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AP Calculus BC Practice Tests

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Free AP Calculus BC Diagnostic Tests

Take the Varsity Learning Tools free diagnostic test for AP Calculus BC to determine which academic concepts you understand and which ones require your ongoing attention. Each AP Calculus BC problem is tagged down to the core, underlying concept that is being tested. The AP Calculus BC 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 BC Diagnostic Test 1

Questions: 45
Test Difficulty:
Average Time Spent: 2 hrs 15 mins

AP Calculus BC Diagnostic Test 2

Questions: 45
Test Difficulty:
Average Time Spent: 2 hrs 46 mins

AP Calculus BC: even the name of the course may strike fear into many students; while AP Calculus AB tests easier (“A”) and intermediate (“B”) concepts, AP Calculus BC begins with the intermediate (“B”) concepts and tests the most difficult (“C”) concepts found in an introductory calculus class. If you’re nervous about missing crucial information in your AP Calculus class, need to figure out how the AP Calculus BC exam is structured, or want to find some excellent free resources you can use while studying for AP Calculus BC, you’ve come to the right place. After reading this guide, you’ll feel less apprehensive about AP Calculus BC and ready to take on its most challenging topics.

AP Calculus BC is a course that many high school students take in order to earn college credit. Before taking AP Calculus, students should have successfully completed four years of high school math. In particular, they should have encountered and mastered advanced concepts in basic functions, analytic geometry, trigonometry, and algebra before attempting to take an AP Calculus course. AP Calculus BC courses pertain to single-variable functions, covering all of the information taught in AP Calculus AB courses in addition to more advanced topics. Because of this, colleges usually grant students credit for whatever course they offer that typically follows their most basic introductory calculus courses. Students thus do the work of two introductory calculus classes in one AP course when taking AP Calculus BC, which makes for a course that is extremely challenging, but potentially very rewarding.

Students who successfully complete AP Calculus BC courses are invited to take the AP Calculus BC exam to demonstrate what they have learned and potentially earn college credit. The AP Calculus exam lasts for three hours and fifteen minutes and consists of a 45-question, 105-minute multiple-choice section and a six-question, 90-minute free-response section. Each of these sections is weighted equally, and each is divided into two parts. The first part of the multiple-choice section consists of twenty-eight questions and lasts for fifty-five minutes, and during this section, students may not use calculators. The second half of the multiple-choice section lasts for fifty minutes and consists of seventeen questions; during this section, students should use graphing calculators, as some questions will require them. The AP Calculus BC exam assumes that the calculators students use can do four things: graph functions, solve for functions’ zeros, calculate a function’s derivative, and calculate a definite integral’s value. Students’ scores on the multiple-choice section of the AP Calculus BC exam are determined only by the number of correct answers they submit; incorrect answers and skipped problems do not affect their scores. So, guessing is highly encouraged on the AP Calculus BC exam, as it cannot hurt students’ scores.

Like on the exam’s multiple-choice section, the AP Calculus BC exam’s free-response section begins by giving students thirty minutes to answer two questions while using a graphing calculator, and concludes by giving students an hour to answer four questions without using a calculator. Students are allowed to continue to work on their answers for the first part of the free response section after the first thirty minutes have elapsed; however, they are not allowed to use calculators when continuing or editing their responses. Showing one’s work is particularly important during the free-response sections of the AP Calculus BC exam. After completing the AP Calculus BC exam, students not only receive a score for the exam overall, but also an AP Calculus AB subscore, which is derived from exam questions that ask about topics covered both in AP Calculus AB and in AP Calculus BC.

One of the best places to find free AP Calculus BC resources for free online is at Varsity Tutors’ Learning Tools website. In particular, you can find AP Calculus BC Practice Tests here, each of which function like a little quiz you can use to test your skills. You can focus on particular type of problem, or choose to do problems drawn from various AP Calculus BC topics; the choice is yours. After you complete a free AP Calculus BC Practice Test, you get to see such data as how well you did in comparison to other who answered the same problems, and how much time it took you to complete each problem. You also get to access full explanations for each question, so if you missed a problem, you can figure out where you went wrong and prevent yourself from making the same mistake again.

