Name:
Period:
Date:
Algebra 1 Common Semester 1 Final Review
Like PS4
1. How many surveyed do not like PS4 and do not like X-Box?
Like X-Box
2. What percent of people surveyed like the X-Box, but not the
PS4?
Yes
No
Total
Yes
45
91
No
8
32
Total
53
123
3. What is the conditional relative frequency of people surveyed
who like PS4, given that they like X-Box?
4. Based on the table below, what is the joint relative frequency of the people surveyed who do not
have a job and have a savings account?
Have a job
Have a savings
account
Yes
No
Yes
134
66
No
16
84
5. The table below shows the results of a survey of students’ favorite subjects. What is the relative
frequency that a student’s favorite subject is not English?
Subject Science English Math
Total
24
48
28
6. The fuel economy in miles per gallon of several vehicles is given below. Use this data to make a
box plot.
Data Set A
miles per gallon
28.5 18.0 19.6 21.1 22.0 24.0 16.9
27.2 15.2 18.0 21.5 29.0 18.0 28.0
In exercises 7 – 12, use the box and whisker plot to find the given measure.
7. Least value
9. Greatest value
11. Range
8. Median
10. Third quartile
12. First quartile
Make a box and whisker plot for each set of data.
13. Hours of exercise per week: 0, 7, 2, 5, 12, 2, 0, 9
14. Number of cars in a parking lot: 12, 35, 20, 17, 24, 30, 28, 16
15. The environmental club is selling water bottles for $8 and tote bags for $12 to raise $240 to
donate to charity. Complete the table and write the linear equation for the fundraising goal.
Water
Tote
Bottles
Bags
0
0
15
16. A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and
solve an equation to find the number of hours of labor spent repairing the car.
Solve each equation.
1
(6 x  4)  5(2 x  8)
17. 2
18. 3b+12 +b = 30 + 4b
3
1
(d  12)  (2d  6)
2
19. 2
21. 5(2c + 7) -3c = 7(c + 5)
k
7
22.  9
20. 3(-5y+2) = 21
Solve the inequality. Graph the solution.
23. -9 < m – 6
26. 4k – (3-3k) > 2
24. -3z > 6 + 3z
27. -3y > 8 or 2y – 6 > 2
25. 4n + 3 < 6n + 8 – 2n
28. -1 < c + 2 < 3
Write an equation for the nth term of the arithmetic sequence. Then fine a10.
29. -3, -1, 1, 3 ….
30. 2, -3, -8, -13 …
31. 3, 14, 25, 36 …
32. 15, 11, 7, 3 …
Determine if the sequence is arithmetic. If so:
a.
b.
c.
d.
find the common difference
write the next three terms
write the explicit rule
graph
33. 1, 5, 9, 11 …
34. -11, -7, 3…
35. -7, -2, 3, 8 …
36. What is the common difference of the sequence represented in the table?
Time in minutes, m
2
Elevation of a scuba
-4
diver in feet, f(n)
37. Write an explicit rule for the sequence.
38. Find the elevation of the diver after 15 minutes.
4
-8
6
-12
Find the rate of change for of each line
39.
40.
41.
42.
43.
44.
For each line below, determine whether the slope is: positive, negative, zero, or undefined (circle one).
45. positive, negative,
zero, or undefined
46. positive, negative,
zero, or undefined?
47. positive, negative,
zero, or undefined?
Write a rule for each table using algebraic notation.
48.
49.
X
0
2
4
6
X
-2
0
2
4
Y
-4
6
16
26
50. The graph below shows the relationship between the
number of tortilla chips and total number of calories of the
chips. Find and interpret the slope.
Write an equation of the line in slope-intercept form.
51.
Find the x- and y-intercepts of each equation.
52. 𝑦 = 3𝑥 − 12
54. 𝑦 = 5𝑥 − 12
53. −8𝑥 = −4𝑦 + 12
55. 9𝑥 − 6𝑦 = −24
Y
0
6
12
18
Graph the linear function.
3
56. y   x  4
2
57. y  2 x  3
58.
y  x5
60. y  
5
x4
2
61. x  3
59. y  2
Use the graph of f and g to describe the transformation from the graph of f to the graph of g.
62.
63.
f(x) = x – 5, g(x) = -f(x)
The graph of the parent function f(x) = x is shown on the coordinate grid. Write the function
that represents the indicated parameter change.
64. m increased, b unchanged
___________
65. m decreased, b unchanged
___________
66. m unchanged, b increased
___________
67. m unchanged, b decreased
__________
Find the linear function graphed on the coordinate grid, state the
value of m and the value of b.
