Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function that can be written as $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, where $n$ is a positive integer and $a_n 
eq 0$.

Question 2

A chemical reaction's rate $R$ is modeled by the quadratic equation $R = -2t^2 + 8t + 5$, where $t$ is time in seconds. What is the maximum rate, and at what time does it occur?

Accepted Answer

Maximum rate is $13$ at $t = 2$ seconds.

Question 3

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

Accepted Answer

$x = 2$ and $x = 3$

Question 4

A hospital tracks the number of patients $P$ admitted each day using the linear equation $P = 12d + 30$, where $d$ is the number of days since the start of the month. How many patients are admitted on day 5?

Accepted Answer

$P = 90$

Question 5

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

Accepted Answer

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

Question 6

A company’s profit $P$ in thousands of dollars is modeled by $P(x) = -4x^2 + 40x - 36$, where $x$ is the number of units sold (in thousands). What is the number of units sold that maximizes profit?

Accepted Answer

$x = 5$

Question 7

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

Accepted Answer

$x = 2$, $y = 3$

Question 8

A ball is thrown upward and its height $h$ in meters after $t$ seconds is given by $h = -5t^2 + 20t + 2$. What is the maximum height reached by the ball?

Accepted Answer

$22$ meters

Question 9

Which of the following is the correct solution for $\frac{2x}{x-1} = 4$?

Question 10

A biologist models the population of bacteria by $N(t) = 500e^{0.2t}$, where $t$ is time in hours. What is the population after $5$ hours?

Accepted Answer

$N(5) = 500e^{1} \approx 1359.14$

Question 11

Which of the following is the correct solution to the quadratic equation $3x^2 - 12x + 9 = 0$?

Question 12

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. Which equation models the total cost $C$ for $m$ miles?

Accepted Answer

$C = 25 + 0.20m$

Question 13

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

Accepted Answer

$x - 2$

Question 14

A student invests $\$1000$ in an account that earns $5\%$ annual interest, compounded yearly. What is the amount after $3$ years?

Accepted Answer

$1000(1.05)^3 \approx \$1157.63$

Question 15

Which of the following is the correct solution to $|2x - 3| = 7$?

Accepted Answer

$x = 5$ or $x = -2$

Question 16

A rectangular garden has a length that is $3$ meters longer than its width. If the area is $40$ square meters, what are the dimensions of the garden?

Accepted Answer

Width $= 5$ m, Length $= 8$ m

Question 17

Which of the following is the correct solution to $x^2 + 4x + 4 = 0$?

Accepted Answer

$x = -2$ (double root)

Question 18

A pharmacist needs to mix a $10\%$ saline solution with a $30\%$ saline solution to get $100$ mL of a $25\%$ solution. How much of the $10\%$ solution should be used?

Accepted Answer

$25$ mL

Question 19

Which of the following is the correct solution to $\log_{2}(x) = 5$?

Accepted Answer

$x = 32$

College Algebra Syllabus and Study Guide Overview

Study Guide - Practice Questions

Study Guide - Flashcards