Question 1

Which of the following best describes the zero-factor property used to solve quadratic equations?

Accepted Answer

If $ab = 0$, then $a = 0$ or $b = 0$.

Question 2

Simplify the expression: $2x^3y^2 \cdot 3x^2y^4$.

Accepted Answer

$6x^5y^6$

Question 3

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

Accepted Answer

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

Question 4

A rectangular garden has a length that is 3 meters more than twice its width. If the width is $w$ meters, which expression represents the area of the garden?

Accepted Answer

$2w^2 + 3w$

Question 5

Simplify the rational expression: $\frac{x^2 - 4}{x + 2}$.

Accepted Answer

$x - 2$

Question 6

Which of the following is the correct solution to the equation $2x^2 - 8 = 0$?

Accepted Answer

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

Question 7

Evaluate the function $f(x) = 3x^2 - 2x + 5$ for $x = -1$.

Accepted Answer

$10$

Question 8

Which of the following is the domain of the function $f(x) = \frac{1}{x-3}$?

Accepted Answer

$x 
eq 3$

Question 9

Simplify the radical expression: $\sqrt{50}$.

Accepted Answer

$5\sqrt{2}$

Question 10

A chemist mixes a solution with a concentration of $x$ grams per liter. If the total amount of solution is $3x + 2$ liters, which expression represents the total grams of solute?

Accepted Answer

$x(3x + 2)$

Question 11

Which of the following is the correct simplification of $\frac{2x^2y}{4xy^2}$?

Accepted Answer

$\frac{x}{2y}$

Question 12

Solve for $x$: $x^2 + 6x + 9 = 0$.

Accepted Answer

$x = -3$

Question 13

Which of the following is a correct application of the laws of exponents: $(x^3)^2$?

Accepted Answer

$x^6$

Question 14

A student is analyzing the function $f(x) = x^2 - 4x + 3$. What are the zeros of the function?

Accepted Answer

$x = 1$ and $x = 3$

Question 15

Which of the following is the correct simplification of $\sqrt{18x^2}$?

Accepted Answer

$3x\sqrt{2}$

Question 16

A medical researcher is analyzing the growth of bacteria, which doubles every hour. If the initial amount is $P_0$, which expression represents the amount after $t$ hours?

Accepted Answer

$P_0 \cdot 2^t$

Question 17

Which of the following is the correct solution to the equation $x^2 - 5x + 6 = 0$?

Accepted Answer

$x = 2$ or $x = 3$

Question 18

Simplify the expression: $\frac{3}{x} + \frac{2}{x}$.

Accepted Answer

$\frac{5}{x}$

Question 19

Which of the following is the correct simplification of $\frac{x^2 - 16}{x - 4}$?

Accepted Answer

$x + 4$

Question 20

A company’s profit $P$ (in dollars) from selling $x$ units is given by $P(x) = -2x^2 + 40x - 100$. What is the maximum profit?

Accepted Answer

$300$

Intermediate College Algebra Syllabus and Course Overview

Study Guide - Practice Questions

Study Guide - Flashcards