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AP Calculus BC Past Papers & Drilling: Series, Polar, Advanced Integrals
TUTORZONE ORIGINAL DRILLING MOCK · AP CALCULUS BC
Written to the College Board exam format: Section I multiple choice, 42 questions, 1 h 40 min, 50% (Part A 29 questions no calculator, Part B 13 graphing calculator); Section II free response, 6 questions, 1 h 30 min, 50%. This drilling mock demonstrates 4 Section II questions (series, polar, advanced integrals, Maclaurin series) with answers and techniques.
What is in the AP Calculus BC exam?
Direct answer: Section I multiple choice, 42 questions, 1 h 40 min, 50%; Section II free response, 6 questions, 1 h 30 min, 50%.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Section II (Free Response) | 6: Part A calculator 2, Part B no calculator 4 | 50% | 1 h 30 min |
| Section I (Multiple Choice) | 42: Part A 29, Part B 13 | 50% | 1 h 40 min |
AP Calculus BC drilling technique: in Section II show steps, substitute, and answer. Use a/(1-r) for geometric series; use substitution for advanced integrals; know the Maclaurin formulas.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the College Board AP Calculus BC format (Section II free response) and the answers are our own, not College Board past papers or marking references.
Every answer was recomputed programmatically.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Section II (Free Response) | 50% | about 15 min per question | show steps then substitute |
| Section I (Multiple Choice) | 50% | about 2 min 20 s per question | eliminate clearly wrong options |
What is the geometric series sum formula?
Direct answer: S = a / (1 – r), for |r| < 1.
Section II: free-response drilling (4 demonstrated)
Demonstrates a geometric series, polar area, a substitution integral and a Maclaurin series.
Question 1 (10 marks)
Find the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + …
Question 2 (10 marks)
Find the area enclosed by the polar curve r = 2.
Question 3 (10 marks)
Find the indefinite integral of x e^(x^2) dx.
Question 4 (10 marks)
Write the first four terms of the Maclaurin series for e^x.
How is the integral of x e^(x^2) dx computed?
Direct answer: substitute u = x^2 (du = 2x dx), giving (1/2)e^(x^2) + C.
Answers and marks per question
Question 1
Ratio r = 1/2; sum = a/(1-r) = 1/(1-1/2) = 2 (10).
Question 2
This is a circle of radius 2; area = pi r^2 = 4 pi (10).
Question 3
Substitute u = x^2, du = 2x dx: (1/2)∫e^u du = (1/2)e^(x^2) + C (10).
Question 4
e^x = 1 + x + x^2/2! + x^3/3! + … (10).
Which topics does this paper drill?
Direct answer: geometric series, polar area, substitution integrals, Maclaurin series.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Series formula | Sum as 1/(1+r) | Geometric sum is a/(1-r) | Sum = 2 |
| Polar area | Using 2 pi r | Area is pi r^2 | 4 pi |
| Substitution half | Integral as e^(x^2) | du = 2x dx, divide by 2 | (1/2)e^(x^2)+C |
How to use this paper
First drill: all 4 questions with no references.
Mark it: check series formulas, polar area and substitution.
Second drill: redo three to seven days later, aiming for a faster finish.
What should I do after drilling this paper?
Direct answer: log questions with wrong series formulas or substitution; redo in three to seven days; and drill Section I multiple choice.
FAQ
Is this a College Board past paper?
No. The questions and answers are TutorZone originals, not College Board past papers or marking references.
What does AP Calculus BC test?
Section I multiple choice, 42 questions, 1 h 40 min, 50%; Section II free response, 6 questions, 1 h 30 min, 50%.
What is the geometric series sum formula?
S = a / (1 – r), for |r| < 1.
Official references
| Resource | What to check |
|---|---|
| College Board AP Calculus BC exam page | Confirm the format and question counts |
| https://www.tutorzone.com.hk/en-ap-calculus-ab-mock-2027/ | AP Calculus AB drilling mock |
Related: practice area · AP Calculus AB drilling mock
Next step: find a tutor / register as a tutor
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