ALGEBRA 1
MIDTERM TOPICS
Chapter 1
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1-1 Variables and Expressions
1-1 Order of Operations
1-3 Properties of Numbers
1-4 The Distributive Property
1-5 Equations
1-6 Relations
1-7 Functions
1-8 Interpreting Graphs of Functions
Chapter 2
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2-1 Writing Equations
2-2 Solving One-Step Equations
2-3 Solving Multi-Step Equations
2-4 Solving Equations with the Variable on Each Side
2-5 Solving Equations Involving Absolute Value
2-6 Ratios and Proportions
2-7 Percent of Change
2-8 Literal Equations and Dimensional Analysis
2-9 D=rt Word Problems
Chapter 3
 3-1 Graphing Linear Equations
 3-3 Rate of Change and Slope
 3-4 Direct Variation
Chapter 4
 4-1 Graphing Equations in Slope-Intercept Form
 4-2 Writing Equations in Slope-Intercept Form
 4-4 Parallel and Perpendicular Lines
Chapter 5
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5-1 Solving Inequalities by Addition and Subtraction
5-2 Solving Inequalities by Multiplication and Division
5-3 Solving Multi-Step Inequalities
5-4 Solving Compound Inequalities
5-5 Inequalities Involving Absolute Value
Chapter 6
 6-1 Solving Systems by Graphing
 6-2 Solving Systems by Substitution
 6-3/6-4 Solving Systems by Elimination
***To study for this exam you should complete the review packet, review your notes, and
look at old tests and quizzes.
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Page 1
Indicate the answer choice that best completes the statement or answers the question. You must show all of
your work on separate paper.
1. Write an algebraic expression for 3 times x squared minus 4 times x.
a. 3(2x) – 4x
b. 4 – 3x
c. 3x2 – 4x
d. 3(x2 – 4x)
2. Write a verbal expression for 3n – 8.
a. the product of 3, n, and 8
b. 8 less than the product of 3 and n
c. 3 times n less than 8
d. n minus 8 times 3
3. Evaluate 4 + 5 • 7 – 1.
a. 139
b. 15
c. 34
4. Evaluate 3(16 – 9) + 12 3.
a. 33
b. 25
c. 41
d. 38
d. 28
5. Evaluate m2 + mtp if m = 3, t = 4, and p = 7.
a. 93
b. 87
c. 100
d. 23
6. Which equation illustrates the Additive Identity Property?
a. 8(9 + 0) = 8(9)
b. 4(0) = 0
c. 8 • 1 = 8
d.
7. Evaluate 16 • 1 + 4(18 2 – 9).
a. 20
b. 0
c. 16
d. 80
8. Simplify 7x2 + 10x2 + 5y3.
a. 22x2y3
b. 17x2 + 5y3
c. 22x4 + y3
9. Simplify 2(7n + 5m – 3m).
a. 14n + 2m
b. 9n + 7m
c. 9n + m
10. Simplify 3(5a + b) + 4(a + 2b).
a. 9a + 5b
b. 19a + 3b
c. 19a + 11b
d. 17x4y3 + 5
d. 14n + 4m
d. 9a + 9b
11. Find the solution of 3n – 13 = 38 if the replacement set is {12, 14, 15, 17, 18}.
a. 12
b. 15
c. 17
d. 18
12. Ari is jogging at an average rate of 2.25 meters per second. Find the time it will take him to jog 270 meters.
a. 1 minute
b. 2 minutes
c. 3 minutes
d. 12 minutes
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Page 2
13. Which statement best describes a daily stock price?
a. The price was unchanged then increased sharply.
b. The price was unchanged then decreased sharply
c. The price rose sharply then leveled off.
d. The price declined sharply then leveled off.
Use the graph to answer each question.
14. What is the domain of the relation?
a. {–4, –2, –1, 0, 1, 2, 3, 4}
b. {–4, –1, 0, 2, 3, 4}
c. {–4, –2, –1, 0, 1, 4}
d. {–4, 4}
15. Which is a true statement about the relation?
a. The relation is not a function.
b. The value of x increases as y decreases.
c. The value of x increases as y increases.
d. The relation is a linear function.
16. Determine which relation is a function.
a.
b.
c.
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d.
Page 3
Use the graph.
17. Interpret the y-intercept of the graph.
a. Anna owes $10 before any payments.
b. Each payment Anna makes is $50.
c. Anna owes $500 before any payments.
d. Anna pays off the loan in 10 payments.
18. Translate the following sentence into an equation.
The product of five and a number y is two less than the quotient of four and y.
a.
b.
c.
d.
19. Translate the following equation into a verbal sentence.
a. x times seven minus five times y equals x divided by two.
b. The product of x and seven minus five times y equals the quotient of x and two.
c. x times the difference of seven and the product of five and y equals the quotient of x and two.
d. x times the sum of seven and five times y equals x divided by two.
20. Solve x – 12 = 5.
a. –17
b. –7
c. 17
21. Solve 6z = –84.
a. –90
b. –78
22. Solve
a. 49
c. –14
d. 7
d. –504
.
b. –49
23. Solve 2 + 7y = 44.
a.
b. 35
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c. 16
d. –16
c. 49
d. 6
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24. A number is divided by four. The result is added to five. This result is multiplied by three to give 27. What is the
number?
a. 16
b. 1
c.
d.
25. Evaluate | 3f – 2g | + 2 if f = –2 and g = 1.
a. –2
b. 4
c. 6
d. 10
26. Solve | 2n + 5 | = 11.
a. {3, –3}
b. {3, –8}
c. {8, –8}
27. What ratio forms a proportion with
a.
b.
c.
28. Solve the proportion
a. 4
b. 28
c. 56
?
d.
.
d. 16
29. Solve 9a + 28 = 4a + 3.
a. –30
b. –20
c.
d. –5
30. Solve
a. 0
d. no solution
.
b. all numbers
c. no solution
31. Solve 4(3r – 2) = –3(r + 7).
a.
b.
c.
–
32. Solve 3b = 6v – 3b, for v.
a. 6b – 6
b. b
c. b – 6
d. 41
d. –13
d. 0
33. Find the percent of change. original: 45 new: 54
a.
b. 25%
c.
d. 20%
%
%
34. Find the discounted price. radio: $45.00 discount: 30%
a. $15.00
b. $31.50
c. $36.00
d. $42.00
35. Teri begins walking east at 2 miles per hour at 1:00 P.M. If Cindy leaves from the same point 30 minutes later walking
east at 3 miles per hour, when will she catch Teri?
a. 2:30 P.M.
b. 1:30 P.M.
c. 2:00 P.M.
d. 3:00 P.M.
36. PHOTOCOPIES Black and white copies cost $0.05 each, and color copies cost $0.49 each. The equation 0.05x +
0.49y = 5 represents the number of black and white copies (x) and color copies (y) that can be made with $5. If no color
copies are made, how many black and white copies can be made with $5?
a. 200
b. 100
c. 25
d. 10
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37. If (a, –7) is a solution to the equation 8a = –3b – 5, what is a?
a. –17
b. 2
c. 8
d. 17
38. What is the slope of the line through (2, –8) and (4, 1)?
a.
b.
c.
d.
39. Which equation is not a linear equation?
a. 2x + 5y = 3
b. y = –10
c. 5 = 3xy
d.
y=
+4
40. What is the slope of the line through (–4, –6) and (9, –6)?
a.
b.
c. 0
d. undefined
41. In 2005, MusicMart sold 12,000 CDs. In 2010, they sold 14,550 CDs. What is the rate of change in the number of
CDs sold?
a. 2550 per yr
b. 510 per yr
c. –510 per yr
d. 2400 per yr
42. Which is the graph of
a.
?
b.
c.
d.
43. If y varies directly as x and y = 5 when x = 8, find y when x = 9.
a.
b.
c.
d. 6
44. SPRINGS The amount a spring stretches varies directly as the weight of the object attached to it. If an 8-ounce weight
stretches a spring 10 centimeters, how much weight will stretch it 15 centimeters?
a. 16 oz
b. 6 oz
c. 10 oz
d. 12 oz
45. Which line shown below is the graph of x + 2y = 6?
a. r
b. n
c. t
d. v
46. Which equation has a graph that is a horizontal line?
a. x – 7 = 0
b. 2y + 3 = 4
c. x = y
d. x + y = 0
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47. What is the standard form of
?
b. x – 2y = 8
a. x + 2y = 0
c. 2x – y = 10
d. 4x – 2y = 0
48. Write an equation in function notation for the relation.
a. f (x) = –2x
b. f (x) = x – 2
c. f (x) = –x + 2
d. f (x) = 2x + 2
49. What is the slope-intercept form of the equation of the line with a slope of
a. y = 4x
b.
y=
x
c.
d.
y=x+
y+
and y-intercept at the origin?
=x
50. Which equation is graphed below?
a. y – 2x = –4
b. 2x + y = –4
c. 2x + y = 4
d. y – 4 = 2x
51. Which is an equation of the line that passes through (4, –5) and (6, –9)?
a.
b.
c. y = –2x + 3
d. y = 2x – 3
y= x–3
y= x+3
52. What is the standard form of the equation of the line through (6, –3) with a slope of
a. –2x + 3y = 24
c. 3x – 2y = 24
?
b. 2x – 3y = 21
d. 3x – 2y = –21
53. What is the equation of the line through (–2, –3) with an undefined slope?
a. x = –2
b. y = –3
c. –2x – 3y = 0
d. –3x + 2y = 0
54. Find the slope-intercept form of the equation of the line that passes through (–1, 5) and is parallel to 4x + 2y = 8.
a. y = –2x + 9
b. y = 2x – 9
c. y = 4x – 9
d. y = –2x + 3
55. If line q has a slope of –2, what is the slope of any line perpendicular to q?
a. 2
b. –2
c.
d.
