The tests are from and The test has an answer key included; however, for some reason, the exam does not. The College Board provided answers for the free-response questions in a separate document, but there is no official answer key available for the exam's multiple-choice section.
The answer key linked below is unofficial, but no one has publicly disagreed with any of the answers, so it's highly likely that it's correct. Because these exams are from a while back, they both have some format differences compared to the current AP Calculus AB exam. But looking through these old exams can give you a sense of the test format, and you can work some of the questions as practice, too. Both of these sections are divided into two parts. For reference, here's the current format of the exam:.
You can only use a calculator for certain sections of the AP exam. Both released exams have the same total number of multiple-choice and free-response questions as the current exam. However, the test does not have separate parts for the free-response section, and students were allowed to use a calculator to answer all six questions. Neither the multiple-choice nor the free-response sections of the exam were separated into different parts, and students were allowed to use their calculator for the entire exam.
The multiple-choice section was also only 90 minutes long, instead of minutes. When you take these exams for practice, it's not worth the time and effort needed to try and figure out which questions you wouldn't be allowed to solve with a calculator today.
Instead, take the tests with the calculator and timing rules that were in place when the tests were administered. These variations between current and past exams do mean that these two complete released exams don't give quite as accurate a representation of the current AP exam as the complete released exams for other AP subjects do. However, they are still very useful because they cover the same content and are worded the same way as the current exam.
Towards the end of this guide I'll explain exactly how to use these resources and others. The College Board often reuses multiple-choice questions for multiple exams, so there are typically few official multiple-choice problems available for any AP exam, AP Calculus AB included.
Besides the complete practice tests discussed above, there are no full official multiple-choice sections available, but you can check out these official sample questions for Calculus AB. The questions start on page 5, and there are Calculus BC questions listed after the AB questions; be sure you're not accidentally looking at those.
This document contains 16 multiple-choice problems, along with answers and the major skills each question tests. There are also two free-response questions. Fortunately, there are more official free-response questions available and, since they are recent, they provide you with a very accurate idea of what to expect on the real exam. The College Board has released free-response questions from , along with scoring guidelines for each set of questions.
These are a great resource, and you should definitely make use of them during your review. This includes study resources for AB Calc. On Khan Academy's website, there are explanation videos for several dozen previously administered questions, both multiple choice and free response. These videos can be particularly helpful if you've gotten stuck on one of the official practice problems or if you just want to learn step-by-step how to solve a particular problem.
While not developed by the College Board, unofficial practice resources can still be very useful for your studying, particularly because there are so many resources available. For each resource listed below, I explain what is offered as well as how you should make use of the resource.
T hey are roughly listed from highest quality to lowest quality. I f you're looking for practice tests, this book has them: twelve of them, in fact! We love that they're all in one convenient resource, too. This book also breaks down the test concepts into study units, so you can brush up on your weakest skills before you take the AP exam.
The combination of high-quality instruction and excellent practice tests are why this book takes the top spot on our unofficial AP Calculus AB practice tests list! This study book is put out by The Princeton Review, which is a trustworthy test prep company.
Even better: this book contains five practice tests that you can use to assess your current knowledge and gauge how much you're improving as you study. The other nice thing about this study guide is that it breaks down the key concepts of the exam as well.
So if there are skills or ideas you've been struggling with, this book can help you get a better handle on them before test day. Shmoop is the only resource listed in this guide that requires a fee to access any of its resources.
Paying a monthly fee gets you access to a diagnostic exam, as well as eight complete practice tests and additional practice questions. Varsity Tutors has a collection of three diagnostic tests and over short practice quizzes you can use to study for the AP Calc AB exam. The practice quizzes are organized by topic, such as the chain rule and finding the second derivative of a function.
Difficulty levels are also given for each of the quizzes. The diagnostic tests are questions long all multiple-choice. They pretty closely represent what questions from the actual AP exam are like, and, as a bonus, the score results show you how well you did in each topic area so you can focus your future studying on the areas you need the most work in. This site organizes quizzes into the three Big Ideas of Calculus AB, as well as more specific tags you can select you don't need to worry about the Series quizzes, that's just for BC Calc.
After creating a free account, you can access hundreds of practice questions. Questions are ranked as easy, moderate, or difficult, they are not timed, and you see the correct answer plus a detailed explanation after you answer each question.
If that's not enough—or if you want to practice harder skills—there's a paid account option that gives you access to even more AP Calc questions. This site has a question multiple-choice test. The questions typically easier and more basic than those you'd find on the actual AP exam, but if you're just starting your review or want to brush up on the basics, this can be a good resource to use.
This site has four short quizzes, each questions long, along with answer explanations. Two quizzes are multiple-choice, and two are free-response. The free-response questions are much shorter than what you'd encounter on the real AP exam, but you can treat them like slightly more involved multiple-choice questions.
Sample Responses Q6. Please note that these resources do not reflect the updates to the course and exam. AP Students. Not a student? Go to AP Central for resources for educators. Explain your reasoning. Use separation of variables to find an expression for h in terms of t. Find the volume of the solid. Show your work. Using correct units, interpret the meaning of H' 6 in the context of the problem b Explain why there must be at least one time t, for 2 PDF Link Non-Calculator 5 Applications of Integration, Differentiation Average rate of change, absolute extrema, limits 2.
Sketch the solution curve that passes through 0, 2 and the solution curve that passes through 1, 0. Use this equation to approximate f 0. The area of the horizontal cross section of the tank at height h feet is given by the function A, where A h is measured in square feet. The function A is continuous and decreases as h increases. Selected values for A h are given in the table above.
When the height of the water is 5 feet, the height is increasing at the rate of 0. Using the model from part c , find the rate at which the volume of water is changing with respect to time when the height of the water is 5 feet.
Using correct units, explain the meaning of f' 7 in the context of the problem. Give a reason for your answer. The graph of f' consists of a semicircle and three line segments. Justify c Find the absolute minimum value of f on the closed interval [-6, 5]. Justify d For each of f'' -5 and f'' 3 , find the value of explain why it doesn't exist PDF Link Non-Calculator 4 Differential Equations, Analytical Applications of Differentiation Separable differential equations, concavity, linear approximation 1.
Find k' pi. Find m' 2. Justify your answer. Show your work and indicate units b Use a left Riemann sum with four subintervals to estimate the total amount of water removed from the rank. Is this an over or underestimate? The graph of y is shown. Does the graph of f have a relative minimum, relative maximum, or neither at the point -2, 8? At this instant, what is the rate of change of the height of the liquid with respect to time? Use the first 3 nonzero terms of the alternating series to approximate f 1.