Midterm Topics

ALGEBRA 1

MIDTERM TOPICS

Chapter 1

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

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

3-2 Solving Linear Equations by Graphing

3-3 Rate of Change and Slope

3-4 Direct Variation

3-5 Arithmetic Sequences as Linear Functions

Chapter 4

4-1 Graphing Equations in Slope-Intercept Form

4-2 Writing Equations in Slope-Intercept Form

4-4 Parallel and Perpendicular Lines

4-5 Scatter Plots and Liens of Fit

Chapter 5

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

5-6 Graphing Inequalities in Two Variables

***To study for this exam you should complete the review packet, review your notes, and look at old tests and quizzes.

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 / d. / 38
4.Evaluate 3(16 – 9) + 12 3.
a. / 33 / b. / 25 / c. / 41 / 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 / d. / 17x4y3 + 5
9.Simplify 2(7n + 5m – 3m).
a. / 14n + 2m / b. / 9n + 7m / c. / 9n + m / d. / 14n + 4m
10.Simplify 3(5a + b) + 4(a + 2b).
a. / 9a + 5b / b. / 19a + 3b / c. / 19a + 11b / 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
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. / / d. /
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 / d. / 7
21.Solve 6z = –84.
a. / –90 / b. / –78 / c. / –14 / d. / –504
22.Solve .
a. / 49 / b. / –49 / c. / 16 / d. / –16
23.Solve 2 + 7y = 44.
a. / / b. / 35 / c. / 49 / d. / 6
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} / d. / no solution
27.What ratio forms a proportion with ?
a. / / b. / / c. / / d. /
28.Solve the proportion .
a. / 4 / b. / 28 / c. / 56 / d. / 16
29.Solve 9a + 28 = 4a + 3.
a. / –30 / b. / –20 / c. / / d. / –5
30.Solve .
a. / 0 / b. / all numbers / c. / no solution / d. / 41
31.Solve 4(3r – 2) = –3(r + 7).
a. / – / b. / / c. / / d. / –13
32.Solve 3b = 6v – 3b, for v.
a. / 6b – 6 / b. / b / c. / b– 6 / 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
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
Use the following information.
The number of students seated in each row of an auditorium form an arithmetic sequence, as shown in the table.

45.How many students are seated in the 15th row?
a. / 46 / b. / 58 / c. / 59 / d. / 195
46.Which formula can be used to find the number of students seated in any given row?
a. / an= 4n / b. / an= 4n – 1 / c. / an= n + 3 / d. / an= 3n + 1
47.Which line shown below is the graph of x + 2y = 6?

a. / r / b. / n / c. / t / d. / v
48.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
49.What is the standard form of ?
a. / x + 2y = 0 / b. / x – 2y = 8 / c. / 2x –y = 10 / d. / 4x – 2y = 0
50.Determine which sequence is an arithmetic sequence.
a. / –16, –12, –8, –4, . . . / b. / 4, 8, 16, 32, . . .
c. / 1, 4, 2, 5, 3, . . . / d. / 1, 1, 2, 3, 5, . . .
51.Which equation describes the nth term of the arithmetic sequence –12, –14, –16, –18, . . .?
a. / an= –2n – 10 / b. / an= –12 – 2n / c. / an= 10n – 2 / d. / an= –2n + 10
52.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
53.What is the slope-intercept form of the equation of the line with a slope of and y-intercept at the origin?
a. / y = 4x / b. / y = x / c. / y = x + / d. / y + = x
54.Which equation is graphed below?

a. / y – 2x = –4 / b. / 2x + y = –4 / c. / 2x + y = 4 / d. / y – 4 = 2x
55.Which is an equation of the line that passes through (4, –5) and (6, –9)?
a. / y = x – 3 / b. / y = x + 3 / c. / y = –2x + 3 / d. / y = 2x – 3
56.What is the standard form of the equation of the line through (6, –3) with a slope of ?
a. / –2x + 3y = 24 / b. / 2x – 3y = 21
c. / 3x – 2y = 24 / d. / 3x – 2y = –21
57.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
58.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
59.If line q has a slope of –2, what is the slope of any line perpendicular to q?
a. / 2 / b. / –2 / c. / / d. /
60.The graph of data that has a strong negative correlation has
a. / a narrow linear pattern from lower left to upper right.
b. / a narrow linear pattern from upper left to lower right.
c. / a narrow horizontal pattern below the x-axis.
d. / all negative x-values.
A scatter plot of data comparing the time in minutes Beverly spends studying for her math test and the score she received on the test contains the ordered pairs (45, 89) and (60, 94).
61.Which is the slope-intercept form of an equation for the line of fit?
a. / 0.573x + 63.2 = y / b. / x + 74 = y
c. / 3x – 46 = y / d. / x + 104 = y
62.Estimate how well Beverly would score on her next test if she spent 20 minutes studying.
a. / 75 / b. / 81 / c. / 84 / d. / 90
Use the scatter plot shown to answer the following questions.

