Unit 4: Expressions, Equations, Inequalities & Circles

Name:______

Class:______

Disponzio & Vasti

Math Formula Sheet

Percent Increase or Decrease:

Percent Error:

Scale Factor:

Solving For Model or Actual: =

Interest: I = PRT

When solving for R convert to a %

When substituting in for R convert to a decimal

Current Balance/Bank Account Balance = Interest + Principal

Discount:The Item’s Cost is under a 100%.

20% is the actual discount on the item.

80% is what you paid for the item after the discount.

Commission: Discounts are applied first. NO COMMISSION ON TAX.

40% commission on all sales

Increased current commission by 30%.

Markup:The profit a stores earns off the sales of their products. =

The population increased by 35%.

Current membership 200, increased by 29%.

Markup Percent: Retail % - 100%

Markup amount: Retail Price – Wholesale Price Macys bought a shirt for $150 and sold the same shirt for $200. The markup or profit for the shirt is $50.

Tax: Increases the cost of an item. The item costs more then 100%.

8% tax included.

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10. A deep sea fiver went 59 feet under the surface, then swam up 31 feet. How many feet below the surface is the diver? / 11. While playing football, Matt lost 3 yards, then gained 21 yards, then lost 4 yards. How many yards did he gain from his three plays? / 12. If you are standing at the top of a mountain 6,684 feet above sea level and there is a submarine 350 below sea level, how much higher is your elevation than the submarine?
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22. / 23. / 24.
25. / 26. / 27.
28. / 29. / 30.
31. / 32. / 33.
34. / 35. / 36.
37. / 38. Evaluate
When and / 39. Evaluate
Whenand
40. Evaluate
When and / 41. Evaluate
When and / 42. Evaluate
When and
43. / 44. / 45.
46. / 47. (6 / 48. Isproportional to?
49. Isproportional to? / 50. Isproportional to? / 51. Isproportional to?
52. / 53. / 54.
55. / 56. Solve for x. / 57. Solve for x.
58. Solve for x. / 59. Solve for x. / 60. Solve for x .

Unit 1 & Unit 2: Review Questions

Unit 3 & Unit 4: Review Questions

Solve for x:

Factor:

Factor:

Factor:

Factor:

Find the scale factor: model’s length is 2 inches and the actual height is 8 ft.

Find the actual height: Model’s height is 4 inches and the Scale Factor is 20 feet per inch

Find scale factor: Toy’s height is 1.5 inches and the car’s height is 30 feet.

Find the model’s height: Building is 66 feet tall and the Scale Factor is 5.5feet per inch

Find percent error: Mike was traveling 75 MPH but the speed limit was 65 MPH.

Find percent error: A block’s length was 13 feet but Paul measured the block to be 18 feet.

Find the percent error: A block weighed 100 lbs. but Susan measured the block to be 180 lbs.

Find the percent error: Sara measured her height to be 5 feet but her Doctor said she was 5.5 feet.

Find the percent increase: started with 40 dollars and ended with 100 dollars.

Find the percent increase: started with 30 dollars and ended with 40 dollars.

Find the percent increase: started with 50 dollars and ended with 65 dollars.

Find the percent increase: started with 8 dollars and ended with 24 dollars.

Find the percent decrease: started with 50 dollars and ended with 25 dollars.

Find the percent decrease: started with 60 dollars and ended with 10 dollars.

Find the percent decrease: started with 100 dollars and ended with 65 dollars.

Find the percent decrease: started with 40 dollars and ended with 5 dollars.

Find the commission: Jim’s salary was 50,000 dollars and he earned 6 percent.

Find the commission: John’s salary was 80,000 dollars and he earned 8.5 percent.

Find the discount: Tim bought shoes for 180 dollars and received a 5 percent discount.

Find the discount: Mike bought shirts for 380 dollars and received a 6.5 percent discount.

Find the sales price: Tim bought shoes for 180 dollars and received a 5 percent discount.

Find the sales price: Mike bought shirts for 380 dollars and received a 6.5 percent discount.

Find the tip amount: Sara spent 35 dollars on a manicure. She gave a 5.5 percent tip.

Find the tip amount: Peter spent 125 dollars on a dinner. He gave a 7.5 percent tip.

Find the total bill: Sara spent 35 dollars on a manicure. She gave a 5.5 percent tip.

Find the total bill: Peter spent 125 dollars on a dinner. He gave a 7.5 percent tip

Find the tax amount: Joe bought a car for $28,000 and was charged a tax rate of 5.5 percent.

Find the tax amount: James bought an iPad for $500 and was charged a tax rate of 8.5 percent.

Find the purchase price: Joe bought a car for $28,000 and was charged a tax rate of 5.5 percent.

Find the purchase price: James bought an iPad for $500 and was charged a tax rate of 8.5 percent.

Find the number of defective chairs: there are 680 chairs and 20 percent were defective.

Find the retail price: A company bought a chair for $175 there was also a 40% markup added.

Find the markup percent: A company bought a couch for $350 and sold for $490.

Find the original price: A table was sold for $378 including an 8% tax.

Combining Like Terms HW Day #1

15.
/ 16.

Combining Like Terms HW Day #2

15.
/ 16.

Distributive Property Challenge Problems

Problem 1:

Problem 2:

Problem 3:

Problem 4:

Problem 5:

Problem 6:

Problem 7:

Problem 8:

Problem 9:

Problem 10:

Aim: How do we evaluate algebraic expressions?

Warm up: What is a variable?

Homework:

NOTES:

Evaluate: To plug in a ______for a variable

Step 1: Plug in value for each variable.

Step 2: Follow order of operations

Step 3: Make sure answer is in simplest form.

Problem 1: Simplify the expression by letting
/ Problem 2Simplify the expression by letting

Problem 3: Simplify the expression by letting

Problem 1: Simplify the expression if

/ Problem 2: Simplify the expression if

Problem 3:Simplify the expression if

/ Problem 4: Simplify the expression if

Problem 5:Four Ones Car Service charges a flat fee of $3.50 for all its customers.

Queens Pickups: $2.50 per mile
Manhattan Pickups: $4.50 per mile.

Susan was picked up in Queens and traveled 35 miles by taxi. How much was her bill?
Peter was picked up in Manhattan and traveled 25 miles by taxi. How much was his bill?

Who paid more for their taxi? Justify your answer.
Problem 6: Sara evaluated the following expression by using for k. Her final answer was 1. What mistake did Sara make when evaluating her expression? Justify your answer using mathematical terminology.

Aim: How can we simplify expressions by combining like terms?

Warm up:Simplify:

NOTES:

Rules For Combing Like Terms:

Get rid of any first

Follow Integer Rules to combine all constants.

Follow Integer Rules to combine all variables that have the same letter and same power.

Like Terms: Unlike Terms:

Problem 1: Simplify.
/ Problem 2Simplify.

Problem 3: Simplify.

Explain if the following expression is in simplest form. Justify your answer.

Aim: How do we use the distributive property ?

Warm up: solve

Homework:

NOTES:

Like Terms: Have the same ______and the same power.

Combine Like Terms:Keep the variable and powerADDthe coefficients.

If there is no number in front of a coefficient it is a 1.

Distributive Property

 * Use the distributive property because the terms inside the parenthesis are not like terms.

 Always combine like terms before distributing value.

Problem 1: Simplify.
/ Problem 2 Simplify.

Problem 3: Simplify.

Problem 1: Simplify.
/ Problem 2: Simplify.

Problem 3: Simplify.
/ Problem 4: Simplify.

Problem 5: Mike said B is equivalent to the following expression . Do you agree with him, justify your answer using mathematical terminology.

Problem 6: Susan simplified the expression below and got . Do you agree with her answer? Justify your answer using mathematical terminology.

Aim: How do we use the distributive property ?

Warm up: solve

Homework:

NOTES:

Step 1: Combine like terms in the parenthesis

Step 2: Perform the distributive property

Step 3: Rewrite Expression.

Step 4: Combine like terms to from a simplified expression:

Problem 1: Simplify.
/ Problem 2 Simplify.

Problem 3: Simplify.

Problem 1: Simplify.
/ Problem 2: Simplify.

Problem 3: Simplify.
/ Problem 4: Simplify.

Problem 5:Mary saidwhenis subtracted from 1 the result is . Do you agree with Mary’s answer? Defend your answer using mathematical terminology.
Problem 6: Danny simplified the expression below and got. What mistakes did he make? Justify your answer using mathematical terminology.

Aim: How do we find equivalent expression ?

Warm up: Can you combine ? Justify.

Homework:

NOTES:

Equivalent Expression: Must always be ______.

Step 1: Simplify the ______side by using order of operations.

Step 2: Simplify the ______side by using order of operations.

Step 3: See if both side are ______.

Problem 1: Are the following expressions equivalent?
/ Problem 2 Are the following expressions equivalent? Justify.

Problem 3: Is equivalent to ? Justify your answer using mathematical terminology.
Problem 1:Are the following expressions equivalent?
/ Problem 2: Are the following expressions equivalent?

