Question 1

Which of the following is the correct solution to the equation $3x + 10 = 4$?

Accepted Answer

$x = -2$

Question 2

Which of the following expressions is equivalent to $a^2 - b^2$?

Accepted Answer

$(a + b)(a - b)$

Question 3

A chemist is mixing two solutions, one with a concentration of $x$% and another with $y$%. If the final mixture is twice as much as the first solution and three times as much as the second, which equation represents the total amount of the mixture?

Accepted Answer

$2x + 3y = 	ext{total mixture}$

Question 4

Which of the following is the correct factorization of $x^2 - 5x + 6$?

Accepted Answer

$(x - 2)(x - 3)$

Question 5

A population of bacteria doubles every 3 hours. If the initial population is $P_0$, which equation models the population after $t$ hours?

Accepted Answer

$P(t) = P_0 \cdot 2^{t/3}$

Question 6

Which of the following is the solution to the inequality $2x - 5 < 7$?

Accepted Answer

$x < 6$

Question 7

Given the function $f(x) = x^2 - 4x + 3$, what is the $y$-intercept?

Accepted Answer

$(0, 3)$

Question 8

A medical researcher is tracking the decay of a drug in the bloodstream, modeled by $C(t) = C_0 e^{-kt}$. If $C_0 = 100$ mg and $k = 0.2$, what is the concentration after 5 hours?

Accepted Answer

$C(5) = 100 e^{-1}$

Question 9

Which of the following is the correct solution to $\frac{2}{3x - 1} = \frac{7}{3x - 1}$?

Accepted Answer

No solution

Question 10

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

Accepted Answer

$f(g(2)) = 2 	imes 4 + 1 = 9$

Question 11

Which of the following is the correct algebraic expression for: 'Twice $x$ is equal to 3 less than half $x$'?

Accepted Answer

$2x = \frac{1}{2}x - 3$

Question 12

Which of the following is the correct solution to the equation $x^2 = 16$?

Accepted Answer

$x = \pm 4$

Question 13

A company’s revenue $R$ is given by $R = 50x - x^2$, where $x$ is the number of units sold. What number of units maximizes the revenue?

Accepted Answer

$x = 25$

Question 14

Which of the following is the correct solution to the system of equations: $x + y = 5$ and $x - y = 1$?

Accepted Answer

$x = 3, y = 2$

Question 15

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

Accepted Answer

$x 
eq 2$

Question 16

A radioactive substance decays according to $A(t) = A_0 e^{-0.1t}$. If $A_0 = 200$ grams, how much remains after 10 hours?

Accepted Answer

$A(10) = 200 e^{-1}$

Question 17

Which of the following is the correct solution to $\log_2(x) = 3$?

Accepted Answer

$x = 8$

Question 18

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

Accepted Answer

$f(2) + g(2) = 4 + 3 = 7$

Question 19

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

Accepted Answer

$x = -2$

Question 20

A car depreciates in value by 20% each year. If its initial value is $V_0$, what is its value after $t$ years?

Accepted Answer

$V(t) = V_0 \cdot 0.8^t$

MATH 206: Algebra & Functions – Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards