Course 3 / Chapter 3 Test
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1. Mr. Frankel bought 9 tickets to a puppet show and spent $65. He bought some children’s tickets for $5 each
and some adult tickets for $9 each. Which system of equations could you use to determine the number of
adult tickets, a, and the number of children’s tickets, c, that he bought?
a.
b.
c.
d.
____
2. Which figure has rotational symmetry with an angle of rotation of
a.
c.
b.
d.
3. The map of Libertytown below uses a coordinate system. Suppose you work at the Visitor Center, which is
located at (0, 0). How would you give someone directions to the coffee shop? For example, to get to the bank,
go 5 blocks east and then 2 blocks north.
North
Bookstore
Library
Bank
Main Street
West
Salon
Coffee Shop
Visitor Center
East
Shore Road
____
?
Drugstore
Movie Theater
South
____
____
a. Go 6 blocks east and then 3 blocks south.
b. Go 5 blocks east and then 4 blocks south.
c. Go 5 blocks west and then 4 blocks south.
d. Go 5 blocks west and then 4 blocks north.
4. In which quadrant is the point (x, y) located if x is negative and y is negative?
a. III
b. IV
c. II
d. I
5. What are the coordinates of the point 4 to the left and 7 above the point (–2, 2)?
a. (9, –6)
b. (2, –5)
c. (2, 9)
d. (–6, 9)
Graph the linear equation.
____
6. y =
a.
y
–4
–2
4
4
2
2
O
____
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
b.
–4
y
c.
4
2
2
2
4
x
4
x
2
4
x
y
d.
4
O
2
–4
–2
O
–2
–2
–4
–4
7. List the lines below in the order of positive slope, negative slope, zero slope, and undefined slope.
y
4
n
2
–4
c
O
–2
2
4
x
–2
a
____
–4
s
a. s, c, n, a
b. c, s, a, n
c. c, s, n, a
8. Which hill described in the table is the steepest? Explain.
Street
Dixie Hill
Bell Hill
Liberty Hill
Horizontal
Distance (ft)
80
80
80
d. a, c, n, s
Vertical Rise
of Street (ft)
40
20
60
a. Bell Hill; it rises one foot for every 4 feet of horizontal travel.
b. Dixie Hill; it rises 2 feet for every 1 foot of horizontal travel.
c. Liberty Hill; it rises 4 feet for every 3 feet of horizontal travel.
d.
Liberty Hill; it rises foot for every 1 foot of horizontal travel.
Write and solve a system of equations to solve the problem.
____
9. You have $10 and save $3 per week. Your friend has $15 and saves $2 per week. After how many weeks x
will you and your friend have the same amount of money y saved?
a.
c.
; 3 weeks
; 5 weeks
b.
d.
; 5 weeks
; 4 weeks
____ 10. A rectangle has a perimeter of 40 ft. Its length is 3 times longer than its width. Find the length y and width x
of the rectangle.
a.
; length: 45 ft; width: 15 ft
b.
; length: 5 ft; width: 15 ft
c.
; length: 15 ft; width: 5 ft
d.
; length: 24 ft; width: 8 ft
____ 11. At the half-time show, a marching band marched in formation. The lead drummer started at a point with
coordinates (–4, 2) and moved 4 steps down and 1 step left.
a. Write a rule to describe the translation.
b. What were the coordinates of the drummer’s final position?
a.
c.
b.
d.
____ 12.
has vertices P(6, 3), Q(–1, –1), and R(–5, –2). The triangle is translated right 6 units and down 3 units.
Without graphing, find the coordinates of , , and .
a.
c.
(0, 0), (–7, –4), (–11, –5)
(12, 6), (5, 2), (1, 1)
b.
d.
(12, 0), (5, –4), (1, –5)
(0, 6), (–7, 2), (–11, 1)
____ 13. Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of one star are (–3, –2). The
star is translated left 6 units. What are its new coordinates?
a. (–9, –2)
b. (3, –2)
c. (–3, 4)
d. (–3, –8)
____ 14. Does the fractal below have reflectional symmetry? If so, how many lines of symmetry does it have?
a. yes; one
b. yes; six
____ 15. Copy
. Draw the image of
c. yes; three
d. no
after a rotation of 270º about the origin.
y
F
H
O
D
x
y
a.
F
y
c.
H'
F
H'
H
H
O
O
x
F'
F'
D'
D
D
y
b.
