Question 1

Which of the following correctly translates the phrase: 'Thirteen less than one quarter of some number' into a mathematical expression?

Accepted Answer

$$\frac{1}{4}x - 13$$

Question 2

Evaluate $$3(x - 7) + 2$$ for $$x = 10$$ using the order of operations.

Accepted Answer

$$11$$

Question 3

Simplify the expression $$2x + 3(5x - 7).$$

Accepted Answer

$$17x - 21$$

Question 4

Solve for $$x$$: $$\frac{2}{3}x = 30.$$

Accepted Answer

$$x = 45$$

Question 5

Which property of exponents is used to simplify $$(a^m)^n$$?

Accepted Answer

Power Rule: $$a^{mn}$$

Question 6

A rectangular mirror has a length three times its width, and its perimeter is $$120 cm. $$What is the width?

Accepted Answer

$$15 cm$$

Question 7

Simplify $$-7t^2 + 3t$$ + $$5t^3$$ - $$t^3$$ + $$2t^2 - t$ by combining like terms.

Accepted Answer

$$4t^3$$ - $$5t^2 + 2t$

Question 8

Convert $$0.00583 to $$scientific notation.

Accepted Answer

$$5.83 	imes 10$$^{-3}$$

Question 9

Solve for $$y in $$the equation $$2x + 3y = 4.$$

Accepted Answer

$$y = \frac{4 - 2x}{3}$$

Question 10

Which of the following is the correct result of multiplying $$(m^5$$ $$n^2)(m^3$ n p^0$)$?

Accepted Answer

$$m^8$$ $$n^3$$

Question 11

A chemical reaction produces $$4.92 	imes 10^3$ grams of a compound. How many grams is this in decimal notation?

Accepted Answer

$$4920$$

Question 12

Simplify $$6^{-3}$$ \cdot $$6^{-5}$$ and write the answer without negative exponents.

Accepted Answer

$$\frac{1}{6^8$}$$

Question 13

Solve for $$h in $$the formula $$V = lwh.$$

Accepted Answer

$$h = \frac{V}{lw}$$

Question 14

Divide and write the result in scientific notation: $$\frac{5.5 	imes 10^6$}{2.2 	imes 10$$^{-3}$$}.$$

Accepted Answer

$$2.5 	imes 10^9$

Question 15

Which of the following is the correct equivalent expression for $$-5(2a + 3b)$$ using the distributive law?

Accepted Answer

$$-10a - 15b$$

Question 16

A rectangular garden has a width that is one-third its length, and its perimeter is $$32 m. $$What is the length?

Accepted Answer

$$12 m$$

Question 17

Simplify $$\frac{y^9$}{y^2$}$$ using the properties of exponents.

Accepted Answer

$$y^7$$

Question 18

Which of the following is the correct translation for 'The sum of two variables'?

Accepted Answer

$$x + y$$

Question 19

Simplify $$[10 - (a - b)]^2$$ for $$a = 7$$ and $$b = 2.$$

Accepted Answer

$$25$$

Question 20

A medical lab uses $$8.92 	imes 10$$^{-3}$$ liters of a reagent in a test. How many liters is this in decimal notation?

Accepted Answer

$$0.00892$$

College Algebra Foundations: Operations, Properties, and Problem Solving

Study Guide - Practice Questions