Austin Independent School District
Department of Curriculum and Instruction
Mathematics
Numerical Fluency
Algebra II, PreCalculus and Math Models
Mathematics
1st Six-Weeks
2008 - 2009
Problems #1-1 - #1-25
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-1
Work this problem and justify your
answer.
In a high school auditorium, 1
junior and 2 sophomores are seated
randomly together in a row.
What is the probability that the 2
sophomores are seated next to each
other?
1
A
9
2
C
3
1
B
3
5
D
6
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-2
Jamal has a game with 2 groups of
tiles. The first group of 26 tiles is
labeled with all the letters of the
alphabet. The second group of
10 tiles is numbered 0 through 9. If
Jamal draws 1 letter tile and 1
number tile at random, what is the
probability that he will draw a letter
in his name and an odd number?
1
A
13
1
C
4
5
B
52
7
D
26
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-3
Work this problem and explain your
solution.
A weather forecaster states that there
is a 20% chance of rain on each of the
next three days. To the nearest whole
percent, what is the probability that it
will not rain at all over the next threeday period?
A 51%
B 80%
C 40%
D 64%
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-4
Jordan likes only blue jelly beans. He
has a box of 100 jelly beans that
contains equal numbers of red, blue,
green, yellow, and orange jelly beans.
Jordan randomly pulls out a jelly
bean. Then he pulls out a second one
without replacing the first. What is
the probability that both jelly
beans are blue?
2
A
5
39
C
199
1
B
25
19
D
495
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-5
Work this problem and justify your
answer.
A car dealer has six used minivans for
sale. The mileage on the minivans is
shown in the table below.
Minivans
Color
White
Tan
Black
Silver
Blue
Maroon
Mileage
(thousands of miles)
90
35
110
15
32
150
The car dealer plans to describe the minivans’
mileage in a newspaper by using one of the
following data measures. Which measure of the
data would make the vehicles appear to have the
lowest mileage?
A Mean
B Median
C Range
D Mode
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-6
The senior class sold carnations
during a fund-raiser. The bar
graph shows the number sold for
each color of carnation.
Ramiro plans to make a circle graph
of the data in the bar graph.
Approximately what percent of
the circle graph should represent red
carnations?
A 40%
C 20%
B 50%
D 30%
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-7
The circle graph below shows the
results of a fair number cube being
tossed 20 times.
Which table matches the data
presented in the circle graph?
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-7
Continued
Which table matches the data presented in
the circle graph?
A
Number Landing
Face Up
Frequency
One
Two Three Four
Five Six
1
3
3
Number Landing
Face Up
Frequency
One
Two Three Four
Five Six
3
3
3
Number Landing
Face Up
B Frequency
One
Two Three Four
Five Six
1
3
3
Number Landing
Face Up
Frequency
One
Two Three Four
Five Six
3
3
5
B
C
D
B
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4
4
5
3
4
4
5
5
3
3
3
3
1st Six Weeks 2008-2009
7/3/08
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-8
The table below shows the cost of
fertilizer, depending on the amount
purchased.
Cost of Fertilizer
Number of
Cost
Pounds
5
$1.95
20
$6.95
50
$15.95
100
$28.95
Which conclusion can be made based on
information in the table?
A The cost of 10 pounds of fertilizer
would be more than $4.00.
B The cost of 200 pounds of fertilizer
would be less than $57.00.
C The cost of fertilizer is always more
than $0.35 per pound.
D The cost of fertilizer is always less
than $0.30 per pound.
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-9
Work the following problem.
Two race cars travel at constant
speeds in the same direction around a
track. The faster car travels 186 miles
per hour and completes 50 laps each
time the slower car completes 47.6
laps. Which is a reasonable estimate
of the slower driver’s speed?
A Between 180 mph and 185 mph
B Between 175 mph and 180 mph
C Between 145 mph and 150 mph
D Between 135 mph and 140 mph
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-10
Work this problem on your paper.
