Name: ________________________
Class: ___________________
Date: __________
ID: A
8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1,
MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1
The table below shows the relationship between the length and the width of a rectangle.
If the length of the rectangle is 10 inches, what is the width of the rectangle?
A.
B.
C.
D.
13 inches
21 inches
22 inches
29 inches
1
Name: ________________________
____
2
ID: A
At an amusement park, the roller coaster rides are 5 tickets each, and the ferris wheel rides are 2
tickets each. The graph below shows the combination of rides that can be paid with 50 tickets.
Based on this graph, which statement is TRUE?
F.
G.
H.
I.
The range is discrete with an upper limit of 10 rides.
The range is continuous with an upper limit of 10 rides.
The domain is discrete with an upper limit of 10 rides.
The domain is continuous with an upper limit of 10 rides.
2
Name: ________________________
____
3
ID: A
Ray works at a grocery store. The table shows the relationship between the number of hours Ray
works and the amount of money he earns.
If this pattern continues, how much will Ray earn for working 10 hours?
A.
B.
C.
D.
____
4
$50.00
$56.25
$62.50
$68.75
The graph shows the distance a train traveled over time.
Which inequality BEST represents the range of this function?
F.
G.
H.
I.
3
Name: ________________________
____
5
ID: A
The graph shows the rate of descent of a parachutist after his parachute opened at an altitude of
3,500 feet.
Based on the graph, which BEST represents the altitude of the parachutist 2.5 minutes after his
parachute opened?
A.
260 feet
B.
800 feet
C . 1,000 feet
D. 1,340 feet
4
Name: ________________________
____
6
ID: A
The linear graph below shows the number of grams of protein in different amounts of peanut
butter.
The slope of the line is
F.
G.
H.
I.
Which statement BEST describes the meaning of the slope?
There are 25 grams of protein in 5 tablespoons of peanut butter.
There are 5 grams of protein in 25 tablespoons of peanut butter.
There is 1 gram of protein in 5 tablespoons of peanut butter.
There are 5 grams of protein in 5 tablespoons of peanut butter.
5
Name: ________________________
____
7
ID: A
Which BEST represents the slope of the line shown below?
A.
B.
C.
D.
____
8
The graphed line passes through points
and
What is the slope of the line?
F.
G.
H.
I.
6
Name: ________________________
____
9
ID: A
The graph below shows the number of tomatoes needed to prepare batches of spaghetti sauce.
Which statement is TRUE according to this graph?
A. Divide the number of tomatoes by 5 to find the number of batches they will
yield.
B. Divide the number of tomatoes by 8 to find the number of batches they will
yield.
C . Multiply the number of batches by 10 to find the number of tomatoes needed.
D. Multiply the number of batches by 15 to find the number of tomatoes needed.
7
Name: ________________________
____
ID: A
10 Paul had saved $120 to spend during his vacation this summer. The graph below shows his
expenditures every day during his vacation. What part of the graph represents the point where
Paul has used up all of his money?
F.
the y-intercept
G. the x-intercept
H. the length of the line
I.
the slope of the line
8
Name: ________________________
____
ID: A
11 Mara started working after school and plans to save enough money to visit her cousin in New
York within the next two years. The graph below shows Mara’s savings per month.
What does the y-intercept of the line segment represent?
A.
B.
C.
D.
Mara had no money in savings when she began working.
Mara had $50 dollars in savings when she started working.
Mara saves $50 each month.
Mara saves $300 each month.
9
Name: ________________________
____
ID: A
12 Rayna paid a $200 fee to join a health club and then a $50 fee per month to use the club. The total
amount of money (t) paid can be represented by the equation
the number of months of club use.
where m represents
Nora paid a $100 fee to join another health club and then a $75 fee per month to use the club,
which can be represented by the equation
The graph below shows the fees paid by Rayna and Nora.
In what month will both Rayna and Nora have paid an equal amount of money to their health
clubs?
F.
G.
H.
I.
