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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.

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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

A function is continuous everywhere if it is:

  1. a rational function
  2. a polynomial
  3. a piecewise jump
  4. 1/x
Show answer & explanation
✓ Answer: B — a polynomial
Polynomials have no breaks.
Q2 · Difficulty 1/3

The derivative represents an instantaneous:

  1. sum
  2. area
  3. rate of change
  4. average
Show answer & explanation
✓ Answer: C — rate of change
The derivative is an instantaneous rate.
Q3 · 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.
Q4 · Difficulty 1/3

∫ x³ dx =

  1. x⁴ + C
  2. 4x³ + C
  3. x⁴/4 + C
  4. 3x² + C
Show answer & explanation
✓ Answer: C — x⁴/4 + C
Power rule: x⁴/4 + C.
Q5 · Difficulty 1/3

The constant multiple rule: d/dx (c·f) =

  1. f′
  2. c·f′
  3. c
  4. f
Show answer & explanation
✓ Answer: B — c·f′
Constants factor out of derivatives.
Q6 · Difficulty 1/3

Acceleration is the derivative of:

  1. position
  2. velocity
  3. time
  4. distance only
Show answer & explanation
✓ Answer: B — velocity
a(t)=v′(t).
Q7 · Difficulty 1/3

The rate of change of a quantity is given by its:

  1. derivative
  2. limit
  3. average
  4. integral
Show answer & explanation
✓ Answer: A — derivative
Derivatives give rates of change.
Q8 · Difficulty 1/3

If f′(x) > 0 on an interval, f is:

  1. decreasing
  2. increasing
  3. constant
  4. concave down
Show answer & explanation
✓ Answer: B — increasing
Positive derivative = increasing.
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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.