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AP Calculus AB Practice Tests

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Free AP Calculus AB Diagnostic Tests

Take the Varsity Learning Tools free diagnostic test for AP Calculus AB to determine which academic concepts you understand and which ones require your ongoing attention. Each AP Calculus AB problem is tagged down to the core, underlying concept that is being tested. The AP Calculus AB diagnostic test results highlight how you performed on each area of the test. You can then utilize the results to create a personalized study plan that is based on your particular area of need.

AP Calculus AB Diagnostic Test 1

Questions: 40
Test Difficulty:
Average Time Spent: 1 hrs 12 mins

AP Calculus AB Diagnostic Test 2

Questions: 45
Test Difficulty:
Average Time Spent: 4 hrs 23 mins

AP Calculus AB Diagnostic Test 3

Questions: 40
Test Difficulty:
Average Time Spent: 5 hrs 39 mins

For many high school students, an AP course in any subject represents a serious undertaking. The large amount of content it covers, the workload it demands, and the necessary preparation it requires for its corresponding AP exam all combine to make AP classes formidable challenges. AP Calculus (AB) is certainly a demanding class for these reasons; however, by approaching the course in the right way, you can master it and attain your best score on the AP Calculus AB exam. Whether you need top Calculus tutors in Albany, Calculus tutors in Milwaukee, or top Calculus tutors in Albuquerque, working with a pro may take your studies to the next level.

AP Calculus (AB) is essentially divided into two main topics: differentiation and integration. The course usually begins with a discussion of limits and continuity, which then builds up to consider the limit definition of a derivative. From there, rules of differentiation are discussed. So, for this first part of AP Calculus (AB), it is essential to understand not only the limit of differentiation, but the different rules (i.e. the power rule, quotient rule, product rule, and others) for finding a derivative of a given function. Finally, understanding the meaning of derivatives and finding critical points is also crucial to success in the class.

The second half of AP Calculus (AB) focuses on integration. This part starts with the definition of an integral and Riemann Sums (left point, right point, and midpoint) as a lead-in to the concept of an integral being the area under a given function over a specific domain. From there, techniques of integration are introduced, some of which are straightforward (i.e. the power rule of integration), and some of which are more complex (integration by substitution, integration by parts, and trigonometric substitution). The latter category often requires extensive practice, for it can be as much a challenge to know which integration technique to apply to a specific problem as it can be to evaluate the integral. 

The second half of AP Calculus (AB) concludes with different applications of integration, which includes finding the volumes of solids generated by revolving a given area around a given axis. These problems also require practice, as different methods are again involved, from the shell method to the disk and washer methods. Again, the challenge is determining which method to use, in addition to actually evaluating the integral. Fortunately, on the AP exam, these types of problems either allow the use of a calculator, or simply ask for the given integral to be set up, but not evaluated. Regardless, one can almost plan on encountering a question on the AP exam that involves the volume of a solid. Varsity Tutors offers resources like a  free AP Calculus AB Diagnostic Tests to help with your self-paced study, or you may want to consider an AP Calculus AB tutor.

Speaking of the AP exam, it consists of a multiple-choice section (45 questions in 1 hour and 45 minutes) and a free response section (6 questions in 90 minutes). Both sections have parts where a calculator is allowed, and parts where it is not. The multiple-choice section typically asks for an integral to be evaluated numerically, for a function to be graphed, or for both of these tasks to be accomplished. The free response section involves conceptual questions, where calculations are simple enough so as to not require a calculator. As with all AP exams, time management is essential, particularly on the multiple-choice questions. If a question proves to be too difficult, it is best either to skip it entirely, or take an educated guess (but only after eliminating at least one response). After all, all multiple-choice questions on the AP Calculus (AB) exam are worth the same number of points!

To prepare for the test, be sure to be familiar with the main topics of the course and confident in applying them in problems. Knowledge of the main theorems is also important, including the Fundamental Theorem of Calculus, the Mean Value Theorem, and the Extreme Value Theorem, to name but a few. With mastery of these, and sufficient practice, it is quite possible to score very well on the AP exam and do well in AB calculus! 

