Download Objective 1: Numbers, Operations, and Quantitative Reasoning

Objective 1: Numbers, Operations, and Quantitative Reasoning
8.1A: Compare and order rational numbers in various forms, including
integers, percents, and positive and negative fractions and decimals.
2003 #42:
A librarian arranged some books on the shelf using the Dewey decimal system. Choose
the group of book numbers that is listed in order from least to greatest.
F
G
H
J*
549.010, 549.101, 549.02, 549.3
392.4, 397.46, 399.53, 399.062
101.2, 101.04, 104.21, 110.0
834, 834.19, 834.2, 834.29
2004 #25:
Which fraction is between
A
1
2
B
3
5
C*
5
7
D
7
8
2
3
and ?
3
4
2006 #31
2
1
7
Several stores are having sales. The prices are reduced by 62.5%, , 75%, , and
.
3
2
10
Which list shows the price reductions from greatest to least?
A
B*
C
D
1 2 7
75%, 62.5%, , ,
2 3 10
7 2
1
75%, , , 62.5%,
10 3
2
7
1 2
75%,
, 62.5%, ,
10
2 3
7
2 1
75%,
, 62.5%, ,
10
3 2
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Objective 1: Numbers, Operations, and Quantitative Reasoning
8.1B: Select and use appropriate forms of rational numbers to solve
real-life problems, including those involving proportional relationships.
2003 #2:
A bag of mixed Yummy Gummies contains 26% green, 34% red, 24% blue, and 16%
yellow gummies. Carla put 250 mixed gummies in a bowl. Which proportion can be
used to find y, the total number of yellow gummies in the bowl?
F
16
250
=
100
y
G*
16
y
=
100 250
H
100
y
=
16
250
J
16 150
=
100
y
2003 #45:
An electronic device counted 3,962 vehicles passing through an intersection during a
7-hour period. If the number of vehicles passing through this intersection per hour
remains the same, which proportion can be used to find x, the number of vehicles that
would be counted by the device during a 9-hour period?
A
x
7
=
3,962 9
B*
3,962 x
=
9
7
C
7
9
=
x 3,962
D
16
7
=
3,962 x
2
Objective 1: Numbers, Operations, and Quantitative Reasoning
2004 #40:
Carlos, Jackie, Lester, and Margie ate lunch at a restaurant. The total amount of the bill,
1
including tax and tip, was $44.60. Carlos paid $15.00, Jackie paid of the bill, Lester
4
paid 20% of the bill, and Margie paid the rest of the bill. Who paid the greatest part of
the bill?
F*
G
H
J
Carlos
Jackie
Lester
Margie
2006 #27
The Texas state flag is rectangular and has a width-to-length ratio of 2:3. Which of the
following can be used to find l, the length of a Texas state flag with a width of 28
inches?
A
B*
C
D
2 + 28 = 3 + l
2 l
=
28 3
2 28
=
3 l
2 · 28 = 3 · l
3
Objective 1: Numbers, Operations, and Quantitative Reasoning
8.1C: Approximate mentally [and with calculators] the value of irrational
numbers as they arise from problem situations. (  , 2 )
2003 #30:
The area of a square is 125 square meters. Which best represents the length of a side
of the square?
F
G*
H
J
10.8 m
11.2 m
11.9 m
12 m
2004 #42:
Mr. Harrington wrote four irrational numbers on the board and asked Jared to choose
the number closest to 3. Which irrational number should Jared choose?
F
6
G*
10
H
12
J
14
2006 #18
The area of a square is 83 square meters. Which of these is closest to the length of
each side of the square?
F*
G
H
J
9.1 m
9m
8.9 m
8m
4
Objective 1: Numbers, Operations, and Quantitative Reasoning
8.1D: Express numbers in scientific notation, including negative
exponents, in appropriate problem situations.
2003 #46:
A certain bacterium measures approximately 0.000015 millimeter in length. How is this
length expressed in scientific notation?
F*
G
H
J
1.5 × 10-5mm
1.5 × 10-4 mm
0.15 × 105 mm
15 × 104 mm
2004 #3:
The diameter of a blood cell is measured in micrometers. A micrometer is 0.000001
meter. Which expression represents this number in scientific notation?
A
B
C*
D
1.0 × 107
1.0 × 106
1.0 × 10-6
1.0 × 10-7
2004 #43:
The sun’s core temperature reaches close to 2.7 × 107 degrees Fahrenheit. Which of
the following represents this temperature in standard notation?
A
B
C*
D
270,000°F
2,700,000°F
27,000,000°F
270,000,000°F
2006 #13
Mr. Loya stated that the circumference of Earth at the equator is 24,902.4 miles. Which
expression represents this number in scientific notation?
A*
B
C
D
2.49024 × 10 4
24.9024 × 10 4
249.024 × 10 4
2.49024 × 10 5
5
Objective 1: Numbers, Operations, and Quantitative Reasoning
8.2A: Select and use appropriate operations to solve problems and justify
the selections.
2003 #9:
Jasmine has an average of 95 on 15 quiz grades. If her teacher drops Jasmine’s lowest
grade, a 72, which equation can be used to find n, Jasmine’s new quiz average?
A
n=
95  72
14
B*
n=
(95  15)  72
14
C
n=
(95  15)  72
15
D
n=
95(72  15)
14
2004 #6:
The Webster Junior High faculty includes 37 teachers. The principal’s and teachers’
annual salaries total $1,266,140. If the principal’s salary is $54,250, which equation
can be used to find s, the average salary for a teacher at Webster Junior High?
