Question 1

Which of the following is the correct simplification of the expression $\sqrt{50} + 2\sqrt{8}$?

Accepted Answer

$7\sqrt{2}$

Question 2

A chemist mixes two solutions, one with a concentration of $x$ percent and another with a concentration of $2x$ percent, to obtain 10 liters of a solution with a concentration of $1.5x$ percent. If the chemist uses $y$ liters of the first solution, which equation models this scenario?

Accepted Answer

$x y + 2x (10 - y) = 1.5x (10)$

Question 3

Which of the following is the solution set for the inequality $2x - 5 > 9$?

Accepted Answer

$x > 7$

Question 4

A circle has the equation $x^2 + y^2 - 6x + 8y = 0$. What are the coordinates of its center?

Accepted Answer

$(3, -4)$

Question 5

Which of the following is the correct factorization of the polynomial $x^2 - 5x + 6$?

Accepted Answer

$(x - 2)(x - 3)$

Question 6

A patient’s medication dosage is modeled by the equation $D = \frac{mg}{kg} 	imes w$, where $w$ is the patient’s weight in kilograms. If the prescribed dosage is $5 \frac{mg}{kg}$ and the patient weighs 70 kg, what is the total dosage?

Accepted Answer

$350\ mg$

Question 7

Solve the system of equations: $\begin{cases} 2x + 3y = 12 \ x - y = 1 \end{cases}$

Accepted Answer

$(3, 2)$

Question 8

Which of the following is the solution to the quadratic equation $x^2 - 4x - 5 = 0$?

Accepted Answer

$x = 5$ or $x = -1$

Question 9

A company’s profit $P$ (in dollars) from selling $x$ units of a product is given by $P = -2x^2 + 40x - 100$. What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $300$ at $x = 10$ units

Question 10

Which of the following is the correct simplification of the expression $\frac{2x^2 - 8}{4x}$ for $x 
eq 0$?

Accepted Answer

$\frac{x - 2}{x}$

Question 11

Which of the following is the correct solution to the equation $|3x - 7| = 5$?

Accepted Answer

$x = 4$ or $x = \frac{2}{3}$

Question 12

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 13

Which of the following is the correct solution set for the inequality $x^2 - 4x + 3 < 0$?

Accepted Answer

$1 < x < 3$

Question 14

A quadratic equation models the height $h$ (in meters) of a ball thrown upward from the ground as $h = -4.9t^2 + 19.6t$, where $t$ is time in seconds. After how many seconds does the ball reach its maximum height?

Accepted Answer

$2$ seconds

Question 15

Which of the following is the correct result of performing the operation $(3 + 2i) + (5 - 7i)$, where $i$ is the imaginary unit?

Accepted Answer

$8 - 5i$

Question 16

A rectangular garden has a length that is 3 meters more than twice its width. If the area of the garden is $99\ m^2$, what is the width of the garden?

Accepted Answer

$6\ m$

Question 17

Which of the following is the correct simplification of the expression $\frac{5}{x} + \frac{2}{x+1}$?

Accepted Answer

$\frac{5(x+1) + 2x}{x(x+1)}$

College Algebra Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards