Question 1

Which region in the first Venn diagram (with FLOUR, EGG, MILK) represents the set of ingredients needed to make pancakes?

Accepted Answer

The intersection of FLOUR, EGG, and MILK

Question 2

Given the Venn diagram labeled $$A \cap B$$, what does the shaded region represent?

Accepted Answer

The intersection of sets $$A$$ and $$B$$

Question 3

In the third Venn diagram, what is the relationship between sets $$A$$ and $$B$$?

Accepted Answer

They are disjoint sets

Question 4

Which of the following best describes the shaded region in the fourth Venn diagram labeled $$A \cup B$$?

Accepted Answer

All elements in $$A$$, $$B$$, or both

Question 5

According to the order of operations chart, which operation should be performed first in the expression $$3 + 4 	imes 2^2$?

Accepted Answer

Exponentiation

Question 6

What is the correct order to simplify the expression $$8 - 2 	imes (3 + 5)^2$?

Accepted Answer

Parentheses, exponents, multiplication, subtraction

Question 7

Which property is illustrated by the equation $$a + (b + c) = (a + b) + c$$?

Accepted Answer

Associative Property of Addition

Question 8

What is the result of applying the distributive property to $$2(x + 3)$$?

Accepted Answer

$$2x + 6$$

Question 9

Which of the following is the correct factorization by grouping for $$x^2 + 7x + 2x + 14$?

Accepted Answer

$$(x^2 + 7x) + (2x + 14) = x(x + 7) + 2(x + 7) = (x + 7)(x + 2$$)$$

Question 10

Which of the following is a perfect square trinomial?

Accepted Answer

$$x^2 + 6x + 9$

Question 11

What is the result of factoring $$x^2 - 16$?

Accepted Answer

$$(x - 4)(x + 4)$$

Question 12

Which of the following is the correct factorization for $$x^3 + 27$?

Accepted Answer

$$(x + 3)(x^2$ - 3x + 9)$$

Question 13

If $$A = \{1, 3, 5, 7\}$$ and $$B = \{3, 4, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3\}$$

Question 14

Which of the following is the correct application of the product rule for exponents: $$a^3$$ \cdot $$a^5$$?

Accepted Answer

$$a^{8}$$

Question 15

What is the greatest common factor (GCF) of $$15x^2y$$ - $$10xy^2 - 5xy$?

Accepted Answer

$$5xy$$

Question 16

Which of the following is the correct factorization for $$x^2 - 6x + 9$$ - $$y^4$$?

Accepted Answer

$$(x - 3)^2$ - (y^2$)^2$$ = [(x - 3) - $$y^2$$][(x - 3) + $$y^2$$]$

Question 17

If $$x = -2$$, $$y = 5$$, $$z = -3$$, what is the value of $$-4x^2 - 7y + 4z$?

Accepted Answer

$$-4(-2)^2 - 7(5) + 4(-3) = -16 - 35 - 12 = -63$

Question 18

Which of the following is the correct factorization for $$6a^2 - 11a + 4$?

Accepted Answer

$$(3a - 4)(2a - 1)$$

Review of College Algebra: Sets, Real Numbers, and Polynomials

Study Guide - Practice Questions