW7duxYQJEwLKRir4uwj+rhz2vwBO+R7HA5jnzxCR7wCYYCr731FsF5El8V6v90hJSUmWf8PKlSvxwgsvdPvC48ePY/HixZ22v/LKK3jppZcwf/78iBpQUFCAxx9/PGReSkpKRHUAxlSGt956K2699dZOefv2nZnZ4ZJLLom4zpUrVwY893q9R8IUPQ2gJuKKDV1O16CqdSLyOoAb/M0RkdEw7l26B2fuXfoGwBaL700UPcXFxeZLoQpA16xZo91ZuHBhwGvMl3xHjBihlZWV3dZhh6qqKn377bc7UvC4nqNHj6rL5epo29NPPx1RvWvWrOl0ilNcXPwTje5huRfA0eB2mNIpAHOi2SYmdvz24PuyNk5GVfXVV18N+LFPmzZNH3744YBtc+fODft6O5WVlQUHgoD8uXPnBvTPHDhwoNs6rY6TcTLB6O/ZHSLAHAMwK9rtYWKQsfx9qVob8VtdXa2jRo0KCEifffaZNjY2amZmZsDr161bp9Hg9XoDrm5deeWVunTpUp0yZUpAe+69994u6+npiN9oJBi3LswG8F3wruvY7jQMMta+L/+DSO5dUlWdP39+QP5dd92lfmvXrg3I83g8WlFRoU778MMPNTk5ucurOfn5+VpbWxvy9d3duzRr1qxijdF/EFPfSwwyFr8v85Pu7sK+/vrrO20Lnu6hsLAwoMz111+v0bBly5aAe5T8yeVy6bx587S6urrTa/ryXdhMfTfZFWRsDFZ9OnWaGe+CCy7ITkpK2rhnz54xCEFEcPXVV2PBggWYM2cORowYEapYTKgqtm7dil27dqGmpgajR49GYWEhcnNzO8pUV1fjtddew7p167Bp0yYEf34/r9e7r7m5ecbXX39dHqXmUz/B1QqsCTv9ZmFh4bLS0tIf19TUhJ070+VyoaCgAFdddRWmTZuGSy65pGN+3r6itbUVH330Ed59912899572LFjB06fDj/cxePxfJubm/vz7du3/yyKzaR+hEHGGlvn+O3PTHP83q9ccoS6wCBjjaXVCsrLyx84cuRImqU3EEF6ejrOOeccnHvuuRg5ciTS0tKQlpaGYcOGwe12Izk5GUOGDEF8fDzi4uIQH28sbNnW1ob29na0traiqakJTU1NaGhoQF1dHWpra1FbW4tjx47hyJEjOHr0KKqqqsKe/oTTl1croL6JE4lbw3WX+vi6S9T3MMhYY8sKkjU1NTP379/fp1eQzMnJ2e/xePr1CpLUNzDIWMO1sIksYpCxxtYgE0pGRsaQGTNmFMXFxRW2tLSMa2pqymxsbBzV0NAwvKmpKam5uTmxoaEhvrm52dXW1ib+VSMBdKwmGR8fr0lJSafdbndbUlJSS3JycrPb7T4xZMiQyuTk5EOJiYl729vbt2/cuLGkoqKi0dEPRAMeO36tcTzIRJOIuAD8DYBcAOcCOARgL4yZ486eD0oxxSBjTXysG2AXESmEMWVlfojsj0RkiapujnKziAa8s+JIRkRyAHwGwN1FsTYAV6rqtui0is5WPJKxpt8HGRERAO8DmOrb1AZj/tsqGGtGjzYVPwggm6dO1Bvs+LXmbAgyOQDMl6T/WVVX+vIEQAmAQlP+OFUtjWIT6SzDIGONy0phEfGKyCci8qkvfSIi3qAyK035n4rIj+xtcid5Qc//7H/gO2JZG5Q/3uH2EJGJpY5fVd0jIh8AuMO0+dcArgEAEZkC4Ic4E50PAXjOhnZ2pRzAfb7HLaoaPNAu+J6rQw63h4hMLJ8uiUgKgF0Azjdt/ntVfUNE3gdQZNp+raq+2ftm9oxv4u23YVzSBoxlRCaranus2kT9Hzt+rbF8CVtV60Xk+wA2mDb/SkSGITDA/DZWAUZE/gggC8aplH/uia8BLGKAIYquHnf8ishzAMxrorTizA59AMBFqlrfu+b1jIg0AUgK2vxHAD9QVatLlxAFGOhHMr51v94H4L9B+iJV3RW2fC+CzFAYp01ZQVkKYIaqboqwntsBPBUm+xtVvbAHbTsKIB2dO7Y/BlCgqq1W6yTyY5CR4KBRp6rDw5Xv8YhfVT3pO216KyhrVaQBxtSG4KMOv3Dbu2vbOSISD2PszPMA/FOJTgbwAIDQq8kRgJA/Igpix3ekqmfLdz0s+HOYg2dvbysI9fpRvazTFqraBmCLiFwH4CtT1gwwyHSpP/51jSa7jkBKS0sVxqDRXwHYDuCnAN5Q1Sd6W7eTRKQOwNCgzX8B8JaqPhlcvsdBRkRSAfw2RNYNIjJfVV+KsKodAB4Kk9dtn46IPAJgnO/p16r6Y3O+qu4VkVoA/hn9xkbYLiJH7dy5EwD+R1UfBwARWQdjzfM+HWRgXODxT5+iAH4GYDOAfxORFFX9ublwb/pk1gBYaNrUjjPrM1cDmKiqVT2q3Fo7XoKx4BkANAIYqqqnTfleGCsw+r2nqtOcbhedvewe8ev7gz0RwH8AeEpVn7ahbseJyG0A/kFV/9H3/DoAT6jqRHM5SyN+TZXPQWCAeReAOXqNALCqJ3X3wMemx0NguuLlm/rh3i7KE8WMcdcLAOBaAG/AmJ7k85g1yLrBAL41PU8CMNbXH9qhJ4PxPAD+ijN9L+0wOlTLYPR9ZJqKL1DVP1hrtzUici6MS+b+D3YaRmf0XgBzAGSbip8EMEFVDzvZJjq7OXF1SUTiACwB8CCAUf3hJl4RyYARC26Dse8/C+AKGGcTDf5yPTmSeQaBnbvPqernvmVEgvtWnhYRRzuCVfUIgLkAmn2bXDD+MtyHwABzGsbNkwww1GeIyE0A4Bsk+p8APADCXg7uS1S1AsCjMGLCJhij64+aAwxg/QbJeTCmT/A7DuBh05u+CKOX3M+DKJw2qeqfYVw12h+myFcALlPV551uC5FF94jISN/jGwC8o6rHY9mgSPnGyq1V1UxVPRfGjAdfdSrXD47KLBGRNACTYFxx+gbAlzCuOvF2ArKFXadLjY2N6na7t8OYzfEbGJez/1VV3+9t3dEgIpfDmOUgF8aZwjoAm1T1NwHlzrYgQ+Q0O68u+S5OZAM45Tv171dE5GUA5wDIAPARgPnB/UkMMkQWcdKqQL6zhwRVrQyZzyBDZA2DjDU9GidDRL1nGidzVmOQISJHMcgQkaMYZIjIUQwyRDEyUC66MMgQkaMYZIjIUQwy/YyIuHyjRIn6Bf5Y+wkRGeGboKsBwAkR+Z2IuGPdLuq5gTJOprdz/FIU+Nb0Xg/jxs8VAEYC+L7v3+ti2DSibvG2Ahv4Jhx6FcBoGNMPrhGR7wJYBmPyrHnmm8Z8E3/tDlkZUKOqE4LqHwfjFvptqlrk2/YlgAsB/K2qfmj3Z6LwBvqSKFbxSMYGqtouIs/AONr4pW+53qdgHGncE2KWMxeMdaFCCXUKe8r377AQ28YAYJChPotBxiaq+qaI/B7A9wDshDHP8TOqujVE2WMikhC8vQsHYUxvOsE3ebMCuNiXl9G7llOsDJSzCJ4u2ch3y/tuGNOTHgDwneCpCH3lUhB+2YsGVX0wxGumAXgNQAqMIHMAxjwkt3PGv+jiXdjW8EjGXm0w1gQHjJUTkmFcDQo2GMAdYeqohjGZdABVfVdEJgC4EsZsf/45jI/2rslEzmKQsdcvYKzWUAvf6RKMxbqCnQRwU5g6ToXaKCIP+OpeoqoqIlNhBLXPettoIicxyNhERKbDWPPpCIwV9j4AcKOI3KiqL5vLquopAJGusOl3IYAfAEgVkWwYHb5/6I9TNpJBRAZEvwz7ZGzgGxT3BYzTl7mq+icRWQDgRRiTQ09U1epevscFAJ6Hsa4NYFwyv11VT/SmXrKOl7CtYZDpZ0RkBIBmVW2MdVsGKgYZaxhkiCxikLGG9y4RxchA+QPPIENEjmKQISJHMcgQkaMYZIhiZKDMJ8MgQ0SOYpAhIkcxyBCRoxhkiGKE42SIiGzAIENEjmKQISJHMcgQxQjHyRAR2YBBhogcxSBDRI5ikCGKEY6TISKyAYMMETmKQYaIHMUgQxQjHCdDRGQDBhkichSDDBE5ikGGKEY4ToaIyAYMMkTkKAYZInIUgwxRjHCcDBGRDRhkiMhRDDJE5CgGGaIY4TgZIiIbMMgQkaMYZIjIUQwyRDHCcTJERDZgkCEiRzHIEJGjGGSIYmSgjJP5f65EPZIJ14b3AAAAAElFTkSuQmCC" /> </span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">Notice that both of these tell you something about the X-axis and run left and right in the original equation, like the X-axis does on the graph. </span></span><br />
<br />
<b><span style="font-family: "arial" , "helvetica" , sans-serif;">3. FIND THE HORIZONTAL ASYMPTOTE by reducing the leading variable. </span></b><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"> <img alt="" 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" /> </span><br />
