Question 1

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

Accepted Answer

$x \leq 7$

Question 2

A company’s profit $P$ (in thousands of dollars) is modeled by the quadratic function $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $18$ thousand dollars at $x = 2$ thousand units.

Question 3

Which of the following is the solution to the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 1$

Question 4

A ball is thrown upward from the top of a 50-meter building with an initial velocity of $20$ m/s. Its height $h$ (in meters) after $t$ seconds is given by $h(t) = -5t^2 + 20t + 50$. After how many seconds does the ball hit the ground?

Question 5

Which of the following is the correct factorization of the polynomial $x^3 - 4x^2 - 7x + 10$?

Accepted Answer

$(x - 5)(x + 1)(x - 2)$

Question 6

If $f(x) = 3x^2 - 2x + 1$, what is $f(-2)$?

Accepted Answer

$f(-2) = 17$

Question 7

Which of the following is the solution to the equation $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 8

A radioactive substance decays according to the formula $A(t) = A_0 e^{-0.03t}$, where $A_0$ is the initial amount and $t$ is time in years. If the initial amount is $100$ grams, how much remains after $10$ years? (Round to the nearest gram.)

Accepted Answer

$74$ grams

Question 9

Which of the following is the domain of the function $f(x) = \dfrac{1}{x^2 - 9}$?

Accepted Answer

$x 
eq 3$ and $x 
eq -3$

Question 10

Solve for $x$: $\sqrt{x + 5} = 4$.

Accepted Answer

$x = 11$

Question 11

A car rental company charges a flat fee of $\$30$ plus $\$0.20$ per mile driven. If your total bill was $\$50$, how many miles did you drive?

Accepted Answer

$100$ miles

Question 12

Which of the following is the solution to the equation $2^{x+1} = 16$?

Accepted Answer

$x = 3$

Question 13

If $f(x) = x^2 - 4x + 3$ and $g(x) = 2x - 1$, what is $(f \circ g)(2)$?

Accepted Answer

$f(g(2)) = 0$

Question 14

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

Accepted Answer

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

Question 15

A rectangular garden has a length that is 3 meters more than twice its width. If the area is $99$ square meters, what are the dimensions of the garden?

Accepted Answer

Width $= 6$ m, Length $= 15$ m

Question 16

Which of the following is the sum of the first $5$ terms of the arithmetic sequence with first term $a_1 = 3$ and common difference $d = 4$?

Accepted Answer

$55$

Question 17

If $x^2 + 6x + 8 = 0$, what are the solutions for $x$?

Accepted Answer

$x = -2$ and $x = -4$

Question 18

Which of the following is the inverse function of $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \dfrac{x - 5}{2}$

Question 19

A bank offers an annual interest rate of $6\%$ compounded quarterly. If you invest $\$1000$, how much will you have after $2$ years? (Round to the nearest dollar.)

Accepted Answer

$1127$

Question 20

Which of the following is the solution to the equation $\dfrac{2}{x} + 3 = 5$?

Accepted Answer

$x = 1$

College Algebra Syllabus and Course Overview

Study Guide - Practice Questions

Study Guide - Flashcards