Free CLEP College Algebra Practice Questions

Sample Practice Questions

Try these 10 sample questions from the CLEP College Algebra practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Combine x³ · x⁵ into a single power, assuming x is a nonzero real number.

   1. A.x raised to the eighth powerCorrect answer: A
   2. B.x raised to the fifteenth power
   3. C.x squared
   4. D.twice x raised to the eighth power

   Explanation: The tutorial states, "When mult. like bases you add your exponents". Adding 3 and 5 gives x⁸; multiplying or subtracting the exponents applies a different operation.

   Reference: College Algebra Tutorial 2: Integer Exponents — Multiplying Like Bases With Exponents, Example 4

2. 2Solve 3x + 7 = 19 for x.

   1. A.Positive fourCorrect answer: A
   2. B.Positive six
   3. C.Twenty-six thirds
   4. D.Negative four

   Explanation: The tutorial explains that "if two expressions are equal to each other and you add or subtract the exact same thing to both sides, the two sides will remain equal." Subtract 7 and divide by 3 to get x = 4.

   Reference: College Algebra Tutorial 14: Linear Equations in One Variable — Addition and Subtraction Properties

3. 3Among the relations given, which is a function of its first coordinate?

   1. A.{(1, 2), (1, 3), (2, 4)}
   2. B.{(1, 2), (2, 2), (3, 4)}Correct answer: B
   3. C.{(1, 2), (2, 3), (2, 4)}
   4. D.{(1, 2), (2, 3), (1, 4)}

   Explanation: The tutorial states, "A function is a relation that assigns to each input number EXACTLY ONE output number." In the correct relation each input occurs once; repeated outputs are allowed.

   Reference: College Algebra Tutorial 30: Introduction to Functions — Function

4. 4Among these square roots, which value belongs to the rational number system?

   1. A.√2
   2. B.√3
   3. C.√5
   4. D.√9Correct answer: D

   Explanation: The tutorial defines a rational number as "a rational number is a number that can be written as one integer over another." It identifies "roots of numbers that are not perfect roots" as irrational. √9 = 3/1 is rational; 2, 3 and 5 are not perfect squares.

   Reference: Intermediate Algebra Tutorial 3: Sets of Numbers — Rational Numbers

5. 5For a nonzero real number y, simplify y⁹ / y⁴.

   1. A.y raised to the thirteenth power
   2. B.y raised to the thirty-sixth power
   3. C.y raised to the fifth powerCorrect answer: C
   4. D.y raised to the negative fifth power

   Explanation: The quotient rule says, "when you divide like bases you subtract their exponents". Subtract the denominator exponent from the numerator exponent: 9 − 4 = 5.

   Reference: College Algebra Tutorial 2: Integer Exponents — Dividing Like Bases With Exponents, Quotient Rule

6. 6What is the solution set of 4(x − 2) = 4x − 8 over the real numbers?

   1. A.{−8}
   2. B.All real numbersCorrect answer: B
   3. C.{2}
   4. D.The empty set

   Explanation: The tutorial states, "An equation is classified as an identity when it is true for ALL real numbers for which both sides of the equation are defined." Distribution makes both sides equal to 4x − 8 for every real x.

   Reference: College Algebra Tutorial 14: Linear Equations in One Variable — Identity

7. 7A chemical sample initially contains 200 grams and retains 80% of its mass after each hour. Which function gives the mass M(t), in grams, after t whole hours?

   1. A.M(t) = 200(0.8)^tCorrect answer: A
   2. B.M(t) = 200(1.8)^t
   3. C.M(t) = 200 − 0.8t
   4. D.M(t) = 200(0.2)^t

   Explanation: The university states, "The positive constant \(b\) is called the base or the growth factor of the exponential function." Retaining 80% means multiplying by 0.8 each hour, so M(t) = 200(0.8)^t.

   Reference: PreCalculus: Exponential Functions — Exponential Function, growth factor

8. 8Which decimal representation corresponds to an irrational real number?

   1. A.A nonterminating, nonrepeating decimalCorrect answer: A
   2. B.A terminating decimal
   3. C.A nonterminating decimal repeating 27
   4. D.A decimal equal to 5/8

   Explanation: The tutorial describes an irrational number: "It is a non-repeating, non-terminating decimal." Terminating and repeating decimals are rational.

   Reference: Intermediate Algebra Tutorial 3: Sets of Numbers — Irrational Numbers

9. 9If t is a real number, which expression is equivalent to (t⁴)³?

   1. A.t raised to the seventh power
   2. B.t raised to the twelfth powerCorrect answer: B
   3. C.t raised to the four-thirds power
   4. D.three times t to the fourth power

   Explanation: The tutorial states, "when you raise a base to two exponents, you multiply those exponents together". Thus (t⁴)³ = t¹².

   Reference: College Algebra Tutorial 2: Integer Exponents — Base Raised to two Exponents, Power Rule

10. 10Determine whether 2(x + 3) = 2x + 5 has real-number solutions, and identify the complete solution set.

    1. A.{5}
    2. B.{6}
    3. C.The empty setCorrect answer: C
    4. D.All real numbers

    Explanation: The tutorial says, "Whenever your variable drops out AND you end up with a FALSE statement, then after all of your hard work, there is NO SOLUTION." Here simplification gives 6 = 5.

    Reference: College Algebra Tutorial 14: Linear Equations in One Variable — Inconsistent Equations