Monroe City School District
Study Guide
Algebra 1 - Midterm
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1. Which graph is the most appropriate to describe a quantity decreasing at a steady rate?
A.
C.
B.
D.
2. Which answer shows another way of writing the expression below?
4(3b) - 2(3b + 1)
A. 2b + 1
B. 2b - 2
C. 6b + 1
D. 6b - 2
3. Use the equation below to answer this question.
C = 0.25m + 30
The equation above models the total cost of Sharla’s cell phone bill, where C is the dollar amount of the bill
and m is the number of minutes she used the phone. Which of these represents the independent variable?
A. C
B. 0.25
C. m
D. 30
4. Which of the following is true?
A. 15 is whole, natural, and an integer but is not rational.
B.
is whole, natural, an integer, and is rational.
C. -87.3 is not rational, but it is an integer.
D. -13 is whole, an integer, and is rational.
13 ?
C. It is a natural number but not a whole
number.
B. It is an integer but not a rational number. D. It is an irrational number but not a
natural number.
5. Which statement best describes the number
A. It is a whole number but not an integer.
1
Revised 2009
Match the equation with its graph.
6. 3x – 7y = –21
A.
C.
B.
D.
7.
Write the following numbers from least to greatest.
2.53,
A.
B.
8.
,
-
,
, -
,
,
2.5
,
2.53
-
,
,
C. 2. 53,
,
, -
D. 2. 53,
,
, -
Gracie Ann works 30 hours per week and makes $6.50 an hour and t tips. Which expression
represents the amount of money she earned in one week, including tips?
A. (6.50)(30)(t)
B.
t
C. 30 + 6.50 + t
D. (30)(6.50) + t
9. Opening a savings account at Bayou Bank requires at least $250. So far, Emily has $106. Which inequality
shows how many more dollars, d, Emily needs to open the savings account?
A. d + 106 ≥ 250
B. d + 106 ≤ 250
C. d - 106 ≥ 250
D. d - 106 ≤ 250
2
10. Which of the scatter plots shows a positive correlation?
C.
A.
B.
D.
11. Which expressions do not have a value of 0?
I.
8 – 3[126 ÷ 2 – 10]2
II.
3[(52 + 12 – 37)(120 + 100)]
III.
(50 – 49)2 + 1
A. I and II
B. I and III
C. II and III
D. None of these
12. A blank tropohy costs $20. Each letter engraved on the trophy costs $3. Which expression models the cost
of a trophy with n letters engraved?
A. 20 + 3n
B. 20n + 3
C. (20 + 3)n
3
D. 20 + 3 + n
13. Which graph shows the best trend line for the following data.
Practice (weeks)
6
8
10
12
14
16
18
Score
21
20
24.5
26.5
36.5
38
45.5
A.
C.
B.
D.
14. Two local gyms, Star Fitness and Pump-up, charge a one-time enrollment fee and a regular monthly fee. The
total amounts charged by both gyms are modeled by the functions below.
Star Fitness f(x) = 25x + 60
Pump-Up
f(x) = 30x + 25
Which statement is true?
A.
B.
C.
D.
Pump-Up charges a greater enrollment fee than Star Fitness.
Pump-Up charges a greater monthly fee than Star Fitness.
The monthly fee at Star Fitness is the same as the monthly fee at Pump-Up.
The enrollment fee at Star Fitness is the same as the enrollment fee at Pump-Up.
4
15. Identify the mapping diagram that represents the relation and determine whether the relation is a function.
ÏÔ
¸Ô
ÔÌÓ (−3,− 6), (−1,− 6), (5,− 6), (8,− 6) Ô˝˛
A.
C.
The relation is a function.
The relation is not a function.
B.
D.
The relation is not a function.
The relation is a function.
16.
A submarine dives 5,230 feet below the surface of the water. After several days of surveillance, the
submarine ascends 1,220 feet. Express the depth of the submarine after this move as an integer.
A. 3,110 feet
B. -3110 feet
C. -4,010 feet
D. 4,010 feet
17.
1
2
Evaluate the expression if x = 2 , y = -8, and z = 5 .
10(x + z) – y
5
A. -3 7
B. 1
C. 14
18.
Which inequalities have the same solution?
I.
II.
III.
A.
B.
C.
D.
x + 7 > 6x + 12
4 – 10x > 14
2(1 – 3x) – 4 > 10 + 3(2 – x)
None have the same solution.
I, II, and III have the same solution.
I and II only have the same solution.
II and III only have the same solution.
5
D. 17
19. If the goal is to hit the bull’s-eye, which target shows the most accurate throws?
A. Target 1
B. Target 2
C. Target 3
20. Which measurement would be the most precise?
D. Target 4
A. Nearest
cup
C. Nearest
cup
B. Nearest
cup
D. Nearest
cup
21.
Camille drove 156 kilometers from her home to New Iberia in 1
hours. Which unit is most reasonable
to determine her average speed?
A. Kilometer per hour
B. Hour per kilometer
C. Miles per hour
D. Meters per second
22.
Hailey is parachuting over the Grand Canyon. At a time of 25 second, she is at a height of 2,225 feet, and
at a time of 35 seconds, she is at a height of 2,115 feet. Determine the rate of change, and include the
meaning in your answer.
A. Hailey’s speed is -11 feet per second.
C. Hailey’s speed is
B. Hailey’s speed is -
D. Hailey’s speed is 11 feet per second.
feet per second.
feet per second.
23.
Which of the following choices includes a family of lines with the same slope but with different
y-intercepts?
5
1
A. 5x – 2y = 10 and y = 2 x – 5
C. y = - 2 x + 3 and 2x – y = 6
3
B. 4x + 3y = 15 and y = - 4 x + 7
5
D. y = 6 x – 8 and 5x – 6y = 8
6
24. Which of these best describes the relation shown?
A. The domain is {-2, -1, 3, 5, 6}.
C. The domain is {-2, -1, 3, 5, 6, 7}.
B. The domain is {-2, -1, 3, 5, 6}.
D. The range is {-8, -2, -1, 4, 6}.
25. Gene created this flow chart before he started painting some walls.
What step is performed after sanding a patch?
A. patch wall
C. check for holes in walls
B. clean walls
D. check for exposed wood or drywall
7
26. Derek approximated the perimeter of the rectangle below as 1,500 mm.
Which statement best describes Derek's approximation?
It is slightly lower than the actual perimeter since each side was rounded to the
nearest 10.
B. It is slightly higher than the actual perimeter since each side was rounded to the
nearest 10.
C. It is significantly lower than the actual perimeter since each side was rounded to
the nearest 100.
D. It is significantly higher than the actual perimeter since each side was rounded to
the nearest 100.
A.
27. Use the graph below to answer this question.
A.
B.
C.
D.
The mailing cost depends on the weight of the letter.
The weight of the letter depends on the mailing cost.
The mailing cost and weight depend on the number of letters being mailed.
The number of letters being mailed depends on the mailing cost and weight.
8
28. The amount of money produced by the government each day is close to 635 million dollars.
How is 635 million written in scientific notation?
A. 6.35 x 10 6
B. 6.35 x 10 7
C. 6.35 x 10 8
D. 6.35 x 10 9
Short Answer
Write an algebraic expression for the phrase.
29. 2 times the quantity d minus 9
30. A pair of shoes costs $46.99 and the state sales tax is 4%. Use the formula C = p + rp to find the total cost of
the shoes, where C is the total cost, p is the price, and r is the sales tax rate.
Simplify the expression.
ÈÍ
˘˙
2
31. 3 ÍÍÍÍ (13 − 1) ÷ 2 ˙˙˙˙
Î
˚
32. 1.7m2 + 6.5n − 4n + 2.5m2 − n
33. Name the set(s) of numbers to which –5 belongs.
34. Evaluate the expression (ab) 2 for a = 5 and b = 4.
Solve the proportion.
35.
x + 1 10
=
15
18
36.
w + 14
3
=
4w + 6
4
37. a. Find the value of a.
b. Find the value of the marked angles.
9
38. The length of a rectangle is 7 centimeters less than twice its width. The perimeter of the rectangle is 34 cm.
What are the dimensions of the rectangle?
Write an inequality to model the situation.
39. Thomas earned $44 or more.
40. The French club is sponsoring a bake sale. If their goal is to raise at least $115, how many pastries must they
sell at $2.50 each in order to meet that goal? Write and solve an inequality.
Find the slope of the line.
41.
Write the slope-intercept form of the equation for the line.
42.
Graph the inequality.
43. x ≥ 2
10
Solve the inequality. Then graph your solution.
44. q −
1 1
>
2 3
45. –5q < –10
46. −2 ≤ 2x − 4 < 10
Write a function rule for the table.
47.
x
–2
–1
0
1
f(x)
–6
–3
0
3
48. A snail travels at a rate of 2.55 feet per minute.
a. Write a rule to describe the function.
b. How far will the snail travel in 9 minutes?
Find the constant of variation k for the direct variation.
49.
x
–2
1
3
4
f(x)
–7
3.5
10.5
14
50. A map has a scale of 1 cm : 19 km. Two cities are 4.7 cm apart on the map. To the nearest tenth of a
kilometer, what is the actual distance corresponding to the map distance?
51. Susan earns a 5% commission on her computer sales. If she earned a $80.31 commission on a sale of a new
system, what was the price of the system?
52. Find the greatest possible error for the measurement 0.991 g.
11
The pair of figures is similar. Find x. Round to the nearest tenth if necessary.
53.
Write an equation in point-slope form for the line through the given point with the given slope.
54. (4, –6); m =
3
5
Graph the equation.
1
55. y + 1 = (x + 1)
4
Graph the function.