Problem 3 Are the following expressions equivalent?
/ Problem 4: Are the following expressions equivalent?

Problem 5: Determine which expressions are equivalent. Justify your answer using mathematical terminology.

Example 1: /
Example 2: /
Problem 6: Sara said the following expressions are equivalent. Do you agree with her reasoning? Justify your answer using mathematical terminology. .

Aim: How do we find equivalent expressions

Warm up: Can you combine ? Justify.

Homework:

NOTES:

Equivalent Expression: Must always be ______.

Step 1: Simplify the ______side.

Step 2: Simplify the ______side.

Step 3: See if both side are ______.

Problem 1: GameStop has a supply of for the new PlayStation. The demand for PlayStation is . Does GameStop’s supply equal GameStop’s demand? / Problem 2 Chipotle’s monthly expenses equal. Their total monthly revenue is represented by . Does Chipotle’s revenue equal their total expenses?
Problem 3: Gap’s total expenses for November equal. During November Gap’s total monthly revenue is represented by Does Gap have enough revenue to cover their total expenses in November? Justify.
Problem 1:Are the following expressions equivalent?
/ Problem 2: Are the following expressions equivalent?

Problem 3:Starbucks’ monthly expenses equal. Their total monthly revenue is represented by . Does Starbucks’ revenue equal their total expenses? / Problem 4: Home Depot has a supply of for paint in May. The demand for paint in May is . Does Home Depot’s supply equals their customers demand?
Problem 5: Sara said the follow expressions were equal. Do you agree with her assessment? Justify.

Problem 6: Best Buy is trying to figure out if theirvideo game supply of Star Wars is enough to meet the demand of their customers.

The video game supply of Star Wars is represented by .
The demand for the Star Wars game is represented

Will Best Buy be able to meet the needs of their customers? Justify your answer using mathematical terminology.

Aim: How do we solve a two-step equation

Warm up: Solve

Homework:

NOTES:

Solving A Two-Step Equation

Step 1: Distribute

Step 2: Combine like terms

Step 3: Use inverse operations to get ride of the ______.

Step 4: Isolate the variable by diving or multiplying by the reciprocal.

Problem 1: Solve for x.
/ Problem 2 Solve for x.

Problem 3: Sara said m has to be equal to 30. Do you agree with her? Justify your answer.

Problem 1: Solve for y.
/ Problem 2: Solve for s.

Problem 3: Solve for x.
/ Problem 4: Solve for m.

Problem 5: A number n, is multiplied by then increased by . If the answer is equal to . How could you use a 2-step equation to find the value of n? Justify your answer using mathematical terminology.
Problem 6: Sara said the value of p would have to be . Justify what mistake Sara made and how to solve this problem correctly?

Aim: How do we write equation

Warm up: solve

Homework:

NOTES:

Writing A Two-Step Equation

Step 1: Determine Constant. A Constant is only paid/done ______
Step 2: Determine Coefficient. A Coefficient happens monthly, weekly, daily.
Step 3: Determine Variable. A Variable is what is being ______for.
Step 4: Write what the variable represents. Let x = monthly rates.

Problem 1: World’s Gym charges a one-time set up fee of $50. Then a monthly fee of $60. If Susan has $500 to spend on her membership, how many months can Susan go to the gym? / Problem 2 White Glove Transportation charges a destination fee of $250. A $99 fee per hour is then applied. If Mary Spends $1,042 on her move, how many hours did she spend moving?
Problem 3: Of the 1850 books in the library, there are four times as many books in the teen section than in the sci-fi section. How many books are in each section?

Could the amount of books in the sci-fi section ever exceed the number of books in the teen section? Justify.

Problem 1: Verizon charges a one-time set up fee of $150. Their monthly fee is $120. If Jen has $1,500 to spend on her cell phone bill, use an equation to determine how many months Jen could afford? / Problem 2: UPS Freight charges a flat fee of $370. A fuel charge of $89.50 is applied per day. Britney Spent $1,533.50 on her shipment. Use an equation to determine how long her package was in transit for?
Problem 3: Peter is driving cross-country. He already drove miles. He then drives miles each day. If Peter traveled , use an equation to determine how many days he spent travelling? / Problem 4: Mike is training for a marathon. He already ran miles. He than runs miles each day to complete his training. If Mike ran , use an equation to determine how many days he spent training for a marathon?
Problem 5: How does each equation differ? Would you use the same strategies to solve each equation? Justify.

