Name:___________________________________ Date:________________________

7th Math Unit 1 TestProportional Reasoning

Part Points Skill Tested

IMultiple Choice _____ / 26 points

Solve word problems with rates and proportions

Identify the constant of proportionality in tables in graphs

Write an equation based on a graph

IIOpen Response _____ / 18 points

Compare unit rates with fractional parts. Represent proportional relationships using

an equation. Explain what a point (x, y) on the graph of a

proportional relationship means in terms of the situation.

IIIConstructed

Response

_____ / 23 points

Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane.

Compute unit rates associated with ratios of fractions in the context of measured quantities

Use unit rates to solve problems Write equations to find the missing values of

a quantity

_____ / 67 points Total Score

Parent Signature Date Student Signature DatePart I Multiple Choice (2 points each)

%

1) Bruce said it takes 20 minutes to complete a page of math homework. He creates the following table.

Homework (pages) 1 2 3 4

Time (min) 20 40 60 80

Which of the following is NOT true for this data?

a) The table does not show a proportional relationship.

b) The ratios are the same for all table entries.

c) The constant of proportionality is 20.d) The table shows a proportional

relationship because the unit rate is the same no matter how many pages of homework Bruce does.

2) If it takes Emily 35 of an hour to walk 3

miles, then what is her unit rate?

a) 0.2 mi/hr.b) 1.8 mi/hr.c) 3.6 mi/hr.d) 5 mi/hr.

3) Jessica’s apple pie recipe calls for 3½ cups of flour and 8 apples. How many cups of flour will she need if she uses 16 apples?

a) 4.5 cupsb) 7 cupsc) 7.2 cupsd) 11.5 cups

4) Look at the graph below.

What is the correct equation for the line shown in the graph?

a) y = ½ xb) x = ½ yc) y = 2xd) y = x

5) Timothy’s earnings vary directly with the number of hours he works. He worked 40 hours and earned $660.00. What equation represents the relationship between the number of hours Timothy works, h, and his earnings, e?

a) e = 11.50hb) e = 16.50hc) e = 40hd) e = 66h

7) The graph below shows the relationship between the distance a taxi travels and the cost of the taxi.

Is the relationship proportional?

a) The relationship is proportional because the graph is a straight line.

b) The relationship is not proportional because the graph does not pass through the origin.

c) The relationship is not proportional because the graph is not a straight line.

d) The relationship is proportional because the cost increases as the distance increases.

8) Mr. Creech’s little truck can travel 25 miles on one gallon of gas. The cost of gas is $3.75 per gallon. Which equation would calculate the total cost of gas, y, based on the number of miles traveled, x?

a) y = 0.11xb) y = 0.15xc) y = 1.50xd) y = 6.67x

9) What is the constant of proportionality based on the graph below?

a) $0.25/lb.b) $1.00/lb.c) $4.00/lb.d) $16.00/lb.

12) Carli’s class built some solar-powered robots. They raced the robots in the parking lot of the school. The graph below shows the distance d, in meters, that each of the three robots traveled after t seconds.

How fast is robot B traveling?

a) 23 meters per second

b) 23 seconds per meter

c) 112 meters per second

d) 112 meters per second

13) A train traveled 16 of the distance

between two cities in 23 hour. At this rate,

how many hours will it take the train to travel the entire distance between these two cities?

a) 19 hour

b) 14 hour

c) 113 hours

d) 4 hours

Part II. Open Response (3 points each)Show your work on a separate piece of paper.

14)

Based on the graph above, how much

would 312 pounds of shrimp cost?

Answer__________________

15) Jack and Jill are reading the same

chapter from the same book. Jack read 47 of

the chapter in 13 hour and Jill read 35 of the

chapter in 14 hour. Who is reading at a

faster pace? Explain.

Answer___________________________________

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_________________________________________15) The graph below shows the number of servings in different amounts of frozen yogurt. Use the graph for the next two questions.

a) Write an equation that gives the number of servings y, in x pints of frozen yogurt.

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b) Malory extends the frozen yogurt graph so that is passes through the point (8, q). What is the value of q? What does this point represent?

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16) If 34 pound of candy cost $20.50, how

much would 1 pound of candy cost?

17) The graph below shows the area, y, (in square feet) that a robotic vacuum cleans in x minutes.

a. Write an equation in the form of y = kx to represent the unit rate.

b. What does the equation mean?

c. Use the equation to find the area cleaned in 5 minutes.

18) Two cars leave from the same city at the same time and drive in the same direction. The table shows the distances traveled by each car.

Determine whether the relationship between the number of hours traveled and the number of miles traveled is proportional for each car. Use the table to explain how you determined your answers.

19) It took a sloth 34 of an hour just to travel 12 of a meter. At that rate, how far can the

sloth travel in 5 hours?

20) Use the graph below to answer the following questions.

a) What is Mahesh’s unit rate?

b) How many pages does Anna read in an hour (notice the x-axis is in minutes!)?

c) Who reads faster? Explain.