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;">4. FIND THE Y-INTERCEPT by reducing the constants.</span></b><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> <img alt="" src="data:image/png;base64,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" /> </span><br />
<span style="color: blue;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;">Notice that these two run up and down like the Y-axis and determine points on the Y-axis.</span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> Done. Sketched. <img alt="" src="data:image/png;base64,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" /></span> </span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><br /><span style="font-size: large;"><b>Other conditions tell even more about the graph.</b></span><br /><br />-- Suppose in step 3, the exponent on the denominator’s variable is larger than the one on the numerator. <span style="color: blue;">Think of ‘end behavior,’ what happens way out there at infinity.</span> If the leading coefficient of the demominator is LARGER than the one in the numerator, the fraction gets very, very small at infinity -- almost nothing. So the horizontal asymptote is 0.<br /><br />-- Suppose reducing the leading coefficients leaves a variable in the numerator, like y = x or y = x/3. This indicates a SLANT (or SKEW) ASYMPTOTE, which is not considered “horizontal” even though it goes through the y-axis. <span style="color: blue;">Notice that it also goes through the x-axis. </span><br /><br />-- Suppose there is no constant in the numerator. <span style="color: blue;">Fill in a place holder, 0.</span> Then the fraction is zero divided by something and equals zero.<br /><br />-- Suppose there is no constant in the denominator. <span style="color: blue;">Again, fill in a place holder, 0.</span> The fraction becomes division by zero, which is undefined and the graph never crosses the y-axis.<br /><br />-- Look at a bunch of rational graphs. <span style="color: blue;">Notice that asymptotes are like the poles of a magnet. They repel the graph.</span> The segments separated by the asymptotes act in a similar way. In MOST (but not all) cases, if the graph is heading up on one side of the asymptote, the other side will NOT follow the same pattern. Simple rational expressions generally occupy only 2 quadrants formed by the vertical and horizontal asymptotes: I and III, or II and IV.<br /><br /><br /><span style="font-size: large;"><b>FINDING THE BLACK HOLES OF A RATIONAL EQUATION</b></span><br /><br />As problems become more complicated, factoring and reducing become necessary.</span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> <img alt="" 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" /> This reduced form gives a vertical asymptote at x = -1, but x can not equal +3 either because it was part of the original equation. Although there is no vertical barrier at x = 3, the graph will skip over that point and create a hole.</span></span></span><br />
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" 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<span style="font-size: large;"><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">WHAT DOES THE GRAPH LOOK LIKE WHEN THERE ARE 2 VERTICAL ASYMPTOTES?</span></span></span></b></span><br />
<span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"><span style="font-size: small;">The principle of repulsion....</span></span></span></span><b><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> </span></span></span></b></span><br />
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" 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uZHH33Ex8lb4fr16/D39ze0to8e+ie6NHlOTg5iYmKk1jPkWHD+/HkEBgbms9bhbnRp8qNHjyI6OjqXtQ61U1xcjICAAN2Xky5NfuDAAURERGS0vafnQilFSUkJDQoKOspai7vRnclrampQWFhIvby8tjqahh7aoW1RWlqK0NBQ85tvvlnf2n566J/ozuT79+9HYmLi9ZUrV+r+SZ4zXLp0CR06dPCIMtKdyffs2YNu3bpJ/RYlxwKDwYCIiAjdj5EDOjR5ZmYmOnbs+DlrHWqnoKAAoaGhrQ4f6gVdmfzChQswGAzmkpKSz5xJRw/t0LbIz89HWFjYybb200P/RFcm/+abb9CvX7/Cr776SvdzpJ3l1KlTCA4O9ohpD7oy+ddff42uXbt+yVqHFsjLy4O/v//3rHUogW5Mfv78eeTm5prbtWv3Dmstaqe0tBQ+Pj7mFStWXGCtRQl0Y/INGzYgNTW1YPny5bf8RJ+96KEd2hqnTp1CXFycrCm2euif6MLklFJs3LgRCQkJH7DWogUKCgrQsWPHYtY6lEIXJv/pp5/g7e1tXLVqFTe5DA4ePIjIyEiPeZagC5OvX78egwYN+o61Dq1w6NAhhIaG7mStQyk0b/ILFy5g165d5vj4+LmuSlMP7VBb1NTUoKioiBoMBlkT2PTQP5Hzw1iqvuIvvfQSLl++fGD79u2DXZgsBaDI1VV66eaff/4Z8+fPr8rOzg6Vsz9f1ZYxpaWl2LJlC01MTJzBWotWOHz4MGJjY8+w1qEkmjb5e++9h8GDB+csW7Ysj7UWrXDs2DFERUX9wlqHkmjW5OXl5Vi3bh1NSkqa6eq09dAOtcX3339PQ0JCPpG7vx76J5ptk8+ePRsXL148/q9//auvq