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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.

Mini practice paper: 8 questions

Mixed-difficulty questions from across the Calculus AB syllabus. Tap "Show answer" after each to check yourself.

Q1 · Difficulty 1/3

The derivative gives the slope of the:

  1. secant line
  2. tangent line
  3. x-axis
  4. normal line
Show answer & explanation
✓ Answer: B — tangent line
f′(x) is the slope of the tangent at x.
Q2 · Difficulty 1/3

The constant of integration C is needed for:

  1. definite integrals
  2. indefinite integrals
  3. derivatives
  4. limits
Show answer & explanation
✓ Answer: B — indefinite integrals
Indefinite integrals include + C.
Q3 · Difficulty 1/3

Evaluate lim(x→2) (3x + 1).

  1. 5
  2. 6
  3. 7
  4. 9
Show answer & explanation
✓ Answer: C — 7
Direct substitution: 3(2) + 1 = 7.
Q4 · Difficulty 1/3

d/dx[7] =

  1. 7
  2. 1
  3. 0
  4. x
Show answer & explanation
✓ Answer: C — 0
The derivative of a constant is 0.
Q5 · Difficulty 1/3

dy/dx = 2x has general solution:

  1. x² + C
  2. 2 + C
  3. x³/3
  4. 2x²
Show answer & explanation
✓ Answer: A — x² + C
∫2x dx = x² + C.
Q6 · Difficulty 1/3

lim(x→∞) (1/x) = ?

  1. 0
  2. 1
  3. ∞
  4. −1
Show answer & explanation
✓ Answer: A — 0
As x grows large, 1/x approaches 0.
Q7 · Difficulty 1/3

d/dx (x⁴) =

  1. 4x³
  2. x³
  3. 4x⁴
  4. 3x⁴
Show answer & explanation
✓ Answer: A — 4x³
Power rule: 4x³.
Q8 · Difficulty 1/3

d/dx[x⁵] =

  1. 5x⁴
  2. x⁴
  3. 5x⁶
  4. 4x⁵
Show answer & explanation
✓ Answer: A — 5x⁴
Power rule: 5x⁴.
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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.