Unit 1: Relationships Between Quantities
N.Q.1-3: Quantities and Units
1. Convert 8 miles to yards.
2. Convert 45 miles per hour to feet per minute.
3. Convert 15,000 feet to miles.
4. When Mary goes to school, she drives at an average speed of 55 miles per hour. It takes one hour for Mary to travel to school. Her car travels 20 miles per gallon of gas. Gas costs $3.30 per gallon. How much does Mary spend to travel each mile to school?
$0.165 cents per mile
How much money does Mary spend per trip?
$9.08 per trip (one-way), $18.15 round trip
5. Bob is taking a road trip. He will drive an average speed of 75 miles per hour on the trip. The trip will take a total of 3 hours and 30 minutes. His car travels 24 miles per gallon of gas, and gas costs $3.48 per gallon. How much will Bob spend to travel each mile on his trip?
$0.145 cents per mile
How much will his trip cost (one-way)?
6. The formula for velocity is v = d/t, where d is distance and t is time. If distance is measured in meters and time is measured in seconds, what is the unit rate for velocity?
Meters per second
7. A box has a volume of 5 m3, a length of 200 cm, and a width of 500 cm. What is the height of the box?
50 centimeters (0.5 meters)
8. A rectangle has an area of 4 m2 and a length of 50 cm. What is the width of the rectangle?
800 centimeters (8 m)
9. How many feet are equivalent to ¼ mile?
10. A rectangular fish tank contains 3,240 cubic inches of water. The dimensions of the base of the fish tank are 12 inches x 18 inches. How tall is the fish tank?
11. Lauren is building a tree house with her dad. The dimensions of the floor are 9 feet by 6 feet. What is the area of the floor, measured in square yards?
12. What is the area of a circle with a circumference of 31.4? (Use 3.14 for pi)
*Remember, C = 2(pi)r and A = (pi)r2.
13. What is the circumference of a circle with an area of 28.26? (Use 3.14 for pi)
14. The rate of water filling a cylinder is represented by the formula r = V/t, where V is the volume measures in meters cubed and t is the time measured in seconds. What is the unit measure for the rate of water filling the cylinder?
Meters3 per second
A.SSE.1, 1a, 1b: Structure of Expressions
15. [using the formula A = P(1 + r)t] An amount of $800 is deposited into a bank account that pays 5% annual interest. What would be the bank account balance after 8 years?
16. An amount of $1200 is deposited into a bank account that pays 3.5% annual interest. What would be the bank account balance after 6 years?
17. [using the formula C = 0.075mt where C is calories burned, m is body weight and t is number of minutes spend jogging) If a person has a body mass of 120 pounds, what would the coefficient for t be?
18. Two different formulas for calories burned are represented: C1 = 0.072mt and C2 = 0.018mt. One of the activities is running, and one of the activities is walking. Which formula would you expect to go with each activity?
C1 goes with running, C2 goes with walking
19. The potential energy of an object is found by the formula PE = mgh, where m is mass, g is 9.8 m/s2 (acceleration of gravity), and h is height. If the mass of an object is 10 grams, what would the coefficient of h be?
20. The formula for the growth of a bacteria’s population is A = Po(1.789)0.06t, where Po is the initial population and t is the time in hours. If you begin with 150 bacteria, how many of the bacteria can you expect after 80 hours?
21. The formula for the growth of a bacteria’s population is A = Po(1.789)0.06t, where Po is the initial population and t is the time in hours. If you begin with 150 bacteria, how many of the bacteria can you expect after 80 hours?
A.CED.1-4: Equations and Inequalities
22. Two angles of a triangle measure 40o and 100o. What is the measure of the third angle?
23. Two angles of a triangle measure 23o and 78o. What is the measure of the third angle?
24. An ant colony starts off with only 10 ants. The colony doubles every day. How long will it take for the ant colony to have at least 1000 ants?
25. When Facebook first started, it only had 500 users. The number of people on facebook quadrupled every 2 weeks. How long will it take for Facebook to have at least 1,000,000 users?
26. Joy starts off with $25 and she makes $7 each week. Brad starts off with $18 and he makes $10 each week.
a)What are the equations for Joy and Brad’s income with x being the number of weeks they work?
Joy: y = 25 + 7x Brad: y = 18 + 10x
b) How much do Joy and Brad both have after 7 weeks of work?
Joy: $74 Brad: $88
27. Mickey only has $20 to spend at the restaurant. He wants to order at least one entrée and at least one drink. Entrees cost $8 and drinks cost $2. What are all the possible combinations of entrees and drinks Mickey can get?
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2) 1st number entrée, 2nd number drinks
28. You only have $40 to spend at Six Flags. Burgers cost $12 each and drinks cost $5. What possible combinations of burgers and drinks can you get at Six Flags?
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3) 1st number burgers, 2nd number drinks
29. The squirrel population in Australia doubles every year. If there are 3,000 squirrels this year, how many squirrels will there be 3 years from now?
