OpenExam.
All examsCLEP College AlgebraFoundation path
View coverage
FREE ORIGINAL PRACTICE · ANSWERS & EXPLANATIONS

CLEP College Algebra Practice Questions & Answers

Connect expressions, functions and graphs through original college-algebra practice and illustrated explanations.

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

Open free practice Read the sample questions

Free access · No sign-up · No personal progress recorded on this page

What this practice covers

College Algebra foundation pilot

Multiple-choice and numeric foundation exercises; not a full official exam simulation.

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.

Check the coverage map and remaining gaps
CHOOSE A STARTING POINT

Topics in this foundation path

The examples below span 4 of 4 learning domains. Counts describe the current catalog, not the exam's official weighting.

Algebraic operations

7 lessons · 128 question variants

Equations & inequalities

6 lessons · 96 question variants

Functions & properties

7 lessons · 112 question variants

Number systems & operations

4 lessons · 64 question variants

TRY A QUESTION. FOLLOW THE REASONING.

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 01Algebraic operations

Powers, roots and equivalent forms

For x ≠ 0, x^9/x^5 = x^k. What is k?

  1. 45
  2. 9/5
  3. 4
  4. 9

Answer: 4

  1. The bases are equal, so subtract exponents in the quotient.
  2. The nonzero restriction belongs to the original denominator.
  3. The requested value is 4. Substitute or reverse the operation to check this result.
Compare the other answer choices
9

Cancel the entire denominator without changing the numerator exponent.

45

Multiply the exponents as if the expression were a power of a power.

9/5

Divide the exponents rather than subtracting them.

Learn: Powers, roots and equivalent forms Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 02Equations & inequalities

Linear equations, systems and boundaries

Solve (2x − 5)/3 = 8. What is x?

Write a numeric answer.

Answer: 29/2

  1. Multiply both sides by 3.
  2. Add the subtracted constant before dividing by the coefficient of x.
  3. The requested value is 29/2. Substitute or reverse the operation to check this result.
Learn: Linear equations, systems and boundaries Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 03Functions & properties

Functions, composition and inverse inputs

The two function rules are shown in the table. Find f(g(2)).

Table: f(t)=2t+1; g(t)=t squared minus 3.Open full-size diagram ↗
  1. 6
  2. 22
  3. 5
  4. 3

Answer: 3

  1. First evaluate g at the given input.
  2. Feed that output into f; do not multiply f and g.
  3. The requested value is 3. Substitute or reverse the operation to check this result.
Compare the other answer choices
5

Multiply f(x) and g(x) instead of composing.

6

Double x squared but not the entire inner output x squared minus three.

22

Reverse the order and calculate g(f(x)).

Learn: Functions, composition and inverse inputs Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 04Number systems & operations

Complex numbers without losing the sign

What is the real part of (6 + 3i)(2 − i)?

Write a numeric answer.

Answer: 15

  1. Multiply the real terms and the two imaginary terms.
  2. Since i² = −1, the product of 3i and −i contributes positive 3 to the real part.
  3. The requested value is 15. Substitute or reverse the operation to check this result.
Learn: Complex numbers without losing the sign Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 05Algebraic operations

Read and combine polynomial structure

In the expansion of (x + 4)(x + 3), what is the coefficient of x?

  1. 7
  2. 1
  3. 3
  4. 4

Answer: 7

  1. The x terms come from the two cross products.
  2. Add their coefficients while keeping the x² and constant terms separate.
  3. The requested value is 7. Substitute or reverse the operation to check this result.
Compare the other answer choices
1

Report the leading coefficient of x squared.

3

Keep only the second cross term.

4

Keep only the first cross term.

Learn: Read and combine polynomial structure Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 06Equations & inequalities

Quadratic equations and discriminants

What is the sum of the roots of 3x² − 27x + 5 = 0?

Write a numeric answer.

Answer: 9

  1. For ax² + bx + c = 0, the root sum is −b/a.
  2. Use the signed coefficient b rather than only its magnitude.
  3. The requested value is 9. Substitute or reverse the operation to check this result.
Learn: Quadratic equations and discriminants Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 07Functions & properties

Transformations and graph features

The function y = 2(x + 3)² − 5 has its vertex at (h,k). What is h?

  1. 13
  2. 3
  3. -3
  4. 0

Answer: -3

  1. The inner expression equals zero at the vertex.
  2. Solve x plus the constant equal to zero; the positive sign inside indicates a left shift.
  3. The requested value is -3. Substitute or reverse the operation to check this result.
Compare the other answer choices
0

Assume vertical stretching leaves the vertex at input zero despite the horizontal shift.

3

Read the inner plus sign as a rightward rather than leftward shift.

13

Report the y-intercept instead of the vertex input.

Learn: Transformations and graph features Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 08Number systems & operations

Sequences, factorials and binomial choices

An arithmetic sequence starts at 7 and has common difference 4. What is term 9?

Write a numeric answer.

Answer: 39

  1. Count one fewer step than the term number.
  2. Add that many common differences to the first term.
  3. The requested value is 39. Substitute or reverse the operation to check this result.
Learn: Sequences, factorials and binomial choices Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 09Algebraic operations

Factor to expose a useful feature

Factor 8x² + 12x as 4x(ax + b). What is b?

  1. 2
  2. 1/3
  3. 12
  4. 3

Answer: 3

  1. Divide the linear term by the factored-out term.
  2. The x cancels and the remaining coefficient is b.
  3. The requested value is 3. Substitute or reverse the operation to check this result.
Compare the other answer choices
2

Report a, the other coefficient inside the parentheses.

12

Leave the original linear coefficient unchanged after factoring.

1/3

Reverse the division used to recover b.

Learn: Factor to expose a useful feature Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

QUESTION 10Equations & inequalities

Absolute value as a distance

What is the larger solution of |x − 6| = 9?

Write a numeric answer.

Answer: 15

  1. The solutions lie the stated distance to either side of the center.
  2. The larger solution is the center plus the nonnegative distance.
  3. The requested value is 15. Substitute or reverse the operation to check this result.
Learn: Absolute value as a distance Practice this topic

Reference basis: CLEP College Algebra exam overview; Siyavula Grade 10 foundation reference. These are original learning questions, not questions reproduced from the references.

BUILD ON WHAT YOU NOTICED

Turn one question into a learning route

Start with the lesson linked to an unfamiliar topic, try a focused set in the practice studio, then return to the review cards. Your practice progress stays in this browser.

Explore the study guide Start free practice

Scope, sources and review notes

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

  • Foundation pilot: selected college-algebra skills, not complete syllabus coverage.
  • No official score conversion or guaranteed college credit.
  • Question mix and timing are not a full CLEP simulation.
  • Fees and appointment availability require confirmation with the official provider.
  • 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.

REFERENCECLEP College Algebra exam overview

scope, timing, calculator and content proportions

TEXTBOOKSiyavula Grade 10 foundation reference

Shared algebra foundations; not a complete source for college algebra