Austin Independent School District
Bureau of Curriculum
Mathematics
Numerical Fluency
Algebra II, PreCalculus, Math
Models
Mathematics
3rd Six-weeks
2009-2010
Numerical Fluency #3-1 through #3-19
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-1
Work this problem and justify your
answer.
An artist studies human proportions in
order to make realistic drawings. He
observes that a person’s kneeling height,
3
y, is of the person’s standing height, x.
4
Which equation best represents this
relationship?
3
A y= x
4
3
B y=- x
4
3
C y=x–
4
3
D y=x+
4
AISD Secondary Mathematics Department
Page 1 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-2
The graph shows the number of gallons of
gas used by Maria’s car as a function of
the number of miles driven.
About how many gallons of gas will
Maria need for a 170-mile trip?
A 7 gal
B 8.5 gal
C 9.5 gal
D 11 gal
AISD Secondary Mathematics Department
Page 2 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-3
Karen jogs at a steady pace up a hill in
her neighborhood. She then runs down
the hill, and her speed increases. Which
graph best describes this situation?
AISD Secondary Mathematics Department
Page 3 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-4
The table below shows independent and
dependent values in a functional
relationship.
Independent Dependent
0
5
1
6
2
9
3
14
Which function best represents this
relationship?
A f (x) = 2x2 + 5
B f (x) = x2 + 5
C f (x) = 2x + 5
D f (x) = x + 5
AISD Secondary Mathematics Department
Page 4 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
Numerical Fluency #3-5
Which graph best represents the
inequality x + 2y  -14?
A
C
B
D
AISD Secondary Mathematics Department
Page 5 of 21
2009-2010
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-6
Which of the following tables describes a
functional relationship between dependent and
independent quantities?
A
C
x
-1
0
-2
0
x
-2
-2
-1
-1
y
0
-1
0
-2
y
2
-2
1
-1
AISD Secondary Mathematics Department
Page 6 of 21
B
D
x
1
0
2
-1
y
1
0
2
-1
x
0
1
1
-1
y
0
0
-1
1
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-7
Which equation best describes the
relationship between x and y shown in the
table below?
A y = 3x
B x = 3y
C x = 3y2
D y = 3x 2
AISD Secondary Mathematics Department
Page 7 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-8
Work this problem on your paper.
The basketball team is ordering T-shirts
to sell for a fund-raiser. The team paid
$275 for the shirts and will sell them for
$12 each. The relationship between the
number of shirts sold and the team’s
profit from the sale of the shirts
can be represented by the function
f (n) = 12n – 275, in which n represents
the number of shirts sold. What is the
dependent quantity in this functional
relationship?
A The number of shirts sold
B The amount the team paid for the
shirts
C The team’s profit from the sale of the
shirts
D The selling price of the shirts
AISD Secondary Mathematics Department
Page 8 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-9
Work the problem and justify your solution.
A department store had a 20%-off sale on
all clothing items. Which statement best
represents the functional relationship
between the sale price of an article of
clothing and the original price?
A The original price is dependent on the
sale price.
B The sale price is dependent on the
original price.
C The sale price and the original price
are independent of each other.
D The relationship cannot be
determined.
AISD Secondary Mathematics Department
Page 9 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-10
Let a represent the average speed in
miles per hour a car traveled on a
trip. Let f(t) represent the distance
in miles the car had traveled hours
after the beginning of the trip. The
function f(t) is best represented by
—
A t 2+ a
B at 2
C t+a
D at
AISD Secondary Mathematics Department
Page 10 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-11
Nancy purchased 5 more pounds of
pecans than she did of almonds.
Pecans cost $4.25 per pound, and
almonds cost $5.50 per pound. If x
represents the number of pounds of
almonds Nancy bought, which
expression represents the total cost
of the nuts she purchased?
A 19.50x + 21.25
B 19.50x + 48.75
C 9.75x + 48.75
D 9.75x + 21.25
AISD Secondary Mathematics Department
Page 11 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-12
Justify your solution to this problem.
What is the domain of the function shown
on the graph?
A -3  x  3
B -3 < x < 3
C -5 < x  4
D -5  x < 4
AISD Secondary Mathematics Department
Page 12 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-13
A music store gives its customers a free
CD for every five used CDs they trade in.