A company ordered 20-boxed lunches for $157.60. If each boxed lunch cost the same amount of money, create an equation to find out how much one boxed lunch cost.
A trailer will be used to transport 60-kilogram crates to a store. The weight limit on a trailer is 1,528 kilograms. If an 88-kilogram box was already loaded, what is the greatest amount of crates a trailer can carry?

Problem 6: Mrs. Disponzio has $350 to spend on parking and admission to the zoo. Parking will cost $26 and tickets cost $22.50 per person, with tax included.
Part A: Write and solve an equation that can be used to determine the number of people Mrs. Disponzio can bring including herself.
Part B: Would your answer in Part A change if Mrs. Disponzio decided to not include herself in the amount of people she can bring to the zoo? Justify your answer.

Aim: How do we solve a two-step equation

Warm up: solve

Homework:

NOTES:

Solving A Two-Step Equation with Variables on Both Sides of the Equal Sign

Step 1: Distribute

Step 2: Combine ______terms.

Step 3: Bring the variable to one side of the equal sign.

Step 4: Use inverse operations to solve the 2-step equation.

Problem 1: Solve for x.
/ Problem 2 Solve for x.

Problem 3: Danny said you would have to subtract in order to get the correct answer. Explain to Danny how to solve this problem correctly.

Problem 1: Solve for y.
/ Problem 2: Solve for s.

Problem 3: Solve for x.
/ Problem 4: Solve for m.

Problem 5: The perimeter of a pentagon is 20.5 cm. Four sides have the same length and the other side has a length of 1.6 cm.
Part A: How long is side N? Justify your answer using mathematical terminology.
Part B: Create and equation with variables on both sides of the equal sign that when solved will have the same value as N in Part A.
Problem 6: Danny said you could not solve for R because the coefficient is and you can’t solve for R if the coefficient is a negative. Explain to Danny how he can solve for R without getting a negative coefficient.

Aim: How do we solve a two-step equation

Warm up: solve

Homework:

NOTES:

Solving A Two-Step Equation with Variables on Both Sides of the Equal Sign

Remember touse inverse operations when solving a 2-step equation.

Problem 1: Solve for y.
/ Problem 2 Solve for x.

Problem 3: Explain the steps needed to solve for x.

Part B: How would you prevent yourself from making a mistake when solving for x? Justify.
Problem 1: Solve for y.
/ Problem 2: Solve for s.

Problem 3: Solve for x.
/ Problem 4: Solve for m.

Problem 5: Create a rubric for a struggle student on how to solve for x.

Part B: Danny says a rubric does not prevent a student from making mistakes? Do you agree with him? Justify.
Problem 6: Solve for a.

Part B: Would you distribute the negative or the first? Justify your answer.

Aim: How do we solve an inequality

Warm up: Solve

Homework:

NOTES:

At Most: Less than or equal to.

At Least: Greater than or equal to.

Less Than: Less than

Greater Than: Greater than

Problem 1: Mike has at most $150 to spend on t-shirts. If each shirt cost $22. How many t-shirts can he buy? / Problem 2 Ryan has $500 to spend on a PlayStation and games. If the system cost $400 and each game cost $35, how many games could Ryan afford?
Part B: An 8.85% sales tax was added to Ryan’s total purchase. Would the tax affect how many games Ryan could afford? Justify your answer.
Problem 3:John is trying to save at least $256.49 to buy a new IPhone. John has $40 in his savings account and can afford to save $38 a week from his allowance. How many weeks will it take John to get his new phone?
Problem 1: Solve for y.
/ Problem 2: Solve for x.

Problem 3: Morgan has at most $150 to spend on clothing. She bought a skirt for $30 and spends the rest of her money on shirts. If each shirt costs $25. What is the greatest number of shirts Morgan could buy? / Problem 4: Peter has $750 to spend on clothing. He bought a pair of jeans for $90 and spent the rest of his money on sneakers. Each pair of sneakers cost $95. How many sneakers could Peter afford?
Problem 5:Amanda wants to ride her bike 80 miles this week. She already rode 18 miles this week. Use an inequality to determine the mean number of miles,Amanda would need to ride her bike each day to achieve her goal?
Part B: Danny said Amanda would have to bike 8.8 miles a day. What mistake did Danny make? Justify your answer using mathematical terminology.
Problem 6: Mary has at most $1,400 to spend on new furniture. She purchased a table for $989.50 and needs to spend the rest of her money on chairs. Each chair costs $65.50.

Will Mary be able to afford 8 chairs? Justify
Mary found a coupon for 50% off the table, would this affect the amount of chairs Mary could buy? Justify.