In how many fewer minutes will a taxi
complete a 10-mile drive at an average
speed of 40 miles per hour than at an
average speed of 30 miles per hour?
A 5 minutes
B 10 minutes
C 8 minutes
D 13 minutes
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-11
Amber is making a patchwork quilt
using 3 different types of fabric. Each
type of fabric is cut into rectangles.
The first fabric is cut into pieces
measuring 3 inches by 5 inches.
The dimensions of the rectangles of the
second type of fabric are 125% those
of the first type, and the dimensions of
the third type of fabric are 125% those
of the second. What are the
approximate dimensions of the third
type of fabric?
A 3.75 in. by 6.25 in.
B 4.69 in. by 7.81 in.
C 5.50 in. by 7.50 in.
D 4.25 in. by 6.25 in.
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-12
Work this problem on your own
paper.
A leap year occurs when the number
of a year is a multiple of 4. However,
year numbers that are multiples of 100
are not leap years unless they are
multiples of 400. Which is not an
example of a leap year?
A 2440
B 2400
C 2340
D 2300
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-13
Rectangle MNPQ has diagonals that
intersect at point X.
Which of the following represents point X?
7
A ( , -2)
2
13
C (, -4)
2
13
B(
, 4)
2
7
D (- , 2)
2
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-14
For a sports banquet Coach Mackey
must use the rectangular tables in the
school cafeteria. The diagram below
shows the seating arrangements that
Coach Mackey can use at 1 and 2
tables.
Which expression can be used to
determine the number of people who
can sit as a group if y tables are
joined to form 1 long table?
A
B
C
D
6y
4(y + 1)
3(y + 1)
2(2y + 1)
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-15
Work this problem.
Look at the series of circles below with
their areas shown.
If the pattern continues, what would
be the approximate circumference of
the sixth circle in this series?
A 18.85 centimeters
B 37.70 centimeters
C 31.42 centimeters
D 25.13 centimeters
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-16
Work each problem on your own
paper.
As part of a classroom assignment,
Kimberly was given this geoboard to
2
model the slope of .
3
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-16
Continued
If the peg in the lower left-hand corner
represents the origin on a coordinate
plane, where could Kimberly place a
rubber band to represent the given
slope?
A From peg V to peg W
B From peg V to peg X
C From peg V to peg Y
D From peg V to peg Z
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-17
Work this problem on your own
paper.
Chase wanted to find 3 consecutive
whole numbers that add up to 81. He
wrote the equation
(n - 1) + n + (n + 1) = 81. What does
the variable n represent in the
equation?
A The least of the 3 whole numbers
B The middle of the 3 whole numbers
C The greatest of the 3 whole
numbers
D The difference between the least
and greatest of the 3 whole numbers
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-18
Gina works at a clothing store where
she earns a weekly salary plus a
percent of her total weekly
sales as a commission. The graph
below shows the amount, y, that Gina
will earn in one week if she
sells x dollars’ worth of clothing.
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-18
continued
The table below shows Gina’s sales for
four weeks.
Gina’s Clothing Sales
Week 1
$750
Week 2
$600
Week 3
$900
Week 4
$850
Which number best reflects the total
amount of money she earned in sales
commission for this four-week period?
A $310
B $3100
C $800
D $1110
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-19
Work this problem on your own
paper.
On Friday Daniel wrote a check for
$158. The following Monday he
deposited $60 into his bank account.
On Wednesday the bank informed
him that he had overdrawn his
account by $8. If Daniel made no
other transactions between Friday and
Wednesday, what was his balance
before he wrote the check on Friday?
A $90
B $98
C $106
D $210
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-20
Work this problem on your own
paper. Be sure to justify your solution.
How many 2-inch cubes can be
placed completely inside a box that
is 8 inches long, 2 inches wide, and
6 inches tall?
A 8
B 12
C 24
D 48
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-21
Work this problem on your own
paper and justify your solution.
Marsha brought cookies to school. She
gave a third of her cookies to Ana.
