G7 U1 Assessment
Name: _________________________________________ Date:________________
Grade 7 Unit 1 Analyzing Proportional Relationships 1. Fred can paint a 30 foot fence in 5 hours. Which of the following is true? (only one answer)
A
The unit rate is 6 feet in one hour.
B
The unit rate is 30 feet in 5 hours.
C
The unit rate is 1 foot per 1/6 hours.
D
none of these
2. If a beanstalk grows 2 inches per day, how many inches will it grow in two weeks?
A
14 inches.
B
28 inches.
C
7 inches
D
12 inches.
3. Eric can build 72 model racecars in 3 days. How many can he build in one day?
A
12 cars
B
22 cars
C
16 cars
D
24 cars Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 1
4.
For each of the following, circle yes if the fractions are equal and no if they are not equal. A B C D
5.
28 12 6 12 8 13 21 12
𝑎𝑛𝑑
14
𝑎𝑛𝑑
1
𝑎𝑛𝑑
1
𝑎𝑛𝑑
6
2
6 90 16
yes
no
yes
no
yes
no
yes
no
The tables below give the dimensions of two rectangular prisms. What is the Proportion of prism 1 to prism 2?
length width height A B C D 6.
Prism 1 50 in 30 in 50 in
Prism 2 30 in 20 in 30 in
5 2 5 3 3 2
They are not proportional.
Phil worked 2 hours on Monday and earned $18, 4 hours on Tuesday and earned $36 dollars. If there was a constant of proportionality between his hours and his earnings, how much would he earn on Wednesday if he worked 5 hours? A
45 dollars
B
50 dollars
C
42 dollars
D
55 dollars Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 2
7.
Jerry recorded some values in a laboratory on the graph below. Which two values share proportionality? Hint: find the ratio between the x and y value of each point. Point 1 2 3 4
8.
A
Points 1 and 4
B
Points 2 and 4
C
Points 1 and 3
D
None are proportionate.
x 1 2 3 9
y 3 4 9 10
The amount of sugar needed for a cookie recipe is proportional to the number of cookies. A batch of 39 cookies calls for 3 tbsp. sugar. What is the constant of proportionality between cookies and tablespoons of sugar?
A
12
B
8
C
13
D
5
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 3
9.
Roy eats a lot of meat, but his stomach hurts if he eats too much. His doctor says to eat a 5 to 3 ratio of vegetables to meat. How many pounds of vegetables should he eat if he ate 6 pounds of meat this week? A
10
B
11
C
12
D
13
10. The total distance d that Ann drives is proportional to the number t of hours that she drives at a constant rate r. Which of the following is the equation that expresses the relationship between her distance driven and the numbers of hours she drives. A
t=r • d
B
r=d • t
C
d=r • t
D
r=I • d • k
11. Ned purchases n bottles of water at p dollars per bottle. The total cost c is proportional to the number of bottles he buys. If there a fee, f on the whole purchase which of the following is the equation that expresses the relationship between his total cost and the number of bottles he buys.
A
c=p • n + f
B
p = c • f +n
C
f = n • c +p
D
n=p•c+f Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 4
12. Jen reads a certain amount of pages per hour. The page number she ends up on is proportional to the number of hours she reads. If Jen’s teacher says she does not have to read the first 5 pages of the book, which of these is the equation that expresses the relationship between the pages Jen is on the number of hours she reads.
A
t=r • p +5
B
5=t+p•r
C
r=t • p +5
D
p=r • t +5
13.
Stan’s boss lost all the paper work for his employee’s wage. He is trying to figure out How much Stan makes per care washed, (r). The paper work that hasn’t been lost States that Stan once made 55 dollars for 10 cars and 33 dollars for 6 cars washed. Help Stan’s boss calculate r, the unit rate.
A
5.2 dollars/ car washed
B
6 dollars/car washed
C
5.5 dollars/ car washed
D
4.8 dollars/ car washed
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 5
14. The graph below shows Phil’s distance and time on his run. Find the unit rate. miles y
•
2
• hours x
A
3 miles/hour
B
4 miles/hour
C
5 miles/hour
D
6 miles/hour
15. A sweater is on sale for 30% off. If the original price was $15, what is the sale price?
A
$9.50
B
$10.50
C
$11.50
D
$12.50
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 6
16.
John Joy washes dishes for t minutes, at a rate of 6 dishes per hour. The total amount of dishes washed, w, is proportional to the number of hours she works. Write an equation that expresses the relationship between total work done and the number of hours she works. Graph this equation and use it to predict how many hours it takes to wash 15 dishes.
17. A dinner costs $24 plus an 8% tax. What is the total? Show your work.
18. The price of a gallon of gas at a service station has dropped from $4 to $3.50. What is the percent decrease? Show your work.
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 7
19. A couple has dinner at a restaurant where there is a 10% deal off the price before tax. However there is a 10% sales tax on the price after the discount. Does the tax end up canceling out the deal? Explain how you know.
20.
The balance b in Harry’s savings account is proportional to the number m of months he has the account, depositing money at a constant rate of 800 dollars per month. Write and graph the equation that represents this. Hint: Scale the y axis.
