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# How to Pass the AP® Calculus Exam

Updated: Jul 25

Tips on how to pass the AP® Calculus exam, from a former teacher, AP exam reader, and current AP Calculus tutor.

Before you dive into your study plan to pass the AP Calculus exam, consider the tips for studying and succeeding on the AP Calculus exam below. These tips are even more important if you don’t have a full month to study for the exam. Also, I recommend revisiting these tips the night before the AP exam to earn some last minute points!

### How to Study for the AP® Calculus Exam:

1. Practice! Do as many AP® level questions as possible, including multiple choice questions (MCQs) and free response questions (FRQs). Practicing early will build your confidence in knowing what the question is asking and being able to solve it. See the 7 best resources to study for AP Calculus tests to get practice problems matching the rigor of the AP exam.

2. Know what FRQs to expect. Especially on the AB exam, the topics assessed are consistent from year to year. The challenge is that the prompts are presented in different ways, with functions, graphs, and tables. For the AB FRQs, you should expect questions on accumulated rates, particle motion, differential equations, area/volume, and a graph prompt. Generally, the graph alternates with a derivative and integral prompt from year to year so check out the previous year's exam to predict which will be on this year's exam. There will also be a question with a table that will ask you to estimate a derivative (using average rate of change) and integral (using a Riemann sum or trapezoid rule).

3. Study what you don’t know. I know it builds confidence to get the right answer, but you’ll make bigger gains in minimizing weaknesses instead of sharpening strengths. One caveat: I recommend skipping Optimization and Related Rates. It's beneficial to know these applications especially if you're pursuing an engineering or STEM career, but as far as passing the AP exam, I personally wouldn't prioritize reviewing/learning these concepts. The problems take too much time and there are so many different geometric formulas that I wouldn't bother memorizing. Knowing derivative rules is much more important.

4. Make notecards to memorize derivative rules including the power rule, product rule, quotient rules, trig derivatives, inverse trig derivatives, exponential derivatives (and do them backwards to practice your antiderivatives). Bonus: make notecards of the Theorems too, including Fundamental Theorem of Calculus, Intermediate Value Theorem, Mean Value Theorem, and Extreme Value Theorem.

5. Know your justifications. Make sure your justifications are Calculus based (including a derivative)! See some examples in the table below. For example, to justify where F has a relative minimum, you must include F'(x) in your reasoning. Saying "F changes from decreasing to increasing at that point" will not earn you the justification point even though the statement is correct; the reader is looking for a Calculus based justification including a derivative. Make sure you also know justifications for particle motion questions. And read more about first and second derivative test justifications.

### Tips for the Free Response portion of the AP® Calculus Exam:

1. Clearly answer the question asked. Include a justification or units if it asks. Make sure to use f, f', g, g'', etc. instead of "the function," "the graph," or "it."

2. Write everything in the box provided. Anything in the margins will not be scored.

3. No need to write an essay or even full sentences. Again, just answer the question.

And don’t waste time explaining how to do a problem or adding units if it's not asked. It won’t earn you any points.

4. The computations are generally straightforward. If you’re caught up solving a complicated equation, pause for a moment to see if you can come up with a different way to solve the problem.

5. Write down your set up for calculator questions. For example, in the 2018 Free Response #2 shown below, you earn 2 points for the set up and only 1 point for the answer. If you're not very quick with the calculator, you could write down your set up for all parts of the question first, then go back and solve everything on your calculator, time permitting.

6. If you do something incorrectly, cross it out or erase it. If you have two separate answers or two ways to solve the problem, the grader will average those points earned.

7. Don’t simplify numerical answers like e + (1/5)/2 - sin(0). It wastes time and if you simplify incorrectly, you won’t earn credit.

8. Round to 3 decimal places. I know it’s specific but don’t lose points when you have the correct answer. Fun fact: if you don't feel confident in rounding, just write the first 3 decimal places or even 4! The reader will only look at the first 3 decimals places for accuracy. And they accept both truncating (keeping the first 3 decimal places exactly as they are) or rounding. You won't earn the answer point if you write less than 3 decimal places, and you lose even more points if you round to different decimal places throughout the problem.

9. You’re allowed to go back to the first two Calculator questions even after the first 30 minutes has passed; you just won’t have a calculator. You can still set up integrals (see tip #5 above) to earn points!

10. Understand what the questions is asking. College Board explains what different verbs are asking the student to do. A common error I see is for absolute minimum/maximum questions. For a relative min/max, we generally create a sign chart and use the justifications listed in the table above. For an absolute min/max, I recommend the "candidate's test," making a table with the critical numbers and endpoints, plugging them back into f(x). If the question asks where the absolute min/max occurs, we're looking for the x-value. If the question asks what the minimum/maximum value of f(x) over a given interval is, we're looking for the y-value.

11. Be aware of eligibility points. For Mean Value Theorem (MVT), the prompt typically says "f is a differentiable function" then the specific part of the question asks to show there exists a time c, a<c<b, where f'(c)=2, for example. One point will be awarded for saying, "Since f is differentiable, therefore f is continuous and MVT applies." You don't have to explicitly mention MVT, but you do need to mention the hypotheses of MVT being differentiable over (a,b) and continuous over [a,b]. Even if you correctly apply the MVT, showing the average rate of change equals 2, you will not earn that point if you don't mention the hypotheses being met. In other words, you're not eligible for the second point if you don't state the continuity and differentiability requirement.

The same goes for L'Hospital's Rule. Instead of saying the limit approaches 0/0, the reader is looking for you to say the limit of the numerator equals 0 and the limit of the denominator equals 0 so L'Hospital's Rule applies. Then you can go on and take the derivative of the numerator and denominator to evaluate the limit.

## Tips on how to pass the AP® Calculus Exam:

Once you’ve reviewed the curriculum, review these tips the night before you take the exam.

1. Eliminate answers on the multiple choice. Given the answer choices below, could you make an educated guess without even knowing the question? Choice (A) looks completely different than the others so I would eliminate that. Then look at the coefficients. Choice (D) has all integer coefficients but the other three choices have fraction coefficients so I would eliminate (D). Then both (A) and (B) have 1/3 as the last coefficient so without knowing the question, I would guess (B).

2. All questions boil down to being about a limit, derivative, or integral (or series in BC). If you’re stuck, ask yourself which topic is being assessed. A rate is typically a derivative question and to undo a rate would require an integral. Once you determine a question wants you to evaluate an integral, make sure you can determine which integration technique to use.

3. Relax! You don’t need a perfect to pass. Scoring changes from year to year but in the released 2008 scoring guide, about 36%-47% correct will earn a 3, 48%-62% will earn a 4, and 63% or above will earn a 5!

4. Find the problems you know how to do and solve them first. You won’t likely have the time to get to every problem (and that’s okay because remember you don’t need a perfect score). Go back through a second round for the more difficult problems.

5. Get your graphing calculator ready. Double check it’s in radian mode and that you have spare batteries.

### Need help reviewing?

If you're unsure if your free response answers are earning the points outlined on the scoring guidelines or if you need more quality practice problems or individual help reviewing for the AP exam, consider hiring an AP Calculus tutor or joining me in Calculus Crew. Calculus Crew is an online Calculus community where students meet with me, a veteran AP Calculus teacher, twice a week for group sessions. The sessions focus on challenging test questions and incorporate previous AP exam questions, both multiple choice and free response, to help you prepare for the AP exam. We even look at my predictions for the FRQs each year and solve similar questions. I want you to have the best chance of passing the AP exam. I know you've worked hard learning Calculus this year and you can succeed on this exam! Best of luck!

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