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High School Pre-Calculus practice questions and exam guide
150 multiple-choice questions and 165 flashcards, organised into 10 chapters, written to the Common Core HS Pre-Calculus / typical course standards blueprint. Every question carries a full rationale.
- 315 total items
- 150 multiple choice
- 165 flashcards
- 10 chapters
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About the High School Pre-Calculus exam
Common Core HS Pre-Calculus / typical course standards — covers: functions and inverses, polynomial/rational/exponential/logarithmic functions, trigonometric functions and identities, analytic trigonometry, sequences and series, conic sections, vectors, polar coordinates, parametric equations, limits introduction, complex numbers. Preparation for AP Calculus. MCQs reference public mathematical pre-calculus standards.
CoStudy's High School Pre-Calculus bank holds 315 items organised into 10 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
What the High School Pre-Calculus bank covers
Each chapter follows a domain of the published exam outline. Practise one on its own (chapter URLs are in the app and on this page for navigation; they are not sitemap targets):
- Functions and Their Graphs16 questions
- Polynomial and Rational Functions16 questions
- Exponential and Logarithmic Functions16 questions
- Trigonometric Functions16 questions
- Analytic Trigonometry: Identities and Equations16 questions
- Applications of Trigonometry: Laws, Vectors, Polar16 questions
- Systems of Equations and Matrices12 questions
- Conic Sections and Parametric Equations14 questions
- Sequences, Series, and Probability14 questions
- Limits and Introduction to Calculus14 questions
Free High School Pre-Calculus practice questions
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
Functions and Their Graphs
f(x) = x² and g(x) = x + 1. Find (f ∘ g)(2).
- 5
- 9
- 4
- 3
Answer: B — 9
B) Correct — (f ∘ g)(2) = f(g(2)) = f(3) = 9. A) Computes (g ∘ f)(2) = g(4), applying the functions in the wrong order. C) Finds f(2) and never applies g. D) Finds g(2) and never applies f.
Polynomial and Rational Functions
How many distinct real zeros does f(x) = x³ − 4x² + 4x have?
- 2
- 3
- 1
- 0
Answer: A — 2
A) Correct — f(x) = x(x − 2)², with zeros 0 and 2 (2 repeated). B) Counts the repeated zero twice; the question asks for distinct zeros. C) Misses the zero at x = 0. D) Misses both zeros.
x + 3 is a factor of p(x) exactly when:
- p(3) = 0
- p(−3) = 0
- p(0) = −3
- the constant term is 3
Answer: B — p(−3) = 0
B) Correct — By the Factor Theorem, x − c is a factor when p(c) = 0; here c = −3. A) Gets the sign of c wrong. C) Confuses the factor with the y-intercept. D) The constant term alone does not decide factors.
Exponential and Logarithmic Functions
Solve log₃ x = 4.
- x = 12
- x = 64
- x = 7
- x = 81
Answer: D — x = 81
D) Correct — Rewrite as 3⁴ = x. A) Multiplies the base by the exponent. B) Computes 4³ instead of 3⁴. C) Adds the base and the exponent.
What is the inverse of f(x) = eˣ?
- 1/eˣ
- ln x
- e^(−x)
- log₁₀ x
Answer: B — ln x
B) Correct — ln and eˣ undo each other. A) Is the reciprocal, not the inverse. C) Is the reflection across the y-axis. D) Uses the wrong base.
Trigonometric Functions
Convert 60° to radians.
- π/6
- π/2
- 60π
- π/3
Answer: D — π/3
D) Correct — Multiply by π/180: 60π/180 = π/3. A) Is 30°. B) Is 90°. C) Forgets to divide by 180.
Analytic Trigonometry: Identities and Equations
Simplify sin² x + cos² x.
- 0
- sin 2x
- 1
- 2
Answer: C — 1
C) Correct — This is the Pythagorean identity. A) Mixes up the identity with sin² x − sin² x. B) Confuses it with a double-angle formula. D) Treats each term as 1.
Applications of Trigonometry: Laws, Vectors, Polar
The Law of Sines states:
- a/sin A = b/sin B = c/sin C
- c² = a² + b² − 2ab cos C
- a + b = c
- sin A + cos A = 1
Answer: A — a/sin A = b/sin B = c/sin C
A) Correct — Each side is proportional to the sine of its opposite angle. B) Is the Law of Cosines. C) Is false for any triangle. D) Is not an identity.
Systems of Equations and Matrices
A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 1]]. Find AB.