If you need extra practice with AP Calculus (AB) material or are looking for a good place to start, try taking some free AP Calculus (AB) Practice Tests offered by Varsity Tutors. Each Practice Test consists of 10 to 12 AP Calculus (AB) problems; you can think of Practice Tests as being like little quizzes which you can use to hone your skills. Each question is accompanied by a detailed explanation of how to find its answer, and after finishing each Practice Test, you can compare how you did to the scores that others received, as well as view data about how long you took to answer each question. The more Practice Tests you do, the better idea you will have as to your strengths and weaknesses in AP Calculus (AB), and focusing on the material you understand the least and reviewing the material you understand well will help you prepare for the AP exam! In addition to the AP Calculus AB Practice Tests and Calculus tutoring, you may also want to consider using some of our AP Calculus AB Flashcards.

Another one of Varsity Tutors’ Learning Tools that you can take advantage of are the Full-Length AP Calculus (AB) Practice Tests. It’s not a bad idea to begin your preparation by taking one of the free online practice tests to help you create an individualized study plan. These tests are like the actual exam, giving you an opportunity to get familiar with the test’s length and scope. The results page is just like the one for the concept-specific practice tests, and includes precise explanations and helpful information on each of the relevant concepts. Plus, the complete practice tests provide the perk of streamlining your AP Calculus (AB) review by showing you which skills have you have mastered, and those you have not. Once you know what you’d like to focus on, you can use any of the other Learning Tools to brush up on your skills. To check your progress, just take a Full-Length AP Calculus (AB) Practice Test periodically as you work toward test day!

 

Free AP Calculus AB Practice Tests

Our completely free AP Calculus AB practice tests are the perfect way to brush up your skills. Take one of our many AP Calculus AB practice tests for a run-through of commonly asked questions. You will receive incredibly detailed scoring results at the end of your AP Calculus AB practice test to help you identify your strengths and weaknesses. Pick one of our AP Calculus AB practice tests now and begin!

Practice Tests by Concept

Acceleration practice test

Questions: 1
Test Difficulty:
Average Time Spent: 30 secs

Finding the derivative at a point practice test

Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 56 secs

Analysis of curves, including the notions of monotonicity and concavity practice test

Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 7 secs

How to find equation of line by graphing functions practice test

Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 40 secs

Interpretation of the derivative as a rate of change practice test

Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 40 secs

Modeling rates of change, including related rates problems­ practice test

Questions: 1
Test Difficulty:

How to find differentiable of rate practice test

Questions: 1
Test Difficulty:
Average Time Spent: 57 secs

Finding the second derivative of a function practice test

Questions: 11
Test Difficulty:
Average Time Spent: 12 mins

Chain rule and implicit differentiation practice test

Questions: 12
Test Difficulty:
Average Time Spent: 14 mins

Derivative rules for sums, products, and quotients of functions practice test

Questions: 1
Test Difficulty:

Finding value practice test

Questions: 8
Test Difficulty:
Average Time Spent: 4 mins

Differentiable rate practice test

Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 51 secs

Finding the derivative of a function practice test

Questions: 13
Test Difficulty:
Average Time Spent: 1 mins 50 secs

Calculating limits practice test

Questions: 2
Test Difficulty:
Average Time Spent: 40 secs

Relationship between differentiability and continuity practice test

Questions: 1
Test Difficulty:

Finding regions of concavity and convexity practice test

Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 27 secs

How to find acceleration practice test

Questions: 1
Test Difficulty:
Average Time Spent: 40 secs

Equations involving derivatives practice test

Questions: 12
Test Difficulty:
Average Time Spent: 8 mins

How to find area of a region practice test

Questions: 4
Test Difficulty:
Average Time Spent: 8 mins

Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ' practice test

Questions: 3
Test Difficulty:

Finding derivatives practice test

Questions: 40
Test Difficulty:
Average Time Spent: 14 mins

How to describe points by graphing functions practice test

Questions: 1
Test Difficulty:
Average Time Spent: 18 secs

Slope of a curve at a point practice test

Questions: 2
Test Difficulty:

Area practice test

Questions: 4
Test Difficulty:
Average Time Spent: 3 mins

Finding regions of increasing or decreasing value practice test

Questions: 5
Test Difficulty:
Average Time Spent: 4 mins

Corresponding characteristics of the graphs of ƒ, ƒ', and ƒ'' practice test

Questions: 1
Test Difficulty:

How to find continuous on the interval by graphing functions practice test

Questions: 1
Test Difficulty:
Average Time Spent: 25 secs

Relationship between the concavity of ƒ and the sign of ƒ'' practice test

Questions: 1
Test Difficulty:

