10 free sample questions with answers and explanations. See how you'd score on the real CLEP exam.
Which of the following is equivalent to (2^3)^2?
Explanation
To find the equivalent expression, we apply the power of a power rule, which states that (a^m)^n = a^(m*n). In this case, (2^3)^2 = 2^(3*2) = 2^6. This rule is a fundamental property of exponents, allowing us to simplify expressions with multiple layers of exponents. The correct answer, 2^6, demonstrates the application of this rule. The distractors are incorrect because they do not apply the power of a power rule correctly: option "2^6" incorrectly adds the exponents, option "2^8" raises 2 to the power of the product of 3 and 3, option "2^9" raises 2 to the power of the product of 3 and 3 plus 1, and option "2^12" raises 2 to the power of the product of 3 and 4.
What is (2x - 3y)^2?
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.
What is the constant term of the expansion of (x + 1/x)^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.
What is the 3rd term in the expansion of (x + 2)^5?
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.
What is the formula for the nth term of the sequence 1, 4, 9, 16, 25?
Explanation
n² is correct because the sequence is obtained by squaring the term number, so the nth term is n².
What is the sum of the first 5 terms of the sequence 2, 4, 6, 8, 10?
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.
Solve the inequality: x > 3 + 2x
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.
Solve for x: x/4 = 9
Explanation
36 is correct because multiplying both sides of x/4 = 9 by 4 gives x = 36, applying the rule of solving linear equations.
What is the inverse of the function f(x) = e^x?
Explanation
ln(x) is correct because the inverse of the exponential function e^x is the natural logarithm function ln(x), since e^(ln(x)) = x and ln(e^x) = x.
If f(x) = 2x + 1 and g(x) = (x-1)/2, are f and g inverse functions?
Explanation
Inverse functions satisfy the condition that their composition equals the input, meaning f(g(x)) = x and g(f(x)) = x. Since f(g(x)) and g(f(x)) both simplify to x, f and g are indeed inverse functions.