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

Question 1

Which of the following best describes the graph of the function $f(x) = \sqrt{x}$?

Accepted Answer

It is defined for $x \geq 0$ and increases slowly as $x$ increases.

Question 2

Given the system of equations: $\begin{cases} x + y = 4 \ x - y = 2 \end{cases}$, what is the solution $(x, y)$?

Accepted Answer

$(x, y) = (3, 1)$

Question 3

Which of the following is the correct formula for the sum of the first $n$ natural numbers?

Accepted Answer

$S = \dfrac{n(n+1)}{2}$

Question 4

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 5

Which of the following is the correct notation for the summation of $x_i$ from $i=1$ to $n$?

Accepted Answer

$\sum_{i=1}^{n} x_i$

Question 6

Given the quadratic function $f(x) = -x^2 + 4x - 3$, what is the vertex of the parabola?

Accepted Answer

$(2, 1)$

Question 7

Which of the following best describes the solution set of the equation $|x| = 5$?

Accepted Answer

$x = 5$ or $x = -5$

Question 8

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

Accepted Answer

$f(g(2)) = 2 \cdot 4 + 1 = 9$

Question 9

Which of the following graphs best represents a function that is increasing for all $x$ in its domain?

Accepted Answer

A straight line with positive slope

Question 10

Given the data points $(1,2), (2,4), (3,6), (4,8)$, what type of relationship is best represented?

Accepted Answer

Linear

Question 11

If $\sum_{i=1}^{4} i^2$ is calculated, what is the result?

Accepted Answer

$30$

Question 12

Which of the following is the solution to $2x - 5 = 9$?

Accepted Answer

$x = 7$

Question 13

If $A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$, what is $A$ called?

Accepted Answer

Identity matrix

Question 14

Which of the following is the correct formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Question 15

If $f(x) = x^2 - 4x + 3$, what are the zeros of the function?

Accepted Answer

$x = 1$ and $x = 3$

Question 16

Which of the following is the correct formula for the slope of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

Key Concepts in College Algebra: Functions, Graphs, and Matrices

Study Guide - Practice Questions