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AP Exams · Calculus AB · Calculus BC

AP Calculus AB & BC Practice Test

Build AP Calculus readiness with original limits, derivatives, integrals, series, representations, and exam-strategy questions.

AP Calculus practice sets

This page combines AP Calculus AB and AP Calculus BC preparation in one canonical hub. It provides five short practice sets with 10 original questions each, covering limits, continuity, differentiation, integration, differential equations, parametric and polar functions, vector-valued functions, infinite series, and mathematical communication.

Skills covered

  • Limits and continuity — limit laws, continuity, the Intermediate Value Theorem, and the Squeeze Theorem
  • Differentiation — derivative rules, tangent slopes, motion, related rates, optimization, and the Mean Value Theorem
  • Integration — accumulation, the Fundamental Theorem of Calculus, Riemann sums, differential equations, and volume
  • BC extensions — parametric, polar, and vector-valued functions plus power series and endpoint convergence
  • Communication — analytical, graphical, numerical, verbal, calculator, free-response, and error-analysis strategy

AP Calculus AB and BC scope

College Board describes AP Calculus AB around limits, differentiation, integration, differential equations, and applications. AP Calculus BC includes the AB foundation and adds parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series. This page keeps AB and BC on one URL while clearly labeling BC-only practice.

College Board’s current AP Calculus information also notes a hybrid digital exam with multiple-choice questions viewed in Bluebook and handwritten free-response answers returned in paper booklets. Exam timing, question counts, calculator rules, and other administration details can change, so check the current course and exam description before test day. College Board reports updates effective with the May 2027 exams.

How to use this page

Start with one untimed set to identify a topic gap, then use timed sets to build pacing. For every missed item, identify the representation and theorem or rule involved, read the explanation, and solve a new similar problem.

These questions are original supplemental practice. They are not official College Board questions, secure AP Exam content, a score predictor, an AP Classroom assignment, or a substitute for current AP policies and course materials.

For current scope and preparation, review the AP Calculus AB course page, the AP Calculus AB exam page, the AP Calculus BC overview, the AP Calculus AB and BC Course and Exam Description, and the AP calculator policy.

For more study options, visit AP Exam Tests or explore College Readiness Tests, High School Course Tests, and Pomodoro.

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AP Calculus Practice Questions

A 10-question AP Calculus AB and BC practice set on ap calculus ab and bc: integration, accumulation, and differential equations, with answers and explanations.

Read the function, graph, table, series, or scenario carefully. Choose the best answer and review the explanation after each response.

10 Questions
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C 0I 0U 10
1. QuestionMultiple choice

What is ∫ 2x dx?

Please select an answer first.

Correct answer: A

The correct answer is x² + C.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: The antiderivative of 2x is x², and an arbitrary constant is included.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The antiderivative of 2x is x², and an arbitrary constant is included.

2. QuestionMultiple choice

What does the Fundamental Theorem of Calculus connect?

Please select an answer first.

Correct answer: B

The correct answer is Differentiation and definite integration.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: The theorem connects accumulation through integration with derivatives.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The theorem connects accumulation through integration with derivatives.

3. QuestionMultiple choice

If F(x) = ∫₀ˣ f(t) dt, what is F′(x) when f is continuous?

Please select an answer first.

Correct answer: C

The correct answer is f(x).

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: The Fundamental Theorem gives the derivative of the accumulation function as f(x).
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The Fundamental Theorem gives the derivative of the accumulation function as f(x).

4. QuestionMultiple choice

What does ∫₁⁴ v(t) dt represent when v is velocity?

Please select an answer first.

Correct answer: D

The correct answer is Net change in position from t = 1 to t = 4.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: The integral of velocity gives displacement, or net position change.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The integral of velocity gives displacement, or net position change.

5. QuestionMultiple choice

A left Riemann sum for an increasing positive function on [a,b] is generally what type of estimate for the integral?

Please select an answer first.

Correct answer: A

The correct answer is An underestimate.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: Left endpoints lie below an increasing function on each subinterval.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Left endpoints lie below an increasing function on each subinterval.

6. QuestionMultiple choice

What is the general solution of dy/dx = 3x²?

Please select an answer first.

Correct answer: B

The correct answer is y = x³ + C.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: Integrating 3x² with respect to x gives x³ + C.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Integrating 3x² with respect to x gives x³ + C.

7. QuestionMultiple choice

In a slope field, a short segment with positive slope indicates what?

Please select an answer first.

Correct answer: C

The correct answer is A solution curve is increasing at that point.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: The slope field gives the local rate of change for solution curves.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The slope field gives the local rate of change for solution curves.

8. QuestionMultiple choice

For dP/dt = kP, what type of model is represented when k is constant?

Please select an answer first.

Correct answer: D

The correct answer is Exponential growth or decay.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: A rate proportional to the current amount produces exponential behavior.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

A rate proportional to the current amount produces exponential behavior.

9. QuestionMultiple choice

What is the average value of f on [a,b]?

Please select an answer first.

Correct answer: A

The correct answer is (1/(b-a)) ∫ₐᵇ f(x) dx.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: Average value is the accumulated integral divided by the interval length.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Average value is the accumulated integral divided by the interval length.

10. QuestionMultiple choice

A region has area 12 square units and is rotated about an axis. Which method is commonly used to find the resulting volume?

Please select an answer first.

Correct answer: B

The correct answer is Set up an integral using disks, washers, or shells.

  1. Identify the representation: Determine whether the AP Calculus practice prompt gives a formula, graph, table, verbal description, or numerical value.
  2. Apply the calculus idea: Volumes of revolution are modeled by an appropriate integral of cross-sectional areas or shells.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Volumes of revolution are modeled by an appropriate integral of cross-sectional areas or shells.

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Frequently asked questions about AP Calculus Practice Tests

Does this page include both AP Calculus AB and BC?

Yes. It uses one canonical page and labels BC extensions such as parametric, polar, vector-valued functions, and infinite series.

What is the main difference between AP Calculus AB and BC?

BC includes the AB foundation and additional topics including parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series.

Are these official College Board questions?

No. These are original supplemental questions. Use AP Classroom, Bluebook previews, AP Central, and current College Board course materials for official preparation.

Can I use a calculator on the AP Calculus exam?

Calculator rules depend on the exam part and current College Board policy. Review the current calculator policy and approved-device information before test day.

Will the AP Calculus format stay the same?

Students should check the current Course and Exam Description because College Board has announced updates for the May 2027 exams.