Summer Packet Review Chapter 1 sections 1 through 5

Summer Packet ReviewChapter 1sections 1 through 5

1.1 Evaluate Algebraic Expressions means substitute a value or to “plug in” a number Evaluate Evaluate the expression when x = 5 a. 7x b. 12 + x

1.1 Evaluate Algebraic Expressions Read and write powers

1.1 Evaluate Algebraic Expressions Read and write powers Write the power in words and as a product. Nine to the fifth power. m to the third power.

1.2 Apply Order of Operations 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 These type of operations should be done first.

1.2 Apply Order of Operations 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! Evaluate the expression.

1.2 Apply Order of Operations PEMDAS or GEMDAS! Evaluate the expression when y = - 8. Use parenthesis when substituting (or “plugging in”) a value!

1.2 Apply Order of Operations Evaluate the expression when y = - 8. Use parenthesis when substituting (or “plugging in”) a value!

1.3 Write Expressions Translate verbal phrases into expressions. • 8 more than the product of 5 times a number w add 8 to what? multiplication of 5 and w • The quotient of 11 and the sum of 7 and a number x addition of 7 and x 11 divided by what?

1.3 Write Expressions Translate verbal phrases into expressions. • The square of a number y decreased by 13 Subtract 13 Be careful, this is NOT square root! • Four less than quantity 6 times a number n Subtract 4 from what? ORDER MATTERS! 6 multiplies n

1.3 Write and Evaluate an Expression 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 Cost of each notebook Number of notebooks x

1.3 Write and Evaluate an Expression 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 mminutes Time from home to bus stop Time on bus from bus stop to school Time on bus from school to bus stop Time from bus stop to home + + +

1.3 Write and Evaluate an Expression Find a unit rate A rate is a fraction that compares two quantities measured in different units.

1.3 Write and Evaluate an Expression Find a unit rate An airport checks in 460 passengers in 5 hours. Find the unit rate. Simplify the fraction

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. SYMBOL MEANING KEY WORDS

1.4 Write Equations and Inequalities 8 times the quantity of 11 plus a number x is 112. The product of 7 and a number y is no more than 31.

1.4 Write Equations and Inequalities • A number z is more than 8 and at most 15. rewrite • A number zis more than 8 and z is at most 15. Think: z is between 8 and 15 This can be combined to: • A number yis no less than 5 and no more than 13. rewrite • A number yis no less than 5 and y is no more than 13.

1.4 Write Equations and Inequalities Check possible solutions A solution to an equation or inequality is a value that makes the statement TRUE. Check whether the given number is a solution of the equation or inequality.

1.5 Use A Problem Solving Plan STEP 1 Read and Understand the Problem STEP 2 Make a Plan STEP 3 Solve the Problem STEP 4 Look Back • 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?

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: What we know: number of days use d gets $50 each day for food & hotel gets $0.35 for each mile drove 124 miles reimbursed $193.40 Write a Verbal Model reimbursed = miles driven x $/mile + daily allowance/day x number of days

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? Is this a reasonable answer? The trip was 3 days long.

1.5 Use A Problem Solving Plan Solve a multi-step problem 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 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? STEP 2 Make a Plan What we know: pizzas sell for $6 each What we want to know: pizzas cost $4 each # pizzas the team need to sell use p there are 10 players # pizzas each player needs to sell use x want to raise $900 Write a Verbal Model money raised = selling price x # of pizzas - cost x # of pizzas

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? STEP 3 Solve the Problem 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 number of players = total pizzas Each player needs to sell 45 pizzas.

Summer Packet Review Chapter 1 sections 1 through 5