Q: Which of the following correctly applies the order of operations to simplify $$2 + 3 \times 4^2$?

$$2 + 3 \times 4^2$ = 2 + 3 \times 16 = 2 + 48 = 50$$

Q: Evaluate $$x^2 + 2x$ for x = -3$.

$$(-3)^2 + 2$$ \times (-3) = 9 - 6 = 3$$

Q: If $$x = 2$$ and $$y = -1$$, evaluate $$3x^2y$$ - $$2xy^2.$$

$$3 \times 4 \times (-1) - 2 \times 2 \times (-1)^2$ = -12 - 4 = -16$$

Q: A chemical reaction's rate is modeled by $$R = k[A]^2[B]. If$$ $$k = 2$$, $$[A] = 3$$, $$[B] = 4$$, what is $$R$$?

$$2 \times 3^2$ \times 4 = 2 \times 9 \times 4 = 72$$

Question 1

Which of the following correctly applies the order of operations to simplify $$2 + 3 	imes 4^2$?

Accepted Answer

$$2 + 3 	imes 4^2$ = 2 + 3 	imes 16 = 2 + 48 = 50$$

Question 2

Evaluate $$x^2 + 2x$ for x = -3$.

Accepted Answer

$$(-3)^2 + 2$$ 	imes (-3) = 9 - 6 = 3$$

Question 3

A consignment store marks orange labels for a $$25\%$$ discount and green labels for a $$40\%$$ discount. If $$p is $$the original price, which expression represents the discount amount for a green label?

Accepted Answer

$$0.40p$$

Question 4

Simplify the expression $$\frac{2x^2$y}{4xy^2$}$$ and write your answer in standard form.

Accepted Answer

$$\frac{x}{2y}$$

Question 5

Express $$\frac{a$$^{-3}$$b^4$$}{$$a^2b$$^{-1}$$}$$ using positive exponents only.

Accepted Answer

$$\frac{b^5$}{a^5$}$$

Question 6

Find the product and simplify: $$(x - 2)(x^2$ + 2x + 4).$$

Accepted Answer

$$x^3$$ + $$2x^2 + 4x$$ - $$2x^2 - 4x - 8$$ = $$x^3 - 8$

Question 7

Factor completely: $$x^2 - 5x + 6$.

Accepted Answer

$$(x - 2)(x - 3)$$

Question 8

Simplify $$\frac{\sqrt{50}}{\sqrt{2}}$$ and rationalize the denominator.

Accepted Answer

$$5\sqrt{2}$$

Question 9

Ohm's law states $$V = IR. If $$the current is $$3$$ amperes and resistance is $$8$$ ohms, what is the voltage?

Accepted Answer

$$24$$ volts

Question 10

Simplify $$\frac{2x^2$ - 8}{x^2$ - 4}$$ completely.

Accepted Answer

$$2$$

Question 11

Rationalize the denominator: $$\frac{3}{\sqrt{5}}.$$

Accepted Answer

$$\frac{3\sqrt{5}}{5}$$

Question 12

Factor completely: $$x^3 - 27$.

Accepted Answer

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

Question 13

Perform the indicated operation and simplify: $$\frac{x^2$ - 4}{x^2$ + 2x + 4} \div \frac{x - 2}{x + 2}.$$

Accepted Answer

$$\frac{(x^2$ - 4)(x + 2)}{(x^2$ + 2x + 4)(x - 2)}$$

Question 14

Kimberly takes 3 more hours than Arianna to complete a project. Arianna's rate is $$\frac{1}{x}$$, Kimberly's rate is $$\frac{1}{x+3}. $$What is the combined rate if they work together?

Accepted Answer

$$\frac{1}{x} + \frac{1}{x+3}$$

Question 15

Simplify $$\frac{(x^2$ - 9)}{(x^2$ - 6x + 9)}.$$

Accepted Answer

$$\frac{(x - 3)(x + 3)}{(x - 3)^2$}$$

Question 16

If $$x = 2$$ and $$y = -1$$, evaluate $$3x^2y$$ - $$2xy^2.$$

Accepted Answer

$$3 	imes 4 	imes (-1) - 2 	imes 2 	imes (-1)^2$ = -12 - 4 = -16$$

Question 17

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

Accepted Answer

$$(x + 3)^2$

Question 18

Simplify $$\frac{4x^3$y^2$$}{$$8x^2y^4$}$$ using positive exponents only.

Accepted Answer

Question 19

A chemical reaction's rate is modeled by $$R = k[A]^2[B]. If$$ $$k = 2$$, $$[A] = 3$$, $$[B] = 4$$, what is $$R$$?

Accepted Answer

$$2 	imes 3^2$ 	imes 4 = 2 	imes 9 	imes 4 = 72$$

College Algebra Unit 1 Review – Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards