Austin Independent School District
Department of Curriculum and Instruction
Mathematics
Numerical Fluency
Algebra 2, MM, PreCal
Mathematics
4th Six-Weeks
2009-2010
Problems #4-1 through #4-28
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-1
What are the slope and y-intercept of the
equation of the line graphed below?
A
3
4
b  4
B
4
3
b  4
m
m
AISD Secondary Mathematics Dept.
C
3
4
b  3
D
4
3
b  3
Page 1 of 30
m
m
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-2
The graph of a line is shown below.
If the slope of this line is multiplied by –1 and
the y-intercept decreases by 2 units, which
linear equation represents these changes?
A
y  2 x  1
B
y  x  1
C
y  x 1
D
1
y   x 1
2
AISD Secondary Mathematics Dept.
Page 2 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-3
Which equation represents the line that
passes through the points (- 1, 4) and
(3, 2)?
1
7
A y x
2
2
1
9
B y   x
2
2
C y  2 x  7
D y  2 x  3
AISD Secondary Mathematics Dept.
Page 3 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency #4-4
AISD Secondary Mathematics Dept.
Page 4 of 30
2009-2010
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-5
What are the coordinates of the xintercept of the equation  3 y  8  2 x ?
A
(2,0)
B
 0, 8 


3

C
 2 ,0 


3 
D
(4,0)
AISD Secondary Mathematics Dept.
Page 5 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency #4-6
Which graph best represents the
function y  1.75 x  5?
C
A
B
AISD Secondary Mathematics Dept.
D
Page 6 of 30
2009-2010
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-7
Which equation describes the line that
passes through the point (4, 7) and is
parallel to the line represented by the
equation  3x  y  4 ?
A
y  3x  19
B
y  3x  5
C
1
2
y  x5
3
3
D
1
1
y   x8
3
3
AISD Secondary Mathematics Dept.
Page 7 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-8
What is the rate of change of the graph
below?
A 3.5
B 1.67
C 0.6
D –1.67
AISD Secondary Mathematics Dept.
Page 8 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency #4-9
A
B
C
D
AISD Secondary Mathematics Dept.
Page 9 of 30
2009-2010
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency #4-10
A
B
C
D
AISD Secondary Mathematics Dept.
Page 10 of 30
2009-2010
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency #4-11
A
B
C
D
AISD Secondary Mathematics Dept.
Page 11 of 30
2009-2010
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
Numerical Fluency #4-12
What is the slope of the line
identified by 2 y  3( x  2) ?
A
3
B
3

