Question 1

Which of the following is the correct least common multiple (LCM) of $$8$$, $$24$$, and $$40$$?

Accepted Answer

$$240$$

Question 2

Simplify the following expression, assuming all variables are positive: $$\sqrt{27x^4$}$$

Accepted Answer

$$3x^2$$

Question 3

Given the equation $$2x + y = 8$$, which of the following is the correct $$y-$$intercept?

Accepted Answer

$$y = 8$$

Question 4

Find the equation of the line passing through the points $$(1, -3)$$ and $$(2, 5).$$

Accepted Answer

$$y = 8x - 11$$

Question 5

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

Accepted Answer

$$(x - 3)^2$

Question 6

Rationalize the denominator and simplify: $$\frac{5}{\sqrt{2}}$$

Accepted Answer

$$\frac{5\sqrt{2}}{2}$$

Question 7

Write $$0.000102 in $$scientific notation.

Accepted Answer

$$1.02 	imes 10$$^{-5}$$

Question 8

Solve for $$x$$: $$x^2 = 4x$

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Question 9

Factor the polynomial $$2x^2 - 16$ completely.

Accepted Answer

$$2(x - 4)(x + 4)$$

Question 10

Simplify the following expression, assuming all variables are positive: $$\frac{27x$$^{11}$$y^{15}$$}{$$64x^5y^3$}$$

Accepted Answer

$$\frac{27x^6$y^{12}$$}{64}$

Question 11

A car travels 5 mph faster than another car. After 3 hours, they are 267 miles apart, traveling in opposite directions. What is the speed of the slower car?

Accepted Answer

$$45$$ mph

Question 12

Which of the following is the correct prime factorization of $$315$$?

Accepted Answer

$$3^2$$ 	imes 5 	imes 7$$

Question 13

Simplify the complex fraction: $$\frac{2}{x} \div \frac{1}{x-2}$$

Accepted Answer

$$\frac{2(x-2)}{x}$$

Question 14

Multiply and simplify, assuming all variables are positive: $$\sqrt{3} 	imes \sqrt{12}$$

Accepted Answer

$$6$$

Question 15

Change the following expression to exponential notation and simplify: $$\sqrt[3]{x^5$}$$, assuming $$x \u003e 0.$$

Accepted Answer

$$x^{5/3}$$

Question 16

Which of the following is the correct result when rationalizing the denominator of $$\frac{1}{\sqrt{5}}$$?

Accepted Answer

$$\frac{\sqrt{5}}{5}$$

Question 17

Factor the trinomial $$x^2 + 4x + 2$ completely.

Accepted Answer

It is not factorable over the integers.

Question 18

Which of the following is the correct result for $$\frac{4}{5} + \frac{6}{7}$$?

Accepted Answer

$$\frac{34}{35}$$

Question 19

Simplify the following expression, assuming all variables are positive: $$\sqrt[3]{8x^9$y^{12}$$}$

Accepted Answer

$$2x^3y^4$

Question 20

Which of the following is the correct result for $$\frac{28 - 7}{156 \div 13}$$?

Accepted Answer

$$\frac{21}{12}$$

Precalculus Study Guide: Numbers, Expressions, Equations, and Functions

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