Algebra 1 CP
Midterm Review Packet
2014-2015
Name ___________________________________
Teacher _________________________________
Period __________
Due Date ________________________________
Midterm Exam Schedule
Day 1, Wednesday, January 14th
Course
Exam #1
7:25 – 8:55
Exam #2
9:10 – 10:40
Exam #3
11:30 – 1:00
Period
Room
1
2
3
Day 2, Thursday, January 15th
Course
Exam #1
7:25 – 8:55
Exam #2
9:10 – 10:40
Exam #3
11:30 – 1:00
Period
Room
4
5
6
Day 3, Friday, January 16th
Course
Exam #1
7:25 – 8:55
Exam #2
9:10 – 10:40
Exam #3
11:30 – 1:00
Period
7
8
9
Room
Algebra 1 Formula Sheet
Algebra 1 – Midterm Review 2015
1. Translate into an algebraic expression: three times the sum of b and f
2. Translate into an algebraic expression: the quotient of 8 and the difference of x and m
3. Boxes of car parts are stacked on top of each other on a work bench. The table below shows how the height
above the floor of the topmost box depends on the number of boxes. What is a rule for the height? Give the
rule in words and as an algebraic expression.
Number of
Boxes
2
Height (in.)
4
 6 2  36
 6 3  36
 6 4  36
n
?
3
4. What is an inequality that compares the numbers?
70
8
1
2
#5-7 – What property is illustrated by each statement?
______ 5. 2.11  2.1
A. Inverse Property of Multiplication
B. Multiplication Property of 1
C. Identity Property of Addition
D. Identity Property of Multiplication
______ 6. 8  8.3  8.3  8
A. Inverse Property of Multiplication
B. Inverse Property of Addition
C. Commutative Property of Addition
D. Associative Property of Addition
 3  3
______ 7. 2        2
 9  9
A. Associative Property of Addition
B. Commutative Property of Multiplication
C. Inverse Property of Multiplication
D. Commutative Property of Addition
1
8. Simplify:
1
 21m  27 
3
9. Simplify:  8d  3w
#10-19 – Solve each equation for the variable.
10. 7 
h
5
11. 9 
5
n
17
b6
 10
5
12.
3r 5

7 2
13.
14.
x6 x6

5
12
15. 5 10 x  10   5  4 x  4 
16. 70  7  2  2z 
17.
3p 8
 1
5 5
2
18. Solve and justify your steps:
3  y  5  2  5
19. Solve and justify your steps:
2  6p 85p
______ 20. Which equation is an identity?
A. 11   2v  3  2v  8
B. 5w  8  w  6w  2  w  4 
C. 7m  2  8m  4  m
D. 8 y  9  8 y  3
______ 21. Which equation has no solution?
A. 8   5v  3  5v  5
B. 3m  6  5m  7  m
C. 3w  4  w  5w  2  w  2 
D. 7 y  9  7 y  6
22. What equation do you get when you solve the following equation for x?
t  a  t  sx
3
23. What equation do you get when you solve the following equation for y?
by
vy  fb 
t
24. A flock of Canadian geese migrated 1623 miles in 28 days. What was the average rate at which these geese
traveled in miles per day?
#25-27 – Which number is a solution for the inequality?
______ 25. 10.6  b
A. 18
B. 9
C. 7
D. 14
7
______ 26. m 
12
A. 9
B. 5
C. 1
D. 1
______ 27. 3  3x  15
7
11
6
B.
11
C. 5
D. 6
A. 
#28-29 – Graph each inequality. Re-write each inequality using interval notation.
28. k 
9
2
4
29. x  5
______ 30. Which inequality describes the situation?
Let n = the number. A number exceeds 45.
A.
B.
C.
D.
n  45
n  45
n  45
n  45
______ 31. What inequality represents the verbal expression?
All real numbers greater than or equal to 67
A.
B.
C.
D.
x  67
x  67
x  67
x  67
______ 32. What inequality represents the verbal expression?
8 less than a number n is less than 11
A. 11  8  n
B. n  8  11
C. 8  n  11
D. 11  8  n
#33-36 – Solve and graph each inequality.
