Name _________________________________________
Date _______________
8th Grade Quarter 4 Assessment
Standard
SP.1
Show your work. Write your answer on the line to the right.
1. Calvin owns a small ice cream stand. His daily profit, in dollars, and the daily maximum temperature, in degrees Fahrenheit, for two weeks during the summer are shown in the table.
Temperature (F)
90
80
65
60
90
100
75
60
95
90
90
70
85
85
Profit ($)
160
100
50
20
160
160
100
40
140
130
110
80
90
100
a. Make a scatter plot of the data, with temperature along the horizontal axis and profit along
the vertical axis.
b. What can you say about the association between profit and temperature? Explain.
__________________________________________________________________________________________
__________________________________________________________________________________________
8th Grade Quarter 4 Assessment
2. Solve
. Show your work.
2.__________________
EE.7
SP.2
3. Compare the given scatter plots of data to the lines of best fit. Tell
which model better fits the data. Explain your answer.
Graph A
3.__________________
Graph B
y
y
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
x
a. Both scatter plots show data with a strong negative correlation.
The linear model in Graph A fits the data better than the linear model in Graph B.
b. Both scatter plots show data with a strong positive correlation.
The linear model in Graph A fits the data better than the linear model in Graph B.
c. Both scatter plots show data with a strong positive correlation.
The linear model in Graph B fits the data better than the linear model in Graph A.
d. Both scatter plots show data with a strong negative correlation.
The linear model in Graph B fits the data better than the linear model in Graph A.
8th Grade Quarter 4 Assessment
4. Solve. Show your work.
EE.7
EE.7.b
EE.6
4.___________________
–2z + 3 + 7z = –12
5. The triangles below each have a vertical leg, a horizontal leg, and a portion of the same line as the
hypotenuse.
a. Explain how you know that the triangles are similar.
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
b. Use each triangle to determine the slope of the line. Explain why you would expect to get
the same slope.
__________________________________________________________________________________________
__________________________________________________________________________________________
__________________________________________________________________________________________
8th Grade Quarter 4 Assessment
6. Find an equation in slope-intercept for the line of best fit, and tell what
the slope and intercepts represent in terms of the data it models. Give the
slope and intercept to the nearest integer.
Total Cost ($)
SP.3
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
6.__________________
y
1
2
3
4
5
Books Ordered
6
7
8 x
a.
The slope of the best-fit line is 2, and the y-intercept is 4.
The slope, $2 per book, is the typical cost per book.
The y-intercept, $4, is the cost of ordering no books; which is the shipping cost.
b.
The slope of the best-fit line is 4, and the y-intercept is 2.
The slope, $4 per book, is the typical cost per book.
The y-intercept, $2, is the cost of ordering no books; which is the shipping cost.
c.
The slope of the best-fit line is 2, and the y-intercept is 4.
The slope, $2, is the typical cost per book.
The y-intercept, $4, shows that the first two books ordered are free.
d.
The slope of the best-fit line is 4, and the y-intercept is 2.
The slope, $4, is the typical cost per book.
The y-intercept, $2, shows that there is a coupon or other discount worth $2.
7. Which ordered pair is a solution to this system of equations?
7.__________________
EE.8
a.
b.
c.
d.
8th Grade Quarter 4 Assessment
SP.4
8. Suppose the United States House of Representatives voted to pass a bill.
The voting results are shown in the two-way table.
Does the table show any difference in voting patterns between
Democrats and Republicans?
8.__________________
a. There are no differences in voting patterns.
b. More Republicans than Democrats voted “no”, so Republicans were more likely to oppose
the bill than Democrats were.
c. Both Democrats and Republicans tended to favor the bill.
d. Republicans tended to vote “yes” on the bill. Democrats were slightly more likely to vote
“no” than to vote “yes”.
EE.8
9. Don is solving a system of linear equations algebraically, and he
concludes that there are an infinite number of solutions to the system.
What solution process result could have led him to make that conclusion?
a.
b.
c.
d.
