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AP Precalculus Practice Questions & Answers

Build function reasoning through symbolic rules, tables, graphs and original worked examples.

Read 10 original sample questions with worked explanations before opening the practice studio. These examples introduce selected topics from this AP Precalculus foundation path.

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What this practice covers

Foundation pilot for AP Precalculus assessed Units 1–3; Unit 4 explicitly listed outside scope

Foundation MCQ and numeric drills; formal AP free responses require written reasoning.

10 public examples400 question variants in the studio96 task families

Review status: Independent educator review and learner calibration are pending. Use these selected foundation examples alongside the coverage map and current official references.

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Topics in this foundation path

The examples below span 3 of 3 learning domains. Counts describe the current catalog, not the exam's official weighting.

Polynomial and Rational Functions

9 lessons · 160 question variants

Exponential and Logarithmic Functions

7 lessons · 112 question variants

Trigonometric and Polar Functions

8 lessons · 128 question variants

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Sample questions with answers

Work out your answer first, then compare the explanation. This stable selection uses distinct task families across the available learning domains.

QUESTION 01Polynomial and Rational Functions

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

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.
Compare the other answer choices
7

Skip the squaring operation.

9

Omit the vertical shift after squaring.

49

Add the vertical shift inside the square.

Learn: Function change and transformations Practice this topic

Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

QUESTION 02Exponential and Logarithmic Functions

Exponential growth and decay

A culture begins with 60 cells and triples each hour in a model. How many cells does the model predict after 3 hours?

    Write a numeric answer.

    Answer: 1620

    1. There are three one-hour growth intervals.
    2. Multiply by 3 in each interval.
    3. 60×3×3×3=1620.
    Learn: Exponential growth and decay Practice this topic

    Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

    QUESTION 03Trigonometric and Polar Functions

    Angles and the unit circle

    Write 90 degrees as kπ radians. What is k?

    1. 2
    2. 90
    3. 1/2
    4. 1

    Answer: 1/2

    1. A full 180 degrees corresponds to π radians.
    2. The coefficient is 90/180.
    3. Reduce to 1/2.
    Compare the other answer choices
    1

    Use 90 degrees rather than 180 per π radians.

    2

    Reverse the conversion ratio.

    90

    Attach π without converting degrees.

    Learn: Angles and the unit circle Practice this topic

    Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

    QUESTION 05Exponential and Logarithmic Functions

    Logarithms as inverse questions

    What is log₂(8)?

    1. 6
    2. 8
    3. 3
    4. 4

    Answer: 3

    1. The logarithm asks for an exponent on 2.
    2. Check 2^3=8.
    3. The exponent, hence the logarithm, is 3.
    Compare the other answer choices
    4

    Divide the argument by the base rather than taking its logarithm.

    6

    Multiply the exponent by the base after identifying it.

    8

    Report the logarithm argument rather than its exponent.

    Learn: Logarithms as inverse questions Practice this topic

    Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

    QUESTION 06Trigonometric and Polar Functions

    Read a sinusoidal model

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

      Write a numeric answer.

      Answer: 6

      1. Amplitude is half the peak-to-trough distance.
      2. The distance is 19−7=12.
      3. Half is 6.
      Learn: Read a sinusoidal model Practice this topic

      Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

      QUESTION 07Polynomial and Rational Functions

      Zeros, factors and remainders

      What is the remainder when P(x)=x³ + 3x + 4 is divided by x−2?

      1. -10
      2. 4
      3. 10
      4. 18

      Answer: 18

      1. Use the remainder theorem at x=2.
      2. Compute 2³+3(2)+4.
      3. The remainder is 18.
      Compare the other answer choices
      4

      Treat the constant as every possible division remainder.

      10

      Omit the cubic contribution.

      -10

      Evaluate at −2 rather than at the divisor zero 2.

      Learn: Zeros, factors and remainders Practice this topic

      Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

      QUESTION 09Trigonometric and Polar Functions

      Polar coordinates and equivalent points

      A point has polar coordinates (3,0). What is its Cartesian x-coordinate?

      1. 9
      2. 1
      3. 0
      4. 3

      Answer: 3

      1. Use x=r cos(theta).
      2. Cosine at zero is 1.
      3. x=3×1=3.
      Compare the other answer choices
      0

      Use r sin θ for the horizontal coordinate.

      1

      Return the unit-circle coordinate without scaling.

      9

      Square the radius during conversion.

      Learn: Polar coordinates and equivalent points Practice this topic

      Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

      QUESTION 10Polynomial and Rational Functions

      Rational functions and restrictions

      For R(x)=(x²−36)/(x−6), which input is excluded from its original domain?

        Write a numeric answer.

        Answer: 6

        1. A denominator cannot be zero.
        2. Solve x−6=0.
        3. The input 6 remains excluded even though the expression simplifies.
        Learn: Rational functions and restrictions Practice this topic

        Reference basis: AP Precalculus course and syllabus. These are original learning questions, not questions reproduced from the references.

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        Scope, sources and review notes

        Catalog scope record: . This records the saved content mapping, not a guarantee that every external rule is current.

        • Expanded foundation practice, not complete AP coverage or a calibrated AP score estimate.
        • 276 MCQ and 124 numeric learning tasks; these are not formal 2027 MCQ/FRQ proportions.
        • Eight original written extensions use method-based self-assessment; not official AP scoring.
        • Six caption-grounded companions; some selected source evidence is reused for distinct original teaching. Full audiovisual and independent educator review pending.
        • Foundation pilot, not full syllabus coverage or official simulation
        • Question variants are not independent question designs
        • Independent educator review pending
        • Evidence integrity and structure checks do not establish factual or audiovisual fidelity

        Check the exam provider's current information for registration, test rules and official preparation materials. The exam guide collects the relevant official references.

        REFERENCEAP Precalculus course and syllabus

        Syllabus facts; independent content mapping