Question 1

Which of the following is the conjugate of the complex number $3 + 4i$?

Accepted Answer

$3 - 4i$

Question 2

Express $-2.312$ as a fraction in its lowest terms.

Accepted Answer

$-2\frac{39}{125}$

Question 3

Determine the equation of the line passing through the point $(1, -1)$ with gradient $\frac{3}{2}$.

Accepted Answer

$y = \frac{3}{2}x - \frac{5}{2}$

Question 4

Given $A = \{-2, 10\}$, $B = \{-4, 5\}$, and $C = \{0, 10\}$, which of the following represents $A \cup C$?

Accepted Answer

$\{-2, 0, 10\}$

Question 5

Which of the following is the intersection $A \cap B$ for $A = \{-2, 10\}$ and $B = \{-4, 5\}$?

Accepted Answer

$\{\}$

Question 6

Find the equation of the line passing through $(2,3)$ and $(-1,4)$.

Accepted Answer

$y = -\frac{1}{3}x + \frac{11}{3}$

Question 7

Given the quadratic function $f(x) = 2x^2 + 18x + 22$, what is the completed square form?

Accepted Answer

$2(x + 9)^2 - 140$

Question 8

If $f(x) = x^2 - 10x + 12$, what are the roots of $f(x)$?

Accepted Answer

$x = 6,\ x = 2$

Question 9

Let $U = \{1,2,3,4,5,6\}$ be the universal set, $A = \{2,4,6\}$, $B = \{1,2,3\}$. What is $A \cup B$?

Accepted Answer

$\{1,2,3,4,6\}$

Question 10

Which of the following arrow diagrams represents a one-to-one function?

Accepted Answer

The diagram where each element in set A maps to a unique element in set B, with no two elements in A mapping to the same element in B.

Question 11

Which of the following best defines a relation?

Accepted Answer

A relation is a set of ordered pairs where each input may correspond to one or more outputs.

Question 12

Which of the following is the definition of the power set of $A = \{1,2\}$?

Accepted Answer

$\{\{\}, \{1\}, \{2\}, \{1,2\}\}$

Question 13

Which of the following statements about the factor theorem is correct?

Accepted Answer

If $f(a) = 0$, then $(x - a)$ is a factor of $f(x)$.

Question 14

Given $A = \{1,2,3\}$ and $B = \{2,3,4\}$, what is $A \cap B$?

Accepted Answer

$\{2,3\}$

Question 15

Simplify the expression $\sqrt{27} + \sqrt{12}$ as far as possible.

Accepted Answer

$3\sqrt{3} + 2\sqrt{3} = 5\sqrt{3}$

Question 16

If $f(x) = x^2 - 4x + 3$, which value of $x$ makes $f(x) = 0$?

Accepted Answer

$x = 1$ or $x = 3$

Question 17

Which of the following is NOT a function?

Accepted Answer

A relation where one input maps to multiple outputs.

Question 18

Given $A = \{2,4,6\}$ and $B = \{1,2,3\}$, what is $A - B$?

Accepted Answer

$\{4,6\}$

Question 19

If $f(x) = x^2 - 6x + 9$, what is the vertex of the parabola?

Accepted Answer

$(3, 0)$

College Algebra: Key Concepts, Functions, and Equations – Study Notes

Study Guide - Practice Questions