9.__________________
8th Grade Quarter 4 Assessment
10. Which ordered pair is the solution of the system graphed?
10.__________________
EE.8
EE.8.a
EE.8.b
a.
b.
c.
d. (5, -3)
11. Which function has the least rate of change.
11.__________________
F.2
a.
b.
c. Helga earns $12 per hour working at a restaurant.
.
8th Grade Quarter 4 Assessment
12. Which graph shows a function?
12.________________
F.1
a.
c.
b.
d.
13. Determine if the relation represents a function.
13._________________
F.1
x
0
1
2
3
y
–5
–1
3
6
a. The relation is a function.
F.4
b. The relation is not a function.
14. Mariana is 10 years old and has grown 7 inches in 2 years. When she was
8 years old, she was 52 inches tall. Mariana writes and graphs a function
that models her height in inches over time in years. What is the initial value
for this function?
14._________________
8th Grade Quarter 4 Assessment
F.4
15. Miguel mows lawns for his neighbors in the summer time to earn money.
He charges $10 to cover the cost of supplies such as gasoline. He also
charges $20 per hour for the time it takes him to mow the lawn. In a
function that models Miguel’s average hourly wage over time in hours.
What is the slope of the function?
What is the initial value of the function?
15._________________
_________________
16. The two-way table shows the results of a survey about which of two new television series people prefer.
SP.4
Complete the two-way table by finding the cumulative frequencies and the percentages.
Program A
Women 30
5
Men
Total
Program B
Total
10
35
8th Grade Quarter 4 Assessment
17. Graph the equation y =
x+2
EE.5
y
10
10 x
–10
–10
18. The graph shows the distance covered by a three-toed sloth and a giant tortoise. 18._________________
EE.5
Giant tortoise y = 14x
Three-toed sloth y = 12x
Which has the greater rate of speed?
8th Grade Quarter 4 Assessment
19.
EE.8.c
Use the following information to match the statement with the corresponding system of equations. Circle the corresponding system of
equations from the choices below.
While on vacation, Rosa stopped at a souvenir shop to buy keychains and refrigerator magnets for family members and friends. Keychains cost
$2 each, and refrigerator magnets cost $1 each. Let x represent the number of
keychains that Rosa bought, and let y represent the number of refrigerator
magnets.
Rosa bought 12 items and paid a total of $18.
ì x + y = 12
A í
î-2 x + y = 18
ì x + y = 12
B í
î2 x - y = 18
ì x + y = 12
C í
î2 x + y = 18
ì x + y = 18
D í
î2 x + y = 12
EE.7.a
20. Solve the equation and state whether the variable has
one solution, no solution or infinite solutions. Show your work.
20._________________
_________________
3(y - 1) - 2y = -2y + 3(y - 1)
8th Grade Quarter 4 Assessment
F.2
21. Use the graph of f(x), and the table of h(x). Compare the slopes of the linear
functions f(x) and h(x) by stating whether the slope of f (x) is less than,
equal to or greater than h.
21.________________
22. Determine whether the equation is linear:
22.________________
.
F.3
23. Tell whether the equation is a linear equation.
23.________________
F.3
F.5
24. Draw a line graph that corresponds to this situation: a car is moving at a constant speed and then gradually
stops. Show speed on the y-axis and time on the x-axis.
8th Grade Quarter 4 Assessment
25. Write a statement that best tells the story of the graph.
25.______________________________
F.5
______________________________________________
______________________________________________
8th Grade Quarter 4 Assessment
Answer Key
1. a.
b. There is a positive, linear association between profit and temperature. As the temperature
increases, Calvin’s profit tends to increase linearly.
Total Points: 4 (2 points for each part)
2.
z/9 + 5 = 10
z/9 + 5 – 5 = 10 – 5
z/9 = 5
(z/9)9 = 5 × 9
z = 45
Total Points: 4
3.
C
Total Points: 4 (minus 3 for B)
4.