56. y = 4x − 2
57. You measure a piece of rope and find its length to be 1 m. Find the percent error of this measurement. Round
to the nearest hundredth.
58. You roll a standard number cube. Find P(number greater than 5)
59. Refer to the spinner below. Find P(even and not shaded).
60. Evaluate f (x) = 2x 2 − 1 for x = 2.
12
61. Find the domain and range of the relation.
Age of
Person
55
55
28
28
Books
Read
41
37
27
15
The rate of change is constant in the graph. Find the rate of change. Explain what the rate of change
means for the situation.
62.
Solve the equation.
63. 5(y + 6) = 55
64.
2p
+ 22 = 12
9
65. 3.7x + 2.8 = 13.9
66. 2x + 8 = 3x + 5
67. 9d + 2d – 3d + 3 = 2d
13
68.
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
69. Giselle pays $190 in advance on her account at the athletic club. Each time she uses the club, $15 is deducted
from the account. The situation can be modeled by the equation
b = 190 – 15x, where x is the number of visits and b is the total account balance.
a. Graph the equation.
b. Find the account balance after 7 visits.
70. Mateo rents a truck. The table below shows the amount charged, in dollars, for each hour Mateo uses the
truck.
Hours
1
2
3
4
5
Truck Charges
Amount
Charged ($)
125
150
175
200
225
A. What is the slope of this data?
B. What does the slope of this data represent?
14
Essay
71. Use the map to answer the following. Show your work.
a. What is the slope of the line representing Elm Street?
b. Show that Birch Street and Poplar Avenue are parallel.
c. Show that Fir Street is NOT perpendicular to Birch Street.
72. A computer consultant is thinking of renting office space in a building that charges $28 per square foot per
month for office space. She estimates that electricity, telephone, and supplies will cost $500 per month.
a. Define variables and write an equation that describes the consultant’s monthly office expenses.
b. Do her monthly office expenses vary directly with the amount of office space she could rent?
c. What is the greatest amount of space she can afford if she wants to spend no more than $4000 a month on
rent and other expenses? Show your work.
15
ID: A
Monroe City School District
Answer Section
Study Guide
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
D
C
B
D
A
B
D
A
A
B
A
B
B
B
C
D
C
D
B
A
A
D
C
B
B
A
C
SHORT ANSWER
29. ANS:
2(d – 9)
30. ANS:
$48.87
31. ANS:
216
32. ANS:
4.2m2 + 1.5n
1
Algebra 1 - Midterm
ID: A
33. ANS:
integers, rational numbers
34. ANS:
400
35. ANS:
22
3
36. ANS:
4
19
37. ANS:
17; 108º
38. ANS:
length = 9 cm; width = 8 cm
39. ANS:
t ≥ 44
40. ANS:
2.50p ≥ 115; p ≥ 46
41. ANS:
−3
42. ANS:
3
y= x+1
4
43. ANS:
44. ANS:
5
q>
6
45. ANS:
q>2
46. ANS:
1≤x< 7
47. ANS:
f(x) = 3x
48. ANS:
d(t) = 2.55t; 22.95 ft
49. ANS:
k = 3.5
2
ID: A
50. ANS:
89.3 km
51. ANS:
$1606.20
52. ANS:
0.0005 g
53. ANS:
11.5 cm
54. ANS:
3
y + 6 = (x − 4)
5
55. ANS:
56. ANS:
57. ANS:
50%
58. ANS:
1
6
3
ID: A
59. ANS:
1
6
60. ANS:
7
61. ANS:
domain: {28, 55}
range: {15, 27, 37, 41}
62. ANS:
100
−
; value drops $100 every 3 years.
3
63. ANS:
5
64. ANS:
–45
65. ANS:
3
66. ANS:
3
67. ANS:
1
−
2
68. ANS:
plant 1; plant 2
69. ANS:
$85
70. ANS:
a. 25/1
b. $25/hour
4
ID: A
ESSAY
71. ANS:
[4]
a.
b.
c.
[3]
[2]
[1]
72. ANS:
[4]
[3]
[2]
[1]
8−1 7
=
8−4 4
7−7
0
= =0
Birch: (10, 7), (1, 7); m =
10 − 1 9
3−3
0
= =0
Poplar: (10, 3), (1, 3); m =
10 − 1 9
Birch Street and Poplar Avenue both have a slope of 0, so they are parallel.
10 − 2 8
=
Fir: (5, 10), (2, 2); m =
5−2
3
Birch has a slope of 0, so it is horizontal. To be perpendicular, Fir would have to
8
be vertical, but it has a slope of so it is not perpendicular to Birch.
3
two parts correct
one part correct with computational errors in the other parts OR missing
explanations
more than two computational errors OR one computation error and missing
explanations
Elm: (4,1), (8, 8); m =
a. Let E = monthly expenses, and let a = square feet of office space; E = 28a + 500
b. no
c. 125 square feet
two parts correct
one part correct
correct answers without work shown
5