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100+ Free AP Precalculus Practice Questions

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The function f(x) = -2 sin(x) differs from 2 sin(x) by which transformation?

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Key Facts: AP Precalculus Exam

40

multiple-choice questions in Section I of the exam

College Board AP Central

62.5%

share of the exam score from the multiple-choice section

College Board AP Central

1-5

score scale, with 3 or higher typically earning college credit

College Board

3 units

assessed on the exam (Unit 4 is taught but not tested)

College Board AP Central

May 2024

date the first AP Precalculus exam was administered

College Board

28 of 40

multiple-choice questions answered without a calculator (Part A)

College Board AP Central

The AP Precalculus exam runs 3 hours and is split into Section I, a 40-question multiple-choice section worth 62.5% of the score, and Section II, a 4-question free-response section worth 37.5%. Section I Part A allows no calculator (28 questions, 80 minutes) and Part B requires a graphing calculator (12 questions, 40 minutes). The exam assesses only Units 1-3 — polynomial and rational functions (30-40%), exponential and logarithmic functions (27-40%), and trigonometric and polar functions (30-35%); Unit 4 is not tested. Scores range from 1 to 5, and most colleges grant credit for a 3 or higher (source: College Board, apcentral.collegeboard.org).

Sample AP Precalculus Practice Questions

Try these sample questions to test your AP Precalculus exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A polynomial function f has degree 4 with a positive leading coefficient. What is the end behavior of f?
A.As x approaches negative infinity, f approaches positive infinity; as x approaches positive infinity, f approaches positive infinity
B.As x approaches negative infinity, f approaches negative infinity; as x approaches positive infinity, f approaches positive infinity
C.As x approaches negative infinity, f approaches positive infinity; as x approaches positive infinity, f approaches negative infinity
D.As x approaches negative infinity, f approaches negative infinity; as x approaches positive infinity, f approaches negative infinity
Explanation: For a polynomial with even degree and a positive leading coefficient, both ends rise: as x approaches positive or negative infinity, f(x) approaches positive infinity. The even degree makes the two ends behave the same way, and the positive leading coefficient makes them rise rather than fall.
2The average rate of change of a function f on the interval from x = 2 to x = 5 is computed as which of the following expressions?
A.f(5) - f(2)
B.(f(5) - f(2)) / (5 - 2)
C.(f(5) + f(2)) / 2
D.f(5) / f(2)
Explanation: The average rate of change of f over [a, b] is the slope of the secant line: (f(b) - f(a)) / (b - a). Here that is (f(5) - f(2)) / (5 - 2). This measures how much the output changes per unit change in input across the interval.
3Which statement correctly describes the relationship between a zero of a polynomial f and its graph?
A.A real zero of f corresponds to a vertical asymptote of the graph
B.A real zero of f corresponds to a y-intercept of the graph
C.A real zero of f corresponds to an x-intercept of the graph
D.A real zero of f corresponds to a horizontal asymptote of the graph
Explanation: A real zero is a value of x where f(x) = 0, which is exactly where the graph crosses or touches the x-axis. Therefore each real zero corresponds to an x-intercept of the graph of f.
4If a polynomial has a zero at x = 3 with multiplicity 2, what happens to the graph at x = 3?
A.The graph crosses the x-axis at x = 3
B.The graph has a hole at x = 3
C.The graph has a vertical asymptote at x = 3
D.The graph is tangent to (touches but does not cross) the x-axis at x = 3
Explanation: When a real zero has even multiplicity, the graph touches the x-axis at that point and turns back without crossing. A multiplicity of 2 is even, so at x = 3 the graph is tangent to the x-axis.
5The rational function f(x) = (x + 2) / (x - 4) has which vertical asymptote?
A.x = 4
B.x = -2
C.x = 1
D.y = 1
Explanation: A vertical asymptote occurs where the denominator equals zero and the numerator does not. Setting x - 4 = 0 gives x = 4, and the numerator x + 2 is nonzero there, so x = 4 is the vertical asymptote.
6For the rational function f(x) = (3x^2 + 1) / (x^2 - 5), what is the horizontal asymptote?
A.y = 0
B.y = 3
C.y = 1/5
D.There is no horizontal asymptote
Explanation: When the numerator and denominator have equal degree, the horizontal asymptote is the ratio of the leading coefficients. Here both are degree 2 with leading coefficients 3 and 1, so the horizontal asymptote is y = 3/1 = 3.
7A rational function f(x) = (x - 3)(x + 1) / ((x - 3)(x - 5)) has which feature at x = 3?
A.A vertical asymptote
B.An x-intercept
C.A hole (removable discontinuity)
D.A horizontal asymptote
Explanation: The factor (x - 3) appears in both the numerator and denominator, so it cancels. A canceled common factor produces a hole, a removable discontinuity, at x = 3 rather than a vertical asymptote.
8The graph of g(x) = f(x - 3) + 2 is obtained from the graph of f by which transformation?
A.Shift left 3 units and down 2 units
B.Shift right 3 units and down 2 units
C.Shift left 3 units and up 2 units
D.Shift right 3 units and up 2 units
Explanation: Replacing x with x - 3 shifts the graph right by 3 units, and adding 2 shifts it up by 2 units. Inside-the-function changes affect horizontal position in the opposite sign, while outside changes affect vertical position directly.
9If f(x) = x^2 + 1 and g(x) = 2x - 3, what is (f composed with g)(x), written f(g(x))?
A.4x^2 - 12x + 10
B.2x^2 - 1
C.2x^2 + 2
D.4x^2 + 10
Explanation: Substitute g(x) into f: f(g(x)) = (2x - 3)^2 + 1. Expanding (2x - 3)^2 gives 4x^2 - 12x + 9, and adding 1 yields 4x^2 - 12x + 10.
10A function f is invertible. Which condition must f satisfy?
A.f must be a polynomial
B.f must be one-to-one (pass the horizontal line test)
C.f must be increasing on its entire domain
D.f must be continuous everywhere
Explanation: A function has an inverse exactly when it is one-to-one, meaning each output corresponds to exactly one input. Graphically, this is the horizontal line test: no horizontal line meets the graph more than once.