63.Which data are shown by the scatter plot?
a. / (1985, 47), (1995, 31), (2001, 24) / b. / (1985, 50), (2000, 25), (2005, 0)
c. / (47, 1985), (31, 1995), (24, 2001) / d. / (1991, 45), (1995, 35), (2000, 8)
64.Based on the data in the scatter plot, which statement is true?
a. / As x increases, y increases.
b. / As x increases, y decreases.
c. / There is no relationship between x and y.
d. / There are not enough data to determine the relationship between x and y.
65.Based on the scatter plot, what would you expect the y-value to be for x = 1992?
a. / between 40 and 45 / b. / higher than 45
c. / between 30 and 40 / d. / impossible to tell
66.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
67.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.
68.–13 > w + 12
a. / {w|w < –25} / b. / {w|w > –25} / c. / {w|w > –1} / d. / {w|w < –1}
69.x – –
a. / / b. / / c. / / d. /
70. < –3
a. / {m|m > –15} / b. / {m|m < –15} / c. / {m|m < 15} / d. / {m|m > 15}
71.–1.1t4.62
a. / {t|t5.72} / b. / {t|t5.72} / c. / {t|t–4.2} / d. / {t|t–4.2}
72.5z – 4 > 2z + 8
a. / {z|z > 4} / b. / {z|z < 1} / c. / {z|z < 4} / d. / {z|z > 1}
73.7 – 9r – (r + 12) 25
a. / {r|r–3} / b. / {r|r–0.6} / c. / {r|r–3} / d. / {r|r–0.6}
74.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
75.Which of the following is the graph of the solution set of x > 0 or x < –4?
a. / / b. /
c. / / d. /
76.Which compound inequality has the solution set shown in the graph?

a. / –2 < y < 3 / b. / –2 < y3 / c. / y–2 or y < 3 / d. / –2 y < 3
77.Which of the following is the solution set of –3 < 2x + 7 13?
a. / {x| –5 < x3} / b. / {x|x < 3 or x > –5}
c. / {x|x < –5} / d. / {x| –5 x < 3}
78.Which of the following is the graph of the solution set of 7a + 3 ≤ a – 15 or 5a – 3 < 8a?
a. / / b. /
c. / / d. /
79.Which inequality corresponds to the graph shown?

a. / | x – 3 | > 1 / b. / | x – 3 | < 1 / c. / | x – 1 | > 3 / d. / | x – 1 | < 3
80.Which of the following is the solution set of ¨?
a. / / b. / {x | x is a real number.}
c. / / d. / {x | 1 x7}
81.Katrina’s weight is within 8 pounds of her ideal weight of 120 pounds. What is her range of weight?
a. / x112 or x128 / b. / x112 or x128
c. / 112 x128 / d. / 112 x128
82.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)
83.Which inequality is graphed?

a. / y2x – 1 / b. / y2x – 1 / c. / y–2x – 1 / d. / y–2x – 1
84.Alicia has at most $196 to buy a new baseball glove and a new baseball bat. Which inequality represents this situation?
a. / y196 – x / b. / y196 + x / c. / 196 y + x / d. / y –x196
85.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)
86.Which inequality has a solution set of {x | x > 4 and x < 8}?
a. / < 1 / b. / > 1 / c. / < 3 / d. / > 3
87.Beng and Shim have less than $30 for candle-making supplies. The molds x cost $6 each and the wax y is $2 per pound. Which point represents a reasonable number of molds and pounds of wax they could buy?
a. / (3, 4) / b. / (4, 4) / c. / (5, 1) / d. / (3, 6)

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
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.d
47.a
48.b
49.b
50.a
51.a
52.c
53.b
54.a
55.c
56.b
57.a
58.d
59.c
60.b
61.b
62.b
63.a
64.b
65.a
66.c
67.–21
68.a
69.a
70.d
71.d
72.a
73.c
74.b
75.c
76.d
77.a
78.c
79.c
80.c
81.d
82.b
83.c
84.a
85.d
86.a
87.a
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