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 $\sqrt[3]{x^6}$?

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 $\frac{5x^2y}{10xy^2}$?

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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