About the AP Precalculus Exam

AP Precalculus is a College Board course and exam first administered in May 2024 that prepares students for calculus by studying families of functions and how they model the world. The exam has two sections: Section I with 40 multiple-choice questions (Part A, 28 questions, no calculator, 80 minutes; Part B, 12 questions, graphing calculator required, 40 minutes) and Section II with 4 free-response questions in 1 hour. Course Unit 4 (functions involving parameters, vectors, and matrices) is taught but is not assessed on the exam.

Questions

40 scored questions

Time Limit

3 hours total (Section I: 2 hours, Section II: 1 hour)

Passing Score

Scored 1-5; a 3 or higher typically earns college credit

Exam Fee

About $99 per exam (2025-26, US) (College Board)

AP Precalculus Exam Content Outline

30-40% of exam

Unit 1: Polynomial and Rational Functions

Rates of change, polynomial degree, end behavior and zeros, complex zeros, rational asymptotes and holes, transformations, composition, and inverses.

27-40% of exam

Unit 2: Exponential and Logarithmic Functions

Arithmetic and geometric sequences, exponential growth and decay, logarithm properties, inverse relationships, and modeling data with regression.

30-35% of exam

Unit 3: Trigonometric and Polar Functions

The unit circle, sine, cosine, and tangent functions, sinusoidal modeling, identities and equations, inverse trig functions, and polar coordinates and graphs.

How to Pass the AP Precalculus Exam

What You Need to Know

  • Passing score: Scored 1-5; a 3 or higher typically earns college credit
  • Exam length: 40 questions
  • Time limit: 3 hours total (Section I: 2 hours, Section II: 1 hour)
  • Exam fee: About $99 per exam (2025-26, US)

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

AP Precalculus Study Tips from Top Performers

1Learn the four CED function families inside out — for each, know domain, range, zeros, asymptotes, end behavior, and transformations.
2Practice Part A questions by hand: 28 of the 40 multiple-choice questions are answered without a calculator, so build fluency with logs, the unit circle, and factoring.
3Master your graphing calculator for Part B: finding intersections, zeros, and running exponential or sinusoidal regressions quickly.
4Memorize log and exponent properties and the unit-circle values for sine, cosine, and tangent at common angles.
5Do not over-study Unit 4 for the exam — it is part of the course but is not assessed; focus exam review on Units 1-3.

Frequently Asked Questions

How many questions are on the AP Precalculus exam and how long is it?

The AP Precalculus exam is 3 hours long. Section I has 40 multiple-choice questions (2 hours), and Section II has 4 free-response questions (1 hour).

Is a calculator allowed on the AP Precalculus exam?

Partly. Section I Part A (28 questions, 80 minutes) does not allow a calculator, while Part B (12 questions, 40 minutes) requires a graphing calculator. In Section II, Part A requires a graphing calculator and Part B does not.

What units are tested on the AP Precalculus exam?

Only Units 1-3 are assessed: polynomial and rational functions, exponential and logarithmic functions, and trigonometric and polar functions. Unit 4 (parametric, vector, and matrix functions) is taught but not tested on the exam.

How is the AP Precalculus exam scored?

It is scored on the standard AP 1-5 scale. Multiple choice contributes 62.5% and free response 37.5%. Most colleges grant credit for a score of 3 or higher.

When did AP Precalculus start?

AP Precalculus launched in fall 2023, and the first AP Precalculus exam was administered in May 2024.

How much does the AP Precalculus exam cost?

The standard AP exam fee in the US is about $99 per exam for 2025-26. Fee reductions are available for eligible students.