G8 U3 Assessment
Name: _________________________________________ Date:________________
Grade 8 Unit 3 Proportions, Lines and Linear Equations 1. Is the relationship between US dollars and Euros proportional, linear, exponential, or none of these? Five US dollars is worth four Euros, and EU 1.60 equals $2.
A
proportional
B
linear
C
exponential
D
none of these
2. Is the relationship between ounces and cost proportional, linear, exponential, or none of these? Three ounces of toothpaste cost $1.50, and ten ounces cost $4.20 A
proportional
B
linear
C
exponential
D
none of these
3. Angel hair pasta costs $2.50 for 2 pounds. Find the unit cost in dollars per kilogram. There are 2.2 pounds per kilogram.
A
$0.57/kg
B
$1.25/kg
C
$0.63/kg
D
$2.75/kg Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 1
4.
5.
6.
A segment has an endpoint at (4, -3) and a midpoint at (1, 3). Find the other endpoint.
A
(5, 0)
B
(-2, 9)
C
(2.5, 0)
D
(2, 5)
Bee’s Knees Honey sells 11 oz. for $7.15 and a 4 oz. bottle for $2.60. How much would a 20 oz. bottle sell for? A
$0.65
B
$13.00
C
$21.50
D
$30.76
Racer Tony Windsor thinks his car is slower on smaller tracks. He tests his car on a 2 mile loop, then on a 2.5 mile loop. What is his fastest speed on either course? Laps 1 2 3 Total time on 2 mile laps 60 s. 120 s. 180 s. Total time on 2.5 mile laps 72 s. 144 s. 216 s. A
$0.65
B
$13.00
C
$21.50
D
$30.76 Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 2
7.
Luke can eat 40 eggs in an hour. A graph relates minutes and the number of eggs his cellmate, Dragline, can eat. Who eats faster?
3 2.5
Eggs
2 1.5 1 0.5 0 1 minute
2 minutes
3 minutes
4 minutes
Time
A
Luke
B
Dragline
C
They are equally fast.
D
It cannot be determined.
8. In 20 minutes, the printing presses of El Tiempo can make 480 copies. The presses at The Angels’ Examiner produces a copy every 3 seconds. How much faster are the presses at El Tiempo?
A
24 copies/minute faster
B
8 copies/minute faster
C
20 copies/minute faster
D
4 copies/minute faster
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 3
9. If A is (-1, -2) and B is (1, -1), which of the following points is on ⃡𝐴𝐵 ?
A
(3, 1)
B
(4, 1)
C
(5, 1)
D
(6, 1)
3
10. If the slope of a line is − 4, and one point on the line is (-2, 5) while another point is (6, r), find r. 1
A
44
B
2
C
-1
D
8
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 4
11. Tell whether the pair of triangles is similar or not.
A
yes
no
B
yes
no
C
yes
no
D
yes
no
12. What proportion would you set up to find an equation relating x and y, if the point 1 (0, 6) is on the line relating x and y, and the line has a slope of − 2. A B C D
𝑦−(−1⁄2) 𝑥 𝑦−𝑥 −1⁄2 𝑦−6 𝑥 𝑦−𝑥 6
6
=1
6
=1 1
= −2 1
= −2
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 5
13. Write an equation relating x and y, if (-2, 1) and (2, 7) are on the line relating x and y. 2
7
A
y = 3𝑥 + 3
B
y = −3𝑥 − 3
C
𝑦 = 2𝑥 + 4
D
y = −2𝑥 − 2
2
1
3
3
14. Ato Bolton ran 100 meters in 10.0 seconds. Seabiscuit ran 1½ miles in 2½ minutes. How many meters per second faster is Seabiscuit than Ato Bolton? (1600 meters is 1 mile)
A
10 m/sec
B
6 m/sec
C
860 m/sec
D
950 m/sec
15. Find an equation relating x and y, if the point (3, 2) is on the line relating x and y, and the line has a slope of 2.
A
y = 2x + 2
B
y = −2𝑥 + 2
C
𝑦 = 2𝑥 − 4
D
y = 2x − 1
1
7
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 6
16. One bag of charcoal weighs 16 pounds and costs $12. Another bag weighs 40 pounds and costs $28. Explain how you know which is the better deal.
2
17. Sketch a line going through (0, 3) with a slope of 5. Label another point on the line (x, y). Draw two similar triangles formed by the line and the y-axis. Set up proportions and find an equation relating x and y.
18. Albert was faced with this problem: “Find the slope between (-3, 4) and (5, 0).” 5−3
2
1
He wrote down, “0−4 = −4 = − 2” What did he do wrong? What answer should he have gotten?
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 7
19. Matt spent two hours fishing on Saturday and caught eight fish. He spent three and a half hours and caught fourteen fish. Is the relationship between time and fish caught proportional, linear, exponential or none of these? Explain how you know.
20.
Find the coordinates of two evenly spaced points on the line between A (1, 3) and B (6, 5).
