Math Core

This test covers nth roots, rational exponents, simplifying radical expressions, solving radical equations, function composition and inverse functions.

Question 1

Solve $x^4 = 625$ . Give all real solutions.

Separate answers with commas, e.g. 2, -5

Question 2

Which expression is not a real number?

Question 3

Evaluate $64^{-2/3}$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

Solve $x^{3/2} = 125$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

Write $\sqrt[3]{250}$ in simplest form as $a\sqrt[3]{2}$ . What is $a$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

Simplify $4\sqrt{12} + \sqrt{75}$ to the form $a\sqrt{3}$ . What is $a$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Which expression equals $\dfrac{8}{3 + \sqrt{5}}$ with a rational denominator?

Question 8

Solve $\sqrt[3]{4x - 1} + 2 = 5$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

Solve $\sqrt{x + 1} = x - 5$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

Let $f(x) = x^2 - 3$ and $g(x) = 2x + 1$ . Find $f(g(-2))$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

Let $f(x) = x^2 + 1$ and $g(x) = x - 4$ . Find $g(f(x))$ .

Enter an expression, e.g. 3x^2 - 2x + 1

Question 12

Find $f^{-1}(x)$ for $f(x) = \sqrt[3]{2x} - 1$ .

Enter an expression, e.g. 3x^2 - 2x + 1

Question 13

Let $f(x) = \sqrt{x + 3}$ . Find $f^{-1}(5)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 14

The point $(2, -7)$ is on the graph of a one-to-one function $f$ . Which point must be on the graph of $f^{-1}$ ?

Enter a point like (2, -3)