Download Ch 3 and Ch 4 Review Questions

Name: ________________________ Class: ___________________ Date: __________
ID: A
Ch 3 and Ch 4 Review Questions
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
Solve the equation.
____
____
____
____
____
____
____
____
____
____
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____
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1. 5x – 5 = –10
a. –1
b. –3
c. –2
d. 5
2. –2 + 2x = –10
a. –6
b. –2
c. –5
d. –4
x
3.
+9=4
5
a. 65
b. –25
c. 5
d. 20
4. 18 - 2x = –4
a. 11
b. –2
c. –7
d. 2
5. 6d − 10d = 40
a. –10
b. 36
c. 10
d. 44
6. 78 = −2(m + 3) + m
a. –28
b. –42
c. –72
d. –84
7. 6 = 2(x + 8) − 5x
2
1
2
1
a.
b. 3
c. −
d. –3
3
3
3
3
1
8.
y–3=9
4
a. 48
b. 3
c. 36
d. 24
4
4
9.
n+6 =
9
3
1
1
2
1
a. 10
b. 16
c. –4
d. –10
2
2
3
2
10. x − 9 = −6x + 5
a. 14
b. 7
c. 2
d. 21
11. x + 9 = 5(4x − 2)
11
1
a.
b. –1
c. 1
d. −
19
19
12. −6p − 21 = 3p − 12
a. 1
b. 3
c. –3
d. –1
13. The sum of three consecutive integers is 72. Find the integers.
a. 22, 23, 24
b. 25, 26, 27
c. 23, 24, 25
d. 24, 25, 26
14. The fare for riding in a taxi is a $3 fixed charge and $0.80 per mile. The fare for a ride of d miles is $6.75.
Which equation could be used to find d?
a. 3(6.75 + d) = 3
c. 3 + 0.80d = 6.75
b. 0.80 + 3d = 6.75
d. (0.80 + 6.75)d = 3
1
Name: ________________________
ID: A
____ 15. If a number n is subtracted from 25, the result is three less than n. What is the value of n?
a. 14
b. 22
c. 28
d. 11
____ 16. Write the given sentence as an equation.
Tim’s age in 7 years will be three times what it was 19 years ago.
a. 3(t + 7) = t – 19
c. t + 7 = 3(t – 19)
b. t + 19 = 3(t – 7)
d. 3(t + 19) = t – 7
____ 17. In which quadrant is the point (x, y) located if x is positive and y is positive?
a. IV
b. I
c. III
d. II
____ 18. What are the coordinates of the point 4 to the left and 5 above the point (1, 0)?
b. (5, 5)
c. (–3, 5)
d. (5, –3)
a. (5, –5)
Write an algebraic expression for the word phrase.
____ 19. the mass of the package in grams reduced by 536 g
x − 536
a.
b.
x + 536
____ 20. 2b + 3 for b = 12
a. 12
b. 21
8c + 12
for c = 3
____ 21.
c
a. 40
b. 4
5a − b
____ 22. c ⋅
for a = 8, b = 15, and c = 4
5
a. 17
b. 20
____ 23. 21 − |d | for d = –20
a. 41
b. –1
____ 24. 8 |a| − |b | for a = –3 and b = –6
a. 30
b. –18
x
c.
536x
d.
c.
30
d.
27
c.
24
d.
12
c.
29
d.
9
c.
1
d.
–41
c.
18
d.
–30
536
3
____ 25. 3x for x = –3
a. 729
b.
–81
c.
81
d.
–729
____ 26. 4n − 3n − 8 for n = –5
a. 77
b.
–33
c.
107
d.
123
c.
–22
d.
254
2
2
3
____ 27. 4r − 2s for r = 1 and s = 5
a. 38
b. –246
____ 28.
(−h − 3j) 2
for h = 3 and j = –5
h
a. 8
b. −28
c. 108
d. 48
____ 29. You have $20 to spend. You buy socks that cost $3 per pair.
a. Write an expression for the amount of money you have left after buying s pairs of socks.
b. How many pairs of socks did you buy if you have $8 left?
a.
b.
20s − 3; 6 pairs
3s + 20; 4 pairs
c.
d.
2
20 − 3s; 4 pairs
20 − 3s; 3 pairs
Name: ________________________
ID: A
____ 30. Eric earns $11.50 per hour. He plans to buy a guitar amp for $287.50. How long will Eric have to work
before he has enough money to buy the guitar amp?
a. 25 hours
b. 20 hours
c. 26 hours
d. 24 hours
Simplify the expression.
____ 31. −4 4
a. –256
b.