30. A farmer has three times as many carrot plants as potato roots. If there are 24 total plants in his garden, how many are potato roots?
p = 8
31. You have twice as many shirts as you do pants. If you have a total of 18 shirts and pants, how many pants do you have?
p = 6
32. The angles of a triangle measure xo, 3xo, and 6xo. Solve for x.
x = 18
33. [using the formula Profit = Revenue – Cost (P = R – C)] You invested $4,000 in a business. Each unit of the product you produce costs $1.50 to make, and you are selling each product for $3.50. How many units of the product must be sold in order for you to make a profit?
34. Barry has a water bottle company. He spends $15 in production costs on each water bottle, and spends $1,000 a month on factory rental. He sells each water bottle for $20. How many water bottles does he need to sell each month in order to make a profit?
200 water bottles
35. What is the solution to the equation P = 2l + 2w solved for l?
36. What is the solution to the equation F = ma solved for a?
a = F/m
37. What is the solution to the equation V = 2r + s solved for r?
*Extra: Which equation is not equivalent to W = 1500 – 150T? C
15(100 – 10T)
1500(1 – 150T)
125 + 1375 – 10(15T)
d. 10(150 – 15T)
At Metropolis Middle School, the number of cans, N, collected for recycling after a basketball game depends on the number of people, P, who attend the game. The approximate relationship is given by N = 2.5(P – 40) – 100. distribute to get 2.5P - 200
a. Is the relationship between the number of cans collected and the number of people attending linear or not? Explain. yes it’s linear
b. If 400 people attended the game for the semifinals of the district championship, how many cans would you expect to be collected? 800
c. If 300 cans were collected at a game, how many people would you expect to have attended the game? 200
d. If 675 cans were collected at another game, how many people would you expect to have attended that game? 350
Unit 2: Reasoning with Equations and Inequalities
A.REI.1, 3: Transformations of Equations and Inequalities, Solving Equations/Inequalities
38. Is the expression equivalent to 2x + 3?
yes (divide everything by 5)
39. Solve the equation 3y – 6 = 2(x + 1) for y.
40. Solve the equation 4(2x – 3) = 4y + 8 for y.
y = 2x - 5
41. Solve the equation bx – 3 = 12 for x.
x = 15/b
42. Solve the equation 9 = 5 – ax for x.
x = -4/a
43. Solve the inequality 2y + 6 ≥ -3 for y.
y ≥ -9/2
44. Solve the inequality 6 – y < -5
y > 11
45. Solve the inequality 8 – 2y ≤ -2
y > 5
46. Solve this inequality for y: 6a – 3y > 9
y < -3 + 2a
47. Solve this inequality for y: 5y + 2b ≤ -10
48. Solve the equation for n.
n = 15/4
49. Solve the equation for x.
x = 15
50. Solve the equation for a.
a = -30/23
51. Which equation is equivalent to 7a = 3(b – 5) solved for b?
52. Which equation is equivalent 2(n + 7) = -3t solved for t?
53. Solve the following equation: 5(4 – x) = 35.
x = -3
54. Solve the inequality: 2(3 – x) ≥ -4
x ≤ 5
55. Solve the inequality: 9 > -3(4 – x)
7 > x or x < 7
56. Marcia wants to save up for an iPhone. She will save $15 per week from the money she earns working. If an iPhone costs $300, how many weeks will it take her to save enough money?
57. Joe wants to save money for a spring break trip. He will save $16 per week from his job. If his trip will cost a total of $550, how many weeks will it take him to save enough money?
35 weeks (need to round up)
58. Decide whether 2x + 8 + 4 is equivalent to 2(x + 4) + 4. Explain how you know.
59. Joe is getting his first cell phone. His phone will cost $28.99 a month, and he can spend a maximum of $40 a month on his phone. He could add unlimited texting to his phone plan for $15 a month, or he can pay for each text individually. The second option offers an additional rate of $0.10 per text. Joe averages about 10 texts per day. Can Joe afford to add texting to his plan?
Not 1st plan ($43.99) and not 2nd play ($58.99)
60. Your family is finally getting cable! The monthly flat rate fee for service costs $65.00 a month. Your family budget for cable is $90.00 a month. Your family can get an “additional random bundle” of channels for $25.00 a month, or your family can pick channels one-by-one for $2.00 per channel. After doing a survey, your family knows that they want to add on at least 15 channels. Which option can your family afford?
1st plan (costs $90, 2nd plan costs $95)
61. [using the formula d = rt] Two trains, the first traveling 20 miles faster than the second, both start in Chicago and travel in opposite directions. After 5 hours, they are 200 miles apart. We can use the formula below to calculate the rate of the second train:
5(r + 20) + 5r = 200
What is the rate, r, of the second train?
r = 10 mph
62. [using the formula d = rt] Two cars, the first traveling 25 miles per hour faster than the second, start at the same point and travel in opposite directions. After 3 hours, they are 225 miles apart. Write a formula to determine the rate, r, of the second car.
r = 33.33333 mph
63. This equation can be used to find t, the number of hours it takes Moe and Mickey to paint a room.
How many hours will it take them to paint the room? (write answer in terms of hours and minutes)
6/5 hours, or 1 hour and 12 minutes
64. This equation can be used to find h, the number of hours it takes Jane and Jack to clean their rooms.
How many hours will it take them?
