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

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

Q: Evaluate $$x^2 + 2x + 1$ for x = -3$.

$$(-3)^2 + 2$$ \times (-3) + 1 = 9 - 6 + 1 = 4$$

Q: If $$x = 2$$, evaluate $$x^3$$ - $$4x^2 + 5x - 6$.

$$2^3 - 4$$ \times $$2^2 + 5$$ \times 2 - 6 = 8 - 16 + 10 - 6 = -4$$

Question 1

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

Accepted Answer

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

Question 2

Evaluate $$x^2 + 2x + 1$ for x = -3$.

Accepted Answer

$$(-3)^2 + 2$$ 	imes (-3) + 1 = 9 - 6 + 1 = 4$$

Question 3

A consignment store marks items with an orange label for a $$25\%$$ discount. If $$p is $$the original price, which expression represents the discount amount?

Accepted Answer

$$0.25p$$

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 the polynomial $$x^2 - 5x + 6$ completely.

Accepted Answer

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

Question 8

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

Accepted Answer

$$5$$

Question 9

Ohm's law states $$V = IR. If a $$circuit has a current of $$2$$ amperes and resistance of $$13$$ ohms, what is the voltage?

Accepted Answer

$$V = 2 	imes 13 = 26$$ volts

Question 10

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 11

Simplify $$\frac{3x^2$y^3$$}{$$6xy^2$$}$ and express using positive exponents only.

Accepted Answer

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

Question 12

Factor $$x^2 - 9$ completely.

Accepted Answer

$$(x - 3)(x + 3)$$

Question 13

Perform the indicated operation and simplify: $$\frac{2}{x} + \frac{3}{x}.$$

Accepted Answer

$$\frac{5}{x}$$

Question 14

Simplify $$\frac{4x^3$y^2$$}{$$8x^2y$$}$ and write your answer in standard form.

Accepted Answer

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

Question 15

If the original price of an item is $$p$$ and the green label discount is $$40\%$$, what is the expression for the discount amount?

Accepted Answer

$$0.4p$$

Question 16

Factor $$x^2 + 6x + 9$ completely.

Accepted Answer

$$(x + 3)^2$

Question 17

Rationalize the denominator: $$\frac{1}{\sqrt{5}}.$$

Accepted Answer

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

Question 18

Simplify $$\frac{\sqrt{8}}{\sqrt{2}}$$ and rationalize the denominator.

Accepted Answer

$$2$$

Question 19

If $$x = 2$$, evaluate $$x^3$$ - $$4x^2 + 5x - 6$.

Accepted Answer

$$2^3 - 4$$ 	imes $$2^2 + 5$$ 	imes 2 - 6 = 8 - 16 + 10 - 6 = -4$$

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

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