Question 1

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

Question 2

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

Accepted Answer

$P(5) = 500e^{1.5} \approx 2240$

Question 3

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

Accepted Answer

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

Question 4

A pharmacist needs to mix a 10% saline solution with a 30% saline solution to obtain 100 mL of a 20% solution. How many mL of the 10% solution should be used?

Accepted Answer

$50$ mL

Question 5

Simplify the expression $\dfrac{2x^2 - 8x}{4x}$ for $x 
eq 0$.

Accepted Answer

$\dfrac{x - 4}{2}$

Question 6

Which of the following is the solution set for $|2x - 5| = 7$?

Accepted Answer

$x = 6$ and $x = -1$

Question 7

A company’s profit $P$ (in thousands of dollars) is modeled by $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $P(4) = 8$ thousand dollars, at $x = 4$ thousand units

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

Accepted Answer

$f(-2) = 19$

Question 10

Which of the following is the domain of the function $f(x) = \dfrac{1}{x^2 - 4}$?

Accepted Answer

$x 
eq 2$ and $x 
eq -2$

Question 11

A radioactive substance decays according to $A(t) = 100e^{-0.05t}$, where $A$ is the amount remaining after $t$ years. How much remains after 20 years?

Accepted Answer

$A(20) = 100e^{-1} \approx 36.8$

Question 12

Which of the following is the correct simplification of $\sqrt{50} + \sqrt{18}$?

Question 13

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

Accepted Answer

$h_{max} = 22.4$ meters

Question 14

Which of the following is the correct solution to $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 15

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

Accepted Answer

$\dfrac{x + 2}{x}$

Question 16

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 3 years?

Accepted Answer

$V(3) = 20000(0.85)^3 \approx 12251$

Question 17

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

Accepted Answer

$x = -3$

Question 18

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

Accepted Answer

$(f \circ g)(2) = \dfrac{1}{4}$

Question 19

Which of the following is the correct solution to the inequality $3x - 7 < 2x + 5$?

Accepted Answer

$x < 12$

College Algebra (MATH 1000) Syllabus and Topic Outline Study Guide

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