33. x  3  12
34. 12r  24
1
35.  x  5
8
5
36.
x
9
9
#37-40 – Solve each inequality.
37. 12 x  3x  11  4 x  17  9 x 
38. 8n 14  13n  6
39. 2  3x  2   6 x  4
40. 10x 10  7 x  3x  2
#41-44 – Solve and graph each inequality. Re-write each answer using interval notation.
41. 2  2 x  4  8
42. 2  4 x 10  6
6
43. 2 x  2  12
44.
2x 1
 3  4
3
OR
OR
2x  3  7
8x  2
1  6
2
45. Write and graph the compound inequality which represents the phrase:
All real numbers that are greater than 8 and less than 8
#46-47 – Solve and graph.
46. 9 x  27
7
47. 2d  5  9
#48-49 – Solve each equation and check for extraneous solutions.
48. x  10  1
49. 6 n  2  10
#50-51 – Use the Vertical Line Test to determine if each relation is a function.
50.
51.
y
–6
–4
6
6
4
4
2
2
–2
2
4
6
x
–2
–6
–4
–2
2
4
6
x
–2
–4
–4
–6
–6
52. Find the range of f  x  
Range: {
y
2
x  5 for the domain 4, 2,0,3 .
5
}
8
53. Evaluate f  x   4.7 x  1 for x  1 .
54. Identify the domain and range of the relation.
 4, 2 ,  9, 5 ,  4,12 , 8, 8
Domain:
{
}
Range:
{
}
#55-56 – Write the function to describe each graph. Identify the domain and range using interval
notation.
55.
56.
Domain:
Domain:
Range:
Range:
57. The function g  t   2t represents the number of guitar lessons, g  t  , you can complete in t months. How
many guitar lessons can you complete in 7 months?
9
58. In what quadrant is the point  1,5 located?
59. Name a point located in Quadrant III.
#60-63 – Find the slope of each line.
60.
61.
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
62. 1, 7  and 10,1
63.
1
2
3
4
5
x
 3, 1 and 8, 4 
64. What are the slope and y-intercept of the graph of the given equation? y  1.9 x  2.5
65. Write an equation of a line with the given slope and y-intercept. m  5, b  3
66. What equation in slope-intercept form represents the line that passes through  2, 4  and  4,1 ?
10
#67-71 – Graph each equation.
68. y  4 x  3
67. y  x
y
y
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
69. y  1 
1 2 3 4 5 6 7 8 9 10
x
4
 x  1
5
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
x
70. y  2
y
y
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
x
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
x
11
71.
y
3
3
x y 
4
4
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
x
72. What do you expect the slope of the line to be based on the following graph?
y
5
4
3
2
Circle one:
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
Positive Slope
Negative Slope
x
–2
–3
–4
–5
73. Write an equation in point-slope form for a line that passes through  8,3 with m  6 .
74. Write the slope-intercept form of the equation for the line.
12
#75-76 – Write an equation for each line in point-slope form.
75.
y
76.
y
5
5
4
4
3
3
–5
–4
–3
–2
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
#77-78 – Find the x and y-intercepts for each line.
77. 4 x  2 y  24
7
78.  x  4 y  7
5
#79-81 – Write each equation in standard form using integers.
79. y 
81.
1
x5
6
80. y  0.2 x  0.3
3
2
y  x4
7
5
13
#82-84 – Are the lines parallel, perpendicular, or neither? Circle one answer for each pair of equations.
1
82. y   x  12
2
6 x  12 y  21
Parallel
Perpendicular
Neither
1
83. y   x  5
6
24 x  4 y  12
Parallel
Perpendicular
Neither
20 x  12 y  12
Parallel
Perpendicular
Neither
84. y 
5
x3
3
85. Write an equation for the line that is parallel to y 
3
x  8 and passes through  15, 23 .
5
86. Write an equation for the line that is perpendicular to x  3 y  16 and passes through  3, 4  .
14
#87-88 – What type of correlation does each scatter plot demonstrate?
87.
20
88.
y
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
1
2
3
4
5
6
7
8
y
x
9
1
2
3
4
5
6
7
8
9
x
Mistakes at a Piano Recital
y
89. The scatter plot shows the number of mistakes a piano student
makes during a recital versus the amount of time the student
practiced for the recital. How many mistakes do you expect the
student to make at the recital after 6 hours of practicing?