Month
Month
Month
Month
1
3
4
5
10
Name: ________________________
____
ID: A
13 Students in the 8th grade plan to sell printed T-shirts to raise funds. There will be a one-time fee of
$45 for the print design. Printing each T-shirt will cost an additional $7. The T-shirts will be sold
for $10 each. The table below shows the expected expenses and income.
After selling how many T-shirts will the students start earning a profit?
A.
B.
C.
D.
10
15
20
25
11
Name: ________________________
____
ID: A
14 Which graph BEST represents a system of equations with no solution?
F.
H.
G.
I.
12
Name: ________________________
____
ID: A
15 The soccer team sold a total of 20 sandwiches at the game on Saturday. The selling price of a
cheese sandwich was $2, and the selling price of a tuna sandwich was $4. The sandwich sales
totaled $64. The graph below represents this information.
Based on the graph, which statement BEST describes the y-intercept of Line n?
If no cheese sandwiches were sold, then 20 tuna sandwiches were sold.
If no tuna sandwiches were sold, then 20 cheese sandwiches were sold.
If no cheese sandwiches were sold, then 16 tuna sandwiches were sold for
A.
B.
C.
$64.
If no tuna sandwiches were sold, then 32 cheese sandwiches were sold for
D.
$64.
13
Name: ________________________
____
ID: A
16 Sophie purchased 8 candles at a total cost of $32. The red candles cost $3 each and the silver
candles cost $7 each. The equations and graph below can be used to determine the number of each
type of candle Sophie purchased, where x represents the number of red candles and y represents
the number of silver candles.
Number of candles purchased:
Total cost of candles:
What is the number of red candles and silver candles Sophie purchased?
F.
G.
H.
I.
2 red candles, 6 silver candles
3 red candles, 5 silver candles
6 red candles, 2 silver candles
7 red candles, 1 silver candle
14
Name: ________________________
____
ID: A
17 An Economics club holds a fundraiser selling school stickers. The graph below shows the profit, p,
they will make if they sell a certain number of stickers, s.
Which table matches the prediction modeled by the graph?
A.
C.
B.
D.
15
Name: ________________________
____
ID: A
18 A phone company offers a monthly wireless phone plan of 900 minutes for $59.99. Additional
minutes cost $0.40 each. The graph shows the relationship between the cost and minutes offered
by this plan.
Which equation can be used to determine y, the cost for using x minutes per month when the
minutes used exceed 900?
F. y = 59.99
G.
H.
I.
16
Name: ________________________
____
ID: A
19 The graph below shows the number of calories in different amounts of steak.
Which equation BEST represents this relationship?
A.
B.
C.
D.
____
20 Which equation describes the relationship between the values of x and y in the table below?
F.
G.
H.
I.
17
Name: ________________________
____
ID: A
21 The table below shows the lengths, widths, perimeters, and areas of similar rectangles.
Similar Rectangles
Which equation can be used to represent the difference in the perimeters (p) of Rectangle S and
Rectangle Q?
A.
B.
C.
D.
18
Name: ________________________
____
ID: A
22 Richard put one 20-dollar bill in a shoebox the first week of summer for his savings. He added more
bills every week. By the 4th week he had two 20-dollar bills, and by the 9th week he had three
20-dollar bills. Which graph shows the number of 20-dollar bills he saved in 9 weeks?
F.
H.
G.
I.
19
Name: ________________________
____
ID: A
23 The table shows the cost of a taxicab ride for several driving distances.
Which graph BEST represents the relationship between the cost and the distance?
A.
C.
B.
D.
20
Name: ________________________
____
ID: A
24 A school bus was stopped for 2 minutes at a red light. When the light turned green, the driver
accelerated the bus at a steady rate and then continued driving at a constant speed. Next to pick up
students, the driver decreased the speed of the bus until it came to a full stop. Which graph
below BEST represents the speed of the bus over the time described?
F.
H.
G.
I.
21
Name: ________________________
____
ID: A
25 Which scenario BEST describes the graph shown below?
A.
B.
C.
D.
An airplane is parked at a maintenance facility.
A person on a bicycle rides at a constant speed.
