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AP Precalculus Practice Worksheets & Answer Key

Download an 8-question AP Precalculus 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

Function reasoning foundations.

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 · Function change and transformations

For f(x)=x², define g(x)=f(x − 3) + 4. What is g(6)?

  1. 7
  2. 9
  3. 49
  4. 13
Read the answer and explanation

Answer: 13

  1. The inner input is 6 − 3 = 3.
  2. The original function squares that input: f(3)=9.
  3. Add the vertical shift 4: g(6)=13.
Review the lesson
QUESTION 2 · Exponential growth and decay

A culture begins with 40 cells and triples each hour in a model. How many cells does the model predict after 3 hours?

  1. 120
  2. 1080
  3. 360
  4. 3240
Read the answer and explanation

Answer: 1080

  1. There are three one-hour growth intervals.
  2. Multiply by 3 in each interval.
  3. 40×3×3×3=1080.
Review the lesson
QUESTION 3 · Angles and the unit circle

Write 150 degrees as kπ radians. What is k?

  1. 6/5
  2. 150
  3. 5/6
  4. 5/3
Read the answer and explanation

Answer: 5/6

  1. A full 180 degrees corresponds to π radians.
  2. The coefficient is 150/180.
  3. Reduce to 5/6.
Review the lesson
QUESTION 4 · Polynomial structure and end behavior

Let P(x)=6x³ − 7x + 4. What is P(−2)?

    Read the answer and explanation

    Answer: -30

    1. Cube the negative input before multiplying.
    2. The terms are −48, +14, and +4.
    3. Adding gives -30.
    Review the lesson
    QUESTION 5 · Logarithms as inverse questions

    What is log₂(8)?

    1. 6
    2. 8
    3. 3
    4. 4
    Read the answer and explanation

    Answer: 3

    1. The logarithm asks for an exponent on 2.
    2. Check 2^3=8.
    3. The exponent, hence the logarithm, is 3.
    Review the lesson
    QUESTION 6 · Read a sinusoidal model

    A sinusoidal height varies between 7 and 19. What is its amplitude?

      Read the answer and explanation

      Answer: 6

      1. Amplitude is half the peak-to-trough distance.
      2. The distance is 19−7=12.
      3. Half is 6.
      Review the lesson
      QUESTION 7 · Zeros, factors and remainders

      What is the remainder when P(x)=x³ + 5x + 6 is divided by x−2?

      1. 19
      2. 24
      3. 6
      4. 16
      Read the answer and explanation

      Answer: 24

      1. Use the remainder theorem at x=2.
      2. Compute 2³+5(2)+6.
      3. The remainder is 24.
      Review the lesson
      QUESTION 8 · Compose and reverse functions

      If f(x)=6x+1 and g(x)=x², what is f(g(3))?

        Read the answer and explanation

        Answer: 55

        1. Apply the inner function first: g(3)=9.
        2. Apply f to 9: 6(9)+1.
        3. The result is 55.
        Review the lesson

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