(1,266,140  54,250)
37
F
s=
G
s = 1,266,140 +
54,250
37
H
s = 1,266,140 −
54,250
37
J*
s=
(1,266,140  54,250)
37
6
Objective 1: Numbers, Operations, and Quantitative Reasoning
2006 #16
A water tank contains 2,500 gallons. A faucet ttached to the tank releases water at a
constant rate of 5 gallons per minute. If the faucet is left open for 1 hour and no other
water is released, which equation can be used to find r, the number of gallons of water
remaining in the tank?
F
G
H*
J
r = 2,500 ÷ 5
r = 2,500 − 60
r = 2,500 − 60(5)
r = 2,500 ÷ 60(5)
2006 #47
1
1
yards of fabric and 6 yards of trim.
2
4
If the fabric costs $2.79 per yard and the trim costs $1.19 per yard, which equation can
be used to find c, the total cost of covering the bulletin board?
To cover his bulletin board, Mr. Adams needs 1
A
B*
C
D
c = (2.79 + 1.5) + (1.19 + 6.25)
c = (2.79 · 1.5) + (1.19 · 6.25)
c = (2.79 + 1.5) − (1.19 + 6.25)
c = (2.79 · 1.5) − (1.19 · 6.25)
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Objective 1: Numbers, Operations, and Quantitative Reasoning
8.2B: Add, subtract, multiply, and divide rational numbers in problem
situations.
2003 #21:
Three roommates agreed to split the cost of food and rent evenly. Last month they
spent a total of $349.66 for food and $365 for rent. Find the amount that each of the 3
roommates paid.
Record your answer and fill in the bubbles on your answer document. Be sure to use
the correct place value.
2004 #35:
On Friday the low temperature in Nome, Alaska, was −12°F, and the high temperature
was 23°F. How much warmer was the high temperature than the low temperature?
A
B
C
D*
−35°F
−11°F
11°F
35°F
2004 #47:
2
1
ounces of chocolate candy, 4 ounces of hard candy, and 4
3
2
ounces of dried fruit. What is the total weight of the contents of the gift basket?
A gift basket contains 6
A
11
1
oz
6
B
14
1
oz
2
C
14
3
oz
5
D*
15
1
oz
6
8
Objective 1: Numbers, Operations, and Quantitative Reasoning
2006 #11
1
1
1
cups of milk, 2 cups of flour, and 1 cups of other
2
4
3
ingredients. How many cups of milk, flour, and other ingredients are needed to make
36 waffles?
A recipe for 12 waffles calls for 1
A
B*
C
D
1
cups
3
1
15 cups
4
1
12 cups
4
1
51
cups
12
20
9
Objective 1: Numbers, Operations, and Quantitative Reasoning
8.2C: Evaluate a solution for reasonableness.
2003 #11:
Ms. Gonzalez’s monthly electricity bills for March through June were $97.09, $103.96,
$114.73, and $121.82. She estimated that the electricity cost a total of $400.00 over
these 4 months. Which best describes her estimate?
A*
B
C
D
Less than the actual amount because she rounded to the nearest $100
Less than the actual amount because she rounded to the nearest $10
More than the actual amount because she rounded to the nearest $100
More than the actual amount because she rounded to the nearest $10
2003 #26:
Rae’s recipe for lemon-lime punch calls for the following ingredients:
1 quart of apple juice
2
3
cups of lemon-lime soda
4
64 ounces of pineapple juice
2 quarts of cold water
1
cup of lemon juice
4
What is the smallest container that will hold all the ingredients?
F
G
H*
J
A 4-quart container
A 5-quart container
A 6-quart container
A 7-quart container
2004 #16:
Cody’s parents bought a big-screen television for $1,099.99 and a DVD player for
$99.99, including tax. Cody’s parents plan to pay the total amount in 18 equal monthly
payments. What is a reasonable amount for each monthly payment?
F
G
H
J*
$50.00
$150.00
$113.00
$67.00
10
Objective 1: Numbers, Operations, and Quantitative Reasoning
2006 #20
Sean is planning a trip of 1,450 miles. He plans to drive between 250 and 300 miles
each day. At this rate, which is a reasonable number of days it will take Sean to
complete his trip?
F
G*
H
J
Less than 4 days
Between 4 and 6 days
Between 6 and 8 days
More than 8 days
2006 #43
Anthony helps his father with his lawn-mowing service. His father charges from $25.00
to $50.00 per lawn depending on the size of the lawn to be mowed. Last Saturday,
1
Anthony and his father spent 6 hours mowing 3 lawns. If Anthony’s father actually
2
charged $25.00 for the smallest lawn and $50.00 for the largest lawn, about how much
could Anthony’s father have charged for all 3 lawns?
A
B
C*
D
$75
$95
$110
$150
11
Objective 1: Numbers, Operations, and Quantitative Reasoning
8.2D: Use multiplication by a constant factor (unit rate) to represent
proportional relationships for example, the arm span of a gibbon is about
1.4 times its height, a = 1.4h.
2004 #37:
The Childress family went on a camping trip. They paid $28.00 for a 2-night stay at a
campground that allows a maximum stay of 30 nights. Which equation can they use to
find c, the cost of camping at this campground for the maximum number of nights?
A
B
C
D*
c = 60 · 56
c = 30 · 28
c = 28 · 28
c = 30 · 14
2006 #40
Which equation can be used to find m, the number of minutes in h hours?
F
G
H
J*
m = 60 − h
m = h + 60
m = h ÷ 60
m = 60h
12