3 DAYS BEFORE ACT TIPS

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.

1.  REVIEW PREVIOUS WORK
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.

2.  ENGLISH - REVIEW RULES OF GRAMMAR
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.

3.  MATH - REVIEW BASIC ALGEBRA AND GEOMETRY EQUATIONS
Make a list of those that appear in your practice problems.  There are quite a few, but they are always the same.

4.  READING - PRACTICE FINDING SPECIFIC WORDS IN CONTEXT
Take any magazine or newspaper article.  (Magazines are better because the columns are generally  wider and more like the layout of the test.)  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. 

5.  SCIENCE - PRACTICE READING CHARTS AND GRAPHS
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:
      a) what is the independent variable? (What does the x axis represent?)
      b) what is the dependent variable?  (What does the y axis represent?)
      c) pick a spot on the graph and identify the meaning.
Here's an example:

    
      a) hours elapsed 
       b) bacteria 
       c) after 5 hours had elapsed, approximately 23 bacteria were reproducing.

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.

6.  SCIENCE - COMPARE RESULTS
Using the same graphs, analyze results.  In this example, an analysis statement might be "as the hours increase, the number of bacteria reproducing increases."  Personally, I use a shorthand system that looks more like.... 

   ....to take less time than full sentences.

Three days left.....keep working!!!

WHAT THE TEACHERS ARE ASKING ABOUT AP CALC AB

I've recently joined a group of AP Calc teachers who share ideas, ask questions, clarify concepts, discuss scoring protocals, etc. I've learned quite a bit from these folks and hope to share their insights with my students and blog followers. Here are some of the last minute ideas to insure success on the AP Calculus AB test.


* When calculating “total distance” use absolute value of the integral. Even if walking backwards, the distance traveled is still positive.

* Average velocity -- is an integral of the endpoint velocities, ∫[v(b) - v(a)], divided by the difference b-a. (Sum of velocities over the interval divided by the length of time of the interval.)

Average acceleration -- use [v(b) - v(a)] divided by b-a. Think: v(b) IS the integral of v’(b), the integral of acceleration. ∫[v’(b) - v’(a)] / b-a (Sum of accelerations over the interval divided by the length of time of the interval.)......This interpretation is closely related to....

Average rate of change -- is an integral of [f’(b) - f’(a)] divided by the difference b-a.
∫[f’(b) - f’(a)]/b-a (Sum of the rates over the interval divided by the length of time of the
interval.)

* A particle is speeding UP if the velocity and acceleration are both either positive or negative.
A particle is slowing DOWN if the velocity and acceleration are opposite signs.

* A function must be continuous if it is differentiable, but continuity does NOT guarantee differentiability: think of sharp corners and piecewise functions.

* Concavity Theorem: The graph of f is concave UP at (c,f(c)) if f”(c)>0 and concave DOWN if f"(c)<0.

* Intermediate Value Theorem: IVT. (using the abbreviation is acceptable)
Use it to explain that there is an X value, c between a and b, that gives a Y value between the Y values of a and b.

* Mean Value Theorem (think Difference Quotient): MVT (abbreviation is acceptable)
There is at least one point on the graph at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the arc (also known as the slope of the secant).

- If f’ is positive on a closed interval, then f is increasing. (positive slope)
- If f’ is negative, f is decreasing. (negative slope)

* Volume of rotations around vertical lines (x= or the y axis), use x= equations where the variable is y. Indicate domain of integrals as the highest and lowest y values.

* Volume of rotations around horizontal lines (y= or the x axis), use y= equations where the variable is x. Indicate domain of integrals as the highest and lowest x values.

* When finding absolute min/max values, be sure to check the endpoints of a closed interval.

* Explanations need to rely on mathematical reasoning; using a visual interpretation of “the graph” is not sufficient.

Use this collection of last minute reminders from hundreds of AP Calc teachers to earn your best score on the College Board test.

ORGANIZE YOUR RESOURCES (CALCULUS)

Since this is my first year focusing on the Calculus curriculum, final exam time is the perfect opportunity for me to refresh my own study skills. For those who struggle with preparation for the cumulative exam each semester, perhaps seeing how someone else studies could give you some ideas of your own.

My situation is slightly different than the students’. I have 4 Calculus students in 3 different schools, 4 different teachers, and 3 different textbooks (one of which is a newer version of another with many of the same problems, some new ones, and all on different pages!). The organization needed to remember where each student was in the various schedules and what homework I had completed in preparation for tutorials for whom got the better of me and was in need of serious revamping even before I began over Winter Break to study for finals. At that time, I collected all homework and piled up assignments by student, then within each student’s pile, I put things in chronological order.

Some teachers had flitted around the text, while others had followed the order given in the book, so when one student was working on Inverse Trig differentiation, another was working on Related Rates. My solution for organizing was to make 4 lines of work (one for each student), assembled by TOPIC. And that gave me the idea to make my own workbook with notes relating to topic and separated with tabs so I could access my backup materials as needed.

MY TIP TO YOU
You already know I expect you to keep all class notes, homework assignments, tests and quizzes (from the first day of the semester until the day you retire to a nursing home). If you’ve been following my suggestions, this material is already organized by chapter or unit according to the chronological order established by your teacher.

That’s a lot of paper and probably difficult to use as reference. I suggest you acquire either the “Stickies index tabs” (mine are the Staples brand but I think 3M has a version also) or actual binder tab sheets. Mark the tabs according to the topics you’ve studied and separate your work by topic. When you come across a final review question that relates to the Mean Value Theorem, for example, you can easily find your past work on that subject.

Here’s a list of the topics in my newly organized, personal reference binder:

FUNCTIONS
LIMITS

RULES OF DIFFERENTIATION (this is my universal sheet with all of the examples including derivatives of Trig functions, e, and all that sum, difference, quotient, chain rule stuff in one location. Not every text provides the handy list on the book cover, so I have my own to use as reference if I forget a rule or just want to verify my work.)

VELOCITY/ACCELERATION
EXTREMA
MEAN VALUE THEOREM
F’’
OPTIMIZATION
NEWTON’S METHOD
IMPLICIT DIFFERENTIATION
RELATED RATES (by far the most voluminous section complete with examples from the internet. I defy any teacher to find a problem I have not researched and copied the algorithm for solution.)

Finals are fast approaching. You may already have your Final Review Packet. I’m thankful to have the organizing completed before trying to work on 4 entirely different sets of problems from 4 uniquely disparate teachers!! Your study plan will surely be less complicated than mine, so take heart in knowing that STUDYING SMARTER, NOT JUST HARDER has many positive rewards.