2
256
____ 32. (9 ⋅ 6 − 9 ⋅ 2 ) ÷ (4 + 5)
a. 8
b. 32
2
c.
16
d.
–16
c.
140
d.
320
c.
32
d.
160
2
3
____ 33. 4 + (4 ⋅ 2 )
a. 528
b.
48
____ 34. The formula for the volume of a sphere is
4
π r 3 , where r is the radius. Find the volume of a sphere with a
3
radius of 2.6 cm. Use π = 3.14. Round to the nearest hundredth.
b. 41.39 cm3
c. 70.3 cm3
a. 73.58 cm3
____ 35. Identify the property.
d.
28.3 cm3
c⋅1 = c
a. Identity Property of Addition
b. Commutative Property of Addition
c. Commutative Property of Multiplication
d. Identity Property of Multiplication
____ 36. Which of the following is an example of the Distributive Property?
c. 4(9 + 2) = 4 ⋅ 9 + 4 ⋅ 2
a. 4(9 ⋅ 2) = 4 ⋅ 9 + 4 ⋅ 2
b. 4(9 + 2) = 4 + 9 ⋅ 4 + 2
d. 4(9 ⋅ 2) = 4 + 9 ⋅ 4 + 2
Use mental math to simplify the expression.
____ 37. 2(−5)(16)
a. –170
b.
–160
c.
–150
d.
–130
d.
−5a − 10
d.
$26.96
d.
21,281 h
Find the product.
____ 38. −5(a + 2)
a. −5a − 3
b. −5a + 10
c. −5a + 2
____ 39. Use the Distributive Property to find the total cost.
7 pounds of rib roast at $3.93 per pound
a. $27.74
b. $26.95
c. $27.51
____ 40. Use the formula d = rt. Find t for r = 46.6 m/h and d = 456.68 m.
a. 9.8 h
b. 0.1 h
c. 410.08 h
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Name: ________________________
ID: A
____ 41. The formula for the volume of a sphere is V =
3.14 for π . Round to the nearest hundredth.
b. 523.33 cm3
a. 294.38 cm3
4
3
c.
π r 3 . Find the volume of a sphere with a radius of 5 cm. Use
500 cm3
d.
104.67 cm3
Solve by simplifying the problem.
____ 42. The houses on your street are numbered with odd numbers starting with 1 and ending with 201. How many
house numbers contain at least one 7?
a. 30 numbers
b. 28 numbers
c. 24 numbers
d. 20 numbers
Solve using any strategy.
____ 43. A school band has a brass section of trumpet, trombone, and tuba players. There are twice as many
trombones as tubas, and half as many trombones as trumpets. If there are two tubas in the band, what is the
total number of players in the brass section?
a. 8 players
b. 10 players
c. 12 players
d. 14 players
____ 44. A dime is 1.25 mm thick. How many meters high would a stack of dimes worth $50 be?
a. 0.00625 m
b. 6.25 m
c. 625 m
d. 0.625 m
____ 45. Simplify − |−11| .
a. |11|
b. − |11|
c. 11
d. –11
In which quadrant does the point lie? Write the coordinates of the point.
y
A
6
4
2
–6
–4
–2
O
–2
B
2
C
4
6
x
–4
–6
____ 46. A
a.
b.
____ 47. B
a.
b.
quadrant II; ( 6, –4)
quadrant I; (4, 6)
c.
d.
quadrant III; (–4, –6)
quadrant I; (6, 4)
quadrant II; (–2, –4)
quadrant III; (2, 4)
c.
d.
quadrant III; (–2, –4)
quadrant IV; (–4, –2)
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Name: ________________________
ID: A
____ 48. C
a. quadrant IV; ( –2, 2)
c. quadrant III; ( 2, –2)
b. quadrant III; ( –2, 2)
d. quadrant IV; ( 2, –2)
____ 49. If the points (–2, 2), (–4, 4), (2, –2), and (4, –4) are joined to form a straight line, at what point does the line
intersect the y-axis?
a. (0, 0)
b. (4, –4)
c. (2, 0)
d. (0, –2)
____ 50. Tell whether the sequence 7, −16, 30, −62 . . . is arithmetic, geometric, or neither. Find the next three terms
of the sequence.
1
1
1
a. arithmetic; 122, −246, 490
c. arithmetic; −62 , −62 , −62
6
3
2
1
13 31
b. neither; 122, −246, 490
d. geometric; 10 , −1 ,
3
18 108
____ 51. Angela started an exercise program on her thirteenth birthday. She started with fewer than five sit-ups, and
she increased the number of sit-ups by a constant amount each day. By February 7, she was up to 39 sit-ups.