9NWsh2qZJs8OzsbTzzxRH1hYWGgHYcp1j9xF5qsyXNycrBt2zZzcnLyo6y1aIkff/wRCQkJp1jrUBpNmnzOnDkYNWrU5rffftuhZeA8lT179qBTp04e9+6r5kz+xRdfoLy8vLauru45d+Whh3aoNQ0NDcjKyqJ+fn5/s+c4XfRPKKVtBdVw7do12qlTJ3NaWtoM2rZuZwJ1c/q/BeESuL+c9+7dS3v16nXdCX2aDZqqyWfMmIGBAwceXrVqlezRAY7A9u3bkZCQkMVaBws0Y/KPP/4Yp0+fruvQocNw1lq0SEZGBiIjI99nrYMJMqp75uTn59PIyEjz4sWLR1JlmxC6aK7k5OTQrl271juokTp4nGqC6mvymzdvYuLEiRg1atTm9PT03az1aJEtW7agd+/eB1nrYIXqTT59+nSEhYWd27hx4xTWWrTKtm3bEBMT47GvBara5EuXLsWvv/5ak5SU5PKnmp7C/v37QQipW7NmzS7WWlihWpOvX78en3zyScPIkSMHrV69WtGf/KBUP+PkGzZsQEpKisMG5+PkbmLbtm20Q4cOjYsWLfovGfrcEahSecGNHc+6ujoaERFhnj17djcX6NNsUJ3JRYM3zZs373G5J+GGQJXKy50mX7t2LR06dOh5F+nTbFCVyTdt2qQGgzefszIXwI0m7927N50xY8YLLtKn2SD3grud9PR02rlz54b58+crMhbeWlDywrrL5D/88APt1q1brQs0KlYW7go+yvcCfo/JZMKsWbOQlZV1c9KkSfelp6cfY61JD6xYsQKpqanrWetQA0xNfvHiRUyYMAG+vr7FY8aM6Zuenn6NpR69kJ2djZMnTzZ07959AWstqkDm7crlbNu2jUZFRZknTJiwE+IbSmoJ0HhzZfTo0XTChAl/d5FGxcrCXUHxcfKysjJMnDgRixYtMk2aNGna559/PpZSqqqBaZXJsYsjR44gJyenoampySXvvuphnFwxkzc1NWHt2rVISkqiN2/e/M+4ceOi//rXv25SKn9PIS0tDcOGDVv71VdfmVhrUQ0yb1cOYzab6fbt22lycjLt379/+cKFCx9jffuSec6K5AUXNle2b99OExMTq92kT7PBbR1Pk8mErVu3YsWKFTCZTLVDhw5d8eGHH/7ZXfl5OjU1NXjppZfo6NGjZ7PWojZcviRFXl4eNm/ejA0bNiAmJqa8X79+az788MO3HJeoPFpckmLhwoXIzc09kZmZ2dNF0prR/JIUTtfkRqMRhw8fxq5du7Bz506UlZU1pqamHp08efLS5cuXf+sKkZzW+fnnn7Fly5bGxx577CHWWtRImzV5Y2Mjra+vR21tLUpLS3H58mUUFhbi1KlTOH78OI4fP07j4+PrEhMTj8fExGwyGAzrtf7DVFqqyW/cuIHevXvT4cOHL/z000/fc7E8QAc1eZsm9/HxMQcEBCAwMJCGh4ebQkNDayIiIkojIiJOhYaG/hIcHLxl2bJlZQrpVQQtmXzs2LEghPyckZHhrndfNW/yNpsrjY2Nqp1z7i5k9FNUwZIlS1BSUnItOzvbbc0UQohmysMWHmdgvfDWW29h69at9X369EmhlDay1qNmbrlNWn9rrZ948Xger7V4L0opsQwQjP9b8NB4KJW/eGF+m7tjjfWDjdWrVyM2NrYhIyMjUWF9aro+dsUzn2qrRtTYDq2vr8eSJUuQmZlZO378+IGPPPJIgRL5qq0cHEHOwyCPQ22jK4cOHcLkyZMRHx+fHx0dnbp582YlX+zW/+gKhx1Hjx5Feno6srKyGh5++OGl69atW8paE0tmzpzp6+/vP7miomLs1atXk69duxZ99erVoOrqau/a2lqbI4G8JpeARU1uMplodXU1cnJycPDgQezcuRPFxcUNQ4YMyQgLC5v2wQcf1CihRwKmNfmCBQsCa2pq3iwsLJxw7NixuC5dupChQ4eiZ8+eSEpKQqdOnRAZGYmAgAD4+vpK6uQ1uQRKfPEJIV7PP//8ywAQFxdnLC0tpe3btzd36dKlOjY2tqBv377/OHDgwPtg/HM2rPonr732WmJ+fv4n+/btG5SSkuI1YcIEbN26FREREXanZXdNTgjRfdVPKdXFywKeyi13YeshKh4oqIDL0wXgPWLEiH/HxcWZd+zYIWSC5uzck6cLNCuiCwCZMmXKpsjIyKYXX3yRGgwG6gCSafPminJ4p6amnvfx8YnNzc1FSEgIaz2qYfHixal9+/bdlZ+fH7Z3717cfffdrs2AdU2hxgAX114AfJKTk6+kpqbSxsbG31c9Kq/J3a1r+vTpyyIiIppWrlxJm5qaqJNI5sFrcgUYMmTI0V69ekWvWbOGt/VFCCHk8ccf33PkyJHh3333HRk4cKD78qJU9/1Iu3HlEOKjjz66vri4+LmsrCwEBARI5QWLa6DGb4DLhxDT0tL8T548mVdfX39HRkaGQyMmNuBDiEozderUB/ft2zftyJEjkgb3UPwPHTp0ITIyMnr37t3w9fV1e4bc5BK44u5GCPHu0aPH16tXr/a68847XaCKDa4cJ585c+ZtOTk554xGY/SOHTsUMTjA55O7jfHjx2+Mi4tr/8wzz7CWogoIIV55eXkFI0eOjD569KhiBgd4m9wWTrVDJ06cGL979+6zhw8f9urWrVur+6q9Te6q/smYMWOO1tXVpezevRt+fn6ukCYFb5MrRVlZ2dbp06e3aXBPYdq0aR+eO3cu5fDhw+40uG0UGGfVXIAT4+STJk3qExISYq6oqGhjSFcAOh8nnz9//tjw8HDziRMnZJWHk0hq4G1yF2MwGDbMmzePhIWFsZbCnNdffz16x44d21atWkWSkpKY6eBtcgkcbYc++eSTCZmZmafOnTsn2+Rqb5PDif7JsGHDzvXs2bPrmjVrXCzJJrxN7m6qq6v/NnXqVF6LA5g9e/Zrly5d6rprlwp+PtSZ9paOg832na3Qq1evoLCwsMaLFy/KaTv+BlTeJocD/ZP58+eHd+7c2ZSZmWlXWbgAST28JncRPXr0WBYbG+sdGxvLWgpzzp07t2v48OG+Dz74IGspAHhzxWXk5eU98+6777KWwZw5c+aMO3DgwICCAkUWE5AFH11xAZMnTx5aUVER+tBDfFHZ7OzsD1599VUSGhrKWspvcJNLYO902KqqqremTZtGvL293aSIHZTKH32bO3fuM0VFRZ1mzZrlRkX2w03uAo4ePTp48uTJrGUw58CBAyvfeOMN+Pv7s5byO7jJnWTKlCkTwsLC/JKTk1lLYUpaWtqs8vLyyOnTp7OWcgvc5E5SVlaWNnHiRNYymHPs2LE/vfLKK1Bjk42bXAJ72qG5ubkp48aNc6MatsjpnyxevHhQXl5ex6effloBRfbDTe4EU6ZM+YOfn59/z56u/i0qbXH27NmVzz77LAkMDGQtRRJucieora2dredaXA6vvPJKyL59+wbOnq3eX1bkJneCs2fP3jdixAjWMphy5cqVv9x7772qfsWPm1wCOe3QRx55JPLMmTNhw4cPV0ARO9rqn5w+fXr8U089pZAax+Amd5Dw8PDn77vvPuLJb+G//PLLMSdOnIgeO3Ysaymtwk3uIFevXn102LBhrGUwpays7E8PPPAACQ4OZi2lVbjJHeTs2bPJem+qtEVBQcG4J554grWMNuEml6CtduiUKVM6GAyG2wYMGKCQInbY6p8sWLAgPDc3t8P48eMVVmQ/3OQO4O3tPXXAgAG6nJAlF6PROKNPnz6qHRu3hJvcASorK0fde++9rGUw5cqVK49qpbnGTe4AJSUlSZ5u8jNnzvTUisn5m0EStLb+HyGEtGvXLqJ///4Kq2KDVDm8/vrr0YWFhe0GDx7MQJH98JrcTl544YVhUVFRXi5cblhzVFRUPDto0CCitnnjtuAmtxOTyfSIOxeM1wI3bty4V0uT0rjJ7aS8vDy1V69erGUwpbS09C4tlQE3uQStjZMbDIZuffr0UVANW6TGyYuLiztxk+uYoqKi8JSUFNYymJGWluZfVFQUwHJtQ3vhJreD5557LtZkMnnffvvtrKUww9/ff8Qdd9yhiYdAzXCT24G/v/9DiYmJrGUwpaamJiU+Pp61DLvgJpfA1nyN2traezzN5Nb9k7q6ujs7d+7MSI1jcJPbQVVVVU9PM7k1dXV1cdzkOubatWtdPN3k1dXVt3OT65jLly9HeLrJq6qqwrnJdYDUOHn//v19DQaDb0JCAgNF7LDun1y/fj1IaybnE7Rkcs8996SUlZURLy/Prhfq6up827Vrx1qGXXj2FbODpqamlLi4ONYymFNbW+ut9nc6reEml0l9fX0SNzlgNBpJUFAQaxl2wU0ugdQ4eW1tbfcuXbowUMMW6/6J0WiEj4+2Wrnc5DKprq6O4TU50NjYqDmTa0stQyoqKqI8sSa3xmw2a65i1JxgVpSXlwdrbc4GR4CbXAKpcfLy8nK/Dh06MFDDFnt/P0mNcJPLYPjw4T43btwg4eHhrKVwHICbXAZ9+/ZNiIqKInqo1TwRbnIZUEq7R0VFsZbBcRBucgmsa+yGhoY7PNXk9vx+klrhJpdBfX19nCd2OvUCN7kMjEZjJ0+tyfUAN7kMjEZjRGRkJGsZHAfhJpdAYr5GsNYmJbkKPYwocZPLwGQyBWlteimnBW5yGRiNxkCtvSjAaYGbXAYmkymQ1+TahZtcAut26M2bN/091eR8nNxDqK+v9/NUk+sBbnIZ1NfX+7Rv3561DI6DcJPLwGg0evv5+bGWwQrNjyFyk0tAKf3dhW1qaiJae+WL0wI3uQwaGxuJr68vaxkcB+Eml4E7X97Vw+iF2uEmlwFvrmgbbnIZaHEZBk4L3OQy4CbXNtzkMuAm1zaEd3w4euf/ASKGs+kbgWjxAAAAAElFTkSuQmCC" /> </span></span></span><br />