A train gradually gains speed when leaving a station.
A truck gradually slows down and stops for the night.
22
Name: ________________________
____
ID: A
26 A ball is thrown up in the air from 5 feet above the ground level. The ball reached a height of an
additional 6 feet in 5 seconds, and then came down back to ground level in 4 more seconds. Which
graph BEST represents the relationship between the height of the ball and the time?
F.
H.
G.
I.
23
GR 8 Advanced - Topic III Assessment
TEACHER ANSWER KEY
ID: A
8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1,
MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6
Answer Section
MULTIPLE CHOICE
1
ANS: B
Feedback
A
B
C
D
2
13 is halfway between the 9 and the 17
Correct
22 is too high; it is not halfway between 17 and 25
29 would be correct if 10 were halfway between 12 and 16
PTS: 1
DIF: L
REF: Math
OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve
problems related to linear equations, including analysis of domain, range and the difference between
discrete and continuous data.
STA: MA.8.A.1.1
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF203301
ANS: F
Feedback
F
G
H
I
Correct
Chose a false statement because the range is discrete
Chose a false statement because the upper limit for the domain is 25, not 10
Chose a false statement because the domain is discrete and the upper limit is 25
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve
problems related to linear equations, including analysis of domain, range and the difference between
discrete and continuous data.
STA: MA.8.A.1.1
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF206923
1
ID: A
3
ANS: C
Feedback
A
B
C
D
4
After 8 hrs
After 9 hrs
Correct
After 11 hrs
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve
problems related to linear equations, including analysis of domain, range and the difference between
discrete and continuous data.
STA: MA.8.A.1.1
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF212220
ANS: H
Feedback
F
G
H
I
5
Domain and used the highest value on the x-axis
Domain
Correct
Used the highest value on the y-axis
PTS: 1
DIF: L
REF: Math
OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve
problems related to linear equations, including analysis of domain, range and the difference between
discrete and continuous data.
STA: MA.8.A.1.1
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF223429
ANS: B
Feedback
A
B
C
D
Used 3 seconds
Correct
Used 2.25 seconds
Used 2 seconds
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve
problems related to linear equations, including analysis of domain, range and the difference between
discrete and continuous data.
STA: MA.8.A.1.1
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF223430
2
ID: A
6
ANS: F
Feedback
F
Correct
G
H
I
7
Reverses meaning
Slope of 1
PTS: 1
DIF: H
REF: Math
OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for
a real-world problem.
STA: MA.8.A.1.2
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MF200499
ANS: B
Feedback
A
B
Correct
C
D
8
The slope is negative—not positive
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for
a real-world problem.
STA: MA.8.A.1.2
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MF201625
ANS: I
Feedback
F
G
H
I
Negative of the slope
Negative reciprocal of the slope
Reciprocal of the slope
Correct
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for
a real-world problem.
STA: MA.8.A.1.2
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MF214405
3
ID: A
9
ANS: B
Feedback
A
B
C
D
Used (40, 5) and interpreted it as dividing by 5
Correct
y-axis scale is 10
Miscalculated
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for
a real-world problem.
STA: MA.8.A.1.2
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MFIBM15942
10 ANS: G
PTS: 1
DIF: M
REF: Topic III
OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for
a real-world problem.
STA: MA.8.A.1.2
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: Extra Problem Bank
11 ANS: B
PTS: 1
DIF: M
REF: TOPIC III
OBJ: MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for
a real-world problem.
STA: MA.8.A.1.2
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low|Grade 08
MSC: Extra Problem Bank
12 ANS: H
Feedback
F
G
H
I
Began in the same month
Month before intersection
Correct
Last month in graph
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems
related to systems of linear equations.
STA: MA.8.A.1.3
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF222107
4
ID: A
13 ANS: B
Feedback
A
B
C
D
Chose number from row just before income equals expenses
Correct
Chose number from row just before income equals expenses
Does not understand how to identify the unique solution for a system of
equations
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems
related to systems of linear equations.