65. A ferry boat carries passengers back and forth between Staten Island and New York.
It takes 1 hour longer for the ferry to make the trip upstream than downstream.
The ferry’s average speed in still water is 20 miles per hour.
The river’s current is usually 10 miles per hour.
This equation can be used to determine the distance in miles apart the two locations are.
What is d, the distance between Staten Island and New York?
d = 15 miles
66. Which expression represents all values of x for which the inequality is true?
x < -9
67. Which expression represents all values of x for which the inequality is true?
68. Which expression represents all values of x for which the inequality is true?
x < 5
A.REI.6- Solve System of Two Linear Equations
69. A parking meter contains 27 coins consisting only of dimes and quarters. If the meter contains $4.35, how many of each type of coin is there?
16 dimes, 11 quarters
70. A bag contains only nickels and dimes. The value of the collection is $2. If there are 26 coins in all, how many of each coin are there?
12 nickels, 14 dimes
71. 200 tickets were sold to a college’s annual musical performance. Tickets for students were $2.50 and for nonstudents $3.50. The total amount collected was $537. How many nonstudents purchased tickets for the performance?
72. Mary’s cell phone costs $20 a month plus $0.15 per minute. Jim’s phone costs $30 a month plus $0.10 per minute. After how many minutes of use will Mary’s phone cost more than Jim’s?
73. Tommy’s internet costs $30 a month plus $0.50 per minute. Terry’s internet costs $35 a month plus $0.40 per minute. After how many minutes of use will Tommy’s internet plan cost more than Terry’s?
74. Given the system of equations, determine if the given points are solutions of the system:
y = 3 + x
4x – 3y = 8
a) (10, 3) b) (0, 0) c) (17, 20) d) (34, 40)
No No Yes No
75. Solve the system of equations:
infinite solutions 0 = 0
76. Solve the system of equations:
77. Solve this system of equations:
no solution 0 = -4
78. The band director is comparing t-shirt prices from two companies.
Company A charges $10 per shirt plus $2 per letter
Company B charges $15 per shirt plus $1.50 per letter
For what number of t-shirts will the band director’s cost be the same for both companies?
79. Barbara is comparing prices for making bracelets.
Store A charges $5 for the string plus $0.50 per bead
Store B charges $3 for the string plus $1 per bead
For how many bracelets will Barbara’s cost be the same for both stores?
80. A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
5 multiple choice
81. A shop sells twelve-pound bags of potatoes for $12 and eighteen-pound bags of potatoes for $15. If 300 bags of potatoes are purchased for a total of $4140, how many eighteen-pound bags of potatoes were purchased?
180 eighteen-pound bags
82. The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.
19 and 71
83. Eldora and Finn went to an office supply store together. Eldora bought 15 boxes of paper clips and 7 packages of index cards for a total cost of $55.40. Finn bought 12 boxes of paper clips and 10 packages of index cards for a total cost of $61.70. Find the cost of one box of paper clips and the cost of one package of index cards.
paper clips: $1.85 index cards: $3.95
a) Which graph shows a system of equations with no solution?
b) Which graph shows a system of equations with one solution? What is the solution?
c) Which graph shows a system of equations with infinite solutions?
A.REI.12- Graphing Solutions of Equations and Inequalities
85. Use a number line to display the solution to 2x + 4 ≥ 24.
x ≥ 10 (closed circle, shade right)
86. Use a number line to display the solution to 9 – 2x < 5.
x > 2 (open circle, shade right
87. Graph the equation on a coordinate plane: -2x + y = -5
y = 2x – 5 (y-intercept -5 and positive slope up 2 right 1)
88. Graph the inequality on a coordinate plane: 4x + y < -2
y < -4x – 2 (y-intercept 2, negative slope down 4 right 1, dotted line, shade to the left/beneath)
89. Graph the inequality on a coordinate plane: y – 5 ≤ 2x
y ≤ 2x + 5 (y-intercept 5, positive slope up 5 right 1, solid line, shade to the right/beneath)
90. Graph the solution of and on the coordinate plane.
91. Graph the solution of 2x – 2y > -6 and x + y > 2 on the coordinate plane.
y < x + 3 and y > -x + 2
92. Which inequality is represented by the graph below?
y ≤ 2x + 3
93. Which inequality is represented by the number line?
x < -10
94. Which pair of inequalities is shown in the graph? B
A. y < -x – 2 and y > -5x – 2
B. y > -x – 2 and y < -5x + 2
C. y > x – 2 and y > 5x – 2
D. y > -2x – 1 and y < 2x – 5
95. Which pair of inequalities is shown in the graph below?
y > -2 and y < -4x + 2
97. Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation and display it on the graph below. How many people can attend Joann’s party?
50 + 4x < 100 solve to get 12 people who can attend