Q1 · Difficulty 1/3
If f′(x) > 0 on an interval, f is:
- decreasing
- increasing
- constant
- concave down
Show answer & explanation
✓ Answer: B — increasing
Positive derivative = increasing.
AP · · Calculus AB
Free AP Calculus AB
Practice Paper
8 mixed-difficulty practice questions in the style of real AP papers — answers, mark-scheme-style explanations, and the official exam structure all on one page.
Take a Mini Mock →What the real AP Calculus AB paper looks like
Paper 1
Objective and short-answer questions covering the breadth of the specification.
Paper 2
Structured and extended-response questions testing depth of understanding.
Total exam time varies by board and tier — typically 2.5 to 3.5 hours.
Grading: See the official board specification for the current grading scale.
Grading: See the official board specification for the current grading scale.
Mini practice paper: 8 questions
Mixed-difficulty questions from across the Calculus AB syllabus. Tap "Show answer" after each to check yourself.
Q2 · Difficulty 1/3
The chain rule is needed for:
- sums
- x²
- composite functions
- constants
Show answer & explanation
✓ Answer: C — composite functions
It differentiates functions of functions.
Q3 · Difficulty 1/3
The constant of integration C is needed for:
- derivatives
- limits
- definite integrals
- indefinite integrals
Show answer & explanation
✓ Answer: D — indefinite integrals
Indefinite integrals include + C.
Q4 · Difficulty 1/3
dy/dx = 2x has general solution:
- x² + C
- 2 + C
- x³/3
- 2x²
Show answer & explanation
✓ Answer: A — x² + C
∫2x dx = x² + C.
Q5 · Difficulty 1/3
d/dx (10x) =
- x
- 0
- 10
- 10x
Show answer & explanation
✓ Answer: C — 10
Slope = 10.
Q6 · Difficulty 1/3
Evaluate lim(x→2) (3x + 1).
- 9
- 5
- 6
- 7
Show answer & explanation
✓ Answer: D — 7
Direct substitution: 3(2) + 1 = 7.
Q7 · Difficulty 1/3
∫ x² dx =
- 2x + C
- x³ + C
- 3x² + C
- x³/3 + C
Show answer & explanation
✓ Answer: D — x³/3 + C
Power rule for integrals: x³/3 + C.
Q8 · Difficulty 1/3
lim(x→2) (x³) = ?
- 6
- 8
- 12
- 4
Show answer & explanation
✓ Answer: B — 8
2³ = 8 by substitution.
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AP Calculus AB FAQ
What does the AP Calculus AB exam look like?
The AP Calculus AB exam is structured across 2 components. Paper 1: Objective and short-answer questions covering the breadth of the specification. Paper 2: Structured and extended-response questions testing depth of understanding. Total exam time varies by board and tier — typically 2.5 to 3.5 hours.
Can I download a free AP Calculus AB past paper?
Real AP past papers are published directly by AP on their official website. Kramizo doesn't redistribute copyrighted past papers, but we do generate free AI-written practice papers in the exact same style — same command words, same difficulty tier, same mark conventions. Use this practice paper as warm-up, then time yourself on official past papers before exam day.
How is AP Calculus AB graded?
See the official board specification for the current grading scale. Kramizo's practice questions are tagged with difficulty 1-3 mapping roughly to the lower, middle, and top grade boundaries you'll encounter in the real exam.