Question 1

Solve the equation $2x^2 = -24x - 64$ by the zero-factor property. What is the solution set?

Accepted Answer

$\{-4,\ 8\}$

Question 2

Simplify $\frac{1}{i^{27}}$. What is the result?

Accepted Answer

$i$

Question 3

Solve the formula $A = bh$ for $h$.

Accepted Answer

$h = \frac{A}{b}$

Question 4

Simplify $i^{81}$. What is the result?

Accepted Answer

$i$

Question 5

Decide whether the equations $3x - 2 = 8$ and $-3x + 8 = -2$ are equivalent.

Accepted Answer

Equivalent

Question 6

Solve the formula $S = 2\pi rh + 2\pi r^2$ for $h$.

Accepted Answer

$h = \frac{S - 2\pi r^2}{2\pi r}$

Question 7

Write $-\sqrt{-4}$ as the product of a real number and $i$.

Accepted Answer

$-2i$

Question 8

Find the product $(-3 + 2i)^3$ and write the answer in standard form.

Accepted Answer

$9 + 46i$

Question 9

Given roots $-2$ and $7$, which quadratic equation $x^2 + bx + c = 0$ has these solutions?

Accepted Answer

$x^2 + 5x - 14 = 0$

Question 10

Use the quadratic formula to solve $y^2 - 14y = -32$. What is the solution set?

Accepted Answer

$\{7 + \sqrt{17},\ 7 - \sqrt{17}\}$

Question 11

Find the sum $(4 - 6i) + (6 + 4i)$ and write the answer in standard form.

Accepted Answer

$10 - 2i$

Question 12

Solve the equation $x^2 + 4x + 40 = 0$ by completing the square.

Accepted Answer

$\{-2 \pm 6i\}$

Question 13

Solve the equation $x^2 + 14x + 40 = 0$ by the zero-factor property.

Accepted Answer

$\{-10, -4\}$

Question 14

Divide $\frac{2 + 4i}{1 + i}$ and write the answer in the form $a + bi$.

Accepted Answer

$3 + i$

Question 15

Decide whether the statement is true or false: $-14$ is a solution of $2x = -28$.

Accepted Answer

True

Question 16

Decide whether the equation $12(x + 3) = 2(6x + 3) + 30$ is an identity, a conditional equation, or a contradiction. Give the solution set.

Accepted Answer

Identity: (all real numbers)

Question 17

Decide whether the equation $5(2x - 31) = 10x - 155$ is an identity, a conditional equation, or a contradiction. Give the solution set.

Accepted Answer

Conditional: $\{0\}$

Question 18

Find the sum $(2 - 5i) + (5 + 9i)$ and write the answer in standard form.

Accepted Answer

$7 + 4i$

Question 19

Solve the equation $-6x + 1.2 = -56.4 - 1.2x$. What is the solution?

Accepted Answer

$\{12\}$

Question 20

Find the product $(8 - 3i)(7 - 5i)$ and write the answer in standard form.

Accepted Answer

$41 - 61i$

College Algebra Study Guide: Quadratics, Complex Numbers, and Equations

Study Guide - Practice Questions