Q: Which of the following is the correct domain for the function $$f(x) = \frac{1}{x^2$ - 4}$$?

$$x \in \mathbb{R},\ x \neq -2,\ x \neq 2$$

Q: Which of the following is the correct result of multiplying the matrices $$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and $$\begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix}$$?

$$\begin{bmatrix} 4 & 4 \\ 10 & 8 \end{bmatrix}$$

Question 1

A pharmaceutical company models the concentration of a drug in the bloodstream over time using the exponential function $$C(t) = C_0$ e$$^{-kt}$$, where C_0$ is the initial concentration and k$ is a positive constant. If the initial concentration is 100 mg/L and after 3 hours the concentration drops to 50 mg/L, what is the value of k$ (rounded to two decimal places)?

Accepted Answer

$$k = \frac{\ln(2)}{3} \approx 0.23$$

Question 2

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

Accepted Answer

$$x \in \mathbb{R},\ x 
eq -2,\ x 
eq 2$$

Question 3

A company’s revenue is modeled by the polynomial $$R(x) = 2x^3$ - 5x^2$ + 4x - 8. $$According to the Rational Zero Theorem, which of the following is a possible rational zero?

Accepted Answer

$$x = -2$$

Question 4

A hospital uses the function $$f(x) = \sqrt{x - 9} to $$estimate the recovery time (in days) for a patient based on their test score $$x. $$What is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 5

Which of the following statements about the inverse of a function is correct?

Accepted Answer

A function has an inverse if and only if it is one-to-one.

Question 6

A chemical reaction is modeled by the equation $$x^2 - 6x + 9 = 0$. What are the solutions to this equation?

Accepted Answer

$$x = 3$$

Question 7

A population grows according to the function $$P(t) = 500 \cdot 2^t. $$What is the population after 4 years?

Accepted Answer

$$P(4) = 8000$$

Question 8

Which of the following is the correct solution to the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 9

A business uses the function $$f(x) = \log_{10}(x) to $$model the effectiveness of its advertising campaign, where $$x is $$the number of impressions. If the campaign has 1000 impressions, what is $$f(1000)$$?

Accepted Answer

$$f(1000) = 3$$

Question 10

A medical lab uses the function $$g(x) = \frac{1}{x} to $$model the risk of infection based on the number of safety protocols $$x. $$What happens to the risk as $$x$$ increases?

Accepted Answer

The risk decreases and approaches zero.

Question 11

A company wants to solve the system of equations: $$\begin{cases} 2x + 3y = 8 \ x - y = 2 \end{cases}. $$What is the value of $$y$$?

Accepted Answer

$$y = 1$$

Question 12

Which of the following is the result of simplifying $$\frac{\sqrt{50}}{\sqrt{2}}$$?

Accepted Answer

$$5$$

Question 13

A student is asked to factor the polynomial $$x^3$$ - $$4x^2 + 4x$. Which of the following is the correct factorization?

Accepted Answer

$$x(x - 2)^2$

Question 14

A real estate company models the price of a house using the function $$p(x) = 200,000 + 10,000x$$, where $$x is $$the number of bedrooms. If a house has 4 bedrooms, what is its price?

Accepted Answer

$$p(4) = 240,000$$

Question 15

Which of the following is the solution to the equation $$\frac{2}{x} = 5$$?

Accepted Answer

Question 16

A scientist uses the function $$f(x) = x^2$ - 2x + 1 to $$model the concentration of a solution. What is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 17

Which of the following is the correct result of multiplying the matrices $$\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$\begin{bmatrix} 2 & 0 \ 1 & 2 \end{bmatrix}$$?

Accepted Answer

$$\begin{bmatrix} 4 & 4 \ 10 & 8 \end{bmatrix}$$

Question 18

A sequence is defined by $$a_n = 3n + 2. $$What is the 5th term of the sequence?

Accepted Answer

$$a_5 = 17$

Question 19

Which of the following is the correct equation for a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

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