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 8
Grade 7 Unit 1 Analyzing Proportional Relationships 1. Fred can paint a 30 foot fence in 5 hours. Which of the following is true? (only one answer)
A
The unit rate is 6 feet in one hour.
B
The unit rate is 30 feet in 5 hours.
C
The unit rate is 1 foot per 1/6 hours.
D
none of these
2. If a beanstalk grows 2 inches per day, how many inches will it grow in two weeks?
A
14 inches.
B
28 inches.
C
7 inches
D
12 inches.
3. Eric can build 72 model racecars in 3 days. How many can he build in one day?
A
12 cars
B
22 cars
C
16 cars
D
24 cars Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 1
4.
For each of the following, circle yes if the fractions are equal and no if they are not equal. A B C D
5.
28 12 6 12 8 13 21 12
𝑎𝑛𝑑
14
𝑎𝑛𝑑
1
𝑎𝑛𝑑
1
𝑎𝑛𝑑
6
2
6 90 16
yes
no
yes
no
yes
no
yes
no
The tables below give the dimensions of two rectangular prisms. What is the Proportion of prism 1 to prism 2?
length width height A B C D 6.
Prism 1 50 in 30 in 50 in
Prism 2 30 in 20 in 30 in
5 2 5 3 3 2
They are not proportional.
Phil worked 2 hours on Monday and earned $18, 4 hours on Tuesday and earned $36 dollars. If there was a constant of proportionality between his hours and his earnings, how much would he earn on Wednesday if he worked 5 hours? A
45 dollars
B
50 dollars
C
42 dollars
D
55 dollars Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 2
7.
Jerry recorded some values in a laboratory on the graph below. Which two values share proportionality? Hint: find the ratio between the x and y value of each point. Point 1 2 3 4
8.
A
Points 1 and 4
B
Points 2 and 4
C
Points 1 and 3
D
None are proportionate.
x 1 2 3 9
y 3 4 9 10
The amount of sugar needed for a cookie recipe is proportional to the number of cookies. A batch of 39 cookies calls for 3 tbsp. sugar. What is the constant of proportionality between cookies and tablespoons of sugar?
A
12
B
8
C
13
D
5
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 3
9.
Roy eats a lot of meat, but his stomach hurts if he eats too much. His doctor says to eat a 5 to 3 ratio of vegetables to meat. How many pounds of vegetables should he eat if he ate 6 pounds of meat this week? A
10
B
11
C
12
D
13
10. The total distance d that Ann drives is proportional to the number t of hours that she drives at a constant rate r. Which of the following is the equation that expresses the relationship between her distance driven and the numbers of hours she drives. A
t=r • d
B
r=d • t
C
d=r • t
D
r=I • d • k
11. Ned purchases n bottles of water at p dollars per bottle. The total cost c is proportional to the number of bottles he buys. If there a fee, f on the whole purchase which of the following is the equation that expresses the relationship between his total cost and the number of bottles he buys.
A
c=p • n + f
B
p = c • f +n
C
f = n • c +p
D
n=p•c+f Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 4
12. Jen reads a certain amount of pages per hour. The page number she ends up on is proportional to the number of hours she reads. If Jen’s teacher says she does not have to read the first 5 pages of the book, which of these is the equation that expresses the relationship between the pages Jen is on the number of hours she reads.
A
t=r • p +5
B
5=t+p•r
C
r=t • p +5
D
p=r • t +5
13.
Stan’s boss lost all the paper work for his employee’s wage. He is trying to figure out How much Stan makes per care washed, (r). The paper work that hasn’t been lost States that Stan once made 55 dollars for 10 cars and 33 dollars for 6 cars washed. Help Stan’s boss calculate r, the unit rate.
A
5.2 dollars/ car washed
B
6 dollars/car washed
C
5.5 dollars/ car washed
D
4.8 dollars/ car washed
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 5
14. The graph below shows Phil’s distance and time on his run. Find the unit rate. miles y
•
2
• hours x
A
3 miles/hour
B
4 miles/hour
C
5 miles/hour
D
6 miles/hour
15. A sweater is on sale for 30% off. If the original price was $15, what is the sale price?
A
$9.50
B
$10.50
C
$11.50
D
$12.50
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 6
16.
John Joy washes dishes for t minutes, at a rate of 6 dishes per hour. The total amount of dishes washed, w, is proportional to the number of hours she works. Write an equation that expresses the relationship between total work done and the number of hours she works. Graph this equation and use it to predict how many hours it takes to wash 15 dishes.
17. A dinner costs $24 plus an 8% tax. What is the total? Show your work.
18. The price of a gallon of gas at a service station has dropped from $4 to $3.50. What is the percent decrease? Show your work.
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 7
19. A couple has dinner at a restaurant where there is a 10% deal off the price before tax. However there is a 10% sales tax on the price after the discount. Does the tax end up canceling out the deal? Explain how you know.
20.
The balance b in Harry’s savings account is proportional to the number m of months he has the account, depositing money at a constant rate of 800 dollars per month. Write and graph the equation that represents this. Hint: Scale the y axis.
Copyright © Swun Math Grade 7 Unit 1 Assessment, Page 8