Ana then gave a fourth of her cookies
to Cybil. Cybil gave half of her
cookies to Betsy. If Betsy has 2
cookies, how many cookies did Marsha
have in the beginning?
A 18
B 24
C 36
D 48
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-22
A triangle has coordinates A (3, 7),
B (12, -5), and C (2, 0). The altitude
drawn to side AB intersects side AB at
point D (6, 3). If triangle ABC is dilated
by a scale factor of 5, what is the area of
the enlarged triangle?
A
B
C
D
73.5 square units
37.5 square units
937.5 square units
187.5 square units
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-23
A cylindrical piece of pipe insulation is
shown below.
If the insulation is 0.4 inch
thick, what is the
approximate volume of
insulation used?
A
B
C
D
3
107 in.
3
74 in.
3
34 in.
3
40 in.
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1st Six Weeks 2008-2009
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-24
The two bar graphs shown below
represent the populations and land areas
of four states.
Based on the information given in the bar
graphs, which of these four states is most
densely populated?
A
B
C
D
Indiana
Louisiana
Minnesota
Wisconsin
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Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency Problem #1-25
Mrs. Jones has a piece of carpet that is
13 feet long and 2 feet wide. She wants to
cut off a section that is 4 feet long and 1
foot wide. She wants to cut up the
remaining piece of carpet into 25 pieces
that are 1 foot square. Why is this
scenario impossible?
A
B
C
D
A piece 4 feet long by 1 foot wide
cannot be cut from the carpet.
Some pieces of carpet would be left
over.
The carpet cannot be cut into 1square-foot pieces.
There is not enough carpet to cut all
the pieces.
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Algebra II, PreCalculus, Math Models – Numerical Fluency
NF
Problem
TEKS TAKS
SEs OBJ
Problem Source
Answer
Problem #1-1
Problem #1-2
Problem #1-3
Problem #1-4
Problem #1-5
Problem #1-6
Problem #1-7
Problem #1-8
Problem #1-9
Problem #1-10
Problem #1-11
Problem #1-12
Problem #1-13
Problem #1-14
Problem #1-15
Problem #1-16
Problem #1-17
Problem #1-18
Problem #1-19
Problem #1-20
Problem #1-21
Problem #1-22
Problem #1-23
Problem #1-24
Problem #1-25
8.11A
8.11A
8.11A
8.11B
8.12A
8.12C
8.13B
8.13B
8.3B
8.3B
8.3B
8.16A
8.16A
8.16A
8.16A
8.15A
8.15A
8.15A
8.14C
8.14C
8.14C
8.14C
8.14A
8.14B
8.14A
TAKS 2004 Grade 11 #2
TAKS 2004 Grade 11 #14
TAKS Study Guide Grade 11 #85
TAKS Study Guide Grade 11 #86
TAKS Study Guide Grade 11 #89
TAKS Study Guide Grade 11 #91
TAKS Study Guide Grade 11 #90
TAKS 2004 Grade 11 #49
TAKS 2004 Grade 11 #35
TAKS Study Guide Grade 11 #84
TAKS 2004 Grade 11 #39
TAKS 2004 Grade 11 #33
TAKS 2004 Grade 11 #58
TAKS 2004 Grade 11 #36
TAKS Study Guide Grade 11 #101
TAKS 2004 Grade 11 #30
TAKS 2004 Grade 11 #32
TAKS Study Guide Grade 11 #99
TAKS 2003 Grade 11 #7
TAKS 2004 Grade 11 #9
TAKS 2004 Grade 11 #28
TAKS Study Guide Grade 11 #102
TAKS 2005(Oct) Grade 11 #26 adj.
TAKS 2005(Oct) Grade 11 #46 adj.
TAKS 2005(Oct) Grade 11 #54 adj.
C
A
A
D
B
D
C
B
B
A
B
D
A
D
B
A
B
A
A
B
D
C
C
A
D
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
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1st Six Weeks 2008-2009
7/3/08