Functions practice test

Questions: 40
Test Difficulty:
Average Time Spent: 14 mins

Equations practice test

Questions: 40
Test Difficulty:
Average Time Spent: 23 mins

Asymptotic behavior in terms of limits involving infinity practice test

Questions: 1
Test Difficulty:

How to find integral expressions practice test

Questions: 35
Test Difficulty:
Average Time Spent: 15 mins

Differential equations practice test

Questions: 8
Test Difficulty:
Average Time Spent: 9 mins

Graphing functions practice test

Questions: 4
Test Difficulty:
Average Time Spent: 3 mins

An intuitive understanding of continuity practice test

Questions: 2
Test Difficulty:

Lines practice test

Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 9 secs

Understanding continuity in terms of limits practice test

Questions: 1
Test Difficulty:

Differential functions practice test

Questions: 14
Test Difficulty:
Average Time Spent: 9 mins

Calculating limits using algebra practice test

Questions: 4
Test Difficulty:
Average Time Spent: 3 mins

How to find midpoint riemann sums practice test

Questions: 1
Test Difficulty:

How to find differential functions practice test

Questions: 14
Test Difficulty:
Average Time Spent: 7 mins

Integrals practice test

Questions: 40
Test Difficulty:
Average Time Spent: 10 mins

How to solve for time practice test

Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 14 secs

Finding specific antiderivatives using initial conditions, including applications to motion along a line practice test

Questions: 1
Test Difficulty:

