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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 bc: parametric, polar, vector-valued functions, and series, 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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1. QuestionMultiple choice

For x = t² and y = t³, what is dy/dx when t ≠ 0?

Please select an answer first.

Correct answer: C

The correct answer is 3t/2.

  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: Use dy/dx = (dy/dt)/(dx/dt) = 3t²/(2t) = 3t/2.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Use dy/dx = (dy/dt)/(dx/dt) = 3t²/(2t) = 3t/2.

2. QuestionMultiple choice

For a polar curve r = f(θ), what is the first step for finding the area over an interval?

Please select an answer first.

Correct answer: D

The correct answer is Use A = (1/2)∫ r² dθ over the stated interval.

  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 polar area formula integrates one-half the square of r with respect to θ.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The polar area formula integrates one-half the square of r with respect to θ.

3. QuestionMultiple choice

For a vector-valued position r(t) = , what does r′(t) represent?

Please select an answer first.

Correct answer: A

The correct answer is The velocity vector.

  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: Differentiating each component gives the velocity vector.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Differentiating each component gives the velocity vector.

4. QuestionMultiple choice

What is the radius of convergence of a power series centered at 0 if it converges for |x| < 4?

Please select an answer first.

Correct answer: B

The correct answer is 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 boundary distance from the center is the radius of convergence.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The boundary distance from the center is the radius of convergence.

5. QuestionMultiple choice

Which series is geometric?

Please select an answer first.

Correct answer: C

The correct answer is ∑ (1/3)ⁿ from n = 0 to infinity.

  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 geometric series has a constant ratio between consecutive terms.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

A geometric series has a constant ratio between consecutive terms.

6. QuestionMultiple choice

What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?

Please select an answer first.

Correct answer: D

The correct answer is 2.

  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: For first term 1 and ratio 1/2, the sum is 1/(1-1/2) = 2.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

For first term 1 and ratio 1/2, the sum is 1/(1-1/2) = 2.

7. QuestionMultiple choice

A power series is centered at x = 2. What does the center indicate?

Please select an answer first.

Correct answer: A

The correct answer is The series is written in powers of (x - 2).

  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 center appears in the expression (x - 2)ⁿ and anchors the convergence interval.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The center appears in the expression (x - 2)ⁿ and anchors the convergence interval.

8. QuestionMultiple choice

For a parametric curve, when is a horizontal tangent possible?

Please select an answer first.

Correct answer: B

The correct answer is dy/dt = 0 while dx/dt is not 0.

  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 dy/dx is zero when the numerator is zero and the denominator is nonzero.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The slope dy/dx is zero when the numerator is zero and the denominator is nonzero.

9. QuestionMultiple choice

What does a Taylor polynomial approximate near its center?

Please select an answer first.

Correct answer: C

The correct answer is A function using derivatives evaluated at the center.

  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: Taylor polynomials use local derivative information to approximate a function near a point.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Taylor polynomials use local derivative information to approximate a function near a point.

10. QuestionMultiple choice

When testing a power series at endpoints, what should be done?

Please select an answer first.

Correct answer: D

The correct answer is Test each endpoint separately because the ratio test may not decide endpoint behavior.

  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: Endpoint convergence can differ and requires a separate test.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Endpoint convergence can differ and requires a separate test.

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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.