9 Weeks
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. During a sale, customers receive an extra discount if they spend $200 or more. So far, Erin’s purchases total
$135. Which inequality can be solved to show how many more dollars d she must spend to receive the extra
discount?
a.
b.
____
2. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if
there are at least 100 people on the plane. Write a compound inequality to show the possible number of
people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight.
Graph the solutions.
a.
–250
–200
–150
–100
–50
0
50
100
150
200
250
–250
–200
–150
–100
–50
0
50
100
150
200
250
–250
–200
–150
–100
–50
0
50
100
150
200
250
–250
–200
–150
–100
–50
0
50
100
150
200
250
b.
c.
d.
____
3. The maximum capacity of a theater is 471 people. So far, 254 people are seated in the theater. Which
inequality can be solved to show the number of people p that can still enter the theater?
a.
c.
b.
d.
____
4. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can
spend the remainder of the money on music. Write an inequality to show how much he can spend on music.
Then, graph the inequality.
a.
;
s
–500
–400
b.
–300
–200
–100
0
100
200
300
400
500
300
400
500
300
400
500
;
s
–500
–400
c.
–300
–200
–100
0
100
200
;
s
–500
–400
–300
–200
–100
0
100
200
d.
;
s
–500
____
–400
–300
–200
–100
0
100
200
300
400
500
5. Susan wants to find out how long it will take her to bike to a store that is 1 mile away, and then turn around
and walk home. Susan’s average cycling rate is 6 times her walking rate. Write and simplify an expression for
how long it will take Susan to bike to the store, and then turn around and walk home. If her walking rate is 2
miles per hour, how long will it take Susan to bike to the store, and then turn around and walk home?
a.
; It will take Susan of an hour, or 35 minutes, to bike to the store, and then turn
around and walk home.
b.
; It will take Susan 2 hours to bike to the store, and then turn around and walk home.
c.
; It will take Susan of an hour, or 30 minutes, to bike to the store, and then turn around
and walk home.
d.
; It will take Susan
and walk home.
of an hour, or 5 minutes, to bike to the store, and then turn around
____6. .Lawrence's parents pay him a base allowance of $10 per week and $3.20 per hour for extra chores he completes.
Mr. Williams pays Lawrence $7.80 per hour to fix broken washing machines at the laundromat. Which
equation models Lawrence's total weekly income?
a.
c.
b.
d.
7. The Ybarra family is renting a car for a few days. Meinke Rentals charges $20 per day, plus a fixed cleaning
fee of $20. The function
represents the cost to rent a car from Meinke Rentals for d days.
SmartRent charges $25 per day. The function
represents the cost to rent a car from SmartRent for
d days. Graph
and
on the same coordinate plane and describe the transformation that takes
to
.
a.
Cost ($)
____
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
M(d)
S(d)
1
2
3
4
5
6
7
Number of days
A vertical shift down 20 units, followed by a vertical stretch by a factor of 1.25.
Cost ($)
b.
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
M(d)
S(d)
1
2
3
4
5
6
7
Number of days
A vertical stretch by a factor of 1.25, followed by a vertical shift down 20 units.
Cost ($)
c.
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
S(d)
M(d)
1
2
3
4
5
6
7
Number of days
A vertical compression by a factor of 0.75, followed by a vertical shift up 20 units.
Cost ($)
d.
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
S(d)
M(d)
1
2
3
4
5
6
7
Number of days
A vertical shift up 20 units, followed by a vertical compression by a factor of 0.75.
____
8. A factory makes widgets x and gadgets y. Widgets cost $3 and gadgets cost $5 each to make. The boss wants
at least 10 widgets and 20 gadgets per day. Total costs need to be at most $300 per day. What system
represents this situation?
_
____
a.
c.
b.
d.
9. Analisa is paid $300 each week plus commission on her total sales s. If she sells less than $200, she receives
5% commission; if she sells $200 or more, she receives 8%. Which function can be used to find her total pay
P?
a.
c.
b.
d.
____ 10. Mr. Frankel bought 7 tickets to a puppet show and spent $43. He bought a combination of child tickets for $4
each and adult tickets for $9 each. Which system of equations below will determine the number of adult
tickets, a, and the number of child tickets, c, he bought?
a.
b.
c.
d.