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 8
Grade 8 Unit 3 Proportions, Lines and Linear Equations 1. Is the relationship between US dollars and Euros proportional, linear, exponential, or none of these? Five US dollars is worth four Euros, and EU 1.60 equals $2.
A
proportional
B
linear
C
exponential
D
none of these
2. Is the relationship between ounces and cost proportional, linear, exponential, or none of these? Three ounces of toothpaste cost $1.50, and ten ounces cost $4.20 A
proportional
B
linear
C
exponential
D
none of these
3. Angel hair pasta costs $2.50 for 2 pounds. Find the unit cost in dollars per kilogram. There are 2.2 pounds per kilogram.
A
$0.57/kg
B
$1.25/kg
C
$0.63/kg
D
$2.75/kg Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 1
4.
5.
6.
A segment has an endpoint at (4, -3) and a midpoint at (1, 3). Find the other endpoint.
A
(5, 0)
B
(-2, 9)
C
(2.5, 0)
D
(2, 5)
Bee’s Knees Honey sells 11 oz. for $7.15 and a 4 oz. bottle for $2.60. How much would a 20 oz. bottle sell for? A
$0.65
B
$13.00
C
$21.50
D
$30.76
Racer Tony Windsor thinks his car is slower on smaller tracks. He tests his car on a 2 mile loop, then on a 2.5 mile loop. What is his fastest speed on either course? Laps 1 2 3 Total time on 2 mile laps 60 s. 120 s. 180 s. Total time on 2.5 mile laps 72 s. 144 s. 216 s. A
$0.65
B
$13.00
C
$21.50
D
$30.76 Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 2
7.
Luke can eat 40 eggs in an hour. A graph relates minutes and the number of eggs his cellmate, Dragline, can eat. Who eats faster?
3 2.5
Eggs
2 1.5 1 0.5 0 1 minute
2 minutes
3 minutes
4 minutes
Time
A
Luke
B
Dragline
C
They are equally fast.
D
It cannot be determined.
8. In 20 minutes, the printing presses of El Tiempo can make 480 copies. The presses at The Angels’ Examiner produces a copy every 3 seconds. How much faster are the presses at El Tiempo?
A
24 copies/minute faster
B
8 copies/minute faster
C
20 copies/minute faster
D
4 copies/minute faster
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 3
9. If A is (-1, -2) and B is (1, -1), which of the following points is on ⃡𝐴𝐵 ?
A
(3, 1)
B
(4, 1)
C
(5, 1)
D
(6, 1)
3
10. If the slope of a line is − 4, and one point on the line is (-2, 5) while another point is (6, r), find r. 1
A
44
B
2
C
-1
D
8
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 4
11. Tell whether the pair of triangles is similar or not.
A
yes
no
B
yes
no
C
yes
no
D
yes
no
12. What proportion would you set up to find an equation relating x and y, if the point 1 (0, 6) is on the line relating x and y, and the line has a slope of − 2. A B C D
𝑦−(−1⁄2) 𝑥 𝑦−𝑥 −1⁄2 𝑦−6 𝑥 𝑦−𝑥 6
6
=1
6
=1 1
= −2 1
= −2
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 5
13. Write an equation relating x and y, if (-2, 1) and (2, 7) are on the line relating x and y. 2
7
A
y = 3𝑥 + 3
B
y = −3𝑥 − 3
C
𝑦 = 2𝑥 + 4
D
y = −2𝑥 − 2
2
1
3
3
14. Ato Bolton ran 100 meters in 10.0 seconds. Seabiscuit ran 1½ miles in 2½ minutes. How many meters per second faster is Seabiscuit than Ato Bolton? (1600 meters is 1 mile)
A
10 m/sec
B
6 m/sec
C
860 m/sec
D
950 m/sec
15. Find an equation relating x and y, if the point (3, 2) is on the line relating x and y, and the line has a slope of 2.
A
y = 2x + 2
B
y = −2𝑥 + 2
C
𝑦 = 2𝑥 − 4
D
y = 2x − 1
1
7
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 6
16. One bag of charcoal weighs 16 pounds and costs $12. Another bag weighs 40 pounds and costs $28. Explain how you know which is the better deal.
2
17. Sketch a line going through (0, 3) with a slope of 5. Label another point on the line (x, y). Draw two similar triangles formed by the line and the y-axis. Set up proportions and find an equation relating x and y.
18. Albert was faced with this problem: “Find the slope between (-3, 4) and (5, 0).” 5−3
2
1
He wrote down, “0−4 = −4 = − 2” What did he do wrong? What answer should he have gotten?
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 7
19. Matt spent two hours fishing on Saturday and caught eight fish. He spent three and a half hours and caught fourteen fish. Is the relationship between time and fish caught proportional, linear, exponential or none of these? Explain how you know.
20.
Find the coordinates of two evenly spaced points on the line between A (1, 3) and B (6, 5).
Copyright © Swun Math Grade 8 Unit 3 Assessment, Page 8
