Question 1

Which of the following is the correct equation of a line passing through the point $(-2, 5)$ with a slope of $3$?

Accepted Answer

$y = 3x - 1$

Question 2

A chemist is mixing two solutions. The first solution contains $x$ grams of salt per liter, and the second contains $y$ grams per liter. If the total amount of salt in $3$ liters of the first and $2$ liters of the second is $20$ grams, which equation models this scenario?

Accepted Answer

$3x + 2y = 20$

Question 3

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

Accepted Answer

$(4, 3)$

Question 4

What is the domain of the function $f(x) = \sqrt{x-2}$?

Accepted Answer

$[2, \infty)$

Question 5

A rectangle has a length that is two inches longer than its width. If the area is $108$ square inches, what is the width of the rectangle?

Accepted Answer

$12$ inches

Question 6

Which of the following is the solution set for $|2x - 3| = 7$?

Accepted Answer

$\{-2, 5\}$

Question 7

Simplify the expression $\dfrac{2x^2y}{4xy^2}$.

Accepted Answer

$\dfrac{x}{2y}$

Question 8

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

Accepted Answer

$x = 11$

Question 9

A vertical line passes through the point $(4, -2)$. What is its equation?

Accepted Answer

$x = 4$

Question 10

Solve for $x$: $2(x - 3) = 4x + 6$

Accepted Answer

$x = -6$

Question 11

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

Accepted Answer

$(x - 3)(x + 3)$

Question 12

If $f(x) = \dfrac{\sqrt{x-1}}{x-3}$, what is the domain of $f$?

Accepted Answer

$[1, 3) \cup (3, \infty)$

Question 13

Which of the following is the solution to the inequality $2x - 5 < 7$?

Accepted Answer

$x < 6$

Question 14

A right triangle has legs of length $x$ and $6$, and hypotenuse $20$. What is the value of $x$?

Accepted Answer

$x = 16$

Question 15

Which of the following is the simplified form of $\dfrac{\sqrt{50}}{\sqrt{2}}$?

Accepted Answer

$5$

Question 16

Solve for $x$: $\dfrac{x+2}{3} = 4$

Accepted Answer

$x = 10$

Question 17

Which of the following is the solution set for $|x + 1| \leq 4$?

Accepted Answer

$[-5, 3]$

Question 18

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

Accepted Answer

$x = -3$

Question 19

If $g(x) = \dfrac{1}{x-2}$, which value is not in the domain of $g$?

Accepted Answer

$x = 2$

Question 20

Which of the following is the solution to $\dfrac{2x}{x-1} = 4$?

College Algebra Final Exam Review: Key Concepts and Practice Problems

Study Guide - Practice Questions

Study Guide - Flashcards