The AP Calculus AB test is composed of 45 multiple choice questions (MCQs) and 6 free response questions (FRQs), each section weighing 50% of the total grade for a possible score from 1 to 5. In this guide, we will go over the strategies for the multiple choice questions and then work through two more difficult multiple choice questions.
Basic Strategies
The multiple choice section on the AP Calculus AB exam is divided into 30 no calculator questions followed by 15 calculator questions. The free response section is split between 3 no calculator and 3 calculator questions.
1. Prepare Well
Before taking the AB exam, it is important to practice. The AB exam is different from other quizzes, tests, or homework you may have done at school. It is long and comprehensive, with difficult multi-step problems. You should take at least one full-length test to see what it really feels like. You can take official free response practice tests and IAC mock multiple choice test. There is also one full practice test available from the 2012 administration of the exam. You can also download I Aced Calculus Flashcards App, which contains all AB material you need to know, with video explanations, calculator tips, and over 900 multiple-choice practice problems.
2. Read Each Problem Carefully
It may surprise you, but many students answer questions incorrectly or waste valuable time because they misread the problems. Take your time and read the problem to make sure you fully understand what’s being asked. We cannot emphasize enough how important this step is.
3. Think About the Problem
Sometimes it’s best to not jump right into a problem. Oftentimes there are also multiple ways to solve one problem. Before you start solving, consider your options and make a plan. This will help you save time and be more accurate.
4. Keep Moving
You have only a few minutes to work on each problem. In the MCQ section, there’s a huge time crunch. If you spend too much time on a single problem, you might not get to others. Remember, you only need to get around 60%-70% of the problems correct to get a perfect score. If you can’t figure out a multiple choice question, make your best guess and keep moving. Keep in mind, there are no points subtracted for incorrect answers, so make sure to pick an answer for every question.
5. Check Your Work
Set aside some time to check your work for each question. It’s always important to check your work, even briefly, after you answer a question. In the MCQ section, there are answer choices specifically designed to catch students making the most common mistakes. Make sure you don’t fall for those distractor choices.
6. Eliminate Choices
Sometimes you can substitute an answer into the problem to eliminate answer choices. Other times your answer is an expression that involves variables, so you can pick specific values for those variables. For example, if a problem gives a particle’s position in the form \(at^2 + bt + c\) and asks for the value of \(t\) when the particle’s velocity is \(0\), the answer will be in terms of \(a\), \(b\), and \(c\). However, you may let \(a = 1, b = 2, c = 3\) and the particle’s position will be \(t^2 + 2t + 3\) and its velocity will be \(2t+2\), which can be used to eliminate some answer choices. There is another example of selecting specific functions in the second practice problem later on.
Practice Problems
The most important things on the AP Calculus AB exam are your timing and accuracy – as long as you are confident in your answers and making progress on a problem at all times, only minor adjustments to your strategy may be necessary. Below are two sample problems from the first section of AB exams.
Sample AP Calculus AB Problem I
The Mean Value Theorem guarantees the existence of a special point on the graph of \(y=\sqrt{x}\) between \((0,0)\) and \((4,2)\). What are the coordinates of this point?
- \((2,1)\)
- \((1,1)\)
- \((2,\sqrt{2})\)
- \(\left(\frac{1}{2},\frac{1}{\sqrt{2}}\right)\)
- None of the above
First, read the question thoroughly and strategically. What is written at the beginning of the question forces us to recall the formula: what does the Mean Value Theorem (MVT) state? In general, if a theorem has a name, you should memorize it. They include the Fundamental Theorem of Calculus, Intermediate Value Theorem (IVT), Mean Value Theorem (MVT), and Extreme Value Theorem (EVT). The MVT states that for a differentiable function \(f(x)\) on a closed interval \([a,b]\), there exists some \(a\leq c\leq b\) such that
$$f’(c) = \frac{f(b)-f(a)}{b-a}.$$
In this problem, \(a =0\), \(f(a) = 0\), \(b = 4\), \(f(b) = 2\). Substituting these values yields \(f’(c) = \frac{1}{2}\). Since \(f’(x) = \frac{1}{2\sqrt{x}}\), we need to find \(c\) such that \(\frac{1}{2\sqrt{c}} = \frac{1}{2}\), or \(c = 1\). Substituting, \(f(1) = \sqrt{1} = 1\). Hence, the correct answer is choice (B) \((1,1)\). The key steps to this problem that you should double check are the derivative of \(f(x)\) and the slope calculation between \((0,0)\) and \((4,2)\).
Sample AP Calculus AB Problem II
If \(f\) and \(g\) are twice differentiable and if \(h(x) = f(g(x))\), then \(h’’(x) =\)
- \(f’’(g(x))[g’(x)]^2 + f’(g(x))g’’(x)\)
- \(f’’(g(x))g’(x) + f’(g(x))g’’(x)\)
- \(f’’(g(x))[g’(x)]^2\)
- \(f’’(g(x))g’’(x)\)
- \(f’’(g(x))\)
To find \(h’’(x)\), we first use the Chain Rule to find
$$h’(x) = f’(g(x)) g’(x).$$
We now use the Chain Rule and Product Rule to finish the problem:
\[ h’’(x) = f’’(g(x))g’(x)\cdot g’(x) + f’(g(x))\cdot g’’(x) \]
\[ = f’’(g(x))[g’(x)]^2 + f’(g(x))g’’(x), \]
which is choice (A).
If you are under a time crunch or want to double-check your answer, it could be a good idea to pick some specific functions that are easy to work with. For example, we could let \(f(x) = 2x\) and \(g(x) = x^2 + 1\). Then \(h(x) = 2x^2 + 1\) and \(h’’(x) = 4\). We can immediately eliminate choices (C), (D), and (E), since \(f’’(x) = 0\), making all of those choices equal to 0.
Conclusion
This article contains general advice and strategies and you may find some work for you, while others don’t. These general strategies apply to most multiple-choice exams, including the SATs. You can find a sample multiple choice section for the AP Calculus AB exam with solutions here. You can find a complete list of AP Calculus AB free response questions with solutions here. We hope that you learned something from this article and we wish you get a 5 on the exam. We believe that having strategies is always better than going without them. Good luck!
