NJ DOE Unit 2_Grade 3vcs7thgrademath.weebly.com/.../review_sheet_answers.docx · Web viewGrade 7 Unit 3 Review Sheet 1. Alexander walked at a rate of Author Windows SOE Manager Created

Name _______________________ Period _____ Date _______________

Grade 7 Unit 3 Review Sheet

1. Alexander walked at a rate of mile every 20 minutes. What is his walking rate in miles per hour?

Make a proportion:

milesminutes

=

23

20= x

60

Solve for x by cross multiplying

20x = 60 (2/3)20 x = 40

x = 2

2. A store sells a 2 14 pound package of cheese for $9.

What is the unit price of the cheese in the package?

Unit Price = priceitem

= 9

2 14

9 ÷ 94

Leave, Change, Flip

91 * 4

9

36/9

5/27/2023 5:16 AM NJ DOE Unit 3_Grade 7 P a g e | 1

Unit Price of Cheese: $4


3. Monica paints a wall that has an area of 45 15square yards.

She uses 1 35 gallons of paint.

Part A: What is Monica’s rate of paint coverage in square yards per gallon (UNIT RATE)? Show your work.

square yardsgallons

=45 1

5

1 35

=

226585

Dividing Fractions: Leave Change Flip

2265 * 5

8=1130

40=¿

28.25 sq yds /gal

Part B: The label on the paint container states that the average (usual) paint coverage rate is 225 square feet per gallon.

What is the difference in square feet per gallon between Monica’s rate of paint coverage and the rate indicated on the label on the container?

Show your work. (HINT: )

Monica: 28.25sq yds * 9 = 254.25 sq feetor

Set up a proportion:1 square yard9 square feet

=28.25 sq ydsx

Difference: Monica – Label254.25 – 225

29.25 sq ft/gal


4. Mattie runs on a track that is mile long. Today, Mattie ran 5 times around the track in 12 ½ minutes. Did Mattie run faster or slower than 5 miles per hour during today’s run? Use numbers and words to explain how you determined your answer.

Miles Mattie Ran: 5 * ¼ = 5/4 miles

Make and solve a proportion

milesminutes

=

54

12 12

= x60

x = 6 miles per hour

Mattie ran faster than 5 miles per hour during today’s run.

5. Which of the following tables shows a proportional relationship between x and y ?

a. b.

c. d.


Make ratios: yx

23

46

69

812

k = 2/3

x y 3 2 9 427 881 16

x y 3 2 6 4 9 612 8

x y 3 2 6 5 9 812 11

x y3 25 37 49 5


6. Nancy saved money in her piggy bank to buy a music player. She started by saving $40 that she received for her birthday, and then she saved $5 from her allowance each month for 6 months. The table below shows the total amount of money Nancy had saved at the end of each month for 6 months.

Number of Months Total Amount of Money Nina Saved

1 $452 $503 $554 $605 $656 $70

Is the relationship shown in the table between the number of months and the total amount of money Nancy saved a proportional relationship? Explain your reasoning.

No a proportional relationship does not exist because the ratios are not equal and there is no k.


7. For each of the relationships between x and y shown on the graphs in the table below, indicate whether the relationship between x and y is proportional by checking the appropriate box in the table.

Yes No


8. The height of a burning candle over a 10 hour period is shown in the graph below.

Is the height proportional to the time? Explain your answer.

No the height is not proportional to the time because the graph does not go through the origin.


9. The equation below shows the relationship between the number of apples purchased, a, and the total cost of the apples in dollars, c. Based on the equation, what is the cost per apple, in dollars?

a8= c

6

a. $0.75b. $1.33c. $8.00d. $6.00

10. The table below shows the amounts of milk used in relation to the amount of sugar used to bake a cake. Based on the information in the table, how many cups of milk will used for 1 cup of sugar?

Amount of Milk (cups) 14

13

1 12

1 13

Amount of Sugar (cups) 2 14 3 13 1

2 15

Make a ratio and reduce. Choose the easiest pair: 3 and 13

sugarmilk

= 313

9 cups of milk


costapple

=68 = $0.75

11. The graph below shows the relationship between speed and time for freely falling object.

Velocity is defined as the change in speed with respect to time. What is the velocity of the car in meters per second every second?

Look at the graph where time = 1 second and find speed.

Velocity ¿ speedtime ¿ 10m/ s1 sec

12. The number of students attending the seventh-grade class trip is 3 times the number of teachers attending. What is the ratio of teachers to students attending the class trip?

teachersstudents = 1

3


13. A recipe that makes 8 servings requires cups of milk. Which of the following equations can be used to find the number of servings, x, that can be made using 14 cups of milk, based on the recipe?

a.

b.

c.

d.

14. Molly reads 36 pages of a book every hour. Write an equation that models the relationship between x, the number of hours Molly reads,

and y, the number of pages of the book he reads.