____ 11. Lena made 32 ounces of a fruit drink mix using pineapple juice and grapefruit juice. The number of ounces of
pineapple juice in the fruit drink mix is 5 more than 2 times the number of ounces of grapefruit juice in the
fruit drink mix. Which graph shows the number of ounces pineapple juice, x, and the number of ounces of
grapefruit juice, y, in the fruit drink mix? What system of equations was used to create the graph?
a.
c.
b.
d.
____12. .A music store is selling posters and CDs. The store profits $3.00 from each poster sold and $5.00 from each CD
sold. The store needs to make an average profit of $200 per hour to stay in business. Using x as the number of
posters sold and y as the number of CDs sold, write and graph an inequality for the number of each item the
store needs to sell to stay in business. If 15 posters are sold, how many CDs must be sold?
a.
c.
; At most 31 CDs.
; At most 31 CDs.
y
y
72
72
64
64
56
56
48
48
40
40
32
32
24
24
16
16
8
8
8
b.
16
24
32
40
48
56
64
; At least 31CDs.
72
80 x
8
d.
16
24
32
40
48
56
64
; At least 31 CDs.
72
80 x
y
y
72
72
64
64
56
56
48
48
40
40
32
32
24
24
16
16
8
8
8
16
24
32
40
48
56
64
72
80 x
8
16
24
32
40
48
56
64
72
80 x
____ 13. Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake
starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That
tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake
and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have
the same volume of water? What is that volume of water?
a. 5 minutes; 150 gallons
c. 5 minutes; 250 gallons
b. 10 minutes; 150 gallons
d. 10 minutes; 250 gallons
____ 14. A store is selling posters and T-shirts. The store profits $3.00 from each poster sold and $5.00 from each Tshirt sold. The store needs to make an average profit of $200 per hour from the sales. Using x as the number
of posters sold and y as the number of T-shirts sold, write and graph an inequality for the number of each item
the store needs to sell to stay in business. If 15 posters are sold, how many T-shirts must be sold?
a.
c.
; At most 31 T-shirts.
; At most 31 T-shirts.
y
y
72
72
64
64
56
56
48
48
40
40
32
32
24
24
16
16
8
8
8
b.
16
24
32
40
48
56
64
72
; At least 31 T-shirts.
80 x
8
d.
16
24
32
40
48
56
64
72
; At least 31 T-shirts.
80 x
y
y
72
72
64
64
56
56
48
48
40
40
32
32
24
24
16
16
8
8
8
16
24
32
40
48
56
64
72
80 x
8
16
24
32
40
48
56
64
72
80 x
____ 15. A local supermarket sells chicken for $2.49/lb and pork for $3.19/lb. Todd buys c pounds of chicken and p
pounds of pork. Which of the following inequalities represents that Todd only has $40 to spend?
a.
b.
c.
d.
____ 16. The formula for converting degrees Celsius (C) to degrees Fahrenheit (F) is
A chemistry
student knows that the temperature in degrees Kelvin (K) is 273.15 degrees greater than in degrees Celsius, so
the formula to convert degrees Kelvin to degrees Fahrenheit is
What formula can
you use to convert degrees Fahrenheit to degrees Kelvin?
a.
c.
b.
d.
____ 17. When x pounds of force is applied to one end of a lever that is L feet long, the resulting force y on the other
end is determined by the distance between the fulcrum (the lever's pivot) and the end of the lever on which the
x pounds of force is exerted.
The formula relating the forces is
a.
What formula can you use to find the length of the lever?
c.
b.
d.
____ 18. The area A of a trapezoid is given by the formula
two parallel sides. Solve the formula for
a.
b.
, where
and
are the lengths of the
.
c.
d.
____ 19. Which of the following properties would not be used to justify any of the steps below?
a.
b.
c.
d.
Subtraction Property of Equality
Multiplication Property of Equality
Distributive Property
Zero Product Property
____ 20. Which of the following is a graph of the solutions of
a.
OR
?
b.
c.
d.
____ 21. Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book and reads
2 pages every night. How long will it take Latisha to be further in the book than Sal?
a. 3 nights
c. 15 nights
b. 11 nights
d. 71 nights
____ 22. Safety goggles function best at room temperature, or 75 F. A pair of special safety goggles can function at
temperatures that differ from this value by at most 41.3 F. Write and solve an absolute-value inequality to
find the range of acceptable temperatures. Graph the solutions.
a.
–40
–20
0
20
40
60
80
100
120
140
40
60
80
100
120
140
The range of acceptable temperatures is
.
b.
–40
–20
0
20
OR
The range of acceptable temperatures is
.
c.
30
40
50
60
70
80
90
100
110
120
70
80
90
100
110
120
The range of acceptable temperatures is
.
d.
30
40
50
60
OR
The range of acceptable temperatures is
.
Solve the absolute value equation. Graph the solution.
____ 23.
c. x = 1 or x = 1
a. x = 1 or x = 4
–5
–4
–3
–2
–1
0
1
2
3
4
–4
–3
–2
–4
–3
–2
–1
0
1
2
3
4
5
d. x = 2 or x = 1
b. x = 1 or x = 2
–5
–5
5
–1
0
1
2
3
4
–4
5
–2
0
2
4
Solve the inequality. Graph the solution.
____ 24. A furniture maker uses the specification
the specification as an absolute value inequality.
a.
c.
b.
d.
for the width w in inches of a desk drawer. Write
Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)?
____ 25. Let
be the reflection of
in the x-axis. What is a function rule for
?
a.
b.
c.
d.
What transformations change the graph of f(x) to the graph of g(x)?
What is the graph of the absolute value equation?
____ 26.
a.
c.
y
–8
–4
y
16
16
12
12
8
8
4
4
O
4
8
–8
x
–4
–4
b.
d.
y
O
8
x
4
8
x
y
16
4
–4
4
–4
8
–8
O
12
4
8
8
x
–4
4
–8
–8
–12
What is the graph of the absolute value function?
____ 27.
–4
O
–4
a.
c.
y
–12
12
12
6
6
O
–6
6
12
–12
x
–6
O
–6
–6
–12
–12
b.
d.
y
–12
y
12
6
6
O
6
12
x
12
x
6
12
x
y
12
–6
6
–12
–6
O
–6
–6
–12
–12
Compare each function with the parent function. Without graphing, what are the vertex, axis of
symmetry, and transformations of the parent function?
____ 28.
a.
5
5
( , 4) x =  ;
4
4
translated to the left
b.
5
5
( , –4); x = ;
4
4
translated to the left
c.
5
units and down 4 units.
4
5
5
( , 4); x = ;
4
4
translated to the left
d.
5
units and up 4 units.
4
5
5
( , –4); x =  ;
4
4
5
units, up 4 units, and reflected in the y-axis.
4
translated to the right
5
units and up 4 units.
4
What is the graph of each absolute value inequality?
____ 29. y  |x – 1| + 3
a.
–12
c.
y
–6
12
12
6
6
O
6
12
–12
d.
12
6
6
O
6
12
–12
x
–6
O
–6
–6
–12
–12
c.
12
6
6
6
12
x
12
x
6
12
x
6
12
x
y
12
O
6
y
12
y
–6
O
–12
____ 30. |x + 5|  y – 2
a.
–12
–6
–6
y
–6
–12
x
–6
b.
–12
y
–12
–6
O
–6
–6
–12
–12
b.
d.
y
–12
–6
y
12
12
6
6
O
6
12
x
–12
–6
O
–6
–6
–12
–12
6
12
x
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
____ 31. To print custom-designed T-shirts, Maria must pay a $45 fee plus $15 for each T-shirt. What equations could
be used to find the number of T-shirts Maria could print with $390?
a.
b.
c.
d.
e.
____ 32. A department store offers a frequent-buyers reward card. Every time a customer earns 100 or more points, the
customer receives a gift certificate. Each purchase is worth 12 points, and customers automatically earn 25
points when they sign up. Which inequalities could be used to find the number of purchases a customer
needs to make to earn the first gift certificate?
a.
b.
c.
d.
e.
____ 33. Sal is having a yard sale. He plans to sell his old DVDs and CDs. Combined, he has 75 DVDs and CDs. He
prices them at $1.50 per CD and $4.50 per DVD. Let represent the number of DVDs Sal sells and
represent the number of CDs Sal sells. He sells all of his DVDs and CDs and earns $262.50. Which of the
following equations should be included in a system that reflects the constraints of this situation?
a.
b.
c.
d.
e.
____ 34. An object with mass
and an object with mass
whose centers of mass are a distance apart experience
an attractive gravitational force
given by the formula
constant. Solve this formula for
, ,
, and
, where
is the universal gravitational
to determine which equations given below are correct.
a.
b.
c.
d.
e.
f.
g.
h.
Matching
35. The surface area
of a rectangular prism with a given length , width
. Match each task with the resulting formula.
a.
d.
b.
e.
c.
f.
, and height
is
____
1. Solving for the length of a rectangular prism with a given width, height, and surface area
____
2. Solving for the width of a rectangular prism with a given length, height, and surface area
____
3. Solving for the height of a rectangular prism with a given length, width, and surface area
Short Answer
36. An essay must be at least 500 words long to be accepted. Define a variable and write an inequality for the
acceptable number of words in an essay. Graph the solutions.
37. Justin is on the TV game show You Can Price Like a Pro. He is playing the Grocery Store Game. In this
game, Justin is shown six grocery-store items without being shown the prices. He must buy multiples of items
until he has a total between $20 and $21 inclusive. If he doesn’t reach $20 with his first item, he continues
buying items and adding to his total, until he either wins or goes over $21.
Justin began by buying six bottles of hand lotion. One bottle of lotion costs $2.99. That gives Justin a running
total of $17.94. He now considers buying packages of gum.
Part A: Justin guesses that one package of gum costs $0.50. Write a compound inequality to find how many
packages he should buy.
Part B: Solve your compound inequality from part a. Write your answer as a compound inequality.
Part C: Justin can only buy whole packages of gum. Assuming each package actually costs $0.50, how many
could he buy to win the game?
38. A grocery store offers a coupon for $2 off when a customer buys 6 or more bottles of water. The water costs
$1.75 per bottle. Shauna uses the function
to find the total dollars it costs to buy bottles of
water. When she uses the function to find how many bottles she can buy for $5, she finds
, so she
concludes she could buy 3 bottles of water for $5. Explain what error Shauna made.
39. Rod has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he
have?
40. A jet can travel the 6000 km distance between Washington, D.C. and London in 6 h with the wind. The
return trip against the same wind takes 7 h 30 min. Find the rate of the jet in still air and the rate of the wind.
41. Solve the following problem. If extra information is given, identify it.
Sharon earned $460 in simple interest on an investment of $6200. Some of the money earned an interest rate
of 5%, and the rest earned 8%. Her average rate of interest was 7.4%. How much did she invest at each rate?
42. Julius is flying home to Los Angeles, California, from Boston, Massachusetts. His distance away from home
in miles d can be expressed in terms of t hours by the equation
. Graph Julius’s distance away
from home in miles d after t hours, choosing appropriate scales.
43. A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length
x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this
situation.
44. A caterer needs to make at least 20 pounds of a mix of cashews and pecans for a party without spending more
than $55 to buy the nuts. The mix should have at least twice as many cashews as pecans by weight. The
caterer can buy cashews for $2.15 per pound and pecans for $1.80 per pound. Write and graph a system of
inequalities to represent this information. Let x represent the weight of cashews used and let y represent the
weight of pecans used.
algebraically, and explain.
45. In a strategy video game, you want to hire 50 soldiers (knights and archers) to attack the enemy base. Knights
cost 250 gold coins to hire, and archers cost 150 gold coins to hire. You currently have 8900 gold coins. Write
a system of equations to represent the constraints. Explain how each equation constrains the values of the
variables. Then give the solution.