By February 12, she was up to 59 sit-ups.
On what date was Angela’s birthday? How many sit-ups did Angela do on her birthday?
a. January 29; 3 sit-ups
c. January 28; 4 sit-ups
b. January 30; 10 sit-ups
d. February 1; 9 sit-ups
Short Answer
52. Use mental math and the Distributive Property to simplify.
43 ⋅ 6 − 33 ⋅ 6
53. Elise and Miguel both collect baseball cards. Miguel has 2 more than 2 times as many cards as Elise.
Together they have 971 cards.
a. Write an equation to represent this situation.
b. How many cards does each person have?
54. Caitlin had $402 in her bank account. She withdrew $15 each week to pay for a swimming lesson. She now
has $237.
a. Write an equation that can be used to find the number of swimming lessons that she
paid for.
b. How many swimming lessons did she pay for?
c. At the time she had $237, the cost of a lesson rose to $19. How many lessons can she
pay for with her remaining $237?
55. Mandy and 2 friends bought some mechanical pencils at a special sale. They divided some of the pencils
equally among themselves and then gave 3 to Mandy’s little brother. At that time they had 19 pencils left.
Write an equation to find the number of pencils p that they bought at the sale.
56. Miranda opened a checking account with $560 from her summer job. She withdrew the same amount each
week for 13 weeks. Her balance was then $365. Solve the equation 560 − 13m = 365 to find how much
money m she withdrew each week.
57. Use grouping symbols to make the number sentence 7 – 2 × 2 – 1 = 9 true.
5
Name: ________________________
ID: A
58. Four friends are planning a camping trip. At one store, they buy a lantern for $35 and 4 batteries for $4 each.
At another store, they buy hamburgers that cost $15, three bags of chips that cost $2 per bag, and a bag of
hamburger rolls for $4. Each will contribute the same amount of money toward the supplies.
a. Write a numerical expression for the amount the friends spent.
b. How much money does each person need to contribute?
59. A ball is dropped from a height of 9 feet. It hits the floor, bounces, falls back to the floor, bounces again, and
2
so on. On each bounce, the ball returns to of the height from which it just fell.
3
a. Write the first four terms of the sequence of heights from which the ball falls. What
kind of sequence do the heights form?
b. What total vertical distance has the ball traveled by the instant it hits the floor for the
fifth time?
60. Is the sequence 5, 9, 15, ... an arithmetic sequence? Explain.
61. Is the sequence 3, 12, 36, ... a geometric sequence? Explain.
Graph the linear equation.
62. For the function x → 4x − 5, make a table with integer values of x from –4 to 4. Then graph the function.
Explain the shape of the graph.
Essay
63. In the diagram below, each dot represents a positive integer. Each number on the outside of the box
represents the product of the integers in that row or column. Explain how you would solve this problem to
find n.
64. Max left his house and walked on a path 100 ft to Amery’s apartment. He then turned around and walked on
the path half the distance home.
a. Use absolute value of integers to represent the total distance Max traveled.
b. Explain your reasoning and justify your answer.
65. The formula R = s ÷ 10 can be used to determine the equivalent amount of rain when you know the amount
of snowfall.
a. What do you think the variables R and s represent in the formula? Explain.
b. Meg measured 8 inches of snow in the last snowstorm. What is the equivalent amount
of rainfall? Show your work.
66. Draw a coordinate plane. Graph point (–3, 5). Label the quadrants, axes, origin, x-coordinate, and
y-coordinate.
67. One term of an arithmetic sequence is 73, and the next term is 90. The fourteenth term of the sequence is
209. Find the first term of the sequence, and explain how you found it.
6
Name: ________________________
ID: A
68. For the function x → |x| , make a table with integer values of x from –4 to 4. Then graph the function.
Explain the shape of the graph.
Other
69. The Hi-Line School is having an all-school play. The cost of 2 adult and 2 children’s tickets is $24. A child’s
ticket costs half as much as an adult ticket.
a. Write an equation that can be solved to find the cost of an adult ticket. Explain the
variables and values you use in the equation.
b. Find the cost of a child’s ticket. Explain your method.
7
ID: A
Ch 3 and Ch 4 Review Questions
Answer Section
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.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
A
D
B
A
A
D
B
A
D
C
C
D
C
C
A
C
B
C
A
D
D
B
C
C
B
C
B
D
C
A
A
B
B
A
D
C
B
D
C
1
ID: A
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
A
B
B
D
D
D
B
C
D
A
B
A
SHORT ANSWER
52. 60
53.
a. x + 2x + 2 = 971
b. Elise, 323 cards; Miguel, 648 cards
54.
a. 237 + 15p = 402, where p = number of lessons paid for
b. 11 lessons
c. 12 lessons
55. 66 pencils
56. $15
57. (7 – 2) × 2 – 1 = 9
58.
a. [(35 + 4 ⋅ 4) + (15 + 3 ⋅ 2 + 4] ÷ 4
b. $19
59.
