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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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1. Test

AP Calculus Practice Questions

A 10-question AP Calculus AB and BC practice set on ap calculus ab and bc: limits and continuity, 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

What is the value of lim x→2 (3x + 1)?

Please select an answer first.

Correct answer: A

The correct answer is 7.

  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 linear function is continuous, so substitute x = 2 to get 3(2) + 1 = 7.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

A linear function is continuous, so substitute x = 2 to get 3(2) + 1 = 7.

2. QuestionMultiple choice

If f is continuous on [1, 4], which theorem guarantees that f takes every value between f(1) and f(4)?

Please select an answer first.

Correct answer: B

The correct answer is Intermediate Value Theorem.

  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 Intermediate Value Theorem applies to a continuous function on a closed interval.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The Intermediate Value Theorem applies to a continuous function on a closed interval.

3. QuestionMultiple choice

What does lim x→a f(x) = L mean?

Please select an answer first.

Correct answer: C

The correct answer is The values of f(x) approach L as x approaches a.

  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 limit describes the value approached near a, which may differ from the function value at a.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

A limit describes the value approached near a, which may differ from the function value at a.

4. QuestionMultiple choice

For f(x) = |x|, is f continuous at x = 0?

Please select an answer first.

Correct answer: D

The correct answer is Yes, because the left and right limits both equal f(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 corner prevents differentiability, but the function remains continuous at 0.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

The corner prevents differentiability, but the function remains continuous at 0.

5. QuestionMultiple choice

If lim x→3 f(x) = 5 and lim x→3 g(x) = 2, what is lim x→3 [f(x) + g(x)]?

Please select an answer first.

Correct answer: A

The correct answer is 7.

  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: Limit laws allow the sum to be found by adding the two limits.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Limit laws allow the sum to be found by adding the two limits.

6. QuestionMultiple choice

Which condition is required for a function to be continuous at x = c?

Please select an answer first.

Correct answer: B

The correct answer is f(c) is defined, the limit exists, and the limit equals f(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: Continuity at a point requires a defined matching limit.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Continuity at a point requires a defined matching limit.

7. QuestionMultiple choice

A graph has a vertical asymptote at x = 4. What usually happens to f(x) as x approaches 4?

Please select an answer first.

Correct answer: C

The correct answer is The function grows without bound in at least one direction.

  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 vertical asymptote indicates unbounded behavior near the x-value.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

A vertical asymptote indicates unbounded behavior near the x-value.

8. QuestionMultiple choice

If f is differentiable at x = c, what must be true?

Please select an answer first.

Correct answer: D

The correct answer is f is continuous at x = 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: Differentiability implies continuity, although continuity does not imply differentiability.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

Differentiability implies continuity, although continuity does not imply differentiability.

9. QuestionMultiple choice

The function f has a removable discontinuity at x = 2. Which change can make it continuous there?

Please select an answer first.

Correct answer: A

The correct answer is Define f(2) to equal the limit as x approaches 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: A hole can be filled by assigning the matching limiting value.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

A hole can be filled by assigning the matching limiting value.

10. QuestionMultiple choice

What is the purpose of the Squeeze Theorem?

Please select an answer first.

Correct answer: B

The correct answer is To determine a limit by trapping a function between two functions with the same limit.

  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: If two bounding functions approach the same value, the trapped function has that limit.
  3. Check the conclusion: Verify the notation, units, interval, sign, and requested form before selecting the answer.

If two bounding functions approach the same value, the trapped function has that limit.

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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.