Don't Lose Points Unnecessarily on the AP Calculus Exam



Don't Lose Points Unnecessarily on the AP Calculus Exam!

Here are some tips from someone who has graded the exam for five years. These tips are for the Free Response section, not the Multiple Choice section.

Decimal answers must be accurate to three decimal places (rounded or truncated). If the answer is π, all these are acceptable: π, 3.141, 3.142, 3.141592654, and even 3.1412345, because the reader will stop after three decimal places.

Questions have multiple entry points, so do not give up if you can't do the first part! The other parts may not depend on part (a) at all.

Use standard mathematical notation. The first quadrant area under y=x2 from x = 1 to x = 5 must be presented as [pic] , not as fnInt(x^2,x,1,5).

Pay attention to the units. The problem may say "Give units", or "... including units". Be sure to do this.

Crossed out work will not be read. To save time, don't erase, just cross out. However, don't cross out your work unless you know you can do better.

Do not simplify answers. If you make a mistake simplifying, you will not earn the "answer point". Graders will accept any mathematically equivalent form of the answer.

Label graphs properly. Is it the graph of f, f' f", g, g' g " or what?

Don't change the names of things. If the problem has "Let s(t) be the position at time t", do not change s(t) to f(x).

Every pronoun needs an antecedent. "It's increasing because it's positive" will not earn you the "justification" point. Say " f(x) is increasing on the interval (a, b) because f'(x) is positive there. "

Sign charts are not sufficient to justify relative extrema or inflection points. Say something like this: "g(x) has a relative minimum at x=3 because g '(x) changes sign from negative to positive at x = 3".

Interpreting a definite integral – be sure to interpret the limits of integration too. Example: If v(t) ft/sec is the velocity of an object at time t sec, then [pic] = 55 means the change of position of the object is 55 feet from time t = 0 sec to t= 20 sec.

Drawing a solution curve is not "connect the dots". When you sketch a solution curve to a differential equation on top of a slope field containing dashes you have previously drawn, the curve must be tangent to the dashes if it goes through the corresponding points. Your curve must be tangent at the point of the initial condition, but it is best to avoid any other points where you drew dashes, and there's always plenty of empty space to do this. If you go through points that have dashes on the slope field, you must make sure the dashes look like tangents! Best to avoid them.

If a calculator is permitted, use it. On the calculator portion (generally questions 1 – 3 of Free Response), problems (particularly integrations) may be impossible without a calculator. Do not waste time with non calculator methods.

General: These tips are to help you. The grading is not "tricky" and you will do well by doing good calculus. The College Board establishes certain grading policies to make sure all exams will be scored the same way. Being aware of these policies can help you avoid losing points unnecessarily.

Study hard. You will do well!

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