Variables, Expressions, & Properties (1.01-1.04 Test)

Properties of =/+/x

100

Which property uses the fact that a number times its reciprocal always equals 1?

Multiplicative Inverse

200

Which property is illustrated by -2 + 2 = 0?

Additive Inverse

300

Solve for x and state which property is used.

10x = 10

x = 1, Multiplicative Identity

400

DOUBLE JEOPARDY

What is the difference between the reflexive and symmetric properties of equality?

Reflexive has one thing equal to itself. a = a

Symmetric has one equal to another, which means the second equals the first. a = b, means b = a

500

Name the properties used in each step:

5 * 7 * 4 * 2 

= 5 * 2 * 7 * 4

= (5 * 2) * (7 * 4)

= 10 * 28 

= 280 

Commutative Property (x)

Associative Property (x)

Substitution

Substitution

Distr. Prop. & Simplify

100

Use the distributive property: 2(x - 3).

2x - 6

200

Simplify (9x - 2x)(-3).

-21x

300

Simplify 8q² - 7q + 1. 

Already simplified. 

400

Simplify 5k² - 2x + 4(k² - x).

9k² - 8x

500

Factor 5x + 15.

5(x + 3)

Order of Operations

100

DOUBLE JEOPARDY

What is the order of operations?

Parentheses, Exponents, Multiply/Divide, Add/Subtract

or

Grouping Symbols, Exponents, Multiply/Divide, Subtract/Add

200

Evaluate: 14³

2744

300

Evaluate: 35 - 3 * 8

11

400

Evaluate: 23 - 2(17 + 3³)

-65

500

Evaluate 2b + 3c² 

              _______

              4a² - 2b

when a = 8, b = 4, and c = 16.

98/31 or approx. 3.16

Word Problems

100

In 2013, there were 3344 amusement parks and arcades. Suppose by 2018 this number decreased by 148. Write and evaluate an expression to find the number of amusement parks and arcades in 2018.

3344 - 148 = 3196

200

Jocelyn makes x dollars per hour working at the grocery store and n dollars per hour babysitting. Write an expression that describes her earnings if she babysat for 25 hours and worked at the grocery store for 15 hours. 

15x + 25n

300

Tickets to a baseball game cost $35 each plus a $5.50 handling charge per ticket. If Sharon has a coupon for $10 off and orders 4 tickets, how much will she be charged?

4(35 + 5.5) - 10 = $152

400

A rectangle has sides of lengths x + 3 and 2x + 5. Write an expression in simplest form that represents its perimeter.

P = 2(x + 3) + 2(2x + 5) = 8x + 16

500

Consuelo and James are writing an algebraic expression for "three times the sum of n squared and 3." Is either of them correct? Explain your reasoning.

Consuelo: 3(n² + 3)      James: 3n² + 3

DOUBLE JEOPARDY

Consuelo is right. James left out the parentheses around n² + 3. 

Verbal/Alg. Expressions

100

Write a verbal expression for -7x - 5.

-7 times x minus 5.

5 less than -7 times x. 

Others?

200

Using the one of the terms "product, quotient, sum, or difference", write 5m² as a verbal expression.

DOUBLE JEOPARDY

The product of 5 and m squared

300

Write a verbal expression for 4(2x + 6).

4 times the sum of 2x and 6. Others?

400

Twice the difference of 3x and y increased by 5.

Write an algebraic expression and write in simplest form.

2(3x - y) + 5 = 6x - 2y + 5

500

Write an algebraic expression for the following and simplify: 5 times the difference of q squared and r plus 8 times the sum of 3q and 2r.

5(q² - r) + 8(3q + 2r) = 5q² + 24q + 11r