Question 1

A pharmaceutical company is testing a new drug and models the number of bacteria in a culture by the function $N(t) = 500 \cdot 2^{0.3t}$, where $t$ is the number of hours after the drug is applied. After how many hours will the bacteria count reach 4000?

Accepted Answer

$t = 10.0$

Question 2

Solve for $x$: $3(x - 2) + 4 = 2x + 7$. What is the value of $x$?

Accepted Answer

$x = 3$

Question 3

A rectangular garden has a length that is 4 meters more than twice its width. If the perimeter is 44 meters, what is the width of the garden?

Accepted Answer

$w = 8$

Question 4

Which of the following is the solution set for the inequality $2x - 5 \leq 9$?

Accepted Answer

$x \leq 7$

Question 5

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 $h(t) = -16t^2 + 32t$. After how many seconds does the ball hit the ground?

Accepted Answer

$t = 2$

Question 6

Which of the following is equivalent to $(3 + 2i)(1 - 4i)$?

Accepted Answer

$11 - 10i$

Question 7

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

Accepted Answer

$f(-2) = 15$

Question 8

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

Accepted Answer

$x = 3$

Question 9

A circle has the equation $x^2 + y^2 - 6x + 8y = 0$. What are the center and radius of the circle?

Accepted Answer

Center $(3, -4)$, radius $5$

Question 10

Solve for $x$: $\sqrt{x + 5} = 4$

Accepted Answer

$x = 11$

Question 11

Which of the following is the solution to the quadratic equation $2x^2 - 4x - 6 = 0$?

Accepted Answer

$x = 3, x = -1$

Question 12

A right triangle has legs of length $6$ and $8$. What is the length of the hypotenuse?

Accepted Answer

$10$

Question 13

Which of the following is the sum of $\dfrac{3}{4} + \dfrac{5}{6}$?

Accepted Answer

$\dfrac{19}{12}$

Question 14

If $f(x) = x^2 - 4x + 7$, what is the minimum value of $f(x)$?

Accepted Answer

$3$

Question 15

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. If a customer paid $\$45$, how many miles did they drive?

Accepted Answer

$100$

Question 16

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

Accepted Answer

$(2, 3)$

Question 17

Which of the following is the simplified form of $\dfrac{2x^2y}{4xy^2}$?

Accepted Answer

$\dfrac{x}{2y}$

Question 18

A population of bacteria triples every 4 hours. If there are initially 200 bacteria, how many will there be after 12 hours?

Accepted Answer

$5400$

Question 19

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

Accepted Answer

$x = 7, x = -2$

Question 20

A triangle has sides of length $5$, $12$, and $13$. Is this triangle a right triangle?

Accepted Answer

Yes, because $5^2 + 12^2 = 13^2$

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