You may also like to take a Full-Length AP Calculus BC Practice Test. These test your knowledge of the course content as a whole, and ask you to answer questions spanning the full range of topics you’ll need to know by the end of the year. One great way to start your review is by taking one of the complete practice tests. The results you’ll receive can help you to build an AP Calculus BC study plan that meets your needs. The feedback you’ll get from the free comprehensive online tests include the same valuable statistics you get on the topic-focused practice tests, but have the additional benefit of helping to tailor your study sessions by showing you the areas in which you’ll want to bone up. You can use any of the Learning Tools to review, and once you feel ready, you can take another Full-Length AP Calculus BC Practice Test when you’d like to check your progress.

By taking advantage of all of Varsity Tutors’ free AP Calculus BC resources, you can make sure that you don’t miss or misunderstand any AP Calculus BC content, and feel completely prepared for your AP Calculus BC exam!

 

Free AP Calculus BC Practice Tests

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

Practice Tests by Concept

Derivatives practice test

Questions: 40
Test Difficulty:
Average Time Spent: 34 mins

Applications of derivatives practice test

Questions: 22
Test Difficulty:
Average Time Spent: 10 mins

Euler's method and l'hopital's rule practice test

Questions: 17
Test Difficulty:
Average Time Spent: 20 mins

Velocity, speed, acceleration practice test

Questions: 5
Test Difficulty:
Average Time Spent: 13 mins

Computation of derivatives practice test

Questions: 40
Test Difficulty:
Average Time Spent: 21 mins

Chain rule and implicit differentiation practice test

Questions: 8
Test Difficulty:
Average Time Spent: 21 mins

Derivative rules for sums, products, and quotients practice test

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

Derivatives of parametric, polar, and vector functions practice test

Questions: 11
Test Difficulty:
Average Time Spent: 18 mins

Rules of basic functions: power, exponential rule, logarithmic, trigonometric, and inverse trigonometric practice test

Questions: 11
Test Difficulty:
Average Time Spent: 5 mins

Derivative as a function practice test

Questions: 11
Test Difficulty:

Equations involving derivatives practice test

Questions: 1
Test Difficulty:

Finding maximums practice test

Questions: 2
Test Difficulty:

Graphs of f and f' practice test

Questions: 1
Test Difficulty:

The mean value theorem practice test

Questions: 9
Test Difficulty:
Average Time Spent: 7 mins

Derivative at a point practice test

Questions: 2
Test Difficulty:
Average Time Spent: 49 secs

Derivative defined as limit of difference quotient practice test

Questions: 18
Test Difficulty:
Average Time Spent: 8 mins

Instantaneous rate of change, average rate of change, and linear approximation practice test

Questions: 2
Test Difficulty:

Second derivatives practice test

Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 45 secs

Concavity practice test

Questions: 1
Test Difficulty:

Inflection points practice test

Questions: 10
Test Difficulty:
Average Time Spent: 5 mins

Functions, graphs, and limits practice test

Questions: 40
Test Difficulty:
Average Time Spent: 31 mins

Asymptotic and unbounded behavior practice test

Questions: 3
Test Difficulty:
Average Time Spent: 6 mins

Comparing relative magnitudes (exponential growth,logarithmic growth, polynomial growth) practice test

Questions: 3
Test Difficulty:
Average Time Spent: 16 mins

Identifying asymptotes graphically practice test

Questions: 12
Test Difficulty:

Continuity practice test

Questions: 3
Test Difficulty:

Continuity in terms of limits practice test

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

Limits practice test

Questions: 5
Test Difficulty:
Average Time Spent: 3 mins

Calculating limits with algebra (including one-sided limits) practice test

Questions: 1
Test Difficulty:
Average Time Spent: 29 secs

Estimating limits from graphs and tables practice test

Questions: 5
Test Difficulty:

Parametric, polar, and vector functions practice test

Questions: 39
Test Difficulty:
Average Time Spent: 28 mins

Parametric form practice test

Questions: 11
Test Difficulty:
Average Time Spent: 14 mins

Polar form practice test

Questions: 21
Test Difficulty:
Average Time Spent: 2 hrs 6 mins

Vector form practice test

Questions: 7
Test Difficulty:

Integrals practice test

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

Application of integrals practice test

Questions: 18
Test Difficulty:
Average Time Spent: 16 mins

Initial conditions practice test

Questions: 3
Test Difficulty:

Length of curve, distance traveled, accumulated change, motion of curve practice test

Questions: 5
Test Difficulty:
Average Time Spent: 6 mins

Modeling by solving separable differential equations practice test

Questions: 1
Test Difficulty:

Volume of cross sections and area of region practice test

Questions: 10
Test Difficulty:
Average Time Spent: 19 mins

Fundamental theorem of calculus and techniques of antidifferentiation practice test

Questions: 1
Test Difficulty:

Fundamental theorem of calculus with definite integrals practice test

Questions: 7
Test Difficulty:
Average Time Spent: 6 mins

Improper integrals practice test

Questions: 4
Test Difficulty:

Substitution of variables (by parts and simple partial fractions) practice test

Questions: 1
Test Difficulty:

Numerical approximations to definite integrals practice test

Questions: 6
Test Difficulty:
Average Time Spent: 10 mins

Riemann sum: left evaluation practice test

Questions: 3
Test Difficulty:

Riemann sum: midpoint evaluation practice test

Questions: 3
Test Difficulty:

Riemann sum: right evaluation practice test

Questions: 1
Test Difficulty:

Trapezoidal sums practice test

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

Polynomial approximations and series practice test

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

Series of constants practice test

Questions: 14
Test Difficulty:
Average Time Spent: 8 mins

Alternating series with error bound practice test

Questions: 5
Test Difficulty:
Average Time Spent: 15 mins

Geometric series practice test

Questions: 7
Test Difficulty:
Average Time Spent: 16 mins

P-series practice test

Questions: 5
Test Difficulty:
Average Time Spent: 2 mins 49 secs

Ratio test and comparing series practice test

Questions: 14
Test Difficulty:
Average Time Spent: 3 mins

Taylor series practice test

Questions: 12
Test Difficulty:
Average Time Spent: 18 mins

Lagrange error bound for taylor polynomials practice test

Questions: 1
Test Difficulty:

Maclaurin series practice test

Questions: 6
Test Difficulty:
Average Time Spent: 5 mins

Maclaurin series for exponential and trigonometric functions practice test

Questions: 2
Test Difficulty:

Radius and interval of convergence of power series practice test

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

Taylor polynomial approximation practice test

Questions: 12
Test Difficulty:

Practice Quizzes

AP Calculus BC Problem Set 29

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

AP Calculus BC Problem Set 28

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

AP Calculus BC Problem Set 26

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

AP Calculus BC Problem Set 25

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

AP Calculus BC Problem Set 22

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

AP Calculus BC Problem Set 21

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

AP Calculus BC Problem Set 20

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

AP Calculus BC Problem Set 19

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

AP Calculus BC Problem Set 18

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

AP Calculus BC Problem Set 17

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

AP Calculus BC Problem Set 16

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

AP Calculus BC Problem Set 15

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

AP Calculus BC Problem Set 14

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

AP Calculus BC Problem Set 13

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

AP Calculus BC Problem Set 12

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

AP Calculus BC Problem Set 11

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

AP Calculus BC Problem Set 10

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

AP Calculus BC Problem Set 9

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

AP Calculus BC Problem Set 8

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

AP Calculus BC Problem Set 7

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

AP Calculus BC Problem Set 6

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

AP Calculus BC Problem Set 5

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

AP Calculus BC Problem Set 4

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

AP Calculus BC Problem Set 3

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

AP Calculus BC Problem Set 2

Questions: 10
Test Difficulty:
Average Time Spent: 9 mins

AP Calculus BC Problem Set 1

Questions: 10
Test Difficulty:
Average Time Spent: 5 mins
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