However, the store limits the number of
CDs that can be traded in during any one
1
month to 25 CDs. The function y = x
5
describes y, the total number of
free CDs, in terms of x, the number of
used CDs traded in each month. What is
a reasonable domain for this function?
A 0y5
B 0  y  25
C 0  x  25
D 0 x 5
AISD Secondary Mathematics Department
Page 13 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-14
Which equation is the parent function of
the graph represented below?
A
y =x
B
y=x
C
y=x²
D
y=x
AISD Secondary Mathematics Department
Page 14 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-15
At the Dallas-Fort Worth
International Airport, a DC-10, at
4500 feet, is descending toward the
east runway at a rate of 150 feet per
minute, and a 727, at 600 feet, is
climbing at a rate of 75 feet per
minute. Which graph shows when
the two planes will be at the same
altitude?
Answer choices on the next page.
AISD Secondary Mathematics Department
Page 15 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-15 (Continued)
AISD Secondary Mathematics Department
Page 16 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-16
Which expression is equivalent to
2
(3x - 15y) + (9y - 11x)?
3
A -9x – y
B 11x - 21y
C 10x - 4y
D -9x - 26y
AISD Secondary Mathematics Department
Page 17 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-17
Which expression is equivalent to
5n - 2)3n - (5n - 2)(n - 1)?
A n–1
B 3n 2 - 3n
C 10n 2 - 13n + 2
D 10n 2 + n - 2
AISD Secondary Mathematics Department
Page 18 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-18
The graph below shows the decrease in
the value of a personal computer over a
period of 60 months.
Which is a reasonable conclusion about
the value of this personal computer
during the time shown on the graph?
A Its value at 18 months was twice its value
at 36 months.
B Its value at 36 months was half its value at
54 months.
C It depreciated $400 every 18 months.
D It depreciated $200 every 12 months.
AISD Secondary Mathematics Department
Page 19 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency #3-19
Jim recently opened a store. The graph below
shows the store’s weekly sales since it opened.
What can be inferred from this graph?
A The store’s sales have been increasing
since it opened.
B The store’s sales increased for the first 2
weeks after it opened, but then they began
to decrease.
C The store’s sales increased for the first 5
weeks after it opened, but then they
decreased the next 2 weeks.
D The store’s sales increased for the first 5
weeks after it opened, remained constant
the next week, and then decreased the last
week shown.
AISD Secondary Mathematics Department
Page 20 of 21
Austin ISD
3rd Six Weeks
Algebra II, PreCalculus, Math Models
2009-2010
Numerical Fluency Specifications
Matrix
Number
TEKS
SEs
TAKS
OBJ
NF 3-1
NF 3-2
NF 3-3
208
516
516
A1.C
A1.E
A1.E
1
1
1
TAKS Test 2004 Grade 11 #1
TAKS Study Guide Grade 11 #10
TAKS Test 2004 Grade 11 #3
A
B
D
NF 3-4
215
A1.D
1
TAKS Study Guide Grade 11 #9
B
NF 3-5
NF 3-6
215
A1.D
1
TAKS Test 2004 Grade 11 #20
C
515
A1.B
1
TAKS Study Guide Grade 11 #3
B
NF 3-7
NF 3-8
515
A1.B
1
TAKS Test 2004 Grade 11 #31
D
258
A1.A
1
TAKS Study Guide Grade 11 #1
C
NF 3-9
NF 3-10
258
A1.A
1
TAKS Test 2004 Grade 11 #55
B
225
A3.A
2
TAKS Test 2004 Grade 11 #11
D
NF 3-11
NF 3-12
225
A3.A
2
TAKS Study Guide Grade 11 #17
D
259
A2.B
2
TAKS Test 2004 Grade 11 #27
B
NF 3-13
NF 3-14
259
261
A2.B
2
TAKS Study Guide Grade 11 #13
C
A2.A
2
TAKS Test 2004 Grade 11 #34
C
NF 3-15
A2.C
2
TAKS Test 2003 Grade 11 #37
A
NF 3-16
NF 3-17
517
121
121
A4.B
2
TAKS Test 2004 Grade 11 #41
A
A4.B
2
TAKS Test 2003 Grade 11 #25
D
NF 3-18
NF 3-19
517
517
A2.C
2
TAKS Test 2004 Grade 11 #47
C
A2.C
2
TAKS Study Guide Grade 11 #14
D
NF
Problem
Problem Source
AISD Secondary Mathematics Department
Page 21 of 21
Answer