Equation: y = kx

k = yx= pageshours

=3634

=48

k = 48

y = 48x



15. A car consumes 9.6 gallons of gasoline during a 336-mile trip. Write a proportion that can be used to find m, the number of miles that the car can travel using 24 gallons of gasoline if the car consumes gasoline at the same rate consumed during the trip. Do NOT solve the proportion.

milesgallons = 336

9.6= m

24

16. A machine can enlarge a 6-inch by 4-inch rectangular photograph to any of the dimensions shown in the table below. Which equation represents the relationship between the length of the enlargement, and w, the width of the enlargement?

Length (inches)

Width (inches)

12 818 1224 16

a.

b.

c. plug in the lengths from table; see if you get same widths

d.


17. The graph below shows the total number of inches of rain that fell, y,in terms of time the rain fell, x. The time is measured in hours after12:00 P.M., with corresponding to the time 12:00 P.M. Explainthe meaning of the point in the context of this problem.

Point (0,0) means that at 0 hours it rained 0 inches.


18. The graph below shows the distance a car can travel, y, usingx gallons of gasoline. Show your work or explain your answer to each of the following questions.

Part A: How many miles per gallon does the car get?

This is a unit rate question. Find k!

Take point (4, 100). Make a ratio: 100/4 = 25

25 miles/gallon

Part B: How many miles can the car travel using 9 gallons of gasoline?

Use answer from Part A: 25 * 9 = 225 miles

or make and solve a proportion

251

= x9

x = 225 miles


19. The graph below relates y, the distance Kelly walked, to x, the amount of time that Kelly walked.

Part A: What is the value of y when

Look at graph and see that y = 200 when x = 1

or find k by taking point (2, 400)

400/2 = 200

Part B: Explain how you can use your answer to Part A to predict, within the context of the situation, where Kelly is at time t minutes.

Possible Answer:

I can multiply the time in minutes by 200 because Kelly walked at a rate of 200 feet per minute.

or

Since the unit rate is 200 feet per minute, I can multiply the time (t) by 200 to find the distance.


20. The equation below represents the relationship between x and y, where y represents the number of quarts of lemonade that can be made from x scoops of a powder mix.

xy=5

4

Part A: On the grid below, graph the equation

xy=5

4

Part B: Determine the number of scoops of powder mix required to make 4 quarts of lemonade.

scoopsquarts

=45= x

4

x = 3.2


Make a table and graph points

Scoops (x) 2.5 5 10Quarts (y) 2 4 8

21. On a map, inch between locations represents an actual distance of 2 miles between the locations. What is the actual distance, in miles,

between two cities that are inches apart on the map?

scaleactual

=

142

=3 3

4x

x = 30 miles

22. Darryl deposits $5,000 in a simple interest account. He earned $250 in interest after 1 year. Lisa deposited $7,000 into an account that has the same interest rate as Darryl’s account. How much money did Lisa earn in interest after 1 year?

interestdeposit

= 2505000

= x7000

x = $350


23. Joe made a scale drawing of the community pool in his town. The scale drawing is shown below. The pool is rectangular and has a perimeter of 44 meters. What are the length and width, in meters, of the pool? Show your

work.

Perimeter of scale drawing = 4 + 6 + 4 + 6 = 20cmScale: 20cm = 44cm

scaleactual

=2044

=6L

scaleactual

=2044

= 4W

L = 13.2 mW = 8.8 m

24. As a real estate agent, Lauren earns 2.5% commission on her sales. Lauren’s goal is to earn $5,000 in commission this month. What is the dollar amount of sales that Lauren must have this month to earn $5,000 in commission?

a. $5,125b. $12,500c. $20,000d. $200,000


4 cm

6 cm

Make a proportion.

percent100

= commissionsales

Change percent to a fraction.2.5100

=5000x

x = 200,000

25. Use a protractor and a ruler to draw an equilateral triangle with side lengths of 4 inches.

Protractor: All angles in an equilateral triangle should be 60°

Ruler: All sides should be 4inches

26. Use a ruler and a compass to draw an isosceles triangle that meets the following requirements.

At least one side must measure 6 centimeters. At least one side must measure 3 centimeters.

Triangle should have sides 3, 6, and 6. Use compass.


27. Triangle ABC has the following properties.

The length of side AB is 7 centimeters. The length of side BC is 5 centimeters. The measure of angle A is 40 degrees.

Use a protractor and a ruler to draw a triangle that satisfies the properties above.

See “constructing triangles” video on website

AB and AC should be make the 40° angle, not BC

28. Can a triangle be constructed with side lengths of 6 inches, 8 inches, and 13 inches? Use freehand drawings and words to explain your answer.

Yes because the sum of the two shorter lengths (6+8 = 14) is greater than the third length (13).


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NJ DOE Unit 2_Grade 3vcs7thgrademath.weebly.com/.../review_sheet_answers.docx · Web viewGrade 7 Unit 3 Review Sheet 1. Alexander walked at a rate of Author Windows SOE Manager Created