CLEP College Algebra Practice Test Questions

Use these CLEP College Algebra sample questions to review algebraic operations, equations and inequalities, functions, real and complex numbers, and the binomial theorem. The questions include both routine calculations and concept-based applications.

Topics Covered

  • Properties of logarithms
  • Factoring polynomials
  • Quadratic equations
  • Absolute-value inequalities
  • Systems of linear equations
  • Domains of functions
  • Inverse functions
  • Quadratic graph transformations
  • Complex-number operations
  • The binomial theorem

Sample Questions

1. For positive values of x, y, and z, which expression is equivalent to logb(x) + 2logb(y) − logb(z), where b > 0 and b ≠ 1?

  • A. logb((x + 2y)/z)
  • B. logb(xy2z)
  • C. logb(xy2/z)
  • D. logb(x2y/z)
  • E. logb(xz/y2)
Show Answer for Question 1
Answer: C. logb(xy2/z)
Use the power rule to rewrite 2logb(y) as logb(y2).

The product rule combines addition inside one logarithm, and the quotient rule converts subtraction into division. Therefore, the expression becomes logb(xy2/z).

2. Which expression is the complete factorization of x3 − 4x2 − x + 4?

  • A. (x − 4)(x − 1)(x + 1)
  • B. (x + 4)(x − 1)(x + 1)
  • C. (x − 4)(x2 + 1)
  • D. (x + 4)(x2 − 1)
  • E. (x − 2)2(x + 1)
Show Answer for Question 2
Answer: A. (x − 4)(x − 1)(x + 1)
Factor by grouping: x2(x − 4) − 1(x − 4) = (x − 4)(x2 − 1).

Then factor the difference of squares: x2 − 1 = (x − 1)(x + 1).

3. What are the solutions of x2 − 5x − 14 = 0?

  • A. x = −7 and x = 2
  • B. x = −2 and x = 7
  • C. x = 2 and x = 7
  • D. x = −14 and x = 1
  • E. x = 5 ± √14
Show Answer for Question 3
Answer: B. x = −2 and x = 7
Factor the quadratic as (x − 7)(x + 2) = 0.

Set each factor equal to zero. This gives x = 7 or x = −2.

4. Which interval is the solution set of |2x − 3| < 5?

  • A. x < −1 or x > 4
  • B. −4 < x < 1
  • C. −1 ≤ x ≤ 4
  • D. −1 < x < 4
  • E. x > 4
Show Answer for Question 4
Answer: D. −1 < x < 4
Rewrite the absolute-value inequality as −5 < 2x − 3 < 5.

Add 3 throughout and divide by 2: −2 < 2x < 8, so −1 < x < 4. The endpoints are excluded because the original inequality is strict.

5. What is the solution to the system 2x + y = 7 and x − y = 2?

  • A. (1, 5)
  • B. (2, 3)
  • C. (3, 1)
  • D. (4, −1)
  • E. (5, −3)
Show Answer for Question 5
Answer: C. (3, 1)
Add the equations to eliminate y: 3x = 9, so x = 3.

Substitute into x − y = 2: 3 − y = 2, which gives y = 1.

6. What is the domain of f(x) = √(x − 1)/(x − 4)?

  • A. (−∞, 4) ∪ (4, ∞)
  • B. [1, ∞)
  • C. [1, 4) ∪ (4, ∞)
  • D. (1, 4) ∪ (4, ∞)
  • E. (−∞, 1] ∪ (4, ∞)
Show Answer for Question 6
Answer: C. [1, 4) ∪ (4, ∞)
The expression under the square root requires x − 1 ≥ 0, so x ≥ 1.

The denominator cannot equal zero, so x ≠ 4. Combining these restrictions gives [1, 4) ∪ (4, ∞).

7. If f(x) = 3x − 5, what is f−1(x)?

  • A. (x − 5)/3
  • B. (x + 5)/3
  • C. 3x + 5
  • D. 5 − 3x
  • E. 1/(3x − 5)
Show Answer for Question 7
Answer: B. (x + 5)/3
Write y = 3x − 5, then interchange x and y: x = 3y − 5.

Solve for y: x + 5 = 3y, so y = (x + 5)/3.

8. Which statement correctly describes the graph of g(x) = −(x + 2)2 + 3?

  • A. It has vertex (2, 3) and opens upward.
  • B. It has vertex (−2, 3) and opens upward.
  • C. It has vertex (2, −3) and opens downward.
  • D. It has vertex (−2, 3) and opens downward.
  • E. It has vertex (−3, 2) and opens downward.
Show Answer for Question 8
Answer: D. It has vertex (−2, 3) and opens downward.
The vertex form is a(x − h)2 + k. Here, h = −2 and k = 3, so the vertex is (−2, 3).

Because the coefficient a = −1 is negative, the parabola opens downward.

9. Which expression is equal to (3 + 2i)(1 − 4i)?

  • A. −5 − 10i
  • B. 5 − 10i
  • C. 11 − 10i
  • D. 11 + 10i
  • E. −11 + 10i
Show Answer for Question 9
Answer: C. 11 − 10i
Multiply using distribution: 3 − 12i + 2i − 8i2.

Because i2 = −1, the last term becomes +8. Combine terms to obtain 11 − 10i.

10. What is the coefficient of x3 in the expansion of (x + 2)5?

  • A. 10
  • B. 20
  • C. 32
  • D. 40
  • E. 80
Show Answer for Question 10
Answer: D. 40
To obtain x3, choose three of the five factors to contribute x and the remaining two to contribute 2.

The coefficient is C(5, 3) · 22 = 10 · 4 = 40.

How to Use These Questions

Identify the algebraic structure before performing calculations. Look for logarithm rules, common factors, recognizable quadratic forms, domain restrictions, function transformations, or binomial coefficients.

Check solutions in the original equation or system whenever possible. For function questions, distinguish restrictions on inputs from properties of the graph, and remember that inverse functions reverse the original input-output relationship.

These practice questions are not official CLEP questions and are not endorsed by the College Board.

CLEP® is a registered trademark of the College Board, which is not affiliated with StudyGuideZone.com or Mometrix Test Preparation.

 

Last Updated: July 28, 2026