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">And some present wierdnesses like part of the graph crossing the horizontal asymptote, looping around, and finally adopting the behavior we expected. Witness:</span></span></span><br />
<br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> <img alt="" 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" /> <img alt="" src="data:image/png;base64,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" /></span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">--- And another rule breaker....</span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> How does it get that squiggle? No vertical asymptote because it's an imaginary number, but a horizontal asymptote at 0. For X between -sqrt 2 and (roughly) 2.4, the y value is increasing; for all other values it is ever decreasing. While the numerator can turn negative, the denominator will always be positive. </span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> <img alt="" src="data:image/png;base64,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" /> </span></span></span><br />
<br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">--- Here's a cute one that defies the repelling principle.</span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> Will this graph ever enter negative territory? Nope. The fraction will always be positive.</span></span></span><br />
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"></span></span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;"> <img alt="" src="data:image/png;base64,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" 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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: blue;"><span style="color: black;">With just a few morsels of data, the general shape of most rational equation graphs can provide valuable information to check more intricate drawings, as well as inform Calculus questions later in math study.</span> </span></span><br />
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<br />Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-15498828467426037082016-03-20T18:40:00.000-07:002016-03-20T18:40:54.203-07:00COMBINATORIAL PROOF<br />
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COMBINATORIAL PROOF</h2>
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or "TELL ME A STORY" </div>
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Proofs can be approached either as algebraic solutions that show one side can be manipulated to look just like the other (Trig and Inductive proof are common examples) or as ‘stories’ describing how the left side counts the same thing as the right side (combinatorial proof, aka combinatorial agruments). The clue to story telling is restating the math symbols in some form that explains what’s going on. <br /><br />Here are some examples with principles that often apply.<br />
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AN EXAMPLE OF THE RULE OF SUMS</h4>
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<img alt="" src="data:image/png;base64,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" /> </h4>
<span style="color: blue;">First, describe the math purpose.<br /><span style="color: black;">In how many ways can r items be chosen from a sample of n items?</span><span style="color: black;"> </span> </span><br />
<br />
<span style="color: blue;">Next, tell a simple story. </span><br />
The Story: There are n people in the Math club and you need a committee of r people to organize the Awards Dinner. <span style="color: blue;"><i>That's all that's needed for the left side, but (n-1) needs to be addressed for the right side, so...</i></span> One member is named Laurel. In how many ways can the committee be chosen? <br /><br />LEFT HAND SIDE (FHS): (n,r) counts the number of ways a committee of r people can be chosen from all club members. <span style="color: blue;"><i>This situation tells how many different committees are possible, with or without a particular member.</i></span><br /><br />RIGHT HAND SIDE (RHS): <span style="color: blue;"><i>The committee could include Laurel or not include Laurel and the total number of ways to set up the committee is all those WITH Laurel plus all those WITHOUT Laurel.</i></span><br /><br />If Laurel IS already on the committee, there are n-1 people left to choose from and r-1 seats left to fill for the other committee members (n-1,r-1). If Laurel is NOT on the committee, there are only n-1 people to choose from and r places on the committee to fill (n-1,r).<br /><br />CONCLUSION: Using the Rule of Sums, the LHS and RHS count the same thing. Ergo, the sides are equal.<br />
