Foundations of Algebra

Variables and Expressions

100

What is an algebraic expression for the word phrase "8 times a number n?"

8n

200

Write a word phrase for the algebraic expression "q + 5"

q plus 5 5 more than a number q the sum of a number q and 5

300

Explain the difference between numerical expressions and algebraic expressions.

algebraic expressions contain variables and numerical expressions do not

400

Write an algebraic expression for the word phrase "the product of 4 and the sum of a number x and 7."

4(x + 7)

500

You and some friends are going to a museum. Each ticket costs $4.50. If n is the number of tickets purchased, write an expression that gives the total cost of buying n tickets.

$4.50n or 4.5n

Order of Operations and Evaluating Expressions

100

What is the simplified form of 5²?

25

200

What is the simplified form of (2/3)^3?

8/27

300

Simplify (6^2-3^2)÷2

9/2

400

Identify the exponents and base in 4^3

exponent: 3 base: 4

500

You earn $10 for each hour you work at a canoe rental shop. Write an expression for your salary for working h hours. How much will you make for working 40 hours?

10h $400

Real Numbers

100

-12+7

-5

200

3.5 - 1.9

1.6

300

-121 + 100

-21

400

Order these numbers from least to greatest: 1.5, -1/3, -2, 0.3, 0

-2, -1/3, 0, 0.3, 1.5

500

A movie ticket cots $7.75. A drink costs $2.40. Popcorn costs $1.25. What is the total cost for a ticket, a drink, and popcorn?

$11.40

The Distributive Property

100

Simplify 3(x + 8)

3x+24

200

Simplify 4(2y - 3x)

8y - 12x

300

Simplify 5x - 3 - 3x + 6y +4

2x + 6y + 1

400

Deli sandwiches cost $4.95 each. What is the total cost of 8 sandwiches?

$39.60

500

3(x + 4) - 5(x + 2)

-2x + 2

Introduction to Equations

100

Is x=6 a solution of the equation 32 = 2x + 12?

no

200

You can read 1.5 pages for every page your friend can read. Write an equation that relates the number of pages p that you can read and the number of pages n that your friend can read.

1.5n=p

300

Give an example of an equation that is true, an equation that is false, and an open equation.

True: 2 + 3 = 5 False: 4 + 3 = 10 Open: 2x - 10 = 20

400

Write an expression using one variable and division.

x / 12

500

What are the differences between an expression and an equation? Does a mathematical expression have a solution? Explain

Equations have an equal sign and an expression does not. A mathematical expression does not have a solution because there is no equal sign.