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56. A baby blue whale weighed 3 tons at birth. Ten days later, it weighed 4 tons. Assuming the same rate of growth,
which equation shows the weight w when the whale is d days old?
a. w = 10d + 3
b. w = 10d + 4
c. w = 0.1d + 3
d. w = d + 10
57. Bonus For what value of k does kx + 7y = 10 have a slope of 3?
Indicate the answer choice that best completes the statement or answers the question.
Solve each inequality.
58. –13 > w + 12
a. {w | w < –25}
59. x –
b. {w | w > –25}
c. {w | w > –1}
d. {w | w < –1}
b.
c.
d.
b. {m | m < –15}
c. {m | m < 15}
d. {m | m > 15}
–
a.
< –3
60.
a. {m | m > –15}
61. –1.1t 4.62
a. {t | t 5.72}
62. 5z – 4 > 2z + 8
a. {z | z > 4}
b. {t | t 5.72}
b. {z | z < 1}
c. {t | t –4.2}
c. {z | z < 4}
63. 7 – 9r – (r + 12) 25
a. {r | r –3}
b. {r | r –0.6}
c. {r | r –3}
d. {t | t –4.2}
d. {z | z > 1}
d. {r | r –0.6}
64. The sum of two consecutive integers is at most 7. What is the largest possible value for the lesser integer?
a. 1
b. 3
c. 2
d. 5
65. Which of the following is the graph of the solution set of x > 0 or x < –4?
a.
b.
c.
d.
66. Which compound inequality has the solution set shown in the graph?
a. –2 < y < 3
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b. –2 < y 3
c. y –2 or y < 3
d. –2 y < 3
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67. Which of the following is the solution set of –3 < 2x + 7 13?
a. {x | –5 < x 3}
b. {x | x < 3 or x > –5}
c. {x | x < –5}
d. {x | –5 x < 3}
68. Which of the following is the graph of the solution set of 7a + 3 ≤ a – 15 or 5a – 3 < 8a?
a.
b.
c.
d.
69. Which inequality corresponds to the graph shown?
a. | x – 3 | > 1
b. | x – 3 | < 1
c. | x – 1 | > 3
70. Which of the following is the solution set of ¨
a.
b. {x | x is a real number.}
c.
d. | x – 1 | < 3
?
d. {x | 1 x 7}
71. Katrina’s weight is within 8 pounds of her ideal weight of 120 pounds. What is her range of weight?
a. x 112 or x 128
b. x 112 or x 128
c. 112 x 128
d. 112 x 128
72. Which ordered pair is part of the solution set of the inequality 5 – y –3x?
a. (2, –1)
b. (–2, –1)
c. (–3, –5)
d. (3, –5)
73. Alicia has at most $196 to buy a new baseball glove and a new baseball bat. Which inequality represents this
situation?
a. y 196 – x
b. y 196 + x
c. 196 y + x
d. y – x 196
74. Determine which of the ordered pairs are a part of the solution set of y + 3 < 2x – 1.
a. (0, 0)
b. (2, 0)
c. (0, –4)
d. (2, –2)
75. Which inequality has a solution set of {x | x > 4 and x < 8}?
a.
b.
c.
d.
<1
>1
<3
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>3
Page 9
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many
solutions. If the system has one solution, name it.
76.
a. infinitely many
b. no solution
c. one solution; (0, 1)
d. one solution; (1, 0)
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77.
a. one solution; (2, 1)
b. infinitely many
c. no solution
d. one solution; (1, 2)
Use substitution to solve the system of equations.
78. y = 5x + 37
2x – 5y = –1
a. (–8, –3)
c. (–3, –8)
b. (–2, –12)
d. (3, –2)
79. 26 = x – 4y
–4x – 48 = 3y
a. (–6, –8)
b. (2, 10)
c. (5, –10)
d. infinitely many solutions
Use elimination to solve the system of equations.
80. –7x + 10y = 101
–7x + 5y = 61
a. (–3, 8)
b. (3, –8)
c. (–12, 7)
d. (12, –7)
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81. 10x – 4y = –122
–3x + 6y = 75
a. (3, –3)
b. (8, –9)
c. (–3, 3)
d. (–9, 8)
Determine the best method to solve the system of equations. Then solve the system.
82.
a. elimination using subtraction;
b.
elimination using addition;
c. elimination using subtraction;
d.
elimination using addition;
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Page 12
Answer Key
1. c
2. b
3. d
4. b
5. a
6. a
7. c
8. b
9. d
10. c
11. c
12. b
13. d
14. c
15. a
16. c
17. c
18. b
19. c
20. c
21. c
22. a
23. d
24. a
25. d
26. b
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Page 13
27. b
28. b
29. d
30. c
31. a
32. b
33. d
34. b
35. a
36. b
37. b
38. d
39. c
40. c
41. b
42. b
43. b
44. d
45. a
46. b
47. b
48. c
49. b
50. a
51. c
52. b
53. a
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Page 14
54. d
55. c
56. c
57. –21
58. a
59. a
60. d
61. d
62. a
63. c
64. b
65. c
66. d
67. a
68. c
69. c
70. c
71. d
72. b
73. a
74. d
75. a
76. d
77. d
78. a
79. a
80. a
81. d
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82. d
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