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AP Calculus AB Past Papers & Drilling: Limits, Derivatives, Integrals
TUTORZONE ORIGINAL DRILLING MOCK · AP CALCULUS AB
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 (limits, derivatives, integrals) with answers and techniques.
What is in the AP Calculus AB 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 AB drilling technique: in Section II show the steps, substitute, and give the answer. Factor and cancel for limits; use the power rule for derivatives; substitute the limits for definite integrals.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the College Board AP Calculus AB 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 d/dx(x^3)?
Direct answer: 3x^2.
Section II: free-response drilling (4 demonstrated)
Demonstrates a limit, a derivative, an indefinite integral and a definite integral.
Question 1 (10 marks)
Find lim(x->2) (x^2 – 4) / (x – 2).
Question 2 (10 marks)
Find the derivative f'(x) of f(x) = x^3.
Question 3 (10 marks)
Find the indefinite integral of (2x + 3) dx.
Question 4 (10 marks)
Evaluate the definite integral of x^2 dx from 0 to 1.
How is a definite integral evaluated?
Direct answer: find the antiderivative, then substitute the upper and lower limits and subtract.
Answers and marks per question
Question 1
Factorise x^2-4 = (x-2)(x+2); cancelling (x-2) leaves x+2, so the limit is 4 (10).
Question 2
By the power rule, f'(x) = 3x^2 (10).
Question 3
The integral is x^2 + 3x + C (10).
Question 4
The integral from 0 to 1 of x^2 dx = [x^3/3] = 1/3 (10).
Which topics does this paper drill?
Direct answer: limits, derivatives, indefinite and definite integrals.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Direct substitution | Plugging x=2 gives 0/0 | Factorise and cancel first | Limit = 4 |
| Power rule | Derivative of x^3 as 3x | d/dx(x^3)=3x^2 | 3x^2 |
| Definite integral | Just x^3/3 | Substitute 0 and 1 and subtract | 1/3 |
How to use this paper
First drill: all 4 questions with no references.
Mark it: check factorisation, the power rule and integral limits.
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 power rules or integral limits; 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 AB 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 d/dx(x^3)?
3x^2.
Official references
| Resource | What to check |
|---|---|
| College Board AP Calculus AB exam page | Confirm the format and question counts |
| https://www.tutorzone.com.hk/en-alevel-mathematics-9709-paper-1-mock-2027/ | A-Level Mathematics (9709) drilling mock |
| https://www.tutorzone.com.hk/en-ap-precalculus-mock-2027/ | AP Precalculus drilling mock |
Related: practice area · A-Level Mathematics Paper 1 drilling mock · AP Precalculus drilling mock
Next step: find a tutor / register as a tutor
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