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CLEP College Algebra Practice Test

10 free sample questions with answers and explanations. See how you'd score on the real CLEP exam.

Question 1Unit 1: Algebraic Foundations

What is the value of the coefficient of the x^3y^2 term in the expansion of (2x + 3y)^5?

A
A) 120
B
B) 720
C
C) 160
D
D) 40
E
E) 240

Explanation

240 is correct because the binomial theorem states that the coefficient of the x^(n-k)y^k term of (a + b)^n is [n!/(k!(n-k)!)]*a^(n-k)*b^k, so for the x^3y^2 term in (2x + 3y)^5, the coefficient is [5!/(2!(5-2)!)]*(2^3)*(3^2) = 240.

Question 2Unit 1: Algebraic Foundations

What is (2x - 3y)^2?

A
A) 4x^2 - 9y^2
B
B) 4x^2 - 12xy + 9y^2
C
C) 12xy - 9y^2
D
D) 4x^2 + 12xy + 9y^2
E
E) 4x^2 - 9y^2 - 12xy

Explanation

4x^2 - 12xy + 9y^2 is correct because the binomial theorem states that (a - b)^2 = a^2 - 2ab + b^2, so (2x - 3y)^2 = (2x)^2 - 2*(2x)*(3y) + (3y)^2 = 4x^2 - 12xy + 9y^2.

Question 3Unit 1: Algebraic Foundations

What is the constant term of the expansion of (x + 1/x)^4?

A
A) 6
B
B) 2
C
C) 3
D
D) 0
E
E) 4

Explanation

6 is correct because the constant term of (x + 1/x)^4 occurs when two terms contribute x and the other two contribute 1/x, so the constant term is [4!/(2!(4-2)!)] = 6.

Question 4Unit 1: Algebraic Foundations

What is the 3rd term in the expansion of (x + 2)^5?

A
A) 40x^3
B
B) 40x^2
C
C) 20x^4
D
D) 10x^2
E
E) 10x^3

Explanation

40x^3 is correct because the binomial theorem states that the kth term of (a + b)^n is [n!/(k!(n-k)!)]*a^(n-k)*b^k, and for the 3rd term of (x + 2)^5, k = 2, so the term is [5!/(2!(5-2)!)]*x^(5-2)*2^2 = 40x^3.

Question 5Unit 1: Algebraic Foundations

What is the sum of the first 10 terms of the arithmetic sequence with first term 1 and common difference 3?

A
A) 155
B
B) 185
C
C) 165
D
D) 175
E
E) 145

Explanation

165 is correct because the sum of the first n terms of an arithmetic sequence with first term a1 and common difference d is n/2 * (2a1 + (n-1)d), so 10/2 * (2*1 + (10-1)*3) = 165.

Question 6Unit 1: Algebraic Foundations

What is the 10th term of the sequence defined by the recurrence relation an = 2an-1 + 1, with initial term a1 = 1?

A
A) 512
B
B) 1023
C
C) 1024
D
D) 2047
E
E) 2048

Explanation

2047 is correct because applying the recurrence relation 9 times, starting with a1 = 1, yields a10 = 2^10 - 1 = 2047.

Question 7Unit 1: Algebraic Foundations

What is the formula for the nth term of the sequence 1, 4, 9, 16, 25?

A
A) an = n
B
B) an = n²
C
C) an = 2n
D
D) an = n³
E
E) an = 2n + 1

Explanation

n² is correct because the sequence is obtained by squaring the term number, so the nth term is n².

Question 8Unit 1: Algebraic Foundations

What is the sum of the first 5 terms of the sequence 2, 4, 6, 8, 10?

A
A) 60
B
B) 30
C
C) 50
D
D) 20
E
E) 40

Explanation

30 is correct because the sum of an arithmetic series can be found by averaging the first and last terms and multiplying by the number of terms, so (2+10)/2 * 5 = 30.

Question 9Unit 1: Algebraic Foundations

Solve the inequality: x > 3 + 2x

A
A) x > -3
B
B) x < -3
C
C) x < 3
D
D) x > 3
E
E) x < 1

Explanation

x < -3 is correct because subtracting 2x from both sides of x > 3 + 2x gives -x > 3, and then multiplying by -1 and reversing the inequality gives x < -3, applying the rules of solving linear inequalities.

Question 10Unit 1: Algebraic Foundations

What is the value of 2^(-3)?

A
A) -8
B
B) -1/8
C
C) 1/8
D
D) 8
E
E) 1/2

Explanation

1/8 is correct because 2^(-3) = 1/(2^3) = 1/8, applying the rule of negative exponents.

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