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<h4 style="text-align: center;">
AN EXAMPLE OF COMMITTEE CHOSEN FROM A SUBGROUP OF THE POPULATION</h4>
<h4 style="text-align: center;">
USING THE RULE OF PRODUCT </h4>
<h4 style="text-align: center;">
<img alt="" src="data:image/png;base64,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" /> </h4>
<br />
<span style="color: blue;"><i>To make this story create itself, I would "label" each of the variables:</i></span><br />
<span style="color: blue;"><i>n = the total population</i></span><br />
<span style="color: blue;"><i>m = the subgroup </i></span><br />
<span style="color: blue;"><i>k = the committee </i></span><br /><br />A STORY: In how many ways can you select a committee of k people out of a subgroup of m members from a total population of n people?<br /><br /><br />LHS: First select the subgroup (n,m). From these group members, select k to be on the committee (m,k). <span style="color: blue;"><i>This part often seems easy.</i></span><span style="background-color: white;"><span></span></span><br /><br />RHS: First select a k-member committee out of the n-member population (n, k). Next, from the population NOT chosen for the committee (n-k), count the number of possible groups (m) that DO NOT contain people already chosen for the committee (m-k): (m-k) out of (n-k). (n-k,m-k) <span style="color: blue;"><i>Labeling the variables helps to make this side easier to explain.</i></span> <i><span style="color: blue;">OK, so even THAT doesn't appear obvious, but it's a direct translation of the term labels. The problem is defined by applying the math symbols and the labels. The Rule of Products states that if there are A ways of doing something (selecting committee members) and B ways of doing another thing after that (selecting non-committee subgroup members), then there are A times B ways of performing both actions. This problem includes both selecting the subgroup AND the committee, just in an order that seems counter-intuitive. The best bet is to just describe the math as it happens in the problem.</span></i><br /><br />
<br />CONCLUSION: Since both sides count the same thing, they must be equal.<br /><br />
<div style="text-align: center;">
------------------------------------------------------------------------</div>
<br />
<h4 style="text-align: center;">
ANOTHER EXAMPLE USING DIALOGUE AND ALGEBRA</h4>
<h4 style="text-align: center;">
<img alt="" src="data:image/png;base64,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" /> </h4>
<span style="color: blue;"><i>In a problem like this, labeling is a vital part of creating a story. Start by defining that pesky 2n.</i></span><br />
Assume there is a bag of n red marbles and n blue marbles. Total marbles = 2n<br /><br />THE STORY: In how many ways can 3 marbles be chosen?<br /><br />LHS: Total number of ways to pick 3 marbles out of a group of 2n.<br /><br />RHS: Option 1 - all red (n,3)<br /> Option 2 - all blue (n,3)<br /> Option 3 - 2 red and 1 blue (n,2)(n,1)<br /> Option 4 - 1 red and 2 blue (n,1)(n,2)<br /><br />All possible options = <br /> (n,3)+(n,3)+(n,2)(n,1)+(n,1)(n,2) =<br /> 2(n,3) + n(n,2) + n(n,2) =<br /> 2(n,3) + 2n(n,2)<br /><br />CONCLUSION: Since both sides count the same thing, they must be equal.<br />
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In combinatorial proof, the conclusion is always that both sides count the same thing. The trick to <u>EXPLAINING</u> (in common terms) why the sides are equal is to create a story, a situation, from the math symbols displayed. The LHS and RHS are just different ways to count the same number. <br />
<br />
If one side involves a SUM, describe cases that include a segment of the total PLUS the remainder of the total (as in Laurel's case where the committee either includes her or doesn't).<br />
<br />
If products are involved, then the counting likely involves a sequence of steps using Rule of Product. The RHS involves doing the steps in a different order as in the subgroup-committee example.<br />
<br />
