Q: If $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix}$$, what is $$A + B$$?

$$\begin{bmatrix} 3 & 2 \\ 4 & 6 \end{bmatrix}$$

Question 1

Which of the following is the correct definition of the domain of a function $$f(x)$$?

Accepted Answer

The set of all $$x-$$values for which $$f(x) is $$defined.

Question 2

A chemical reaction's rate $$R is $$modeled by the exponential function $$R(t) = 100e$$^{-0.05t}$$, where t$ is time in minutes. What is the rate after 20 minutes, rounded to the nearest whole number?

Accepted Answer

$$R(20) = 100e$$^{-1}$$ \approx 37$$

Question 3

Which of the following equations represents a circle in the $$xy-$$plane?

Accepted Answer

$$x^2$$ + $$y^2 + 4x - 6y + 9 = 0$

Question 4

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 5

Given the function $$f(x) = \sqrt{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 2$$

Question 6

A company’s profit $$P in $$thousands of dollars is given 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 $$P(3) = 2$$ thousand dollars, at $$x = 3$$ thousand units.

Question 7

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 8

Solve the equation $$\log_2$(x-1) = 3$$ for $$x.$$

Accepted Answer

Question 9

Which of the following is the sum of the first 10 terms of the arithmetic sequence $$a_n = 7 + 3(n-1)$$?

Accepted Answer

$$S_{10} = 175$$

Question 10

A patient’s medication level in the bloodstream decreases by 20% every hour. If the initial level is 50 mg, what is the amount after 3 hours?

Accepted Answer

$$50 	imes 0.8^3$ = 25.6 mg$$

Question 11

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 12

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

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 13

A quadratic function models the height $$h (in $$meters) of a ball thrown upward from a building: $$h(t) = -4.9t^2$ + 19.6t + 50. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 14

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 15

Which of the following is the correct solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 16

A parabola opens upward and has its vertex at $$(2, -3). $$Which of the following could be its equation?

Accepted Answer

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

Question 17

Which of the following is the sum of the infinite geometric series $$\sum_{n=0}^{\infty} 5 \left(\frac{1}{3}\right)^n$$?

Accepted Answer

$$\frac{15}{2}$$

Question 18

A rational function has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 1. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \frac{x-1}{x-2}$$

Question 19

If $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \ 1 & 2 \end{bmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{bmatrix} 3 & 2 \ 4 & 6 \end{bmatrix}$$

Question 20

A lottery has 5 winning tickets out of 1000. What is the probability of buying a single ticket and winning?

Accepted Answer

$$\frac{1}{200}$$

College Algebra (MATH-1314) Syllabus and Course Overview

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