How to find solutions to differential equations practice test

Questions: 8
Test Difficulty:
Average Time Spent: 40 mins

How to find value practice test

Questions: 8
Test Difficulty:
Average Time Spent: 2 mins 20 secs

Use of the fundamental theorem to evaluate definite integrals practice test

Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 58 secs

Intervals practice test

Questions: 1
Test Difficulty:
Average Time Spent: 23 secs

Integral expressions practice test

Questions: 35
Test Difficulty:
Average Time Spent: 10 mins

Basic properties of definite integrals (additivity and linearity) practice test

Questions: 12
Test Difficulty:
Average Time Spent: 5 mins

How to find rate of change practice test

Questions: 5
Test Difficulty:
Average Time Spent: 4 mins

How to find the meaning of functions practice test

Questions: 11
Test Difficulty:
Average Time Spent: 6 mins

How to write equations practice test

Questions: 15
Test Difficulty:
Average Time Spent: 6 mins

Riemann sums (left, right, and midpoint evaluation points) practice test

Questions: 24
Test Difficulty:
Average Time Spent: 7 mins

Trapezoidal sums practice test

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 50 secs

How to find velocity practice test

Questions: 3
Test Difficulty:
Average Time Spent: 3 mins

Antiderivatives by substitution of variables practice test

Questions: 1
Test Difficulty:
Average Time Spent: 2 hrs 54 mins

How to find minimum values practice test

Questions: 1
Test Difficulty:
Average Time Spent: 26 secs

Practice Quizzes

AP Calculus AB Problem Set 120

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 119

Questions: 12
Test Difficulty:
Average Time Spent: 41 secs

AP Calculus AB Problem Set 118

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 117

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 116

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 115

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 113

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 112

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 111

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 110

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 109

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 108

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 107

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 106

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 105

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 37 secs

AP Calculus AB Problem Set 104

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 103

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 102

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 101

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 100

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 99

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 98

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 97

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 96

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 95

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 93

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 48 secs

AP Calculus AB Problem Set 91

Questions: 12
Test Difficulty:
Average Time Spent: 8 mins

AP Calculus AB Problem Set 90

Questions: 12
Test Difficulty:
Average Time Spent: 11 mins

AP Calculus AB Problem Set 89

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 23 secs

AP Calculus AB Problem Set 87

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 57 secs

AP Calculus AB Problem Set 86

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 85

Questions: 12
Test Difficulty:
Average Time Spent: 6 mins

AP Calculus AB Problem Set 84

Questions: 12
Test Difficulty:
Average Time Spent: 5 mins

AP Calculus AB Problem Set 83

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 46 secs

AP Calculus AB Problem Set 82

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 81

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 40 secs

AP Calculus AB Problem Set 79

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 23 secs

AP Calculus AB Problem Set 78

Questions: 12
Test Difficulty:
Average Time Spent: 3 mins

AP Calculus AB Problem Set 77

Questions: 12
Test Difficulty:
Average Time Spent: 3 hrs 17 mins

AP Calculus AB Problem Set 76

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 23 secs

AP Calculus AB Problem Set 75

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 24 secs

AP Calculus AB Problem Set 74

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 73

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 72

Questions: 12
Test Difficulty:
Average Time Spent: 24 secs

AP Calculus AB Problem Set 71

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 50 secs

AP Calculus AB Problem Set 70

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 28 secs

AP Calculus AB Problem Set 68

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 46 secs

AP Calculus AB Problem Set 67

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 21 secs

AP Calculus AB Problem Set 66

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 9 secs

AP Calculus AB Problem Set 65

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 35 secs

AP Calculus AB Problem Set 64

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 33 secs

AP Calculus AB Problem Set 63

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 62

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 61

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 60

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 59

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 58

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 11 secs

AP Calculus AB Problem Set 57

Questions: 12
Test Difficulty:
Average Time Spent: 55 secs

AP Calculus AB Problem Set 56

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 20 secs

AP Calculus AB Problem Set 55

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 54

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 53

Questions: 12
Test Difficulty:
Average Time Spent: 4 mins

AP Calculus AB Problem Set 52

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 14 secs

AP Calculus AB Problem Set 51

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 50

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 49

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 48

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 47

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 12 secs

AP Calculus AB Problem Set 46

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 50 secs

AP Calculus AB Problem Set 45

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 44

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 43

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 42

Questions: 12
Test Difficulty:
Average Time Spent: 3 mins

AP Calculus AB Problem Set 41

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 3 secs

AP Calculus AB Problem Set 40

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 39

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 42 secs

AP Calculus AB Problem Set 38

Questions: 12
Test Difficulty:
Average Time Spent: 0 secs

AP Calculus AB Problem Set 37

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 5 secs

AP Calculus AB Problem Set 36

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 48 secs

AP Calculus AB Problem Set 35

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 13 secs

AP Calculus AB Problem Set 34

Questions: 12
Test Difficulty:
Average Time Spent: 30 secs

AP Calculus AB Problem Set 33

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 6 secs

AP Calculus AB Problem Set 32

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 16 secs

AP Calculus AB Problem Set 30

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 33 secs

AP Calculus AB Problem Set 25

Questions: 12
Test Difficulty:
Average Time Spent: 11 mins

AP Calculus AB Problem Set 24

Questions: 12
Test Difficulty:
Average Time Spent: 7 mins

AP Calculus AB Problem Set 23

Questions: 12
Test Difficulty:
Average Time Spent: 7 mins

AP Calculus AB Problem Set 22

Questions: 12
Test Difficulty:
Average Time Spent: 6 mins

AP Calculus AB Problem Set 21

Questions: 12
Test Difficulty:
Average Time Spent: 8 mins

AP Calculus AB Problem Set 20

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 54 secs

AP Calculus AB Problem Set 19

Questions: 12
Test Difficulty:
Average Time Spent: 2 mins 35 secs

AP Calculus AB Problem Set 18

Questions: 12
Test Difficulty:
Average Time Spent: 7 mins

AP Calculus AB Problem Set 17

Questions: 12
Test Difficulty:
Average Time Spent: 35 mins

AP Calculus AB Problem Set 16

Questions: 12
Test Difficulty:
Average Time Spent: 7 mins

AP Calculus AB Problem Set 15

Questions: 12
Test Difficulty:
Average Time Spent: 13 mins

AP Calculus AB Problem Set 14

Questions: 12
Test Difficulty:
Average Time Spent: 47 secs

AP Calculus AB Problem Set 12

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 43 secs

AP Calculus AB Problem Set 11

Questions: 12
Test Difficulty:
Average Time Spent: 36 secs

AP Calculus AB Problem Set 10

Questions: 12
Test Difficulty:
Average Time Spent: 10 mins

AP Calculus AB Problem Set 9

Questions: 12
Test Difficulty:
Average Time Spent: 47 secs

AP Calculus AB Problem Set 8

Questions: 12
Test Difficulty:
Average Time Spent: 54 secs

AP Calculus AB Problem Set 7

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 50 secs

AP Calculus AB Problem Set 6

Questions: 12
Test Difficulty:
Average Time Spent: 1 mins 54 secs

AP Calculus AB Problem Set 3

Questions: 10
Test Difficulty:
Average Time Spent: 2 mins 12 secs

AP Calculus AB Problem Set 2

Questions: 10
Test Difficulty:
Average Time Spent: 7 mins

AP Calculus AB Problem Set 1

Questions: 10
Test Difficulty:
Average Time Spent: 31 mins
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