Question 1

Which of the following is the correct domain of the rational function $$f(x) = \frac{2x+1}{x^2$-9}$$?

Accepted Answer

$$x 
eq 3,\ x 
eq -3$$

Question 2

Simplify the following expression and choose the correct answer: $$\frac{3x^2$}{6x} \cdot \frac{4x}{9}$$

Accepted Answer

$$\frac{2x}{3}$$

Question 3

A chemist is mixing two solutions. The concentration $$C of $$the mixture is given by $$C = \frac{C_1V_1 + C_2V_2}{V_1$ + V_2$}. If$$ $$C_1 = 10$$\%$$, V_1$ = 100 mL$$, $$C_2 = 20$$\%$$, and V_2$ = 200 mL$$, what is the concentration $$C$$?

Accepted Answer

$$15\%$$

Question 4

Which of the following is equivalent to $$\sqrt[3]{x^6$}$$?

Accepted Answer

Question 5

Which of the following is the simplified form of $$\frac{2x^2$ - 8}{4x}$$?

Accepted Answer

$$\frac{x-2}{x}$$

Question 6

If $$f(x) = \frac{1}{x-2}$$ and $$g(x) = \frac{2}{x+3}$$, what is the simplified form of $$f(x) + g(x)$$?

Accepted Answer

$$\frac{x+1}{(x-2)(x+3)}$$

Question 7

Which of the following is the correct solution to the equation $$\sqrt{x+5} = 3$$?

Accepted Answer

$$x = 4$$

Question 8

A biologist is studying the growth of a bacteria population, which doubles every hour. If the initial population is $$P_0$$, which function best models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2^t$$

Question 9

Simplify the expression $$\frac{\sqrt{50}}{\sqrt{2}}.$$

Accepted Answer

$$5$$

Question 10

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$x = 3$$

Question 11

Given the function $$f(x) = \frac{2x}{x^2$-4}$$, which value(s) must be excluded from the domain?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 12

Which of the following is the simplified form of $$\frac{3}{x} + \frac{2}{x}$$?

Accepted Answer

$$\frac{5}{x}$$

Question 13

If $$x = 2 + 3i$$ and $$y = 1 - 2i$$, what is $$x + y$$?

Accepted Answer

$$3 + i$$

Question 14

Which of the following is the correct solution to $$x^2 + 4 = 0$?

Accepted Answer

$$x = 2i$$ and $$x = -2i$$

Question 15

A medical researcher uses the formula $$d = \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$} to $$calculate the distance between two points on an X-ray image. If the points are $$(2,3)$$ and $$(7,11)$$, what is the distance $$d$$?

Accepted Answer

$$\sqrt{89}$$

Question 16

Which of the following is the correct simplified form of $$\sqrt{18} + 2\sqrt{8}$$?

Accepted Answer

$$3\sqrt{2} + 4\sqrt{2} = 7\sqrt{2}$$

Question 17

Solve for $$x$$: $$\frac{1}{x} + \frac{1}{x+2} = 1$$

Accepted Answer

$$x = -1 \pm \sqrt{3}$$

Question 18

Which of the following is the correct solution to the equation $$2x^2 - 8x = 0$?

Accepted Answer

$$x = 0$$ and $$x = 4$$

Question 19

Which of the following is the correct simplified form of $$\frac{5x^2$y}{10xy^2$}$$?

Accepted Answer

$$\frac{x}{2y}$$

Question 20

If $$f(x) = \sqrt{x-1}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 1$$

Study Guide: Rational, Radical, and Quadratic Expressions in College Algebra

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