68. f(x): m = _____, b = _____
69. g(x): m = _____, b = _____
70. h(x): m = _____, b = _____
71. A school sell T-shirts to promote school spirit. The school’s profit is given by the function P9x) = 8x – 150,
where x is the number of T-shirts sold. During the play-offs, the school increases the price of the T-shirts. The
school’s profit during the play-offs is given by the function Q(x) = 16x – 200, where x is the number of T-shirts
sold. Describe the transformation from the graph of P to the graph of Q.
Write an equation in point-slope form of the line with the given information.
72. slope = 3/7; y-intercept = 4
75. Slope = -1/2 passes through ( -6, 10)
73. passes through (4, 7) (-1, 17)
76. (3, 4); m 
74. (2, -6); m  
1
4
1
3
77. (-2, 3); m = 4
Write the point-slope form of the equation with the given characteristics.
78. slope = 3; y-intercept = 5
79. Slope = -3; passes through (-4, 7)
Write an equation of the line that passes through the given point and is parallel to the given line.
80. (1, 2); y = −5x + 4
7
81. 𝑦 = 9 𝑥 − 5 ; passes through (0, 7)
82. (18, 2); 3y − x = −12
83. y = -5x – 3; passes through (7, -11)
Write an equation of the line that passes through the given point and is perpendicular to the given line.
84. (−3, 3); 2y = 8x − 6
86. (8, 1); 2y + 4x = 12
85. y = -3x – 7; passes through (6, 7)
87. y = ½x – 4; passes through (3, -4)
88. You are planning a school carnival. The equipment costs $180 to rent. You plan to charge $4.00
per ticket. You would to have profit of at least $500. Write and solve an inequality that represents the
number of tickets t that you need to sell.
89. You want to purchase a calculator for at most $115. You have saved $30 so far. You earn $7.50
per hours at your job. Write and solve an inequality that represents the number of hours h that you
need to work.
A bowling alley charges $4.00 per game and will rent a pair of shoes for $2.50 for any number of
games. The bowling alley has an earnings goal of $500 for the day.
90. Write a linear equation that describes the problem.
91. Graph the linear equation.
92. If the bowling alley rents 40 pairs of shoes, approximately
how many games will need to be played to reach its goal?
93. An account charges an initial fee of $100 plus a rate of $40 per hour. The function shows the total
fees charged is f(x) = 40x + 100. How would you graph the function change if the accountant raised
his rate to $45 per hour?
A baker sells bread for $3 a loaf and rolls for $1 each. The baker
needs to sell $24 worth of baked goods by the end of the day.
94. Write a linear equation that describes the problem.
95. Graph the linear equation. Make sure to label both axes with
appropriate titles.
96. Use the graph to approximate how many loaves of bread the baker must sell if 12 rolls are sold.
The function y = 3.5x + 2.8 represents the cost y (in dollars) of a taxi ride of x miles.
97. Identify the independent and dependent variables.
98. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the
function.
Opal walked from school to home, which was a distance of 12 miles. She
walked at a rate of 4 miles per hour. The graph represents the remaining
distance Opal had to walk.
99. Find the slope of the line.
100. Find the x-intercept, and explain what it represents in the context.
101. Find and interpret the y-intercept.
102. Write an equation for the line in slope-intercept form.
103. The table below represents the amount of money (in dollars) a Booster Club made washing cars
for a fundraiser. Use this information to find the rate of change in dollars per car.
Draw a graph to represent each situation. Classify each as either discrete or continuous.
104. Two children are selling lemonade. They are charging $2 for a cup. They only sell 12 cups.
105. You decide to hike up a mountain. You climb steadily for 4 hours, then take a 30 minute break
for lunch. Then you continue to climb, slower than before. When you make it to the summit, you
enjoy the view for an hour. Finally, you decide to climb down the mountain.
106. Alma earns $15 an hour. How much does she earn in 4 hours?
Independent Variable: ________________
Dependent Variable:__________________
Function:
Solution:
The data in the table shows the amount of taxes to be paid by married couples filing a joint tax return
for the given taxable income amounts. (Source 2006 IRS Tax Table, www.irs.gov)
y = ax + b
Taxable Income
(thousand dollars)
x
Tax Paid
(dollars)
y
20
30
40
50
60
70
80
90
2249
3749
5249
6749
8249
10621
13121
15621
a = 188.19
b = -2149.48
107. Looking at the regression equation what is the practical meaning of the slope?
108. Use the regression equation and explain the meaning of the y-intercept.
109. Use the linear regression model to predict the amount of tax paid by a married couple with an
income of $52,000. (Explain your answers and show all work)
Use the table to answer the following questions.