- [[4, 2], [10, 4]]
- [[2, 0], [3, 4]]
- [[2, 4], [4, 6]]
- [[3, 2], [4, 5]]
Answer: A — [[4, 2], [10, 4]]
A) Correct — Rows of A times columns of B: [1·2 + 2·1, 1·0 + 2·1; 3·2 + 4·1, 3·0 + 4·1]. B) Multiplies matching entries, which is not matrix multiplication. C) Computes BA; matrix multiplication is not commutative. D) Adds the matrices.
Conic Sections and Parametric Equations
What are the asymptotes of x²/9 − y²/16 = 1?
- y = ±(3/4)x
- y = ±(16/9)x
- There are none
- y = ±(4/3)x
Answer: D — y = ±(4/3)x
D) Correct — For x²/a² − y²/b² = 1, the asymptotes are y = ±(b/a)x. A) Inverts b/a. B) Uses b²/a². C) Every hyperbola has two asymptotes.
Sequences, Series, and Probability
How many ways can 2 people be chosen from 6, when order does not matter?
- 15
- 30
- 12
- 36
Answer: A — 15
A) Correct — C(6, 2) = 6 · 5/2. B) Counts ordered pairs, P(6, 2). C) Multiplies 6 × 2. D) Squares 6.
Limits and Introduction to Calculus
Evaluate lim_{x→0⁺} 1/x.
- −∞
- 0
- ∞
- 1
Answer: C — ∞
C) Correct — For small positive x, 1/x is large and positive. A) Is the left-hand limit. B) Confuses the input with the output. D) Plugs in x = 1.
High School Pre-Calculus flashcards
6 sample cards from the 165 in the bank.
What are the inverse trig functions?
arcsin (sin⁻¹), arccos (cos⁻¹), arctan (tan⁻¹) — return the angle for a given trig value, on restricted ranges.
What test on a graph determines whether a function has an inverse function?
The horizontal line test — if every horizontal line crosses the graph at most once, f is one-to-one and has an inverse.
What is an odd function? Give a graphical property.
f(−x) = −f(x). Symmetric about the origin. Example: x³, sin x.
Worked Example: Find sin(7π/6) using reference angle and unit circle
Step 1: Identify the quadrant. 7π/6 is between π (= 6π/6) and 3π/2 (= 9π/6). So 7π/6 is in Quadrant III. Step 2: Find the reference angle. Reference angle = 7π/6 − π = 7π/6 − 6π/6 = π/6 Step 3: Recall sin(π/6). sin(π/6) = 1/2 Step 4: Apply the quadrant's sign. In Quadrant III, sine is NEGATIVE (only tangent is positive). Final answer: sin(7π/6) = −1/2
What does log(x) mean (without subscript)?
Common log: log₁₀(x).
What kinds of discontinuities are there?
Removable (hole), jump, infinite (asymptote).
Practise the full High School Pre-Calculus bank
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
Open High School Pre-Calculus →
High School Pre-Calculus — frequently asked
What is the High School Pre-Calculus exam?
Common Core HS Pre-Calculus / typical course standards — covers: functions and inverses, polynomial/rational/exponential/logarithmic functions, trigonometric functions and identities, analytic trigonometry, sequences and series, conic sections, vectors, polar coordinates, parametric equations, limits introduction, complex numbers. Preparation for AP Calculus. MCQs reference public mathematical pre-calculus standards.
How is CoStudy’s High School Pre-Calculus bank organised?
It holds 315 items across 10 chapters: Functions and Their Graphs; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Analytic Trigonometry: Identities and Equations; Applications of Trigonometry: Laws, Vectors, Polar; Systems of Equations and Matrices; Conic Sections and Parametric Equations; Sequences, Series, and Probability; Limits and Introduction to Calculus. Free samples on this page include the full rationale, with no account. Chapter counts in the bank are our mix; they are not a promise that the live exam uses the same item counts.
Does CoStudy replace the certifying body?
No. the certifying body owns the outline, the badge, and the sitting rules. This is independent practice with written rationales. We do not sell live items and we do not guarantee a pass.
Where do High School Pre-Calculus fees, cut scores, and pass rates live?
On the certifying body’s site. CoStudy will not invent a sitting fee or a pass rate. If a table on this page lacks a citation, treat it as unverified.
Are these real High School Pre-Calculus exam questions?
No. CoStudy does not have live items. The samples below are original practice written to the published outline, with rationales. Anyone selling “real exam dumps” is describing something you should not buy.