Q: Which of the following correctly applies the order of operations to evaluate the expression $3 + 6 \times 2^2 - (4 + 2)$?

$3 + 6 \times 2^2 - (4 + 2) = 3 + 6 \times 4 - 6 = 3 + 24 - 6 = 21$

Q: A medical researcher models the decay of a drug in the bloodstream with $C(t) = 100e^{-0.2t}$, where $C$ is the concentration in mg/L and $t$ is time in hours. What is the concentration after 5 hours? (Round to the nearest mg/L.)

$C(5) = 100e^{-1} \approx 37$ mg/L

Q: A company wants to maximize profit $P = 3x + 2y$ subject to the constraints $x + y \leq 10$, $x \geq 0$, $y \geq 0$, and $x \leq 6$. What is the maximum profit and at which point does it occur?

Maximum profit is $P = 26$ at $(x, y) = (6, 4)$

Question 1

Which of the following correctly applies the order of operations to evaluate the expression $3 + 6 	imes 2^2 - (4 + 2)$?

Accepted Answer

$3 + 6 	imes 2^2 - (4 + 2) = 3 + 6 	imes 4 - 6 = 3 + 24 - 6 = 21$

Question 2

A chemist needs to convert $3.5 	imes 10^3$ milligrams to grams using scientific notation. Which of the following is correct?

Accepted Answer

$3.5 	imes 10^3$ mg $= 3.5$ g

Question 3

Which of the following is the correct simplification of $\sqrt[3]{x^6 y^3}$, assuming $x, y \geq 0$?

Accepted Answer

$x^2 y$

Question 4

A biologist is studying the growth of a bacteria population modeled by the function $P(t) = 500 \cdot 2^t$, where $t$ is in hours. What is the population after 3 hours?

Accepted Answer

$P(3) = 500 \cdot 2^3 = 500 \cdot 8 = 4000$

Question 5

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

Accepted Answer

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

Question 6

Solve for $x$ in the equation $\dfrac{2x}{x-1} = 4$.

Accepted Answer

$x = 2$

Question 7

A solution to the quadratic equation $x^2 + 6x + 5 = 0$ is:

Accepted Answer

$x = -1$ and $x = -5$

Question 8

Which of the following is the correct simplification of the complex number $(3 + 4i) - (1 - 2i)$?

Accepted Answer

$2 + 6i$

Question 9

A line passes through the points $(2, 3)$ and $(6, 11)$. What is the slope of the line?

Accepted Answer

$2$

Question 10

Which of the following equations represents a line perpendicular to $y = -\dfrac{1}{3}x + 2$?

Accepted Answer

$y = 3x - 5$

Question 11

If $f(x) = 2x + 5$ and $g(x) = x^2$, what is $(f \circ g)(3)$?

Accepted Answer

$f(g(3)) = 2 \cdot 9 + 5 = 23$

Question 12

Which of the following is the inverse function of $f(x) = 3x - 7$?

Accepted Answer

$f^{-1}(x) = \dfrac{x + 7}{3}$

Question 13

Divide $2x^3 - 3x^2 + 4x - 5$ by $x - 2$ using polynomial long division. What is the remainder?

Accepted Answer

$-1$

Question 14

Solve the inequality $x^2 - 4x - 5 < 0$.

Accepted Answer

$-1 < x < 5$

Question 15

A medical researcher models the decay of a drug in the bloodstream with $C(t) = 100e^{-0.2t}$, where $C$ is the concentration in mg/L and $t$ is time in hours. What is the concentration after 5 hours? (Round to the nearest mg/L.)

Accepted Answer

$C(5) = 100e^{-1} \approx 37$ mg/L

Question 16

Solve the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$

Accepted Answer

$x = 2, y = 1$

Question 17

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

Accepted Answer

$x = 32$

Question 18

A company wants to maximize profit $P = 3x + 2y$ subject to the constraints $x + y \leq 10$, $x \geq 0$, $y \geq 0$, and $x \leq 6$. What is the maximum profit and at which point does it occur?

Accepted Answer

Maximum profit is $P = 26$ at $(x, y) = (6, 4)$

Question 19

Which of the following is the correct value of $\sin(30^\circ)$?

Accepted Answer

$\dfrac{1}{2}$

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