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AP Calculus BC practice test

Q: Is this an official AP Calculus BC exam?

No. StudySim writes original practice questions independently. This is not a full-length exam, an official past paper, or a predictor of an official exam score.

Q: Can I practice without signing up?

Yes. These prepared practice questions and their explanations are free to use without an account. They do not require an AI generation request.

Q: How should I use the practice results?

Use the raw number correct and topic breakdown to decide what to review. Difficulty labels are editorial estimates. Results are not converted into an official scaled score.

Q: Does this include every exam task?

No. This bank focuses on multiple-choice skills. Official exams may also require essays, free responses, performances, audio, projects, or other task formats; use official resources for those components.

StudySim's free AP Calculus BC practice test has 24 sample questions with answer explanations. Practice calculus with parametric curves, polar functions, improper integrals, and series. Use the answer explanations to understand the reasoning, then revisit the topics that need more work.

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Sample AP Calculus BC questions

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AP Calculus BC Sample Questions

Practice quiz

1. For x(t) = t² and y(t) = t³ − t, what is dy/dx at t = 2?

2. For x(t) = t² and y(t) = t³ with t > 0, what is d²y/dx²?

3. Which integral gives the length of x = t, y = t² for 0 ≤ t ≤ 1?

4. A curve has polar equation r = 2. What area is swept out for 0 ≤ θ ≤ π/2?

5. A particle has velocity vector ⟨3t, 4t⟩ for t ≥ 0. What is its speed at t = 2?

6. Which improper integral converges?

7. What is ∫ x e^x dx?

8. What is ∫ from 0 to ∞ of e^(−2x) dx?

9. What is the sum of the series Σ from n = 0 to ∞ of 3(1/4)^n?

10. What can be concluded about Σ from n = 1 to ∞ of n/(n + 1)?

11. Which series is conditionally convergent?

12. For Σ from n = 1 to ∞ of n!/3^n, what does the ratio test show?

13. For the alternating series Σₙ₌₁∞ (−1)^(n+1)/n³, what is an upper bound on error after the first four terms?

14. What is the radius of convergence of Σ from n = 0 to ∞ of (x − 2)^n/5^n?

15. What is the interval of convergence of Σ from n = 1 to ∞ of x^n/n?

16. Which is the degree-four Maclaurin polynomial for cos x?

17. If f(x) = Σ from n = 0 to ∞ of x^n/n!, what is f′(0)?

18. Which power series represents 1/(1 + x²) for |x| < 1?

19. The first terms of f(x) are 2 + 3x − 4x² + 5x³. What is f″(0)?

20. Which substitution is useful for ∫ 2x/(x² + 9) dx, and what result follows?

21. Evaluate lim as x → 0 of (e^x − 1 − x)/x².

22. A logistic model is P′ = 0.2P(1 − P/600). At what population is the positive growth rate largest?

23. For r = 1 + cos θ, what is dr/dθ at θ = π/2?

24. For a positive decreasing function f, a right-endpoint Riemann sum estimates ∫₀¹ f(x)dx how?

0 of 24 answered

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Exam at a glance

AP Calculus BC preparation includes Parametric and polar functions, Advanced integration, Infinite series, Power and Taylor series, Differential equations, Integration and accumulation. This StudySim bank provides original multiple-choice skill practice. Consult the official framework for the complete exam format, required tasks, and current policies.

Detail	Information
Content framework	College Board: AP Calculus BC course framework

Source: College Board: AP Calculus BC course framework · Last reviewed Oct 27, 2026

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AP Calculus BC content areas

Parametric and polar functions

Practice parametric and polar functions with original questions and explanations. Topic labels describe this bank, rather than official section weights.

Advanced integration

Practice advanced integration with original questions and explanations. Topic labels describe this bank, rather than official section weights.

Infinite series

Practice infinite series with original questions and explanations. Topic labels describe this bank, rather than official section weights.

Power and Taylor series

Practice power and taylor series with original questions and explanations. Topic labels describe this bank, rather than official section weights.

Differential equations

Practice differential equations with original questions and explanations. Topic labels describe this bank, rather than official section weights.

Integration and accumulation

Practice integration and accumulation with original questions and explanations. Topic labels describe this bank, rather than official section weights.

Study tips for AP Calculus BC

Explain your answer

Before opening the explanation, identify the evidence, calculation, or rule that supports your choice. Explain why the other choices do not fit.

Practice a weak topic

Use the topic and difficulty filters in exam prep, then review your missed questions. These difficulty labels are editorial estimates, not calibrated exam statistics.

Use official exam materials too

Pair these skill checks with official practice materials for pacing, extended responses, and any tasks not represented by multiple-choice practice.

A few useful details

AP Calculus BC FAQ

Is this an official AP Calculus BC exam?

No. StudySim writes original practice questions independently. This is not a full-length exam, an official past paper, or a predictor of an official exam score.

Can I practice without signing up?

Yes. These prepared practice questions and their explanations are free to use without an account. They do not require an AI generation request.

How should I use the practice results?

Use the raw number correct and topic breakdown to decide what to review. Difficulty labels are editorial estimates. Results are not converted into an official scaled score.

Does this include every exam task?

No. This bank focuses on multiple-choice skills. Official exams may also require essays, free responses, performances, audio, projects, or other task formats; use official resources for those components.

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