As the process becomes more obvious, the stories can become more creative. But to start, let's just keep it simple. Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-2238565672586009102016-03-10T22:26:00.001-08:002016-03-10T22:26:26.050-08:004 SIMPLE KEYS FOR INDUCTIVE PROOF <b><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></b><span style="font-family: Arial,Helvetica,sans-serif;">Whether mathematical induction seems routine or complicated, a few simple keys can make the process easier to follow.<br /><br /><span style="font-size: large;"><b>1. Have a structure within which to organize your work.</b></span></span><br />
<b style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"> <img alt="" 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" /></b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"></span></span><br />
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<span style="clear: right; float: right; font-family: Arial,Helvetica,sans-serif; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><b> </b></span><br />1a. The left-hand column will be the same each time. Every teacher will have specific wording intended to describe the process. Additional comments like “Let n = 1” or “Assuming the base case is true for n = k, we will now show that the base case is true for k + 1 and therefore for all integers” will be redundant from problem to problem within the discrete classroom.<br /><br />1b. By keeping the calculations aligned, it will be easier to follow the calculation steps.<br /><br /><span style="font-size: large;"><b>2. Highlight specific information.</b></span> Another organization tool is intended to identify what part of the Inductive Assumption (also called the Inductive Hypothesis) will be used to simplify calculations in the proof. Highlighting the terms can take several forms like underlining or enclosing in brackets. <br /> <br /> <img alt="" 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" /><br /><br /><span style="font-size: large;"><b>3. Use the highlighted form.</b></span> The Induction Step itself follows a predictable steps. The key is to employ strong algebra skills in order to manipulate the left side to look like a simplified right side!<br /><br />Add (k + 1) to the 1 + 2 + 3 + … + k + (k + 1) = (k + 1)(k + 1 + 1) / 2<br />left side and replace<br />k with (k + 1) on the<br />right side<br /><br />Replace the underlined <u> k (k + 1) </u>+ (k + 1) = <u>(k + 1)(k + 2)</u><br />section on the left. 2 2<br /><br />Then do all that elementary Algebra on the left side…..<br /><br />…..adding fractions <u>k (k + 1) + 2(k + 1)</u><br /> 2 <br /><br />…..factor out common terms <u>(k + 1)(k + 2)</u> = <u>(k + 1)(k + 2)</u><br /> 2 2<br /><br /> <span style="color: #6aa84f;"><span style="font-size: large;">QED: the left side looks just<br /> like the right side!</span></span></span><span style="clear: right; float: right; font-family: Arial,Helvetica,sans-serif; margin-bottom: 1em; margin-left: 1em;"><span style="color: #6aa84f;"></span></span><span style="clear: right; float: right; font-family: Arial,Helvetica,sans-serif; margin-bottom: 1em; margin-left: 1em;"><span style="color: #6aa84f;"><span style="font-size: large;"> </span></span><br /><span style="font-size: large;"><b>4. Recognize properties of exponents.</b></span> 'Product' and 'Multiple' induction problems have unique applications. The objective is to pull out the divisor so multiplying it by anything else would prove divisibility. This strategy might require expanding an exponential and using the distributive property. Here’s an example:<br /><br />Prove that 11^n - 4^n is ‘a multiple of 7’ (or is ‘divisible by 7’)<br /><br />Initial Test Step Let n = 1<br /> 11^1 - 4^1 = 11 - 4 = 7 (true)<br /><br />Assume true when 11^k - 4^k is a multiple of 7<br /> n = k <span style="color: #6aa84f;"> Therefore, 11^k - 4^k = 7x<br /> and <u>11^k</u> = 7x + 4^k</span><br /><br />Prove true when 11^(k + 1) - 4^(k + 1) is a multiple of 7<br /> n = k + 1 <br /> <u>(11^k)</u>(11^1) - (4^k)(4^1)<br /><br /> (7x + 4^k)(11^1) - (4^k)(4^1)<br /> 11(7x + 4^k) - (4^k)(4)<br /> 77x + [11(4^k) - 4(4^k)]<br /> 77x + (4^k)(11 - 4)<br /> 77x + (4^k)(7)<br /> 7 (11x + 4^k) <span style="font-size: large;"><span style="color: #6aa84f;"> QED</span></span><br /><br />Often, classroom expectations include some description like “7 times any number is a multiple of 7.” Individual teachers will have a favored statement to use.<br /><br /><span style="font-size: large;"><b>5. Partition integers.