Q: A quadratic equation $ax^2 + bx + c = 0$ has discriminant $D = b^2 - 4ac$. If $D < 0$, what can be said about the solutions?

There are two complex (non-real) solutions.

Q: Which of the following is the correct simplification of $\sqrt{50} - \sqrt{18}$?

$5\sqrt{2} - 3\sqrt{2} = 2\sqrt{2}$

Q: Which of the following is the correct simplification of $\frac{x^2 - 9}{x^2 - 6x + 9}$?

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

Question 1

Which of the following is the correct interval notation for the solution set of the inequality $x^2 - 5x + 6 < 0$?

Accepted Answer

$(2, 3)$

Question 2

A company’s profit $P$ (in thousands of dollars) is modeled by the function $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Question 3

Given the function $f(x) = \frac{2x+1}{x-3}$, what is the domain of $f$?

Accepted Answer

$x 
eq 3$

Question 4

Which of the following is the correct solution to the equation $|2x - 5| = 9$?

Accepted Answer

$x = 7$ or $x = -2$

Question 5

A quadratic equation $ax^2 + bx + c = 0$ has discriminant $D = b^2 - 4ac$. If $D < 0$, what can be said about the solutions?

Accepted Answer

There are two complex (non-real) solutions.

Question 6

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x - 4)(x - 5)$

Question 7

If $f(x) = 3x - 2$ and $g(x) = x^2$, what is $(f \circ g)(x)$?

Accepted Answer

$3x^2 - 2$

Question 8

A line passes through the points $(2, 5)$ and $(6, 13)$. What is the equation of the line in slope-intercept form?

Accepted Answer

$y = 2x + 1$

Question 9

Which of the following is the correct simplification of $\sqrt{50} - \sqrt{18}$?

Accepted Answer

$5\sqrt{2} - 3\sqrt{2} = 2\sqrt{2}$

Question 10

A rational function $f(x) = \frac{x^2 - 4}{x^2 - 1}$ has which vertical asymptotes?

Accepted Answer

$x = 1$ and $x = -1$

Question 11

Which of the following is the correct solution to the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 5$

Question 12

Which of the following is the correct domain for the function $f(x) = \sqrt{x - 4}$?

Accepted Answer

$x \geq 4$

Question 13

If $f(x) = x^2$ and $g(x) = x + 1$, what is $f(g(x))$?

Accepted Answer

$(x + 1)^2$

Question 14

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

Accepted Answer

$x = -2$

Question 15

A rectangular garden has a length that is 3 meters longer than its width. If the area is $40$ square meters, what are the dimensions of the garden?

Accepted Answer

Width: $5$ m, Length: $8$ m

Question 16

Which of the following is the correct simplification of $\frac{x^2 - 9}{x^2 - 6x + 9}$?

Accepted Answer

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

Question 17

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

Accepted Answer

$\frac{1}{5}$

Question 18

Which of the following is the correct solution to the inequality $2x - 3 > 7$?

Accepted Answer

$x > 5$

Question 19

Which of the following is the correct solution to the equation $\sqrt{x + 5} = 4$?

Accepted Answer

$x = 11$

College Algebra Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards