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

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

Decimal answers must be accurate to three decimalplaces (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.

Trace doesn't give three-point accuracy. When you need an intersection point or zero, use the Calc menu or equivalent.

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 , not as fnInt(x^2,x,1,5).

Pay attention to the units. The problem may say "Give units", or "... include units of measure". 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. Simplifying is still an important skill, and these skills are needed on the multiple choice part of the exam.

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 = 55 means "the change of position of the object is 55 feet from time t = 0 sec to t = 20 sec."

Given a table of data, ∆x, ∆t, etc.may not be constant. Be sure to check whether or not the inputs are equally spaced before you set up a Riemann or Trapezoid sum. For example, see Question AB5/BC5 from the 2007 exam.

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, but "be smooth".

If a calculator is permitted, use it for graphing, intersection points, and numerical derivatives and definite integrals. However, do not use fmax, fmin or special programs except to check.

Global (Absolute) max and min on an interval. Best thing to do is make a table showing all the candidates and their function values. The candidates are the critical numbers (f ' = 0 or doesn't exist) and the endpoints.

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!

Even More Tips

If the question asks for units, underline the word "units" so you won't forget. Always attach the unit to a number if possible.

When you solve a differential equation put in a constant of integration in the step where you integrate.

Unsupported answers may not receive any credit, even if they are "numerically correct". i.e., always show the setup.

Be sure to understand the distinction between "displacement" and "distance traveled". (Distance traveled may not be negative, but displacement can be negative.) See 2009 AB 1 / BC 1 and the grading standard for it.

Areas / Volumes that "come out negative" (which usually results from a reversed integrand). How you "make the answer positive" is important.

is not OK

but so area = 5/3is OK

When "Quantity 1" is the derivative of "Quantity 2 " always say so (unless the problem already gives them as f and f ', etc. Example, a question tells you that g is defined by g(x)= . You should immediately write

g '(x) = f(x).

Do not round an intermediate result. If you might need it later, STOre it (unrounded) to a memory location A, B etc., then use the letter in your calculation.

CAS Users (T-89, Nspire, etc.). Use numerical antiderivatives and derivatives (not symbolic) on the calculator part of the exam.

Use the "=" sign properly. For example, x + 5 = 17 = x = 12 is improper.

One tip for the Multiple Choice Part: There is no deduction for wrong answers (i.e. penalty for guessing), so don't leave anything blank on MC.