Q: A hospital uses the function $C(t) = 500e^{0.03t}$ to model the cost of a treatment over time $t$ (in months). What is the cost after 12 months?

$C(12) = 500e^{0.36} \approx 500 \times 1.433 \approx 716.5$

Q: A chemical reaction is modeled by the exponential decay function $N(t) = 1000e^{-0.05t}$, where $N$ is the amount of substance left after $t$ hours. How much remains after 20 hours?

$N(20) = 1000e^{-1} \approx 1000 \times 0.368 \approx 368$

Q: If $A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$, what is $A + B$?

$\begin{pmatrix} 3 & 3 \\ 3 & 5 \end{pmatrix}$

Q: A population grows according to $P(t) = 2000 \cdot 1.05^t$. What is the population after 8 years?

$P(8) = 2000 \cdot 1.05^8 \approx 2000 \cdot 1.477 \approx 2954$

Q: Which of the following is the correct value for the determinant of the matrix $\begin{pmatrix} 3 & 2 \\ 5 & 4 \end{pmatrix}$?

$3 \times 4 - 2 \times 5 = 12 - 10 = 2$

Q: Which of the following is the correct sum for the geometric series $2 + 6 + 18 + 54$?

$S = 2 \left( \frac{3^4 - 1}{3 - 1} \right ) = 2 \left( \frac{81 - 1}{2} \right ) = 2 \times 40 = 80$

Q: Which of the following is the correct property of logarithms for $\log_b (xy)$?

$\log_b (xy) = \log_b x + \log_b y$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $f(x) = 2x^2 - 3x + 5$, what is $f(-2)$?

Accepted Answer

$f(-2) = 19$

Question 3

Which transformation occurs when the function $f(x)$ is changed to $f(x-4)$?

Accepted Answer

The graph shifts 4 units right.

Question 4

A hospital uses the function $C(t) = 500e^{0.03t}$ to model the cost of a treatment over time $t$ (in months). What is the cost after 12 months?

Accepted Answer

$C(12) = 500e^{0.36} \approx 500 	imes 1.433 \approx 716.5$

Question 5

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

Accepted Answer

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

Question 6

Solve the quadratic equation $x^2 - 5x + 6 = 0$.

Accepted Answer

$x = 2$ and $x = 3$

Question 7

A chemical reaction is modeled by the exponential decay function $N(t) = 1000e^{-0.05t}$, where $N$ is the amount of substance left after $t$ hours. How much remains after 20 hours?

Accepted Answer

$N(20) = 1000e^{-1} \approx 1000 	imes 0.368 \approx 368$

Question 8

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

Accepted Answer

$x = 2$, $y = 1$

Question 9

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

Accepted Answer

$(f \circ g)(2) = f(g(2)) = f(3) = 9$

Question 10

Which of the following is the correct logarithmic form of the equation $2^x = 16$?

Accepted Answer

$x = \log_2 16$

Question 11

A business's revenue is modeled by $R(x) = -2x^2 + 40x$, where $x$ is the number of units sold. What number of units maximizes revenue?

Accepted Answer

$x = 10$

Question 12

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

Accepted Answer

$S_5 = 55$

Question 13

If $A = \begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 0 \ 2 & 1 \end{pmatrix}$, what is $A + B$?

Accepted Answer

$\begin{pmatrix} 3 & 3 \ 3 & 5 \end{pmatrix}$

Question 14

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

Accepted Answer

$1 < x < 3$

Question 15

A population grows according to $P(t) = 2000 \cdot 1.05^t$. What is the population after 8 years?

Accepted Answer

$P(8) = 2000 \cdot 1.05^8 \approx 2000 \cdot 1.477 \approx 2954$

Question 16

Which of the following is the correct value for the determinant of the matrix $\begin{pmatrix} 3 & 2 \ 5 & 4 \end{pmatrix}$?

Accepted Answer

$3 	imes 4 - 2 	imes 5 = 12 - 10 = 2$

Question 17

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

Accepted Answer

$S = 2 \left( \frac{3^4 - 1}{3 - 1} ight ) = 2 \left( \frac{81 - 1}{2} ight ) = 2 	imes 40 = 80$

Question 18

Which of the following is the correct property of logarithms for $\log_b (xy)$?

Accepted Answer

$\log_b (xy) = \log_b x + \log_b y$

College Algebra Syllabus and Course Structure Overview

Study Guide - Practice Questions

Study Guide - Flashcards