STA: MA.8.A.1.3
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF222592
14 ANS: I
Feedback
F
G
H
I
Chose pair of lines that will intercept because their slopes are not the same
Confused parallel with perpendicular
Chose both negative slopes
Correct
PTS: 1
DIF: L
REF: Math
OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems
related to systems of linear equations.
STA: MA.8.A.1.3
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MF222691
15 ANS: C
Feedback
A
B
C
D
y-intercept of Line m
x-intercept of Line m
Correct
x-intercept of Line n
PTS: 1
DIF: H
REF: Math
OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems
related to systems of linear equations.
STA: MA.8.A.1.3
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF222824
5
ID: A
16 ANS: H
Feedback
F
G
H
I
Inverted the abscissa and the ordinate
3 + 5 = 8 total candles purchased
Correct
7 + 1 = 8 candles purchased
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.3 Use tables, graphs, and models to represent, analyze, and solve real-world problems
related to systems of linear equations.
STA: MA.8.A.1.3
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF222935
17 ANS: D
Feedback
A
B
C
D
2s + 20 is used instead of 2s – 20
The rate of change is used without subtracting the constant term of 20
20 – 2s is used instead of 2s – 20
Correct
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear
functions.
STA: MA.8.A.1.5
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF200465
18 ANS: I
Feedback
F
G
H
I
Chose the equation to determine the minimum monthly cost when using up to
900 minutes
The entire minimum monthly bill was multiplied by minutes used
Added first 900 minutes again instead of subtracting
Correct
PTS: 1
DIF: H
REF: Math
OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear
functions.
STA: MA.8.A.1.5
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF201020
6
ID: A
19 ANS: B
Feedback
A
B
C
D
Reverses variables
Correct
Reverses variables, the line goes up by 80
The line goes up by 80
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear
functions.
STA: MA.8.A.1.5
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF201116
20 ANS: F
Feedback
F
G
H
I
Correct
Fits x = 6
Fits x = 3
Fits x = 9
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear
functions.
STA: MA.8.A.1.5
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MF208938
21 ANS: B
Feedback
A
B
C
D
Calculated difference in areas
Correct
Calculated difference in perimeters of Rectangle S and Rectangle R
Multiplied instead of adding length and width and multiplied 2 times area of Q
PTS: 1
DIF: H
REF: Math
OBJ: MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear
functions.
STA: MA.8.A.1.5
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF219942
7
ID: A
22 ANS: F
Feedback
F
G
H
I
Correct
Chose a linear relationship: y = 1
Chose a linear relationship: y = x
Chose a linear relationship: x = 1
PTS: 1
DIF: L
REF: Math
OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations.
STA: MA.8.A.1.6
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF202096
23 ANS: B
Feedback
A
B
C
D
Chose an increasing function but one that would not model the data
Correct
Chose a gradually decreasing function but one that would not model the data
Chose an increasing function but one that would not model the data
PTS: 1
DIF: L
REF: Math
OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations.
STA: MA.8.A.1.6
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF222371
24 ANS: F
Feedback
F
G
H
I
Correct
Did not take constant speed into consideration
Did not take the acceleration into consideration
Did not take the stop into consideration
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations.
STA: MA.8.A.1.6
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Low | Grade 08
MSC: ItemCode: MF222595
8
ID: A
25 ANS: D
Feedback
A
B
C
D
Graph would be horizontal line
Graph would be a straight line, positive slope
Graph would curve up
Correct
PTS: 1
DIF: H
REF: Math
OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations.
STA: MA.8.A.1.6
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF222693
26 ANS: F
Feedback
F
G
H
I
Correct
Did not consider the 5 ft starting height
Consider the heights as mentioned in stem
Stopped ball height at 5 ft instead of 0 ft
PTS: 1
DIF: M
REF: Math
OBJ: MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations.
STA: MA.8.A.1.6
TOP: MA.8.A.1 Analyze and represent linear functions and solve linear equations and systems of
linear equations.
KEY: Webb: Moderate | Grade 08
MSC: ItemCode: MF223104
9