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

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

Question 1

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

Accepted Answer

$$f(-2) = 19$$

Question 2

Which of the following is the correct graph for the piecewise function $$f(x) = \begin{cases} x+2 & 	ext{if } x \u003c 0 \ 2x-1 & 	ext{if } x \geq 0 \end{cases}$$?

Accepted Answer

A line with slope 1 for $$x\u003c0$$ and a line with slope 2 for $$x\geq0$$, with a jump at $$x=0$$

Question 3

What is the result of translating the quadratic function $$f(x) = x^2$ 3 units right and 2 units up?

Accepted Answer

$$f(x) = (x-3)^2$ + 2$$

Question 4

If $$f(x) = \sqrt{x}$$ and $$g(x) = x+1$$, what is $$(f \circ g)(x)$$ and its domain?

Accepted Answer

$$(f \circ g)(x) = \sqrt{x+1}$$, domain: $$x \geq -1$$

Question 5

Which pair of functions are inverses of each other?

Accepted Answer

$$f(x) = 2x+3$$, $$g(x) = \frac{x-3}{2}$$

Question 6

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

Accepted Answer

Remainder is $$-3$$

Question 7

Identify the vertical asymptote of $$f(x) = \frac{2x+1}{x^2$-4}.$$

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 8

Solve the polynomial inequality $$x^2 - 5x + 6$$ \u003c 0$$.

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 9

Solve the rational inequality $$\frac{x-1}{x+2} \u003e 0.$$

Accepted Answer

$$x \u003e 1 or$$ $$x \u003c -2$$

Question 10

Solve the exponential equation $$2^{x+1} = 16$ using logarithms.

Accepted Answer

$$x = 3$$

Question 11

Solve the exponential equation $$3^x = 81$$ without using logarithms.

Accepted Answer

$$x = 4$$

Question 12

Solve the logarithmic equation $$\log_{2}(x-1) = 3.$$

Accepted Answer

Question 13

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

Accepted Answer

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

Question 14

Find the determinant of $$\begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}.$$

Accepted Answer

Question 15

Solve the matrix equation $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 5 \ 11 \end{pmatrix}.$$

Accepted Answer

$$x = 1, y = 2$$

Question 16

Solve the system using Cramer's Rule: $$\begin{cases} 2x + 3y = 8 \ x - y = 1 \end{cases}.$$

Accepted Answer

$$x = 2, y = 1$$

Question 17

Evaluate the third-order determinant $$\begin{vmatrix} 1 & 2 & 3 \ 0 & 1 & 4 \ 5 & 6 & 0 \end{vmatrix}$$ using expansion by minors.

Accepted Answer

$$-24$$

Question 18

Write the partial fraction decomposition of $$\frac{5x+3}{(x+1)(x-2)}.$$

Accepted Answer

$$\frac{2}{x+1} + \frac{3}{x-2}$$

Question 19

Solve the nonlinear system by addition: $$\begin{cases} x^2$ + y = 7 \ x + y = 5 \end{cases}.$$

Accepted Answer

$$x = 2, y = 3$$ and $$x = -3, y = 8$$

Question 20

Which of the following graphs represents the solution to the system of inequalities $$y \u003e x + 1$$ and $$y \u003c 2x - 3$$?

Accepted Answer

The region above $$y = x + 1$$ and below $$y = 2x - 3$$

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