Unit 3 Expressions Test Review

6th—Ch. 6 Lessons 1, 2 & 4

7th—Ch. 5 All except Lesson 2

6th 6-1

• Be sure you can write powers as product of the same factor

• Be sure you can evaluate powers

6th 6-2

• Be sure you know the Order of Operations and can use it to find the value of numerical expressions

PE

• Solve using the Order of Operations:

1.) -9 + x (-20 – 8) ÷ (-2) + 6

2.) 96 ÷ + (-25 x 2) – 15(-3)

6th 6-4

• Writing phrases as algebraic expressions– Look for key words that tell you what operation to

do– Choose a variable to represent the unknown

quantity– Translate phrase into expression– Less than!

7th 5-1

• To evaluate an algebraic expression:– 1.) Plug in the value for each variable and rewrite

the expression– 2.) Follow order of operations to solve (show

work step by step)

• Evaluate each expression

3m² @ 4 if m = -3

6s @ 3t if s = 4 and t = -2

• Write expressions from word problems– Key words like each and per tell you where

variable should go and to multiply– Look for other key words to tell you what

operation to use

• Nicole has d dollars in her bank account. On her birthday, she received $150 from family and friends to put into her account. Write an expression to represent the total amount of money now in her account.

• Andy is buying some T-shirts and shorts for his wardrobe. Each T-shirt costs $14 and each pair of shorts costs $18.– Write an algebraic expression to represent the

total cost of buying x T-shirts and y pairs of shorts.– Find the total cost of buying 4 T-shirts and 3 pairs

of shorts.

• Mitchel bought c plates for $6 each. Jennifer bought d plates for $6 each. Write an expression that can be used to find the total amount Mitchel and Jennifer spent for the plates.

7th 5-3

• NEED TO KNOW THE 5 PROPERTIES IN LESSON 3!– Commutative Property (+ or x)– Associative Property (+ or x)– Additive Identity– Multiplicative Identity– Multiplicative Property of Zero

• Name the property shown by each statement.1.) 6 + (b + 2) = (6 + b) + 2

2.) 1 x 4 = 4

3.) 7 + t = t + 7

7th 5-4

• Need to know how to rewrite expressions using the Distributive Property– If you have a negative number on outside of

parentheses and subtraction sign on inside of parentheses, ___________________

– Don’t forget to distribute to the second term inside the parentheses!

• Use the Distributive Property to rewrite each expression

• 1.) -9(x – 8)

• 2.) 4(3y – 12)

7th 5-5

• Simplifying Algebraic ExpressionsSTEPS:1.) Get rid of all subtraction signs (keep, change, opposite)2.) Distribute to get rid of parenthesis (if needed)3.) Show the like terms (circle, underline, box)4.) Simplify*List variable terms first and alphabetically

• Write each expression in simplest form

1.) -4x + 8 + 5x – 6

2.) x – 4 – 12x – 9

• Write each expression in simplest form

3.) -3x – 4(5x + 7)

4.) 6(4a + 3b) – 8a

• Identify the terms, like terms, coefficients, and constants in each expression.

1.) 9 – 5x – 2 + x

2.) -y + 4 – 7y

7th 5-6

• Add linear expressionsSTEPS:1.) Get rid of subtraction signs (keep, change, opposite)2.) Distribute if needed3.) Rewrite without parentheses and show like terms4.) Simplify

• Add

1.) (10x – 5) + (-6x + 4)

2.) (-8y – 2) + 3(-4y – 7)

• Write a linear expression in simplest form to represent the perimeter of the triangle. Find the perimeter if the value of x is 4 inches.

• The table gives the number of laps Pragitha swam each week. Write an expression in simplest form for the total number of laps she swam all four weeks.

Week 1 2 3 4

Laps x + 2 3x 2x + 1 4x – 6

7th 5-7

• Subtract Linear ExpressionsSTEPS:1.) Put a 1 after the subtraction sign in the middle of the two expressions2.) Get rid of subtraction signs3.) Distribute -1 to the second expression4.) Add like terms and simplify

• Subtract.

1.) (12x + 8) @ (x – 2)

2.) (3x – 2) @ (5x – 4)

• Jacob has (4n + 7) crayons. Maria has (3n + 2) crayons. Write an expression in simplest form to show how many more crayons Jacob has than Maria.

– Then evaluate the expression if n = 6.

• The table gives the cost of a gallon of gasoline at two stations. How much more does gasoline cost at Gas For Less than at Cut-Rate? Express your answer as a simplified expression

Cut-Rate –2x + 3.5

Gas for Less x – 1.2

7th 5-8

• Factor Linear ExpressionsSTEPS:1.) Find GCF of both terms2.) Divide both terms by GCF and put in parentheses3.) Put GCF outside of parentheses*Use Distributive Property to check(Don’t forget about bday cake shortcut)

• Factor each expression

1.) 12x + 30 2.) 90x – 15

• A sidewalk has an area that can be represented by the expression (8x + 24) feet. Factor the expression 8x + 24.