Question 1

Which of the following is the correct solution to the equation $2x - 5 = 9$?

Accepted Answer

$x = 7$

Question 2

A chemist is diluting a solution and models the concentration $C$ (in mg/L) after $t$ hours by $C = 100e^{-0.3t}$. What is the concentration after 5 hours? (Round to the nearest mg/L)

Accepted Answer

$C \approx 22$

Question 3

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x - 4)(x - 5)$

Question 4

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 200 	imes 3^{t/4}$

Question 5

Which of the following is the solution set for the inequality $2x + 3 < 7$?

Accepted Answer

$x < 2$

Question 6

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

Accepted Answer

$f(-2) = 15$

Question 7

A ball is thrown upward from the ground with an initial velocity of 32 ft/s. Its height $h$ (in feet) after $t$ seconds is given by $h = -16t^2 + 32t$. When does the ball hit the ground?

Accepted Answer

$t = 2$ seconds

Question 8

Which of the following is equivalent to $\log_{2} 32$?

Accepted Answer

$5$

Question 9

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

Accepted Answer

$9$

Question 10

A car's value depreciates exponentially according to $V = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value after 3 years? (Round to the nearest dollar)

Accepted Answer

$V \approx 12253$

Question 11

Which of the following is the solution to the quadratic equation $x^2 + 6x + 9 = 0$?

Accepted Answer

$x = -3$

Question 12

Simplify the expression $\dfrac{2x^2y}{4xy^2}$ for $x 
eq 0, y 
eq 0$.

Accepted Answer

$\dfrac{x}{2y}$

Question 13

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

Accepted Answer

$x = 3$ or $x = -\dfrac{5}{3}$

Question 14

A radioactive substance decays according to $A = A_0 e^{-0.05t}$, where $A_0$ is the initial amount and $t$ is in years. What is the half-life of the substance? (Round to the nearest year)

Accepted Answer

$t \approx 14$

Question 15

Which of the following is the domain of the function $f(x) = \dfrac{1}{x-4}$?

Accepted Answer

$x 
eq 4$

Question 16

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

Accepted Answer

$19$

Question 17

Which of the following is the solution to the equation $\dfrac{3}{x} = 6$?

Accepted Answer

$x = 0.5$

Question 18

A medication is administered so that its concentration in the bloodstream decreases by 20% every hour. If the initial concentration is 50 mg/L, what is the concentration after 3 hours?

Accepted Answer

$25.6$ mg/L

Question 19

Which of the following is the correct solution to the system of equations: $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 3, y = 2$

Question 20

Which of the following is the correct simplified form of $\sqrt{50}$?

Accepted Answer

$5\sqrt{2}$

College Algebra Study Guide: Key Topics and Concepts

Study Guide - Practice Questions

Study Guide - Flashcards