</b></span> Sometimes it is useful to split up integers into the sum of two other numbers (called Partitioning - a favored activity in early elementary numeracy education). To use it requires recognizing that 9 can be written as (8 + 1) or (5 + 4). So when proving that something is divisible by or a multiple of 8 for example, split up 9 into (8 + 1) and use the distributive property. For example…<br /><br />Given: 18^n -1 is divisible by 17<br />Initial Test Step Let n = 1<br /> 18 - 1 = 17 (true)<br /><br />Assume true when 18^k -1 is divisible by 17<br /> n = k <br /><br />Prove true when 18^(k + 1) - 1 is divisible by 17<br /> n = k + 1 <br /> (18^k)(18^1) - 1 <br /> 18(18^k)-1<br /> <br /> (17 + 1)(18^k) -1<br /> 17(18^k) + 1(18^k -1)<br /> <br />Now might come a lengthy description preferred by a teacher:<br /> 17(18^k) is obviously divisible by 17 AND<br /> (18^k - 1) is assumed divisible by 17 AND the sum<br /> of any multiples of 17 is divisible by 17. <span style="font-size: large;"><span style="color: #6aa84f;">QED</span></span><br /><br /><b><span style="font-size: large;">6. Know how to use Pascal’s Triangle to expand higher power binomials.</span></b> While it is possible to raise a binomial to a higher power through long hand distribution, Pascal will be a work saver. Be ready to recognize what is duplicated and look for ways to factor out the divisor. Watch this…<br /><br />Prove that the sum of the cubes of any 3 consecutive, positive integers is divisible by 9.<br /><br />Set up 3 consecutive, positive integers = x, x + 1, x + 2<br /> Cubes = x^3, (x + 1)^3, (x + 2)^3<br /><br />Base Case x^3 + (x + 1)^3 + (x + 2)^3 is divisible by 9<br /><br />Initial Test Step Let x = 1<br /> 1^3 + 2^3 + 3^3 is divisible by 9 (true)<br /><br />Assume true when<br /> x = k k^3 + (k + 1)^3 + (k + 2)^3 is divisible by 9<br /> <span style="color: #6aa84f;"> Pascal Assistant: k^3 = k^3 <br /> (k + 1)^3 = (k^3 + 3k^2 + 3k + 1)<br /> (k + 2)^3 = (k^3 + 6k^2 +12k + 8)</span><br /><br />Prove true when<br /> x = k + 1 (k + 1)^3 + (k + 2)^3 + (k + 3)^3 is divisible by 9<br /><br /> <span style="color: #6aa84f;"> Pascal Assistant: (k + 3)^3 = (k^3 + 9k^2 + 81k + 27)</span><br /><br /> k^3 + (k + 1)^3 + (k + 2)^3 + 9k^2 + 81k +27 <br /> [k^3 + (k + 1)^3 + (k + 2)^3] + 9(k^2 + 9k + 3)<br /> [assumed divisible by 9] obviously divisible<br /> by 9<br /><br />Well, proof by induction may never be ‘simple,’ but it IS predictable and relies on just a few well-known manipulations. Keep these keys in mind and the task will (eventually) become routine.</span>Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-87999104608345376102016-03-10T16:31:00.002-08:002016-03-10T16:35:54.817-08:00FACTOR DIFFICULT TRINOMIALS<div style="text-align: center;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><b>TWO EASY WAYS TO </b></span></span><span style="font-size: x-large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b> </b></span></span></div>
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<span style="font-size: x-large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>FACTOR</b></span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-size: large;"><b> DIFFICULT TRINOMIALS</b></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Factoring trinomials can sometimes seem like a gigantic task, especially when the numbers get large or there’s a coefficient other than 1 in front of the leading variable. Thinking of the two numbers that multiply up to the constant and also add up to the middle term is actually ‘double think.’ It requires keeping two operations in mind at the same time….ugh. </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">Consider the equation y = 24x^2 + 2x - 35. First, find all the factors of 24. Then find all the factors of 35. Then consider each factor pair of 24 in combination with each factor pair of 35 to see if any of the products add up to 2. My brain is a jumble of numbers at this point… 1 times 24 plus or minus 1 times 35, 2 times 12 plus or minus 1 times 35, 3 times 8 plus or minus 1 times 35, and on and on and on. This is too much work, and as a mathematician, I’m always looking for the “elegant solution.” For the more complicated factoring problems, I prefer systems that reduce calculations to one-at-a-time (and self-correcting would be a bonus).<br /><br />Here are two procedures that exploit methods we’ve already learned for simple problems and avoid some of the typical mistakes.<br /><br /><b><span style="font-size: large;"> BOTTOMS UP</span></b><br /> </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Given: y = 24x^2 + 2x - 35<br /><br />Step 1: multiply the leading coefficient (24)(35) = 840<br /> and the constant, <br /> and rewrite the problem y = x^2 + 2x - 840<br />————————————————————————————-<br />Step 1 turns an ugly trinomial into one that looks more like the first exercises practiced when learning to factor. The next 3 steps should be very familiar.