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

스터디 가이드 - 연습 문제