$$\begin{pmatrix} 3 & 6 \\ 9 & 12 \end{pmatrix}$$

$$\begin{pmatrix} 1 & 3 \\ 2 & 4 \end{pmatrix}$$

$$\begin{pmatrix} 4 & 7 \\ 8 & 15 \end{pmatrix}$$

Question 1

Which of the following is the standard equation of a parabola that opens upwards with vertex at the origin?

Accepted Answer

$$y = ax^2$

Question 2

Given the parabola $$y = 2(x-3)^2$ + 4$$, what are the coordinates of its vertex?

Accepted Answer

$$(3, 4)$$

Question 3

If $$A = \begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \ 5 & 2 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

Question 4

What is the result of multiplying the matrix $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} by $$the scalar $$3$$?

Accepted Answer

$$\begin{pmatrix} 3 & 6 \ 9 & 12 \end{pmatrix}$$

Question 5

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

Accepted Answer

$$2x^2 + 1$

Question 6

What is the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Question 7

If $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$, what is the transpose $$A^T$$?

Accepted Answer

$$\begin{pmatrix} 1 & 3 \ 2 & 4 \end{pmatrix}$$

Question 8

Which of the following is the inverse of the function $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{3}$$

Question 9

A right triangle has legs of length $$5$$ and $$12. $$What is the length of the hypotenuse?

Accepted Answer

$$13$$

Question 10

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 11

Which of the following is an arithmetic progression?

Accepted Answer

$$2, 5, 8, 11, 14$$

Question 12

What is the sum of the first $$5$$ terms of the geometric progression $$2, 6, 18, ...$$?

Accepted Answer

$$242$$

Question 13

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

Accepted Answer

$$\begin{pmatrix} 4 & 7 \ 8 & 15 \end{pmatrix}$$

Question 14

Which of the following is the correct formula for the $$nth $$term of an arithmetic progression with first term $$a$$ and common difference $$d$$?

Accepted Answer

$$a_n = a + (n-1)d$$

Question 15

If $$	an 	heta = 1$$ and $$0 \u003c 	heta \u003c \frac{\pi}{2}$$, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{4}$$

Question 16

Given the system of equations: $$x + y + z = 6$$, $$2x - y + 3z = 14$$, $$-x + 4y - z = -2$$, which method can be used to solve for $$x, y, z$$?

Accepted Answer

Matrix inverse method

Question 17

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \geq 0$$

Question 18

Which of the following is a true trigonometric identity?

Accepted Answer

$$\sin^2$ x + \cos^2$ x = 1$$

Question 19

If the sum of the first $$n$$ terms of an arithmetic progression is $$S_n = 5n + 3n^2$, what is the common difference?

Accepted Answer

$$6$$

Key Topics in College Algebra: Parabolas, Matrices, Functions, Trigonometry, and Sequences

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