140
120
mistakes
100
80
60
40
20
2
4
6
8
10
14 x
12
practice time (hr)
#90-91 - Sketch the graph for each absolute value equation.
90. y  x  2
91. y  x  4  3
y
y
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
x
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
x
15
#92-93 - Write an equation for each translation of y  x .
92. 12 units up
93. 3 units left
#94-95 – Solve each system of equations by graphing both lines.
94.
y  5 x  2
y  2  5 x
95.
y  3x  2
y  3x  4
y
y
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
x
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
x
#96-97 – Use substitution to solve each system of equations.
96.
3x  2 y  7
y  3x  11
97.
y  6x  2
3 y  18 x  12
16
#98-100 – Use elimination to solve each system of equations.
98.
100.
3x  4 y  9
3x  2 y  9
99.
x  3 y  1
5 x  6 y  16
5 x  7 y  32
8 x  6 y  46
#101-103 – Assign a variable. Write an equation and solve each problem.
101. Manny and Emma are both competing in a long jump competition at their school. Manny can jump four
fifths of the distance that Emma can jump. Manny can jump 40 inches. How far can Emma jump?
17
102. Steven wants to buy a $565 bicycle. Steven has no money saved, but he will be able to deposit $30 into a
savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must
pay $65 he owes to his sister. For how many weeks will Steven need to deposit money into his savings account
before he can pay back his sister and buy the bike?
103. Angela and Neil are going to the movies. They each bought one medium popcorn. Neil also purchased a
soft drink. Angela had a $10 gift card to use toward the cost, and Neil paid $19.30. A movie ticket costs $9.00,
and a medium popcorn costs $4.40. How much does a small soft drink cost?
#104-105 – Assign variables and write two equations for each problem. Then solve each problem.
104. Kendra owns a restaurant. She charges $3.00 for 2 eggs and one piece of toast and $1.80 for one egg and
one piece of toast. How much does Kendra charge for an egg? A piece of toast?
18
105. The cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00, and the
chicken wrap costs $1.80. The cafeteria collected $98.80 for selling 70 wraps. How many of the wraps were
vegetarian? Chicken?
#106-107 - Determine if the ordered pair is a solution of the linear inequality.
106. 2 x  4 y  5
107. y  3x  1
 5,1
 3,5
#108-109 - Sketch the graph of each linear inequality.
7
109. y  4 x  2
108. y   x  5
y
y
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
x
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
x
19
#110-111 - Sketch the solution for each system of inequalities.
1
x2
111.
2
y  2 x  3
y  x  2
110.
y  5 x  2
y
y
y
10
9
8
7
6
5
4
3
2
1
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Name one ordered pair that is a solution
of this system of inequalities.
x
–10–9 –8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
1 2 3 4 5 6 7 8 9 10
x
Is (3, 4) a solution to this inequality?
#112-113 - Write the inequality or system of inequalities that best represents each graph.
112.
113.
20
114. A friend makes $15 per hour at his first job and $11 per hour at his second job. His goal is to make at
least $600 per week. He does not want to work any more than 55 hours in a week. Write a system of
inequalities for the given situation and graph the inequalities.
#115-129 – Simplify each expression.
115.
 6.1
116.   5
0
117. 2a 5t 2
118.
119.
 2k  6 j
121.
 3g h   2 g h 
5
3 6 2
9
4k
3 5 4
4
g h
3 5
120. 9
122.
2
5
2
d 8
d5
21
 t5 
123.  4 
3j 
5
 4
124.  
 3c 
2
1
 3 3
125.  n 5 
 
126.
127.  8k
 3k 4 
128.  3 
 2c 

8 5
 m 1m5 
129.  2 
 m 
130. Evaluate
 h 
4 5
2
3
1
for x  2 and y  4 .
2 x 3 y 5
2
131. Simplify the expression. Write your answer using scientific notation.
5 107 9 107 
#132-133 - Re-write each expression using the base only once.
132. 83 85
133. 125 121 121
22