46. The business leader of a toy-making company needs to determine the number n of employees that can be
hired while maintaining a certain profit . Employee wages are dollars per day, and each employee will
make toys on average each day. Each product can be sold for dollars and costs dollars to produce. The
daily overhead cost is dollars. Write an equation for profit, explaining how you obtained the equation. Then
find an equation expressing the number of employees that can be hired as a function of the other variables.
47. You want to know the number of minutes that you can use on a $20.00 phone card. The card company
charges $0.50 for the card and $0.10 for each minute used. The equation
, where m
is the number of minutes on the card, represents this situation. Solve the equation and write a reason for each
step. If necessary, round your answer to the nearest hundredth.
Problem
48. The length of any side of a triangle is less than the sum of the lengths of the other two sides of the triangle. If
three side lengths do not satisfy this requirement, then a triangle cannot be formed from them.
2x
x– 3
7
a. Given the triangle above, use the restriction on side lengths to write three inequalities. Solve all three
inequalities for .
b. What values of will satisfy the inequalities you found in part a? Explain how you know.
c. Give an example of one set of possible side lengths for the triangle above.
49. A fruit juice company makes two kinds of juice blends, each in 1-gallon bottles. The regular mix uses
gallon of orange juice and
and
gallon of pineapple juice, while the tropical mix uses
gallon of orange juice
gallon of pineapple juice. The company wants to maximize its profit from selling bottles of the
regular juice mix and bottles of the tropical juice mix made using the 225 gallons of orange juice and 150
gallons of pineapple juice it currently has on hand.
a. Give four constraints the company must take into consideration to maximize the profit.
b. Graph and shade the region bounded by the constraints from part a.
t
r
c. If the regular juice blend makes a $2.50 profit per bottle sold and the tropical juice blend makes a $1.75
profit per bottle sold, the profit from selling bottles of the regular blend and bottles of the tropical
blend is
. The maximum profit is the maximum value found when evaluating the profit
function at each vertex on the graph (or the point closest to the vertex with values that make sense in
context). What is the maximum profit, and how many bottles of each type of juice blend will be sold to
make that profit? Assume all manufactured bottles are sold.
50. Your classmate Juan missed the lesson on graphing linear equations using slope-intercept form. You attended
the class and want to help Juan understand the material he missed. Assume Juan knows how to graph
Part A: Write an explanation for Juan that describes the y-intercept of a line and what happens to the graph of
as you change the y-intercept. Be specific and consider several cases.
Part B: Write an explanation for Juan that describes the slope m of a line and what happens to the graph of
as you change the slope. Be specific and consider several cases.
51. Al's Auto Shop charges $149 for parts and $53 per hour of labor for a repair job. Edna's Engine Repair
charges a flat fee of $280 for the same job.
Part A: Write a system of equations to represent the situation.
Part B: Graph the system of equations.
Part C: Which shop is cheaper if the job takes 2 hours? 3 hours?
52. Jim is catering a large party. To make one apple pie, he needs 2 pounds of apples. To make one peach pie, he
needs 3 pounds of peaches. There are about 42 pounds of apples in one bushel of apples and 48 pounds of
peaches in one bushel of peaches.
Part A: Write an inequality to represent the possible numbers of pies Jim can make from one bushel of
apples.
Part B: Write an inequality to represent the possible numbers of pies Jim can make from one bushel of
peaches.
Part C: Jim needs to have at least 240 servings of apple pie and 180 servings of peach pie. If one pie contains
6 servings, how many of each type of pie should he make?
Part D: How many bushels of each type of fruit should Jim buy in order to have enough fruit? Will he have
leftover fruit? Explain.
53. A classmate has just solved an equation without checking the answer. Unfortunately, the solution has several
mistakes. Without re-doing the entire problem, go through each step and explain how the step was obtained. If
the step is incorrect, explain the error and the procedure that should have been followed.
Other
54. Ernesto and his family have just finished dinner at a restaurant in a region where meal tax is 5% of the price
of the meal. Ernesto leaves a 17% tip. With tax and tip, the total cost is $58.56. The equation
, where p is the price of the meal without tax or tip, can be used to model this
situation. Determine which of the following could be steps in calculating the price of the meal .
a.
b.
c.
Yes
Yes
Yes
No
No
No
d.
e.
Yes
Yes
No
No