D'
y
d.
D'
D'
F
F
H'
F'
H
H
O
O
x
F'
D
x
x
H'
D
____ 16. What are the coordinates of the point H(–5, 2) after a rotation of 270 about the origin?
a. (–5, –2)
b. (5, –2)
c. (2, 5)
d. (–2, –5)
Write and graph equations to represent income and expenses for the problem. Then find the breakeven point.
____ 17. A cookie shop owner spends $2 on each cookie and $30 on additional expenses. She sells each cookie for $3.
Let y represent income/expenses and x the number of cookies sold.
a. income:
c. income:
expenses:
;
expenses:
;
y
120
100
100
Income/Expenses (dollars)
Income/Expenses (dollars)
y
120
(30, 90)
80
60
40
20
(30, 90)
80
60
40
20
0
0
10
20
30
40
0
x
0
10
Number of Cookies S old
b. income:
expenses:
30
40
x
Number of Cookies S old
d. income:
expenses:
;
y
;
y
120
120
100
100
Income/Expenses (dollars)
Income/Expenses (dollars)
20
(90, 30)
80
60
40
20
(90, 30)
80
60
40
20
0
0
10
20
30
40
Number of Cookies S old
x
0
0
10
20
30
40
x
Number of Cookies S old
____ 18. A vendor sells basketball jerseys for $30 each. He buys the jerseys for $20 each. He pays $70 in shipping
costs. Let y represent income/expenses and x the number of jerseys sold.
a. income:
c. income:
expenses:
;
expenses:
;
y
y
240
240
(7, 210)
(7, 210)
200
Income/Expenses (dollars)
Number of Jerseys Sold
200
160
120
80
40
160
120
80
40
0
0
2
4
6
8
10
0
x
0
2
Income/Expenses (dollars)
b. income:
expenses:
6
8
10
x
10
x
Number of Jerseys S old
d. income:
expenses:
;
y
;
y
240
240
(7, 210)
(210, 7)
200
Number of Jerseys Sold
200
Income/Expenses (dollars)
4
160
120
80
40
160
120
80
40
0
0
2
4
6
8
10
Number of Jerseys S old
x
0
0
2
4
6
8
Income/Expenses (dollars)
____ 19. Use arrow notation to write a rule for finding the coordinates of a point
the origin.
a.
c.
(x, 2y)
(–x, –y)
b.
d.
(x, –y)
(y, –x)
after a rotation of
about
Short Answer
20. Make a table of solutions for y = 2x
or negative.
. Graph the line and find the slope. State whether the slope is positive
21. Monica conducted a survey about whether students bike or drive to school. When she tallied the results, she
found that 120 wheels were used to travel to school.
a. Write an equation to describe the situation.
b. Graph the equation using the intercepts.
c.
What are two possible solutions for the number of bikes and cars used? Assume that
both the number of bikes and the number of cars are not zero.
Solve the system of equations by graphing.
22.
4x + y =
x – y = –2
23. Al’s Auto Shop charges $125 for parts and $50 per hour of labor for a particular auto repair. Edna’s Engine
Repair charges a flat fee of $260 for the same job.
a. Write a system of equations that represents the relationship between repair time and total
cost for each shop.
b. Graph the system of equations.
c. Which shop is cheaper if the job takes 2 hours? 3 hours? Explain how you used the
graph to find the answer.
24. Which translation below is NOT described by the rule
?
Essay
25. At the movie theater, you spend $9.25 on food and $8.50 on each ticket.
a.
Explain how the equation
models the situation.
b.
Complete the solution (5,
). Show your work.
c.
What does the solution represent?
26. Charlie is growing plants in his science class. The equation
relates the height of a plant h in
centimeters to the numbers of weeks w since he planted the plant at 5 cm tall.
Graph the equation.
a.
Find the slope of the graph. What does the slope represent?
b.
Do all the points on the graph apply to Charlie’s situation? Explain.
c.
27. The average cost of a certain computer has decreased since the first year it came onto the market. In the first
year, the average cost of the computer was $6,000. The average cost has since dropped by $250 every year.
Write an equation with two variables to model the situation.
a.
Graph the equation.
b.
Use the graph to find the average cost of the computer 15 years after it first came onto the
c.
market. Explain how you used the graph.
28. The county fair offers two ticket options.
Ticket Option
Admission Price
Price per ride
A
$3
$.40
B
$1
$.80
a.
b.
c.
