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AP Calculus AB Practice Worksheets & Answer Key

Download an 8-question AP Calculus AB worksheet with a separate answer and explanation section. The selected text questions work without a screen or an account.

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Version 2026-10-27 · Original foundation materials · No sign-up

What this collection covers

Calculus AB foundation practice.

This fixed sample includes one question per selected skill before additional families. Questions requiring a separate diagram are excluded from this text worksheet. It is an untimed study resource with working space, rather than an official mock examination.

Author-reviewed learning materials. Independent educator review is pending; question difficulty has not been calibrated with learner results. Check coverage and gaps before planning your preparation.

Inside the printable worksheet

8 original questionsSeparate explanationsUS Letter · PDF · Version 2026-10-27

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Questions included in this PDF

QUESTION 1 · Limits without guessing

Find the limit as x approaches 3 of 2x² + 4.

  1. 10
  2. 22
  3. 18
  4. 98
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Answer: 22

  1. The polynomial is continuous at 3.
  2. Substitute x=3: 2(3)²+4.
  3. The limit is 22.
Review the lesson
QUESTION 2 · Derivative rules and meaning

If f(x)=3x³+5, find f′(4).

  1. 144
  2. 48
  3. 36
  4. 149
Read the answer and explanation

Answer: 144

  1. The power rule gives f′(x)=9x².
  2. The constant term differentiates to zero.
  3. Substitute 4: f′(4)=144.
Review the lesson
QUESTION 3 · Position, velocity and acceleration

An object has position s(t)=4t²+6t meters. Find its velocity at t=5 seconds.

  1. 40
  2. 46
  3. 26
  4. 130
Read the answer and explanation

Answer: 46

  1. Velocity is s′(t)=8t+6.
  2. Evaluate at t=5.
  3. The velocity is 46 meters per second.
Review the lesson
QUESTION 4 · Integrals and numerical accumulation

An antiderivative of 5x^6 is kx^7+C. Find k.

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    Answer: 5/7

    1. Differentiate kx^7 to obtain (7)kx^6.
    2. Match its coefficient to 5.
    3. Thus k=5/7.
    Review the lesson
    QUESTION 5 · Differential equations and initial values

    A solution satisfies dy/dx=x+y. What is its slope at (2,3)?

    1. 5
    2. 6
    3. 2
    4. 3
    Read the answer and explanation

    Answer: 5

    1. A slope field evaluates the differential equation at the specified point.
    2. Substitute x=2, y=3.
    3. The slope is 5.
    Review the lesson
    QUESTION 6 · Area, average value and volume

    Find the area between y=5x and y=0 from x=0 to x=6.

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      Answer: 90

      1. The upper function is the line throughout this nonnegative interval.
      2. Integrate 5x from 0 to 6.
      3. The area is 90 square units.
      Review the lesson
      QUESTION 7 · Choose and justify a theorem

      f is continuous on [0,4] and differentiable on (0,4), with −5≤f′(x)≤8. If f(0)=8, what is the smallest value f(4) could have under these constraints?

      1. 40
      2. 3
      3. -12
      4. 28
      Read the answer and explanation

      Answer: -12

      1. The Mean Value Theorem expresses the total change as an interior derivative times interval length.
      2. The smallest allowed change is −5×4=-20.
      3. Add the initial value to obtain -12. The line f(x)=8−5x attains this bound.
      Review the lesson
      QUESTION 8 · Areas across intersections and sideways slices

      Find the total area between y=x² and y=36 for 0≤x≤12.

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        Answer: 432

        1. The curves cross at x=6 in the interval; the horizontal line is above before that point.
        2. Integrate (36−x²) on [0,6] and (x²−36) on [6,12].
        3. The pieces are 144 and 288; the total is 432.
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