Question 1

Which of the following is the correct definition of the imaginary unit $i$?

Accepted Answer

$i$ is defined as $i = \sqrt{-1}$

Question 2

What is the result of multiplying $(3 + 2i)$ and $(1 - 4i)$?

Accepted Answer

$3 + 2i - 12i - 8i^2 = 3 - 10i - 8(-1) = 3 - 10i + 8 = 11 - 10i$

Question 3

Which of the following is the standard form of the complex number $5 - 3i + 2i$?

Accepted Answer

$5 - i$

Question 4

Solve the quadratic equation $x^2 - 4x + 4 = 0$ using factoring.

Accepted Answer

$x = 2$

Question 5

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

Accepted Answer

$x = 3i$

Question 6

Given the function $f(x) = 2x^2 - 3x + 1$, what is the value of $f(-2)$?

Accepted Answer

$f(-2) = 2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15$

Question 7

Which of the following is the domain of the function $f(x) = \frac{1}{x-5}$?

Accepted Answer

All real numbers except $x = 5$

Question 8

If the graph of a function passes the Vertical Line Test, what does this indicate?

Accepted Answer

The graph represents a function

Question 9

Which of the following is the solution to the equation $|2x - 3| = 5$?

Accepted Answer

$x = 4$ or $x = -1$

Question 10

A rectangle has a long side that is 10 units longer than the short side. If the area is $45$ square units, what are the dimensions of the rectangle?

Accepted Answer

Short side: $5$, Long side: $15$

Question 11

Which of the following is the correct solution to the equation $(x^2 - 2x) - [(1 - 2x) + 2] = 0$?

Accepted Answer

$x = 2$

Question 12

Which of the following is the correct interval notation for the solution to $x^2 < 9$?

Accepted Answer

$(-3, 3)$

Question 13

Which of the following is the correct solution to the inequality $2x + 5 > 9$?

Accepted Answer

$x > 2$

Question 14

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

Accepted Answer

$x = -2$

Question 15

Which of the following is the correct solution to the equation $x^2 = 16$?

Accepted Answer

$x = 4$ or $x = -4$

Question 16

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

Accepted Answer

$x = 0$ or $x = -2$

Question 17

Which of the following is the correct solution to the equation $x^2 - 5x = 0$?

Accepted Answer

$x = 0$ or $x = 5$

Question 18

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

Accepted Answer

$x = -3$

Question 19

Which of the following is the correct solution to the equation $x^2 - 1 = 0$?

Accepted Answer

$x = 1$ or $x = -1$

College Algebra Unit Test 1 Review: Key Concepts and Study Guide

Study Guide - Practice Questions