Other
Write a system of equations that represents the total cost for each ticket option.
Draw a graph to solve the system of equations.
Interpret the solution to the system in terms of cost and number of rides.
29. The coordinates of an ordered pair have the same sign. In which quadrant(s) must the ordered pair lie?
Explain.
30. Without graphing, explain how the graphs of each pair of lines are similar and different.
a.
and
b.
and
31. Suppose you bought some 37¢ stamps and some 23¢ stamps. You spent $4.52 for sixteen stamps.
Write an equation to describe the situation.
a.
If you were to graph the equation, would every point on the line be a solution to the
b.
problem? Explain.
32. How many lines of symmetry does an equilateral triangle have? Describe the lines of symmetry.
33. Is rotating the point L(4, 4)
34. The expression
about the origin the same as reflecting the point over the x-axis? Explain.
represents the slope of a line. For what values of x is the slope of the line positive?
negative? zero? undefined? Explain.
Course 3 / Chapter 3 Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
ANS: A
ANS: C
ANS: C
ANS: A
ANS: D
ANS: A
ANS: C
ANS: D
MSC: NAEP A1f, CAT5.LV18.54, CTBS.LV18.54, ITBS.LV14.A, S9.Adv1.PRA, S10.Adv1.PRA,
TV.LV18.14, TV.LV18.16
9. ANS: C
10. ANS: C
11. ANS: D
12.
13.
14.
15.
16.
17.
18.
19.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
A
C
D
C
A
B
D
SHORT ANSWER –
20. ANS:
x
–1
0
1
y
–1
1
3
y
4
2
–4
–2
O
2
x
4
–2
–4
2; positive
21. ANS:
a. Let b = the number of bikes.
Let c = the number of cars.
b.
Answers may vary. Sample:
b
60
Number of Bikes
50
40
30
20
10
0
0
4
8
12
16
20
24
28
32 c
Number of Cars
c. Answers may vary. Sample: 40 bikes, 10 cars; 20 bikes, 20 cars
22. ANS:
y
4
(1, 3)
2
–4
–2
O
2
4
x
–2
–4
23. ANS:
a. Let y = the total cost.
Let x = the number of hours of labor.
Al’s Auto Shop:
Edna’s Engine Repair:
y
b.
400
350
Al's Auto Shop
Cost (dollars)
300
250
Edna's Engine Repair
200
150
100
50
0
0
1
2
3
4
5
x
Time (hours)
c.
Explanations may vary. Sample: Al’s Auto Shop is cheaper for 2 hours of work. When
the x-coordinate is 2, the y-coordinate of the graph of Al’s Auto Shop is less than the ycoordinate of the graph of Edna’s Engine Repair. Edna’s Engine Repair is cheaper for 3
hours of work. When the x-coordinate is 3, the y-coordinate of the graph of Edna’s
Engine Repair is less than the y-coordinate of the graph of Al’s Auto Shop.
24. ANS:
(1, –5)
ESSAY
(3, –2)
25. ANS:
[4] a.
y represents the total amount of money spent on food and x movie tickets.
51.75
b.
The solution represents the cost of food and 5 movie tickets.
c.
[3] two parts correct
[2] one part correct
[1] correct answer without work shown
27. ANS:
[4] a.
Let c = the average cost of the computer.
Let n = the number of years since the computer first came onto the market.
c = 6,000 – 250n
c
b.
Cost (thousands of dollars)
6
5
4
3
2
1
0
0
4
8
12
16
20
n
Years
$2,250; find the point on the line with an n-coordinate of 15 and then estimate the
c-coordinate.
two parts correct
one part correct
correct answer without explanation
c.
[3]
[2]
[1]
28. ANS:
[4] a.
Let y = the total cost.
Let x = the number of rides.
b.
y
10
Total Cost (dollars)
8
6
(5, 5)
4
2
0
0
2
4
6
8
x
Number of Rides
[3]
[2]
[1]
c. The total cost for both ticket options is the same when five rides are purchased.
two parts correct
one part correct
correct answer without work shown
OTHER
a.
Let x = the number of 37¢ stamps.
Let y = the number of 23¢ stamps.
b.
Only the points in quadrant I with whole numbers for the x- and y-coordinates are valid
solutions. You cannot buy negative or fractional amounts of stamps.
32. ANS:
An equilateral triangle has 3 lines of symmetry—one from each vertex to the middle of the opposite side.