2
9 ft, 6 ft, 4 ft, 2 ft; geometric sequence
3
8
b. 37 ft
9
60. No; sample explanation: 9 − 5 = 4, but 15 − 9 = 6. Since these differences are not equal, there is not a
common difference.
61. No; sample explanation: 12 ÷ 3 = 4, but 36 ÷ 12 = 3. Since these quotients are not equal, there is not a
common ratio.
a.
2
ID: A
62.
y
4
2
–4
–2
2
4
x
–2
–4
ESSAY
63.
[4] Since the numbers outside are found by multiplying the numbers in each row or column,
you can find the values of the dots by dividing. First find the number that belongs in the
lower right corner. 36 ÷ 4 = 9. Next find the number that goes in the top right corner.
45 ÷ 9 = 5. Then find the value of the dot in the upper left corner. 40 ÷ 5 = 8. Finally,
multiply 8 by 4 to find n. So n = 32.
[3] correct values for the three dots, but not n
[2] correct values for two dots OR correct values for one dot and n
[1] correct value for n without work shown
64.
[4] a.
distance = |100| +
1
|−100| = 150
2
Max traveled 150 feet.
b. Max’s house represents zero on the number line. Max walks 100 ft from his house
to Amery’s apartment. Graphically, he moves 100 units away from zero. When he
goes home, he walks in the opposite direction, or –100 ft. This is similar to walking
toward zero. Direction does not matter, so take the absolute value of both 100 and
1
–100. Max walks half the distance home, so multiply |−100| by . Add the two
2
absolute value expressions to find the total distance.
[3] correct procedures, but one computational error
[2] correct answer, but incomplete explanation
[1] correct answer with incorrect or no explanation
3
ID: A
65.
[4]
[3]
[2]
[1]
R represents the amount of rainfall and s represents the amount of snowfall.
R = s ÷ 10
R = 8 ÷ 10
R = 0.8
8 inches of snow is equivalent to 0.8 inch of rain.
minor error in part (b)
one part correct
correct answer without work shown
a.
b.
66.
[4]
8
y
y-axis
(x-coordinate, y-coordinate) 6
(–3, 5)
4
Quadrant II
2
Quadrant I
x-axis
–8
–6
–4
–2
O
2
4
6
x
–2
Quadrant III
Quadrant IV
–4
–6
–8
[3]
[2]
[1]
Student can draw coordinate plane and graph point. Some labels are missing.
Student draws plane and graphs points but does not include any labels.
Student can draw a plane but cannot relate it to graphing points or place labels on the
plane.
4
ID: A
67.
The first term is −12. Since 90 is the next term after 73, the common difference is
90 − 73, or 17. If x is the first term, you would have to add the common difference to
x thirteen times to get to the fourteenth term. So x + 13(17) = 209. Solve this
equation for x.
x + 13(17) = 209
[4]
x + 221 = 209
x = 209 − 221
x = −12
So the first term is −12.
correct reasoning, but one computational error
correct reasoning, but incorrect equation or two computational errors
correct answer without work shown
[3]
[2]
[1]
68.
[4]
x
−4
−3
−2
−1
0
1
2
3
4
|X|
4
3
2
1
0
1
2
3
4
(x, y)
(–4, 4)
(–3, 3)
(–2, 2)
(–1, 1)
(0, 0)
(1, 1)
(2, 2)
(3, 3)
(4, 4)
5
ID: A
OTHER
69.
a.
b.
Let the cost of an adult ticket be represented by a. If a child’s ticket is
1
the cost of an
2
1
adult ticket, then the cost of that ticket is a. Two adult and 2 children’s tickets are
2
1
1
purchased, so that is 2a + 2( a). The total cost is 24, so the equation is 2a + 2( a) =
2
2
24.
To find the cost of a child’s ticket, first find the cost a of an adult ticket by solving the
1
equation 2a + 2( a) = 24. First, simplify expressions. Then combine like terms. Finally,
2
divide to find the value of a.
1
2a + 2( a) = 24
2
2a + a = 24
Simplify.
3a = 24
Combine like terms
3a
24
=
Divide each side by 3.
3
3
a = 8
The cost of an adult ticket is $8, so the cost of a child’s ticket is $4.
6