CLEP College Algebra Practice Questions with Answers: 15 Problems to Try First

CLEP College Algebra can help eligible students earn college algebra credit at participating institutions, but credit rules are set by each college. The current College Board exam page describes a 90-minute exam with approximately 60 questions, routine and nonroutine algebra problems, and an online nongraphing TI-30XS MultiView calculator. Preparation requires more than a casual review because the exam covers algebraic operations, equations and inequalities, functions, and number systems.

This page provides 15 original practice questions spread across all four content areas of the CLEP College Algebra exam, each followed by a complete step-by-step solution.

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CLEP College Algebra: Exam Overview

Content Areas and Weighting

• Algebraic Operations (25%): Exponents and radicals, polynomials, rational expressions, absolute value, logarithm properties
• Equations and Inequalities (25%): Linear, quadratic, absolute value, rational, radical, systems of equations and inequalities, exponential and logarithmic equations
• Functions (30%): Domain and range, evaluation, function algebra (sum, difference, product, quotient, composition), graphs (intercepts, symmetry, transformations), inverses
• Number Systems and Operations (20%): Real and complex numbers, factorials, sequences, binomial theorem

15 CLEP College Algebra Practice Questions

Section A: Algebraic Operations

Problem 1. Simplify: x³ · x⁵.

Solution: When multiplying powers with the same base, add the exponents: x³ · x⁵ = x^(3+5) = x⁸.

Problem 2. Simplify: (2x²y³)³.

Solution: Raise each factor to the power of 3: 2³ · x^(2·3) · y^(3·3) = 8x⁶y⁹. Answer: 8x⁶y⁹.

Problem 3. Factor completely: x² − 9.

Solution: This is a difference of squares: x² − 9 = (x − 3)(x + 3). Answer: (x − 3)(x + 3).

Problem 4. Simplify: log₂(32).

Solution: log₂(32) = log₂(2⁵) = 5.

Section B: Equations and Inequalities

Problem 5. Solve: 2x − 5 = 11.

Solution: 2x = 16; x = 8.

Problem 6. Solve: x² − 5x + 6 = 0.

Solution: Factor: (x − 2)(x − 3) = 0. Solutions: x = 2 or x = 3.

Problem 7. Solve: |2x − 3| = 7.

Solution: Two cases: (1) 2x − 3 = 7 → 2x = 10 → x = 5. (2) 2x − 3 = −7 → 2x = −4 → x = −2. Solutions: x = 5 or x = −2.

Problem 8. Solve the system: 2x + y = 10 and x − y = 2.

Solution: Add the equations: 3x = 12, so x = 4. Substitute: 4 − y = 2, so y = 2. Solution: (4, 2).

Problem 9. Solve: 3^x = 81.

Solution: 81 = 3⁴, so 3^x = 3⁴. Therefore x = 4.

Section C: Functions

Problem 10. Let f(x) = 2x + 1 and g(x) = x². Find (g ∘ f)(3).

Solution: First find f(3) = 2(3) + 1 = 7. Then g(f(3)) = g(7) = 7² = 49.

Problem 11. What is the domain of f(x) = √(x − 4)?

Solution: The expression under the radical must be ≥ 0: x − 4 ≥ 0, so x ≥ 4. Domain: [4, ∞).

Problem 12. Find the inverse of f(x) = 3x − 6.

Solution: Replace f(x) with y: y = 3x − 6. Swap x and y: x = 3y − 6. Solve for y: 3y = x + 6, so y = (x + 6)/3. Inverse: f⁻¹(x) = (x + 6)/3.

Problem 13. The graph of f(x) = x² is shifted 3 units to the right and 2 units down. What is the equation of the resulting function?

Solution: Shift right 3 → replace x with (x − 3). Shift down 2 → subtract 2. Result: f(x) = (x − 3)² − 2.

Section D: Number Systems and Operations

Problem 14. Simplify: (3 + 2i)(1 − i), where i = √(−1).

Solution: Distribute: 3(1) + 3(−i) + 2i(1) + 2i(−i) = 3 − 3i + 2i − 2i². Since i² = −1: = 3 − i − 2(−1) = 3 − i + 2 = 5 − i.

Problem 15. Use the binomial theorem to expand (x + 2)³.

Solution: (x + 2)³ = C(3,0)x³(2)⁰ + C(3,1)x²(2)¹ + C(3,2)x¹(2)² + C(3,3)x⁰(2)³ = 1·x³ + 3·2x² + 3·4x + 1·8 = x³ + 6x² + 12x + 8.

Key CLEP College Algebra Formulas to Know

• Difference of squares: a² − b² = (a − b)(a + b)
• Perfect square trinomial: a² + 2ab + b² = (a + b)²
• Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
• Logarithm rules: log(xy) = log x + log y; log(x/y) = log x − log y; log(xⁿ) = n log x
• Composition: (g ∘ f)(x) = g(f(x))
• Inverse: to find f⁻¹, swap x and y, then solve for y
• Binomial theorem: (a + b)ⁿ = Σ C(n,k) aⁿ⁻ᵏ bᵏ
• Complex multiplication: i² = −1

CLEP College Algebra Study Tips

• Master the function section first: Functions carry the highest weight (30%) and appear in many CLEP questions indirectly. Understanding domain, range, composition, and transformations is essential.
• The calculator is available but limited: The on-screen TI-30XS helps with arithmetic and basic calculations but cannot factor, solve equations symbolically, or graph. Practice algebraic manipulation by hand.
• Know the difference between solving and simplifying: “Solve” means find a value of x. “Simplify” means rewrite in a simpler or factored form. Confusing these instructions leads to losing credit on otherwise understood problems.
• Review absolute value equations carefully: Every absolute value equation produces two cases. Both cases must be checked; sometimes one solution is extraneous.

ViewMath Resources for CLEP Math

ViewMath CLEP College Algebra resources provide topic-by-topic practice, full-length tests, complete answer keys, and worked solutions suitable for self-study before sitting for the CLEP exam. Start with CLEP College Algebra Made Easy if you need guided review, use the CLEP College Algebra Workbook for topic practice, and move to 5 Full-Length Practice Tests for CLEP College Algebra when you are ready for realistic timed practice.