Question 1

Which property allows you to change the grouping of numbers when adding three or more terms, and what is its mathematical expression?

Accepted Answer

Associative Property: $$(a + b) + c = a + (b + c)$$

Question 2

If $$x = 3$$ and $$y = 4$$, what is the value of $$x^2$$ + $$y^2$$?

Accepted Answer

$$25$$

Question 3

Which of the following is the correct definition of a rational number?

Accepted Answer

Any number that can be written as a fraction of two integers

Question 4

What is the result of multiplying $$\frac{2}{3} by$$ $$\frac{3}{4}$$?

Accepted Answer

$$\frac{1}{2}$$

Question 5

Simplify $$\frac{180}{\sqrt{8}}$$ and express your answer in simplest radical form.

Accepted Answer

$$45\sqrt{2}$$

Question 6

Which rule is used to simplify $$x^a \cdot x^b$$?

Accepted Answer

Product Rule: $$x^{a+b}$$

Question 7

What is the value of $$\log_{10}(1000)$$?

Accepted Answer

$$3$$

Question 8

If the ratio of students enrolled at Greenvale and Riverside is $$4:7$$ and Riverside has $$42$$ students, how many does Greenvale have?

Accepted Answer

$$24$$

Question 9

What is the sum of the arithmetic sequence $$7, 10, 13, 16, 19$$?

Accepted Answer

$$65$$

Question 10

Which of the following is the correct expression for the change of base rule for logarithms?

Accepted Answer

$$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$$

Question 11

If $$a = 2$$, $$b = 3$$, and $$c = 4$$, what is the value of $$(a^b)^c$$?

Accepted Answer

$$4096$$

Question 12

Which of the following is the correct method to add $$\frac{3}{8}$$ and $$\frac{5}{12}$$?

Accepted Answer

Find the least common multiple of the denominators, convert both fractions, then add numerators.

Question 13

What is the value of $$\sqrt{50} in $$simplest radical form?

Accepted Answer

$$5\sqrt{2}$$

Question 14

Which property states that $$a \cdot 1 = a$$?

Accepted Answer

Multiplicative Identity

Question 15

If $$x = 2$$ and $$y = 3$$, what is the value of $$\frac{x}{y}$$?

Accepted Answer

$$\frac{2}{3}$$

Question 16

What is the scientific notation for $$7,500,000$$?

Accepted Answer

$$7.5 	imes 10^6$

Question 17

Which of the following is the correct product rule for logarithms?

Accepted Answer

$$\log_b(xy) = \log_b(x) + \log_b(y)$$

Question 18

If $$a = 5$$, $$b = 2$$, and $$c = 3$$, what is the value of $$a^b \cdot a^c$$?

Accepted Answer

$$a^{b+c}$$ = $$5^{2+3}$$ = $$5^5 = 3125$

Question 19

What is the value of $$\log_{10}(x) if$$ $$x = 100$$?

Accepted Answer

$$2$$

Question 20

If the first term of an arithmetic sequence is $$10$$ and the $$9th $$term is $$42$$, what is the common difference?

Accepted Answer

$$4$$

Review of College Algebra: Foundations for Trigonometry

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