STUDY FOR FINALS OR THE ACT?

The question stunned me for a second. It didn't seem like a valid issue, especially considering it came from someone I consider to be educationally grounded. It's akin to asking whether you prefer your right arm or your left. The saying "cutting off your nose to spite your face" comes to mind. So I was caught off guard when asked whether a student should study for finals or the upcoming ACT.

The one-word answer is "BOTH!!"

The real problem for the unprepared student comes when there's only one week left of the semester and snow days pushed the last day of finals to the Friday before the June ACT test. I've known quite a few "crammers" in 20 years of teaching and I've never found one who could handle both final exams and the ACT in the same week. Only through continuous, sustained, long-term study can anyone expect to excel on both classroom assignments and college entrance exams simultaneously.

For those who have postponed study until the last minute there are few options available.
1. There's only one chance to succeed on final exams, so at this point there is no choice but to prepare for them as much as possible before test date. Use the final review packet provided by the classroom teacher and review from work that has been collected throughout the semester. Good luck!!
2. The good news is that there is always another chance to conquer the standardized college entrance exams like the ACT or the SAT. For a small fee, you can transfer your registration for June's test to September or October and still have results in time for early application to most colleges.

That brings me to the whole issue of when to take the ACT. I heard today someone suggesting that students need the practice in taking a bubble test or standardized test or a specific test like the ACT. I could agree that "practice" is an important component to feeling confident, but is it necessary to get up at 6:30, drive to the testing location, and sit for up to 4 hours taking a specific standardized test if it's already apparent that you won't do your best work and will have to take the test again in 3 months anyway? For many public school students, there's little need to "practice" bubbling. We've already taken a raft of these things mandated by the education system. And what is learned by simply taking a test if the results are just a few numbers? If a student doesn't pay for and receive the actual test and his or her actual answers, the exam can't be used to identify errors and mitigate them in the future.

Then came the suggestion that saving a mere $13 by transferring the June testing fee to September doesn't make it worthwhile....make the student take the June test and pay again for the later date, plus the full test report for both. This idea obviously DIDN'T come from a student and it didn't consider the detrimental effect that might come from "bombing" the test. Rescheduling now and creating a plan to study over the summer gives the test taker a reasonable goal to shoot for and obviates the possibility of giving up and just accepting a score that doesn't support the grade point average.

There's another way to gain the "practice." Retired tests are available from most test publishers, so seeing the types of questions asked and the format for questioning can be accomplished without sitting for the proctored exam. If pacing issues are a problem, a kitchen timer can be used efficiently, or the "parental unit" can be recruited to keep track of the stop watch. Sample tests can be scored immediately, providing a more effective study plan than waiting for test results for up to 6 weeks, by which time you've probably forgotten why those answers were chosen in the first place.

In this last week before finals and the June ACT, the question about which to study for is moot. Study time is over for both. Now is the time to review, review, review. If a student has diligently learned the classroom material over the semester, finals should go well. That's the first priority. If more study is necessary in order to reach the optimum goal on a college entrance exam, postponing until the Fall and focusing on preparation over the summer could prove to be the most realistic plan.

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.