<br />————————————————————————————-<br />Step 2: factor the product 840 <br /> (1, 840)</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> (10, 84)<br /> (20, 42)<br /> <span style="background-color: blue;"></span> (24, 35)<br /> </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Step 3: select factors that SUM to <span style="color: blue;"><span style="background-color: white;"> <span style="font-size: x-large;">(28, 30)</span></span></span><br /> the middle term</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">-------------------------------------------------------------------------------------<br /><br />Step 4: enter the factors into binomials y = (x + 30)(x - 28)<br /> <span style="color: #3d85c6;"><i> (Notice that the MIDDLE TERM<br /> determines the sign of the larger <br /> factor, while the CONSTANT tells<br /> if the factors are the same sign or<br /> different signs. A negative constant<br /> indicates the signs are DIFFERENT,<br /> while a positive constant says the<br /> signs are THE SAME.)</i></span><br /><br />Step 5: Divide the integers by the<br /> original leading coefficient y = (x + 30/24)(x - 28/24)<br /><br /> and reduce. y = (x + 5/4)(x - 7/6)<br /><br />NOW, the step that gives the method<br />its name…..<br />Step 6: bring the “BOTTOMS UP” y = (4x + 5)(6x - 7)<br /><br /> <span style="color: #3d85c6;"> <i>(Notice that at Step 5, the problem is set up to solve.)</i></span></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="color: #3d85c6;"><i> </i></span><br /> <br />While this plan makes numbers easier to manipulate, the next alternative approach is also <b>SELF CORRECTING</b>.</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="font-size: x-large;"> DE-FOIL</span></b></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><br />Follow Steps 1- 3 but don’t rewrite the equation.</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Step 1: multiply the leading coefficient (24)(35) = 840<br /> and the constant. <br /><br />Step 2: factor the product 840 <br /> (1, 840) </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> (10, 84)<br /> (20, 42)<br /> (24, 35)<br /> </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Step 3: select factors that SUM to <span style="color: blue;"><span style="font-size: x-large;">(28, 30)</span></span><br /> the middle term</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">---------------------------------------------------------------------------<br /><br />Step 4: Rewrite the equation into one <br /> with the FOUR TERMS that would</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> result from FOIL:<br /><br /> -- the first term comes as is<br /> -- the constant comes as is y = 24x^2…….………- 35<br /><br /> -- instead of the initial middle<br /> term, enter the chosen<br /> factors y = 24x^2 - 28x + 30x - 35</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> <span style="color: #3d85c6;"> <i>(If there are opposite signs, I like to put the negative one first so I don't lose it in the next step.)</i></span><br /><br />Step 5: Now, think about what would<br /> be done to factor any polynomial </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> with four terms........GROUP y = (24x^2 - 28x) + (30x - 35)<br /><br />Step 6: Factor out commons y = 4x(6x - 7) + 5(6x - 7)<br /><br />Step 7: Factor out commons y = (6x - 7)(4x + 5)</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">We do a lot of factoring in Algebra, but once we get to simplifying radical expressions it becomes mandatory to be at ease with the task. One of these alternate methods could be a magic key to making the job less daunting. </span></div>
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Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com0tag:blogger.com,1999:blog-7971595768928070725.post-52755666504797256312015-11-04T17:50:00.000-08:002015-11-04T17:50:35.892-08:00PREPARING FOR CALCULUS SEMESTER 1 FINAL: LIMITS<br />
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Now that the first quarter of the 2015-2016 term is closing, it's time to start reviewing the material for the semester final. Here and in subsequent posts, are "study cards" that summarize concepts that are SURE to be tested. Start reviewing now so finals are a breeze.<br />
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" 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Dr. Sandi Fergusonhttp://www.blogger.com/profile/15041012085453464859noreply@blogger.com1