-2z + 3 + 7z = -12
5z + 3 = -12
5z + 3 – 3 = -12 – 3
5z = -15
5z/5 = -15/5
z = -3
Total Points: 4
2 points if correct to here
3 points if correct to here
4 points if correct to here
1 points if correct to here
2 points if correct to here
3 points if missing negative; 4 points if correct
8th Grade Quarter 4 Assessment
5. a. Possible answer:
To map the smaller triangle onto the larger triangle, translate the smaller triangle 2 units to
the right and 3 units down. This translation maps the smaller triangle’s vertex at (4, 6) to
the larger triangle’s vertex at (2, 3). Dilate the image of the smaller triangle using a scale
factor of 2 and the point (2, 3) as the center of dilation. The image of the smaller triangle
after the translation and dilation completely coincides with the larger triangle, so the triangles
must be similar.
b. For the smaller triangle, the vertical leg has a directed length of 3 because the movement
from the vertex at (2, 3) to the vertex at (4, 3) is downward, while the horizontal leg has a
directed length of 2 because the movement from the vertex at (4, 3) to the vertex at (2, 3)
3
is to the right. So, the slope of the line based on this triangle is - .
2
For the larger triangle, the vertical leg has a directed length of 6 while the horizontal leg has
6
3
a directed length of 4. So, the slope of the line based on this triangle is - , or - .
4
2
The two slopes should be the same because the triangles were shown to be similar. That
means that the directed lengths of the legs of the larger triangle are some scale factor (in
this case, 2) times the directed lengths of the corresponding legs of the smaller triangle.
When you form the ratio of the directed length of the vertical leg to the directed length of the
horizontal leg for the larger triangle, the scale factor divides out, producing the same ratio as
that obtained for the smaller triangle.
Total Points: 4 (2 pt each part)
6.
A. 2 points (student mixed up the slope and y-int but has an understanding of what the slope
and y-int mean)
B. 4 points
C. 1 point (student mixed up the slope and y-int and only shows an understanding of what
slope means)
D. 3 points (student calculated the correct slope and y-int, student understands the meaning
of slope but didn’t understand the meaning of the y-int)
Total Points: 4
7.
C
Total Points: 4 (minus two points for A)
8.
D
Total Points: 4
9.
A
Total Points: 4
8th Grade Quarter 4 Assessment
10.
D
Total Points: 4
11.
B
Total Points: 4
12.
D
Total Points: 4
13.
A
Total Points: 4
14.
52
Total Points: 4
15.
slope is 20
initial value is 10
Total Points: 4 (two points for the slope, two points for the initial value)
16.
Total Points: 4 (two points for the correct frequency totals, two points for the correct
percentages)
8th Grade Quarter 4 Assessment
17.
Slope = -3/5
(2 points)
y-intercept = 2
(2 points)
Total Points: 4 check students graph
18. the giant tortoise
Total Points: 4
19. C
ì x + y = 12
í
î2 x + y = 18
Total Points: 4 (minus 2 for A or B)(minus 4 for D)
20. 3(y – 1) -2y = -2y + 3(y – 1)
3y – 3 – 2y = -2y + 3y – 3
y–3=y–3
y–3+3=y–3+3
y=y
y–y=y–y
0=0
Infinite solutions
Total Points: 4
two points to here
three points to here
four points to here
21. The slope of f is less than the slope of h.
Total Points: 4
22. Yes, it is linear.
Total Points: 4
8th Grade Quarter 4 Assessment
23. No, it is not linear.
Total Points: 4
24.
ANS:
Total Points: 4
25. Possible answer: A worker earns $7.50 per hour for the first 6 hours of work, then volunteers
for the next 8 hours (earning
). Check student answers
Total Points: 4
8th Grade Quarter 4 Assessment
1.
_______/4
Name______________________
Score Sheet
2.
_______/4
21.
_______/4
3.
_______/4
22.
_______/4
4.
_______/4
23.
_______/4
5.
_______/4
24.
_______/4
6.
_______/4
25.
_______/4
7.
_______/4
8.
_______/4
9.
_______/4
10. _______/4
11. _______/4
12. _______/4
13. _______/4
14. _______/4
15. _______/4
16. _______/4
17. _______/4
18. _______/4
19. _______/4
20. _______/4
Total Score _____________/100
8th Grade Quarter 4 Assessment