How to Score a 5 on the AP Calculus Test


Getting ready to take the AP Calculus test? Brush up on these study tips from Olympia, WA tutor Tali H


The AP Calculus exam is rumored to be one of the harder AP tests – especially for those of us who math doesn’t come easily to. The test takes three hours and 15 minutes, and has 45 multiple-choice questions and six short-answer questions. Both types have a non-calculator part and a calculator part. Even though it sounds daunting, with some determination and productive studying, the test should be doable. The following are some tips to help you study effectively.

Get Your Hands on AP Calculus Practice Tests

Even for someone who knows calculus pretty well, acing the test might still be a problem unless you get practice with some actual AP questions to familiarize yourself with the format. So, get your hands on a few AP Calculus practice tests (and yes, I do mean a few and not just one). AP teachers have access to every released AP test. You can also find tests online or in AP Calculus test prep books. Not wanting to spend any money but wanting hard copies, I just went to the library and found quite a selection. You can find almost every released free-response section with the scoring rubric (GO OVER WITH CAREFUL ATTENTION) online at the College Board website. You can also find full-length AP Calculus practice tests on the AP Practice Exams website, plus a ton of other resources and online notes!

Know What the Test Graders Are Looking For

On the short-answer section, you not only need to know how to get the right answer, you also need to know exactly what they’re looking for. The right answer usually gets between 2-4 points, while the actual work of the problem accrues the other 4-7 points. Take a look at an actual 2012 AP question below:

For 0 ≤ t ≤ 12, a particle moves along the x-axis. The velocity of the particle at time t is given by v(t ) = cos(π/6 t ). The particle is at position x = −2 at time t = 0.
(a) For 0 ≤ t ≤ 12, when is the particle moving to the left?
(b) Write, but do not evaluate, an integral expression that gives the total distance traveled by the particle from time t = 0 to time t = 6.
(c) Find the acceleration of the particle at time t. Is the speed of the particle increasing, decreasing, or neither at time t = 4 ? Explain your reasoning.
(d) Find the position of the particle at time t = 4.

Here’s the breakdown for how this question was scored (to see the actual answers, visit the 2012 AP Free-Response Score Guidelines and go to page 7).

(a) 1 : considers v(t)=0
1 : interval
(b) 1: answer
(c) 1 : a(t)
2 : conclusion with reason
(d) 1 : antiderivative
1 : uses initial condition
1 : answer

As can be seen, points are given for coming up with an interval, the antiderivative, using the initial conditions, etc. If you were to give just the answer, you would only get four or maybe five out of the nine points. Plus, what if you get the wrong answer? Then you may end up with no points. However, by showing all your steps, you can get points even if the answer is wrong.

*** Important Tip ***

If you’re not sure an answer from a previous step is right (or if you didn’t know how to get the answer in that step but you know how to do the next step, which requires the previous answer) write “Assume _______ (answer you got or an estimated answer) is correct” at the top of the problem you are now solving. If possible, your next answer will be scored based off of the answer you would get from the “assumed information.”

Time Yourself

Many students know how to do the problems. However, they do not know how to do the problems quickly and efficiently. On the AP test, you will most likely not have time to check your answers multiple times or even once for that matter. The problems are long and with all the additional work you will have to show to make sure that you will be receiving as many points as possible, time will definitely be an issue. So prior to taking the test, practice, practice, practice!

*** Important Tip ***

When you’re practicing, do the same problem multiple times (three times is usually sufficient) back-to-back, attempting to improve your time of completion. First time through, some AP problems can take 20 to 25 minutes. Cutting your time by 10 to 20 minutes is not only a fun challenge but it also shows you what it feels like to solve the problem in the correct amount of time and solidifies the information you’re working with.

Regardless of your intelligence level, AP Calculus is a challenge and requires work. However, the work is worth it. Learning calculus brings your understanding of mathematics, logic, and problem solving to a whole new level. Enjoy the pain, practice the problems, and then practice the problems some more. I highly recommend taking multiple AP Calculus practice tests and investing in a tutor. Having someone to guide you along in such a difficult subject helps you progress smoothly and keeps you from getting frustrated. Check out the selection of Calculus tutors on for additional help.

TaliHTali H. tutors in various academic subjects in Olympia, WA, as well as through online lessons. Since 2010, she has worked with numerous students in elementary, middle, high school, and college in both group settings and one-on-one. Learn more about Tali here! 



Interested in Private Lessons?

Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today!

Newsletter Sign UpPhoto by Akash k

0 replies

Leave a Reply

Want to join the discussion?
Feel free to contribute!

Leave a Reply

Your email address will not be published. Required fields are marked *