2
C
2
3
D
2
AISD Secondary Mathematics Dept.
Page 12 of 30
2009-2010
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-13
What are the slope and y-intercept of a line
that contains the point (5, -1) and has the
same y-intercept as x – 3y = 6?
A
1
3
b6
B
1
5
b  2
m
C
m5
b  2
D
m3
b6
m
AISD Secondary Mathematics Dept.
Page 13 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-14
Given the function y  3.54 x  54.68,
which statement best describes the
effect of increasing the y-intercept
by 33.14?
A The new line is parallel to the
original.
B The new line has a greater rate of
change.
C The x-intercept increases.
D The y-intercept decreases.
AISD Secondary Mathematics Dept.
Page 14 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-15
Ms. Barton determined that the total
cost of her wedding, c, could be
represented by the equation
c  75n  1500, where n is the number
of people attending the wedding. If
Ms. Barton’s wedding cost $8625,
how many people attended the
wedding?
A 135
B 95
C 115
D 75
AISD Secondary Mathematics Dept.
Page 15 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-16
5
The graph of the equation y  x  3 is given
3
below. Graph y  x  1 on the grid.
AISD Secondary Mathematics Dept.
Page 16 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-17
The price, e, of an entertainment system at
Extreme Electronics is $220 less than twice
the price, u, of the same system at Ultra
Electronics. The difference in price between
the system at Extreme Electronics and Ultra
Electronics is $175. Which system of linear
equations can be used to determine the price
of the system at each store?
A
2e  u  220
e  u  175
B
2e  u  220
e  u  175
C
2e  2u  440
e  u  175
D
e  2u  220
e  u  175
AISD Secondary Mathematics Dept.
Page 17 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-18
The amount of an employee’s weekly
pay, p, including a bonus, can be
represented by the inequality
6.00h  100  p  6.50h  125 , where h
represents the number of hours
worked by the employee. If an
employee worked 25 hours, which of
the following is a reasonable amount
for the week’s pay?
A $118.75
B $250.00
C $272.50
D $290.25
AISD Secondary Mathematics Dept.
Page 18 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-19
At a college bookstore, Carla purchased a
math textbook and a novel that cost a total of
$54, not including tax. If the price of the
math textbook, m, is $8 more than 3 times the
price of the novel, n, which system of linear
equations could be used to determine the
price of each book?
A
mn8
m  3n  54
B
mn8
m  3n  54
C
m  n  54
m  3n  8
D
m  n  54
m  3n  8
AISD Secondary Mathematics Dept.
Page 19 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-20
Rita put some hummingbird feeders in her backyard.
The table shows the number of hummingbirds that
Rita saw compared to the number of feeders.
Which equation best describes the relationship between
h, the number of hummingbirds, and f, the number of
feeders?
A
h  2 f 1
B
f  2h  1
C
h f 2
D
h 1
f 
1
2
AISD Secondary Mathematics Dept.
Page 20 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-21
A shaded parallelogram is graphed on the coordinate
grid below.
Which of the following functions describes a line that
would include an edge of the shaded parallelogram?
A
y  2 x  5
B
y  2 x  2
C
y  2 x  9
D
y  2 x  1
AISD Secondary Mathematics Dept.
Page 21 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-22
What is the x-coordinate of the solution
to the system of linear equations
below?
4x  5 y  8
2 x  3 y  18
A
4
B
3
C
3
D
4
AISD Secondary Mathematics Dept.
Page 22 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-23
In 1998 the enrollment at a community
college was approximately 2500
students. In 2002 the enrollment had
increased to 3250 students. If the
enrollment continues to increase at this
rate, what is a reasonable projection of
enrollment for 2010?
A
4750
B
5750
C
6250
D
9000
AISD Secondary Mathematics Dept.
Page 23 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-24
Chase and Sara went to the candy store.
Chase bought 5 pieces of fudge and 3 pieces
of bubble gum for a total of $5.70. Sara
bought 2 pieces of fudge and 10 pieces of
bubble gum for a total of $3.60. Which
system of equations could be used to
determine the cost of 1 piece of fudge, f, and
1 piece of bubble gum, g?
A
5 f  3g  3.60
2 f  10 g  5.70
B
5 f  2 g  5.70
3 f  10 g  3.60
C
f  g  22
7 f  13g  9.30
D
5 f  3g  5.70
2 f  10 g  3.60
AISD Secondary Mathematics Dept.
Page 24 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-25
On Wednesdays an athlete’s schedule
allows no more than 75 minutes for
morning training. One round of a
strength routine, s, requires 8 minutes.
Once round of an endurance routine, e,
requires 12 minutes. Which of these best
represents the time available for the
athlete to spend on strength and
endurance routines on Wednesdays?
A
20( s  e)  75
B
8s  75  12e
C
8s  12e  75
D
12e  75  8s
AISD Secondary Mathematics Dept.
Page 25 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-26
Anna makes hand-painted plates.
Her overhead costs are $750 per
week, and she pays an additional $10
per plate in material costs. If Anna
sells the plates for $25 each, how
many plates does she have to sell
each week before she can make a
profit?
A
20
B
30
C
50
D
75
AISD Secondary Mathematics Dept.
Page 26 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-27
Valerie purchased x tubes of lipstick at $4 each and y
bottles of nail polish at $2 each. She spent less than $12,
not including tax. Use the grid below to graph the
inequality 4 x  2 y  12 .
Which point represents a reasonable number of
lipsticks and bottles of nail polish that Valerie
purchased?
A
(1, 5)
B
(2, 3)
C
(1, 3)
D
(2, 2)
AISD Secondary Mathematics Dept.
Page 27 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
2009-2010
Numerical Fluency #4-28
At a restaurant the cost for a breakfast
taco and a small glass of milk is $2.10.
The cost for 2 tacos and 3 small glasses of
milk is $5.15. Which pair of equations can
be used to determine, t, the cost of a taco,
and m, the cost of a small glass of milk?
A
t  m  2.10
2t  2m  5.15
B
t  m  2.10
3t  3m  5.15
C
t  m  2.10
3t  2m  5.15
D
t  m  2.10
2t  3m  5.15
AISD Secondary Mathematics Dept.
Page 28 of 30
Austin ISD
4th Six Weeks
Algebra II, PreCalculus, Math Models – Numerical Fluency
NF Problem
TEKS
NF #4-1
NF #4-2
NF #4-3
NF #4-4
NF #4-5
NF #4-6
NF #4-7
NF #4-8
NF #4-9
NF #4-10
NF #4-11
NF #4-12
NF #4-13
NF #4-14
NF #4-15
NF #4-16
NF #4-17
NF #4-18
NF #4-19
NF #4-20
NF #4-21
NF #4-22
NF #4-23
NF #4-24
NF #4-25
NF #4-26
NF #4-27
NF #4-28
A.6A
A.6C
A.6D
A.6G
A.6E
A.5C
A.6D
A.6A
A.6C
A.6E
A.5C
A.6A
A.6B
A.6C
A.7B
A.8B
A.8A
A.7C
A.8A
A.7A
A.7A
A.8B
A.7C
A.8A
A.7A
A.7B
A.7C
A.8A
TAKS
OBJ
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
AISD Secondary Mathematics Dept.
Problem Source
TAKS Test Gr 11 2004 #13
TAKS Test Gr 11 2004 #17
TAKS Test Gr 11 2004 #44
TAKS Test Gr 11 2004 #45
TAKS Test Gr 11 2004 #8
TAKS Test Gr 10 2004 #52
TAKS Test Gr 10 2004 #44
TAKS Test Gr 10 2004 #26
TAKS Test Gr 10 2004 #8
TAKS Test Gr 10 2004 #6
TAKS Test Gr 11 2003 #16
TAKS Test Gr 10 2003 #28
TAKS Test Gr 10 2003 #43
TAKS Test Gr 10 2003 #29
TAKS Test Gr 11 2004 #60
TAKS Test Gr 11 2004 #29
TAKS Test Gr 11 2004 #53
TAKS Test Gr 11 2004 #48
TAKS Test Gr 11 2004 #40
TAKS Test Gr 10 2004 #14
TAKS Test Gr 10 2004 #18
TAKS Test Gr 10 2004 #24
TAKS Test Gr 10 2004 #46
TAKS Test Gr 10 2004 #54
TAKS Test Gr 11 2003 #56
TAKS Test Gr 11 2003 #35
TAKS Test Gr 11 2003 #23
TAKS Test Gr 11 2003 #3
Page 29 of 30
2009-2010
Answer
C
A
A
D
D
D
B
C
C
B
A
B
B
A
B
C
D
C
C
A
D
B
A
D
B
D
C
D