Summer Packet Review

Chapter 1

sections 1 through 5

1.1 Evaluate Algebraic Expressions

Evaluate the expression when x = 5

a. 7x b. 12 + x

Evaluate

means substitute a valueor to “plug in” a number

7(5)

35

12 (5)17

Read and write powers

1.1 Evaluate Algebraic Expressions

Read and write powers

Write the power in words and as a product.

1.1 Evaluate Algebraic Expressions

59 Nine to the fifth power.

9 9 9 9 9

3m m to the third power.m m m

PEMDAS or GEMDAS!STEP 1 Evaluate expressions inside parenthesis or grouping symbols.

Parenthesis is not the only type of grouping

Numerator or Denominator

Radical

Absolute Value

1.2 Apply Order of Operations

(3 5)3 5

7

3 5

3 5

These type of operations should be done first.

PEMDAS or GEMDAS!STEP 1 Evaluate expressions inside grouping symbols.

STEP 2 Evaluate powers.

STEP 3 Multiply and divide from left to right.

STEP 4 Add and subtract from left to right.

1.2 Apply Order of Operations

PEMDAS or GEMDAS!1.2 Apply Order of Operations

Evaluate the expression.

4(3 9)

4(12)

48

23(8 2 )

3(8 4)

3(4)

12

PEMDAS or GEMDAS!1.2 Apply Order of Operations

Evaluate the expression.

2 (9 3) 4

2 (12) 4

2 12 4

2 36

PEMDAS or GEMDAS!1.2 Apply Order of Operations

Evaluate the expression when y = - 8.2 3y 2( 8) 3

64 3

61

12 1y

12 ( 8) 1 12 8 1 20 119

Use parenthesis when substituting (or “plugging in”) a value!

1.2 Apply Order of OperationsEvaluate the expression when y = - 8.

10 171

yy

Use parenthesis when substituting (or “plugging in”) a value!

10( 8) 17( 8) 1

80 179

63

9

7

Translate verbal phrases into expressions.

•8 more than the product of 5 times a number w

1.3 Write Expressions

add 8 to what?

multiplication of 5 and w

5 8w

• The quotient of 11 and the sum of 7 and a number x11 divided by what? addition of 7 and x

117 x

Translate verbal phrases into expressions.

• The square of a number y decreased by 13

1.3 Write Expressions

Be careful, this is NOT square root!

Subtract 132 13y

• Four less than quantity 6 times a number nSubtract 4 from what?ORDER MATTERS! 6 multiplies n

6 4n

Use a verbal model to write an expression

Write an expression for the situation.

• Total cost of n notebooks if each notebook costs $1.25

1.3 Write and Evaluate an Expression

Number of notebooks

x Cost of each notebook

n 1.25

$1.25n

Use a verbal model to write an expression

Write an expression for the situation.• The time it takes to get to school and home

again if you walk 5 minutes to the bus stop and ride the bus for m minutes

1.3 Write and Evaluate an Expression

Time from home to bus stop

Time on bus from bus stop to school

5 52 10 minutesm

+ +Time on bus from school to bus stop

+Time from bus stop to home

m m

or 2( 5)m

Find a unit rate1.3 Write and Evaluate an Expression

A rate is a fraction that compares two quantities measured in different units.

mileshour

degreesminute

studentsclass

Find a unit rate

An airport checks in 460 passengers in 5 hours. Find the unit rate.

1.3 Write and Evaluate an Expression

450 passengers5 hoursSimplify

the fraction 90 passengers

hour

90 passengers per hour

1.4 Write Equations and Inequalities

An equation is two expressions that are equal.

Keyword is “is”. Replace “is” with =

An inequality is two expressions that are compared with inequality symbols.

MEANING

SYMBOL KEY WORDS

1.4 Write Equations and Inequalities8 times the quantity of 11 plus a number x is 112.

8 (11 )x 112

8(11 ) 112x

The product of 7 and a number y is no more than 31.7 y 31

7 31y

1.4 Write Equations and Inequalities

and8z 15z

A number z is more than 8 and at most 15.

