Foundations of Algebra Review

Vocabulary

100

State the difference between a constant and a coefficient

Constant: a number without a variable

Coefficient: a number multiplied to/next to a variable

200

Create an expression that shows the sum of (x + 1)² and (-x² + 3x - 12)

(x + 1)² + (-x² + 3x - 12)

300

Create an expression for the product of (2x - 4) and (3 + 5x)

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

400

What are the coefficients in the following expression: 

7 + 4p - 5 + p - 2q

4, 1, -2

500

Given: 7b³ - 5

7 is a ____        b is a ____

3 is a ____       -5 is a ___

7 is a coefficient

b is a variable and a base

3 is an exponent

-5 is a constant

Simplifying Expressions

100

Simplify 3(x + 2)

3x + 6

200

Simplify -4(m + 9)

-4m - 36

300

Simplify 9x - 3x² + 2x

11x - 3x²

400

3y + 2(y - 5) + 1

5y - 9

500

7 - (4x - 6) + 12x

8x + 13

Evaluating Expressions

100

Evaluate 3q - 20 when q = 5

-5

200

Evaluate 25 - (2/3)y when y = 18

13

300

Evaluate d² + 6d when d = -4

-8

400

Evaluate a³ + ab when a = -5 and b = 3

-140

500

Evaluate 2x² - 4x - x + 3 when x = -5

78

Creating Equations

100

Lydia wants to take art classes. Center A charges $15 per hour and a registration fee of $75. If A represents the total charges and h represents the number of hours, write an equation Lydia could use to calculate how much she will spend on art classes.

A = 15h + 75

200

Anna is planning a party for her daughter's birthday. The number of party hats Anna needs is twice as many as the number of balloons. x represents the number of balloons and y represents the number of party hats. Write an equation that represents this situation.

y = 2x

300

Julia is 4 years older than twice Kelly’s age, x. The product of their ages is 96. Write an equation that could be used to find their ages.

x(2x + 4) = 96

or

2x² + 4x = 96

400

Joe has dimes and nickels in his piggy bank totaling $1.45. The number of nickels he has is 5 more than twice the number of dimes, d. Write an equation that could be used to find the number of dimes he has?

0.05(2d + 5) + 0.10d = 1.45

500

Hannah went to the school store to buy supplies and spent $16.  She bought four more pencils than pens and two fewer erasers than pens.  Pens cost $1.25 each, pencils cost $0.55 each, and erasers cost $0.75 each.  If x represents the number of pens Hannah bought, write an equation in terms of x that can be used to find how many of each item she bought.

1.25x + 0.55(x + 4) + 0.75(x - 2) = 16