110. f(4) =
111. g(5) =
112. f(1) =
113. Write the rules for f(x) and g(x).
114. If f(x) = 10, find x.
115. If g(x) = -4, find x.
Hours
0
1
2
3
4
5
f(x)
4
6
8
10
12
14
g(x)
-4
-4.5
-5
-5.5
-6
-6.5
116. For the function {(-1, 2), (3, 3), (1, 5), (0, 2)} write the domain and range of the function.
Domain: _________________________
Range: _________________________
117. Create a mapping diagram for the ordered pairs  2, 4  ,  0, 1 ,  2, 5  .
Is the relation above a function?
Determine whether each of the following is a function.
118. (1, – 2), (2, 1), (3, 6), (4, 13), (5, 22)
123.
119. (7, 4), (5, – 1), (3, – 8), (1, – 5), (3, 6)
124.
120.
121.
125.
122.
For each problem, circle the relation that represents a function.
126.
127.
128.
129.
Write the domain and range of each relation below. Determine if the relation is a function.
130.
131.
Domain: _____ < x < _____
Domain: _____ < x < _____
Range: _____ < y < _____
Range: _____ < y < _____
Function: Yes/No
Function: Yes/No
132.
133.
134.
Domain: _____ < x < _____
Domain: _____ < x < _____
Domain: _____ < x < _____
Range: _____ < y < _____
Range: _____ < y < _____
Range: _____ < y < _____
Function: Yes/No
Function: Yes/No
Function: Yes/No
Find the value of x so that the function has the given value.
135. h(x) = −7x; h(x) = 63
137. m(x) = 4x + 15; m(x) = 7
136. t(x) = 3x; t(x) = 24
138. k(x) = 6x − 12; k(x) = 18
Let c(t) be the number of customers in a restaurant t hours after 8 A.M. Explain the meaning of
each statement.
139. c(0) = 0
141. c(3) = c(8)
140. c(n) = 29
142. c(13) < c(12)
Write a linear function f with the given values.
143. f(0) = 7, f(3) = 1
144. f(0) = 4 and f(1) = -4
145. f(4) = -3, f(0) = -2
Evaluate the function when x = -1 and x = 0.
146. g(x) = 3x2 + 1
147. b(x) = -2x – 4
148. h( x)   x  5
149. The graph represents Joe’s distance from home over time on his walk. What is happening at the
part of the graph labeled “A”?
A. Joe is stopped.
B. Joe is walking away from home.
C. Joe is walking towards home.
D. Joe is slowing down
Match each graph below with the description that best matches it.
150.
151.
152.
153.
154.
155.
A. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start
3 meters away from me and slowly walk away for 8 seconds. Then stand still for 3 seconds
and then walk quickly toward me for 4 seconds.
B. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start
4 meters away from me and slowly walk toward me for 8 seconds. Then stand still for 3
seconds and then walk quickly away from me for 4 seconds.
C. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start
3 meters away from me and quickly walk away for 3 seconds. Then stand still for 8 seconds
and then walk quickly toward me for 3 seconds.
D. Ashley walked up a hill at a steady speed and then increased her speed as she walked down
the hill
E. John was driving in heavy traffic. As he took off from a stoplight, he was able to increase his
speed until he came to another stoplight where he had to brake and decrease his speed
quickly. He came to a stop and when the light turned green, he increased his speed again.
F. John took off from a stop light and increased his speed until he reached the speed limit. He
kept his speed right at the speed limit until he passed a sign saying the speed limit had
increased so he sped up again.
156. Which ordered pair is the solution for the system graphed below?
Write a system of equations in standard form.
157.
158.
Write a system of equations in slope-intercept form.
159.
160.
Compare the slopes and y-intercepts of the graphs of the equations in the linear system to determine
whether the system has one solution, no solution, or infinitely many solutions. Explain.
161. x   3 y  28
163.
x  4 y  36
162. x  2 y  3
 2 x  4 y   20
2 x  3 y  11
 4 x  6 y   22
164. {
𝑦 = 2𝑥 + 1
4𝑥 + 2𝑦 = 2
Solve the system of linear equations. Check your solutions.
−𝟐𝒙 + 𝟐𝒚 = 𝟐
165. {
−𝟕𝒙 − 𝒚 = −𝟗
𝒙 + 𝟐𝒚 = 𝟓
167. {
𝟒𝒙 + 𝟑𝒚 = −𝟓
𝟐𝒙 + 𝒚 = 𝟏𝟏
166. {
−𝟐𝒙 + 𝒚 = −𝟏
−𝟐𝒙 − 𝟑𝒚 = 𝟓
168. {
−𝟑𝒙 − 𝟒𝒚 = 𝟗
𝟑𝒙 + 𝟓𝒚 = 𝟐𝟕. 𝟓
169. {
𝟐𝒙 + 𝟑𝒚 = 𝟏𝟔
170.A humane society has 73 dogs and cats to be adopted. The number of cats is 10 more than twice
the number of dogs. Write a system of equations that represents this situation. How many of each
animal is up for adoption?