A number z is more than 8 and z is at most 15.rewrite

This can be combined to:

8 15z

Think: z is between 8 and 15

A number y is no less than 5 and no more than 13. rewriteA number y is no less than 5 and y is no more than 13.

5y and 13y 5 13y

Check possible solutions

Check whether the given number is a solution of the equation or inequality.

A solution to an equation or inequality is a value that makes the statement TRUE.

1.4 Write Equations and Inequalities

13 17;4a 13 (4) 17

17 17

7 3 10;2b

The statement is trueso 4 is a solution.

7(2) 3 10 14 3 10

11 10False statement so 2 is NOTa solution.

Check possible solutions

Check whether the given number is a solution of the equation or inequality.

A solution to an equation or inequality is a value that makes the statement TRUE.

1.4 Write Equations and Inequalities

4 15;3c 7 8 15;9m

4(3) 15

12 15

The statement is trueso 3 is a solution.

7 (9) 8 15

7 17 15

False statement so 9 is NOTa solution.

STEP 1 Read and Understand the Problem STEP 2 Make a PlanSTEP 3 Solve the ProblemSTEP 4 Look BackA salesman is reimbursed $50 a day for food and lodging. He also receives $.35 for each mile driven. He drives 124 miles and is reimbursed $193.40. How many days was the trip?

1.5 Use A Problem Solving Plan

A salesman is reimbursed $50 a day for food and lodging. He also receives $.35 for each mile driven. He drives 124 miles and is reimbursed $193.40. How many days was the trip?

What we want to know:number of days use d

What we know:gets $50 each day for food & hotel gets $0.35 for each miledrove 124 milesreimbursed $193.40

Write a Verbal Modelreimbursed =

miles driven x $/mile

+ daily allowance/day x number of days

193.40 124 0.35 50 d

193.40 124 0.35 50d

1.5 Use A Problem Solving Plan

A salesman is reimbursed $50 a day for food and lodging. He also receives $.35 for each mile driven. He drives 124 miles and is reimbursed $193.40. How many days was the trip?

193.40 124 0.35 50d 193.40 43.40 50d

193.40 43.4043.40 4 503.40 d

150 50d

150 5050 50d

3 d

Is this a reasonable answer?

The trip was 3 days long.

1.5 Use A Problem Solving Plan

A soccer team is selling pizzas for $6 each. Each pizza costs $4 to make. The team has 10 players and wants to raise $900 for equipment and uniforms. How many pizzas does the team need to sell? How many pizzas will each player sell if every player sells the same number of pizzas?

Solve a multi-step problem1.5 Use A Problem Solving

Plan

STEP 1 Read and Understand the Problem

A soccer team is selling pizzas for $6 each. Each pizza costs $4 to make. The team has 10 players and wants to raise $900 for equipment and uniforms. How many pizzas does the team need to sell? How many pizzas will each player sell if every player sells the same number of pizzas?

1.5 Use A Problem Solving Plan

STEP 2 Make a Plan What we want to know:

# pizzas the team need to sell use p

What we know:pizzas sell for $6 each pizzas cost $4 each there are 10 players

# pizzas each player needs to sell use x

Write a Verbal Modelmoney raised = selling price x # of pizzas - cost x # of pizzas

900 = 6 4

want to raise $900

p p

900 6 4p p

A soccer team is selling pizzas for $6 each. Each pizza costs $4 to make. The team has 10 players and wants to raise $900 for equipment and uniforms. How many pizzas does the team need to sell? How many pizzas will each player sell if every player sells the same number of pizzas?

1.5 Use A Problem Solving Plan

STEP 3 Solve the Problem 900 6 4p p 900 2 p

9002 2

2 p

450 p

STEP 4 Look Back Is this a reasonable answer?

The team needs to sell 450 pizzas.

Have we answered all of the problem ?# pizzas each player needs to sell use x

# pizzas each player sells

= total pizzas

number of players

x 0 45 1045x

Each player needs to sell 45 pizzas.