Q: A savings account earns interest compounded annually at a rate of $4\%$. If you deposit $\$1000$, how much will you have after 3 years? (Use $A = P(1 + r)^t$)

$A = 1000(1.04)^3 \approx 1124.86$

Q: Which of the following is the correct matrix product for $\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix} \times \begin{pmatrix}2 & 0\\1 & 2\end{pmatrix}$?

$\begin{pmatrix}4 & 4\\10 & 8\end{pmatrix}$

Q: A car’s value depreciates according to $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value after 4 years?

$V(4) = 20000(0.85)^4 \approx 10441$

Question 1

Which of the following is the correct solution to the equation $2x^2 - 8x + 6 = 0$?

Accepted Answer

$x = 2 \pm \sqrt{2}$

Question 2

A biologist is modeling the population of a bacteria culture with the function $P(t) = 500e^{0.3t}$, where $t$ is in hours. What is the population after 5 hours?

Accepted Answer

$P(5) = 500e^{1.5} \approx 2241$

Question 3

Which of the following is the correct graph for the function $f(x) = -2x + 4$?

Accepted Answer

A line with slope $-2$ and $y$-intercept $4$

Question 4

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = -5x^2 + 40x$, where $x$ is the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $R(5) = 100$ at $x = 5$

Question 5

Solve the system of equations: $\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$

Accepted Answer

$x = 2, y = 1$

Question 6

Which of the following expressions is equivalent to $\log_{2}(8x)$?

Accepted Answer

$3 + \log_{2}x$

Question 7

A medication’s concentration in the bloodstream is modeled by $C(t) = 20e^{-0.2t}$, where $t$ is in hours. After how many hours will the concentration drop to $5$ mg/L?

Accepted Answer

$t = 6.93$

Question 8

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

Accepted Answer

$1 < x < 3$

Question 9

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

Accepted Answer

$x 
eq 3$

Question 10

A savings account earns interest compounded annually at a rate of $4\%$. If you deposit $\$1000$, how much will you have after 3 years? (Use $A = P(1 + r)^t$)

Accepted Answer

$A = 1000(1.04)^3 \approx 1124.86$

Question 11

Which of the following is the correct matrix product for $\begin{pmatrix}1 & 2\3 & 4\end{pmatrix} 	imes \begin{pmatrix}2 & 0\1 & 2\end{pmatrix}$?

Accepted Answer

$\begin{pmatrix}4 & 4\10 & 8\end{pmatrix}$

Question 12

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

Accepted Answer

$x = 3$

Question 13

A quadratic function models the height $h$ (in meters) of a ball thrown upward as $h(t) = -4.9t^2 + 20t + 1.5$. What is the maximum height reached by the ball?

Accepted Answer

$h_{max} = 21.9$ meters

Question 14

Which of the following is the correct inverse of the function $f(x) = 3x - 7$?

Accepted Answer

$f^{-1}(x) = \dfrac{x+7}{3}$

Question 15

A car’s value depreciates according to $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value after 4 years?

Accepted Answer

$V(4) = 20000(0.85)^4 \approx 10441$

Question 16

Which of the following is the correct solution to the equation $\ln(x) = 2$?

Accepted Answer

$x = e^2$

Question 17

A business uses the function $C(x) = 1000 + 5x$ to model its costs, where $x$ is the number of units produced. If the business sells each unit for $15$, what is the minimum number of units it must sell to break even?

Accepted Answer

$x = 100$

Question 18

Which of the following is the correct solution to the equation $|2x - 5| = 7$?

Accepted Answer

$x = 6$ or $x = -1$

Question 19

Which of the following is the sum of the geometric series $2 + 6 + 18 + 54$?

Accepted Answer

$80$

Question 20

A patient’s temperature $T$ (in $^\circ$F) is modeled by $T(t) = 98.6 + 1.5\sin(\frac{\pi}{12}t)$, where $t$ is hours after midnight. What is the maximum temperature during the day?

Accepted Answer

$100.1^\circ$F

College Algebra with Corequisite Support – Course Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards