10th Grade TAKS - Released Tests - by Objective
Objective
1
Functional relationships
2
Properties and attributes of functions
3
Linear functions
4
Linear equations and inequalities
5
Quadratic and other nonlinear functions
6
Geometric relationships and spatial reasoning
7
Two- and three-dimensional representations of geometric
relationships and shapes
8
Concepts and uses of measurement and similarity
9
Percents, proportional relationships, probability, and statistics
in application problems
10
Mathematical processes and tools used in problem solving
Objective 1:
The student will describe functional
relationships in a variety of ways.
A(b)(1) Foundations for functions.
The student understands that a function
represents a dependence of one quantity
on another and can be described in a
variety of ways.
(A) The student describes independent
and dependent quantities in functional
relationships.
If y is a function of x in the equation
y = x2 – 9, which statement is true?
F
G
H
J
The independent variable x is equal to 9 less
than the square of the dependent variable y.
The independent variable y is equal to 9 less
than the square of the dependent variable x.
The dependent variable y is equal to 9 less
than the square of the independent variable x.
The dependent variable x is equal to 9 less
than the square of the independent variable y.
Correct Answer - H
April 2006 #10
The volume of a rectangular prism is given by the
function V = lwh. Which statement is true?
A
The volume of the prism depends on the
product of only the length and the width.
B
The volume of the prism depends on the
product of only the length and the height.
C
The volume of the prism depends on the
product of the length, the width, and the height.
D
The volume of the prism depends on the
product of only the width and the height.
Correct Answer - C
April 2004 #23
A function is described by the equation
f(x) = x2 + 5. The replacement set for the
independent variable is {1, 5, 7, 12}. Which of the
following is contained in the corresponding set for
the dependent variable?
A
0
B
6
C
7
D
15
Correct Answer - B
Spring 2003 #19
A(b)(1) Foundations for functions.
The student understands that a function
represents a dependence of one quantity
on another and can be described in a
variety of ways.
(B) The student [gathers and records
data, or] uses data sets, to determine
functional (systematic) relationships
between quantities.
The table below shows the relationship between p, the
number of cell phones a company produces, and d, the
number of cell phones that are defective. Which
equation can be used to describe this relationship?
Correct Answer - G
April 2006 #14
Troy borrowed money from his father so that he could
buy a used car. The table shows the remaining
balance, b, of Troy’s loan after each payment. Which
function can be used to describe this relationship?
A
b = 3910 + 225p
B
b = 4135 – 225p
C
b = 2785 + 225p
D
b = 3685 – 225p
Correct Answer - B
April 2004 #35
Which equation best describes the relationship
between x and y in this table?
Correct Answer - D
Spring 2003 #45
A(b)(1) Foundations for functions. The
student understands that a function
represents a dependence of one quantity on
another and can be described in a variety of
ways.
(C) The student describes functional
relationships for given problem situations
and writes equations or inequalities to
answer questions arising from the
situations.
Ms. Adams bought a refrigerator that cost
$1200, including tax. The cost of electricity to
run this refrigerator is estimated at $78 per
year. Which equation best represents c, the total
cost of the refrigerator including electricity over
n years of operation?
A
B
C
D
c = 1200(78n)
c = 1200(n + 78)
c = 1200 – 78n
c = 1200 + 78n
Correct Answer - D
April 2006 #5
A candy company sells chocolate-covered cherries in a
box. The empty box weighs 4.2 ounces. Each piece of
candy weighs at least 1.8 ounces. Which inequality
best describes the total weight in ounces, w, of a box of
chocolate-covered cherries in terms of c, the number of
candies in the box?
A
w ≥ 1.8c + 4.2
B
w ≥ 1.8c – 4.2
C
w ≥ 4.2c + 1.8
D
w ≥ 4.2c – 1.8
Correct Answer - A
April 2004 #49
Vicki works as a salesclerk in a clothing store. She
earns $10 per hour plus a commission of 6% of her
total sales. Which equation represents e, her total
earnings when she works h hours and sells a total
of d dollars in merchandise?
A
e = 10h + 0.06d
B
e = 10h + 0.6d
C
e = 6h + 10d
D
e = 0.06h + 10d
Correct Answer - A
Spring 2003 #7
A(b)(1) Foundations for functions. The
student understands that a function
represents a dependence of one quantity on
another and can be described in a variety of
ways.
(D) The student represents relationships
among quantities using [concrete] models,
tables, graphs, diagrams, verbal
descriptions, equations, and inequalities.
Which data set is best described by the function
y = -2x2 + 5x?
Correct
Answer
H
April 2006 #48
Which inequality best describes the graph
shown below?
F
y ≥ -2x
G
y ≥ -x – 2
H
y ≥ -2x – 2
J
y≥x–2
Correct Answer - G
April 2004 #20
Which mapping best represents the function y
= 2x2 + 1 when the replacement set for x is {1, 0, 3}?
Correct Answer - D
Spring 2003 #43
A(b)(1) Foundations for functions.
The student understands that a function
represents a dependence of one quantity
on another and can be described in a
variety of ways.
(E) The student interprets and makes
inferences from functional
relationships.
The graph below represents Cheyenne’s bicycle trip
from her house to a friend’s house. On which
segment of the graph does it appear that Cheyenne
was riding her bicycle at the slowest pace?
A
r
B
s
C
t
D
u
Correct Answer - A
April 2006 #49
The graph below represents which of the following
relationships between temperature and time?
A
B
C
D
Oven temperature while
a cake is baking
Temperature of water
that is heated on a
stove, removed, and
then allowed to cool
Temperature of a
container of hot tea
after placing several cubes of ice in it
Room temperature of a gym after the air
conditioner is turned on
Correct Answer - B
April 2004 #51
Jake studied the parabola shown below. Which is
an accurate conclusion that Jake could make about
this parabola?
A
The vertex is at
(-2, 0).
B
The minimum value
is at (0, -4).
C
The maximum
value is at (2, 0).
D
The axis of symmetry
is the x-axis.
Correct Answer - B
Spring 2003 #5
Objective 2:
The student will demonstrate an
understanding of the properties and
attributes of functions.
A(b)(2) Foundations for functions.
The student uses the properties and
attributes of functions.
(A) The student identifies [and
sketches] the general forms of linear
2
(y = x) and quadratic (y = x ) parent
functions.
Which of these are characteristics of the parent function of a
quadratic equation?
I. The parent function of a quadratic equation has the vertex
at (0, 0).
II. The parent function of a quadratic equation opens
downward.
III.The parent function of a quadratic equation has the y-axis
as its line of symmetry.
F
I and II only
G
I and III only
H
II and III only
J
I, II, and III
Correct Answer - G
April 2006 #28
A(b)(2) Foundations for functions.
The student uses the properties and
attributes of functions.
(B) For a variety of situations, the
student identifies the mathematical
domains and ranges and determines
reasonable domain and range values for
given situations.
The graph shows the path of a golf ball.
What is the range
of this function?
F
0 < y < 100
G
0 ≤ y ≤ 100
H
0≤x≤5
J
0<x<5
Correct Answer - G
Spring 2003 #
A(b)(2) Foundations for functions.
The student uses the properties and
attributes of functions.
(C) The student interprets situations in
terms of given graphs [or creates
situations that fit given graphs].
A(b)(2) Foundations for functions.
The student uses the properties and
attributes of functions.
(D) In solving problems, the student
[collects and] organizes data, [makes
and] interprets scatterplots, and models,
predicts, and makes decisions and
critical judgments.
The coaches of a group of debate teams answered a survey about
hours of debate team practice and number of team wins. The
graph shows the results of this survey. Based on these results, if a
team practices 4 hours per week next season, which is the best
estimate of the number of debates the team can expect to win?
F
1
G
12
H
16
J
20
Correct
Answer
H
April 2004 #12
A(b)(3) Foundations for functions.
The student understands how algebra
can be used to express generalizations
and recognizes and uses the power of
symbols to represent situations.
(A) The student uses symbols to
represent unknowns and variables.
The area of the shaded portion of the rectangle
shown below is 440 square feet. How can the
area of the unshaded portion of the rectangle be
expressed in terms of x in square feet?
F
440x – 30
G
(30 + x)440
H
(30 – 440)x
J
30x - 440
Correct Answer - J
April 2006 #36
Mrs. Franklin received a 7% raise at her job. If
she was earning x dollars per year before, how
much is she earning now?
F
x+7
G
x + 0.07
H
x + 0.7x
J
x + 0.07x
Correct Answer - J
April 2004 #32
Which equation best represents the area, A,
of the rectangle below?
A
A = 2x + 2(x + c)
B
A = x2 + (x + c)2
C
A = x(x + c)
D
A = 2x(x + c)
Correct Answer - C
Spring 2003 #53
A(b)(3) Foundations for functions.
The student understands how algebra
can be used to express generalizations
and recognizes and uses the power of
symbols to represent situations.
(B) Given situations, the student looks
for patterns and represents
generalizations algebraically.
The squares below show a pattern. Which expression can
be used to determine the number of squares at stage n?
F
5n – 3
G
4n – 2
H
2n2
J
n2 + n
Correct Answer - J
April 2006 #38
Which expression can be used to find the
values of s(n) in the table below?
F
3n
G
5n
H
n+4
J
3n + 2
Correct Answer - J
April 2004 #4
A(b)(4) Foundations for functions. The student
understands the importance of the skills required
to manipulate symbols in order to solve problems
and uses the necessary algebraic skills required to
simplify algebraic expressions and solve
equations and inequalities in problem situations.
(A) The student finds specific function values,
simplifies polynomial expressions, transforms and
solves equations, and factors as necessary in
problem situations.
A rectangle has a length of 2x + 1 and a width of
5x – 4. Which expression best describes the area
of the rectangle?
F
7x – 3
G
14x – 6
H
10x2 – 3x – 4
J
10x2 + 13x – 4
Correct Answer - H
April 2006 #46
In the equation y = 2x2 – 5x – 18, which is a
value of x when y = 0?
A -18
B
1½
C
2
D
4½
Correct Answer - D
Spring 2003 #31
After a ball is dropped, the rebound height of each
bounce decreases. The equation y = 5(0.8)x shows
the relationship between x, the number of bounces,
and y, the height of the bounce, for a certain ball.
What is the approximate height of the fifth bounce
of this ball to the nearest tenth of a unit?
A
20.0 units
B
4.0 units
C
1.6 units
D
1.3 units
Correct Answer - C
Spring 2003 #37
A(b)(4) Foundations for functions. The
student understands the importance of the skills
required to manipulate symbols in order to
solve problems and uses the necessary
algebraic skills required to simplify algebraic
expressions and solve equations and
inequalities in problem situations.
(B) The student uses the commutative,
associative, and distributive properties to
simplify algebraic expressions.
Simplify the expression 6 – 3(5x + 2) – 10x.
F -25x
G
5x + 6
H
8 – 25x
J
12 – 25x
Correct Answer - F
April 2006 #16
Simplify the algebraic expression
5(x + 3)(x + 2) – 3(x2 + 2x + 1).
A 2x2 + 7
B
2x2 + 27
C
2x2 + 7x + 7
D
2x2 + 19x + 27
Correct Answer - D
April 2004 #1
Which expression is equivalent to
5(x2 – 4x) – (x + 1)?
A
5x2 – 21x + 1
B
5x2 – 5x – 1
C
5x2 – 21x - 1
D
5x2 – 5x + 1
Correct Answer - C
April 2004 #25
Simplify the expression 3(x + 1) – 2(3x + 7).
F -3x – 11
G
-3x - 10
H
-3x - 8
J
-3x + 17
Correct Answer - F
Spring 2003 #10
Objective 3:
The student will demonstrate an
understanding of linear
functions.
A(c)(1) Linear functions. The
student understands that linear
functions can be represented in
different ways and translates
among their various
representations.
(A) The student determines whether
or not given situations can be
represented by linear functions.
A(c)(1) Linear functions. The student
understands that linear functions can
be represented in different ways and
translates among their various
representations.
(C) The student translates among and
uses algebraic, tabular, graphical, or
verbal descriptions of linear functions.
Which table best describes points on the line graphed below?
Correct Answer - C
April 2006 #55
Which graph best represents the function y = -1.75x + 5?
Correct Answer - J
April 2004 #52
Which linear function best describes the graph
shown below?
Correct Answer - B
Spring 2003 #49
A(c)(2) Linear functions. The student
understands the meaning of the slope
and intercepts of linear functions and
interprets and describes the effects of
changes in parameters of linear functions
in real-world and mathematical situations.
(A) The student develops the concepts of
slope as rate of change and determines
slopes from graphs, tables, and algebraic
representations.
Which line appears to have a slope of zero?
F
Line n
G
Line k
H
Line w
J
Line p
Correct Answer - H
April 2006 #40
What is the rate of change of the graph below?
F
3.5
G
1.67
H
0.6
J
-1.67
Correct Answer - H
April 2004 #26
What is m, the slope of the line that contains the
points (2, 0), (0, 3), and (4, -3)?
Correct Answer - J
Spring 2003 #46
A(c)(2) Linear functions. The student
understands the meaning of the slope
and intercepts of linear functions and
interprets and describes the effects of
changes in parameters of linear functions
in real-world and mathematical situations.
(B) The student interprets the meaning of
slope and intercepts in situations using
data, symbolic representations, or
graphs.
The graph shows the distance a certain motorbike can travel
at a constant speed with respect to time. Which of the
following best describes the meaning of the slope of the line
representing this situation?
F
The motorbike travels at a
speed of about 8 mph.
G
The motorbike travels at a
speed of about 2.5 mph.
H
The motorbike travels at a
speed of about 5 mph.
J
The motorbike travels at a
speed of about 10 mph.
Correct Answer - J
April 2006 #12
A(c)(2) Linear functions. The student
understands the meaning of the slope
and intercepts of linear functions and
interprets and describes the effects of
changes in parameters of linear functions
in real-world and mathematical situations.
(C) The student investigates, describes,
and predicts the effects of changes in m
and b on the graph of y = mx + b.
What will happen to the slope of line p if the line is shifted
so that the y-intercept increases and the x-intercept
remains the same?
F The slope will change
from positive to
negative.
G The slope will change
from negative to
positive.
H The slope will
increase.
J The slope will
decrease.
Correct Answer - H
April 2004 #8
Which best describes the effect on the graph of
f(x) = 4x + 8 if the y-intercept is changed to -3?
F
The slope decreases.
G
The new line passes
through the origin.
H
The x-intercept
increases.
J
The y-intercept
increases.
Correct Answer - H
Spring 2003 #24
A(c)(2) Linear functions. The student
understands the meaning of the slope
and intercepts of linear functions and
interprets and describes the effects of
changes in parameters of linear functions
in real-world and mathematical situations.
(D) The student graphs and writes
equations of lines given characteristics,
such as two points, a point and a slope,
or a slope and y-intercept.
Which linear equation represents the line passing
through points R and S?
F
y = 1.5x – 4.5
G
y = 1.5x + 4.5
H
y = 0.5x – 4.5
J
y = 0.5x + 4.5
Correct Answer - F
April 2006 #2
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?
Correct Answer - G
April 2004 #44
Which of the following describes the line
containing the points (0, 4) and (3, -2)?
Correct Answer - A
Spring 2003 #9
A(c)(2) Linear functions. The student
understands the meaning of the slope
and intercepts of linear functions and
interprets and describes the effects of
changes in parameters of linear functions
in real-world and mathematical situations.
(E) The student determines the intercepts
of linear functions from graphs, tables,
and algebraic representations.
What is the x-coordinate of the x-intercept of the
function ⅔y = -6x + 12?
F
12
G
18
H
-9
J
2
Correct Answer - J
April 2006 #26
Which coordinate points represent the x- and yintercepts of the graph shown below?
F
(0, -4) and (6, 0)
G
(-4, 0) and (0, 6)
H
(6, 0) and (-4, 0)
J
(0, 6) and (0, -4)
Correct Answer - G
April 2004 #6
What is the y-intercept of the function f(x) = 3(x – 2)?
F
3
G
1
H
-2
J
-6
Correct Answer - J
Spring 2003 #26
A(c)(2) Linear functions. The student
understands the meaning of the slope and
intercepts of linear functions and interprets
and describes the effects of changes in
parameters of linear functions in real-world
and mathematical situations.
(F) The student interprets and predicts the
effects of changing slope and y-intercept in
applied situations.
A(c)(2) Linear functions. The student
understands the meaning of the slope
and intercepts of linear functions and
interprets and describes the effects of
changes in parameters of linear functions
in real-world and mathematical situations.
(G) The student relates direct variation to
linear functions and solves problems
involving proportional change.
Objective 4:
The student will formulate and use
linear equations and inequalities.
A(c)(3) Linear functions. The student
formulates equations and inequalities
based on linear functions, uses a
variety of methods to solve them, and
analyzes the solutions in terms of the
situation.
(A) The student analyzes situations
involving linear functions and
formulates linear equations or
inequalities to solve problems.
A chemist started an experiment with 5 grams of a
chemical. The chemical was used at a rate of 0.01
gram per minute. Which equation best describes
the relationship between c, the amount of chemical
remaining in grams, and t, the time in minutes?
F
c = 5.01t
G
c = 4.99t
H
c = 5 – 0.01t
J
c = 0.01t – 5
Correct Answer - H
April 2006 #50
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?
Correct Answer - F
April 2004 #14
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?
F
y = -2x + 5
G
y = -2x – 2
H
y = -2x + 9
J
y = -2x – 1
Correct Answer - G
April 2004 #18
At Northwest Electronics audiotapes cost $5.00 per
package, and videotapes cost $10.00 per package.
Which inequality best describes the number of packages
of audiotapes, a, and the number of videotapes, v, that
can be purchased for $45.00 or less?
F
5a + 10v < 45
G
10a + 5v ≤ 45
H
5a + 10v ≤ 45
J
10a + 5v < 45
Correct Answer - H
Spring 2003 #4
A(c)(3) Linear functions. The student
formulates equations and inequalities
based on linear functions, uses a variety
of methods to solve them, and analyzes
the solutions in terms of the situation.
(B) The student investigates methods for
solving linear equations and inequalities
using [concrete] models, graphs, and the
properties of equality, selects a method,
and solves the equations and inequalities.
The length of each leg of an isosceles triangle is
5 centimeters more than twice the length of the
base. If the perimeter of this isosceles triangle is
95 centimeters, what is the length of the base?
A
17 cm
B
21 cm
C
30 cm
D
39 cm
Correct Answer - A
April 2006 #39
What is the value of y if (3, y) is a solution to the
equation 5x – 3y = 18?
F
3
G
1
H
-1
J
-11
Correct Answer - H
Spring 2003 #34
A(c)(3) Linear functions. The student
formulates equations and inequalities
based on linear functions, uses a variety
of methods to solve them, and analyzes
the solutions in terms of the situation.
(C) For given contexts, the student
interprets and determines the
reasonableness of solutions to linear
equations and inequalities.
In 2004 a married couple could have calculated
their estimated income tax, t, for that year using
the equation t = 0.25c – 6525, in which c represents
their combined taxable income. If a married
couple had a combined taxable income between
$60,000 and $64,000, which of the following is a
reasonable amount for their income tax?
F
$6,525
G
$8,975
H
$13,869
J
$15,500
Correct Answer - G
April 2006 #20
The 1998 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?
F
4750
G
5750
H
6250
J
9000
Correct Answer - F
April 2004 #46
A(c)(4) Linear functions. The
student formulates systems of linear
equations from problem situations,
uses a variety of methods to solve
them, and analyzes the solutions in
terms of the situation.
(A) The student analyzes situations
and formulates systems of linear
equations to solve problems.
Norma and Lauretta went to a store to buy DVDs on sale for
$5 each, tax included. Norma purchased two and a half times
as many DVDs as Lauretta purchased. Together they
purchased 14 DVDs. Which system of linear equations can
be used to determine n, the number of DVDs Norma
purchased, and l, the number of DVDs Lauretta purchased?
F
n + l = 14
n = ½l
G
5n + 5l = 14
l = ½n
H
n + l = 14
n = (5/2)l
J
n + l = 14
l = (5/2)n
Correct Answer - H
April 2006 #32
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?
F
5f + 3g = 3.60
2f + 10g = 5.70
G
5f + 2g = 5.70
3f + 10g = 3.60
H
f + g = 22
7f + 13g = 9.30
J
5f + 3g = 5.70
2f + 10g = 3.60
Correct Answer - J
April 2004 #54
The length of a rectangle is equal to triple the
width. Which system of equations can be used
to find the dimensions of the rectangle if the
perimeter is 85 centimeters?
F
l=w+3
2(l + w) = 85
G
l = 3w
2l + 6w = 85
H
l = 3w
2(l + w) = 85
J
l=w+3
2l + 6w = 85
Correct Answer - H
Spring 2003 #20
A(c)(4) Linear functions. The student
formulates systems of linear equations
from problem situations, uses a variety
of methods to solve them, and
analyzes the solutions in terms of the
situation.
(B) The student solves systems of
linear equations using [concrete]
models, graphs, tables, and algebraic
methods.
If the system of linear equations 2x + y = 1 and
y = (-½)x +1 are graphed on the same
coordinate grid, which of the following is the
solution to this system of linear equations?
A
(2, 0)
B
(0, 2)
C
(0.5, 0)
D
Not here
Correct Answer - D
April 2006 #47
What is the x-coordinate of the solution to the
system of linear equations below?
4x + 5y = 8
2x – 3y = -18
F
-4
G
-3
H
3
J
4
Correct Answer - G
April 2004 #24
Which graph best represents a solution to this
system of equations?
2x – 3y = 0
x + 2y = -7
Correct Answer - J
Spring 2003 #36
Marcos had 15 coins in nickels and quarters. He
had 3 more quarters than nickels. He wrote a system
of equations to represent this situation, letting x
represent the number of nickels and y represent the
number of quarters. Then he solved the system by
graphing. What is the solution?
A
(6, 9)
B
(5, 10)
C
(9, 6)
D
(10, 5)
Correct Answer - A
Spring 2003 #47
A(c)(4) Linear functions. The student
formulates systems of linear equations
from problem situations, uses a variety
of methods to solve them, and
analyzes the solutions in terms of the
situation.
(C) For given contexts, the student
interprets and determines the
reasonableness of solutions to
systems of linear equations.
Objective 5:
The student will demonstrate an
understanding of quadratic and
other nonlinear functions.
A(d)(1) Quadratic and other nonlinear
functions. The student understands
that the graphs of quadratic functions
are affected by the parameters of the
function and can interpret and describe
the effects of changes in the parameters
of quadratic functions.
(B) The student investigates, describes,
and predicts the effects of changes in a
on the graph of y = ax2.
Which lists the functions of the form y = ax2 in
order from the widest to the narrowest graph?
Correct Answer - B
April 2006 #37
What is the effect on the graph of the
equation y = -4x2 when the equation is
changed to y = 4x2?
A The graph of y = 4x2 is translated 8 units
down.
B
The graph of y = 4x2 is a reflection of
y = -4x2 across the x-axis.
C
The graph of y= 4x2 is translated 8 units
up.
D
The graph of y = 4x2 is a reflection of
y = -4x2 across the y-axis.
Correct Answer - B
April 2004 #17
The graph of the function y = x2 is given below.
How will the graph be affected if the coefficient of
x2 is decreased to ¼?
F
The parabola will
be wider.
G
The parabola will
be narrower.
H
The parabola will
be translated up.
J
The parabola will
be translated down.
Correct Answer - F
Spring 2003 #22
A(d)(1) Quadratic and other nonlinear
functions. The student understands
that the graphs of quadratic functions
are affected by the parameters of the
function and can interpret and describe
the effects of changes in the parameters
of quadratic functions.
(C) The student investigates, describes,
and predicts the effects of changes in c
on the graph of y = x2 + c.
Shirley graphed a function of the form y = ax2 + c.
She then translated the graph 8 units up, resulting
in the function y = –⅔x2 + 5. Which of the
following best represents Shirley’s original
function?
F
y = –⅔x2 + 13
G
y = –⅔x2 – 13
H
y = –⅔x2 + 3
J
y = –⅔x2 – 3
Correct Answer - J
April 2006 #18
How does the graph of y = x2 differ from the graph
of y = x2 – 4?
A
The graph of y = x2 – 4 is wider than the graph
of y = x2.
B
The graph of y = x2 – 4 is shifted to the left of
the graph of y = x2.
C
The graph of y = x2 – 4 is shifted down from
the graph of y = x2.
D
The graph of y = x2 – 4 is narrower than the
graph of y= x2.
Correct Answer - C
April 2004 #45
A(d)(1) Quadratic and other nonlinear
functions. The student understands
that the graphs of quadratic functions
are affected by the parameters of the
function and can interpret and describe
the effects of changes in the parameters
of quadratic functions.
(D) For problem situations, the student
analyzes graphs of quadratic functions
and draws conclusions.
An object was dropped from a height of 250 meters and fell to
the ground. The graph below shows the change in h, the
objects height in meters, with respect to t, the time in seconds.
According to the graph, which time interval best represents
when the object was at 140 meters above the ground?
F
Between 3 seconds
and 3.25 seconds
G
Between 3.75 seconds
and 4 seconds
H
Between 3.5 seconds
and 3.75 seconds
J
Between 3.25 seconds
and 3.5 seconds
Correct Answer - J
April 2006 #22
The graph below shows h, the height in meters of a
model rocket, versus t, the time in seconds after the
rocket is launched. From the graph, what conclusion
can be made about the flight of the rocket?
A
The rocket reached its maximum
height after 2.5 seconds.
B
At 0 seconds, the rocket was 2
meters off the ground.
C
The height of the rocket
was 0 meters when it was
launched.
D
The rocket was in flight for 5
seconds.
Correct Answer - B
April 2004 #55
The sales record for a recent hit CD at Tony’s
Music Store is shown on the graph below. Which
statement best describes the sales of this CD?
A
Sales rapidly increased,
reached a peak, and then
gradually decreased.
B
Sales gradually increased,
reached a peak, and
then leveled off.
C
Sales rapidly increased,
reached a peak, and then
rapidly decreased.
D
Sales remained constant
throughout the time period.
Correct Answer - C
Spring 2003 #1
A(d)(2) Quadratic and other
nonlinear functions. The student
understands there is more than one
way to solve a quadratic equation and
solves them using appropriate
methods.
(A) The student solves quadratic
equations using [concrete] models,
tables, graphs, and algebraic methods.
The polynomial x2 + x – 6 is modeled below using
algebraic tiles. What are the solutions to the
equation x2 + x = 6?
A
-3 and -2
B
-3 and 2
C
3 and -2
D
3 and 2
Correct Answer - B
Spring 2003 #27
A(d)(2) Quadratic and other
nonlinear functions. The student
understands there is more than one
way to solve a quadratic equation
and solves them using appropriate
methods.
(B) The student relates the
solutions of quadratic equations to
the roots of their functions.
Which graph best represents an equation that has
the roots x = -7/2 and x = 1/2?
Correct Answer - G
April 2006 #42
What are the roots of the function graphed below?
F
(-1, -9) and (0, -8)
G
(0, -4) and (2, 0)
H
(-4, 0) and (2, 0)
J
(0, 2) and (0, -4)
Correct Answer - H
April 2004 #40
What are the roots of the quadratic equation
x2 – 3x + 2 = 0?
A
-2 and -1
B
-2 and 1
C
2 and -1
D
2 and 1
Correct Answer - D
Spring 2003 #25
A(d)(3) Quadratic and other
nonlinear functions. The student
understands there are situations
modeled by functions that are neither
linear nor quadratic and models the
situations.
(A) The student uses [patterns to
generate] the laws of exponents and
applies them in problem-solving
situations.
Marlena was asked to find an expression that is
not equivalent to 212. Which of the following is not
equivalent to the given expression?
F
(22)6
G
(28)4
H
(26)(26)
J
(23)(29)
Correct Answer - G
April 2006 #54
Which expression is equivalent to
Correct Answer - C
?
April 2004 #33
The area of a rectangle is 144a8b4 square units. If
the width of the rectangle is 8a2b2 units, what is the
length in units?
A
18a6b2 units
B
136a6b2 units
C
152a10b6 units
D
1152a10b6 units
Correct Answer - A
Spring 2003 #41
Objective 6:
The student will demonstrate an
understanding of geometric
relationships and spatial reasoning.
(8.6) Geometry and spatial
reasoning. The student uses
transformational geometry to
develop spatial sense. The student
is expected to
(A) generate similar shapes using
dilations including enlargements and
reductions;
Look at the cylinder shown below.
Which of the following cylinders is similar to the one shown?
Correct Answer - C
April 2006 #35
A copy machine can enlarge or reduce letters
proportionately. Which would not be an
enlargement or reduction of the letter below?
Correct Answer - J
April 2004 #16
Identify the drawing that shows Figure 1 under dilation to
produce Figure 2, using center of dilation (0, 0) and a scale
factor of ½.
Correct Answer - H
Spring 2003 #40
The graph below shows ∆XYZ and similar ∆X’Y’Z’. Which
statement is true when transforming ∆XYZ to ∆X’Y’Z’.
F
All the corresponding
angles will increase
by a multiple of 3.
G
All the corresponding
angles will increase
by a scale factor of ⅓.
H
All the corresponding
sides are proportional,
with a scale factor of 3.
J
All the corresponding
sides are proportional,
with a scale factor of ⅓.
Correct Answer - H
Spring 2003 #44
(8.6) Geometry and spatial
reasoning. The student uses
transformational geometry to
develop spatial sense. The student
is expected to
(B) graph dilations, reflections, and
translations on a coordinate plane.
∆KQR is translated so that R is mapped to
R’. Which ordered pair best represents
either point K’ or point Q’?
F
K’ (-3, 6)
G
Q’ (-4, -1)
H
K’ (5, -2)
J
Q’ (-3, -2)
Correct Answer - J
April 2006 #4
Pentagon PQRST is graphed on the coordinate grid
below. Which of the following points would be the
location of S’ if pentagon PQRST is dilated by a scale
factor of 2 and has a center of dilation at (0, 0)?
F
(-6, 4)
G
(2, -6)
H
(4, -6)
J
(4, -3)
Correct Answer - H
April 2006 #34
At what coordinates should vertex Z be placed to
create a quadrilateral WXYZ that is similar to
quadrilateral PQRS?
F
(24, 16)
G
(24, 24)
H
(20, 20)
J
(16, 24)
Correct Answer - F
April 2004 #10
If quadrilateral TUVW is reflected across the
x-axis, to become quadrilateral T’U’V’W’,
what will be the coordinates of W’?
F
(-4, -2)
G
(-4, 2)
H
(2, -4)
J
(4, -2)
Correct Answer - G
April 2004 #28
Identify the location of point P under translation
(x + 3, y – 2).
A
(3, -2)
B
(2, 3)
C
(-1, 0)
D
(2, 0)
Correct Answer - D
Spring 2003 #17
∆RST is translated so that R is mapped to R’. Which
set of ordered pairs best identifies points S’ and T’.
F S’ (8, 3), T’(3, 8)
G S’(4, 3), T’(9, 8)
H S’(10,-1), T’(12,-9)
J S’(10,3), T’(5,4)
Correct Answer - G
Spring 2003 #54
(8.7) Geometry and spatial
reasoning. The student uses
geometry to model and describe the
physical world. The student is
expected to
(D) locate and name points on a
coordinate plane using ordered pairs
of rational numbers.
Which of the following ordered pairs best
represents the location of point T?
Correct Answer - G
April 2006 #6
The circle shown below has a diameter of 10 units.
Which of the following ordered pairs best
represents the location of the center of the circle?
Correct Answer - J
April 2006 #52
A portion of isosceles trapezoids NPRT is shown on the
grid below. At what coordinate should vertex T be
placed to make NP parallel to RT in order to complete
isosceles trapezoid NPRT?
A
(-2, -2)
B
(-3, -2)
C
(-2, -3)
D
(-4, -5)
Correct Answer - C
April 2004 #37
Which point on the grid satisfies the conditions
x ≥ 5 and y < -1?
F
W
G
X
H
Y
J
Z
Correct Answer - F
April 2004 #48
A
M
B
N
C
P
D
Q
Correct Answer - B
Spring 2003 #51
Objective 7:
The student will demonstrate an
understanding of two- and threedimensional representations of
geometric relationships and shapes.
(8.7) Geometry and spatial
reasoning. The student uses
geometry to model and describe the
physical world. The student is
expected to
(A) draw solids from different
perspectives;
The drawing shows the top view of a 3-dimensional object.
Which of the following drawings best represents this 3dimensional object?
Correct Answer - C
April 2006 #1
Which of the following shapes could not
represent a top, front, or side view of a
trapezoidal prism?
A
A square
B
A trapezoid
C
A rectangle
D
A triangle
Correct Answer - D
April 2006 #11
Lee designed a table that appears to be a cone with a
wooden board passing through it, as shown below. Which
of the following best represents a top view of this table?
Correct Answer - B
April 2006 #45
The drawing shows the top view of a structure built with
cubes as well as the number of cubes in each column of the
structure. Which 3-dimensional view represents the same
structure?
Correct Answer - H
April 2004 #56
The drawing shows a view of a building. Which
drawing best represents the top view of this building?
Correct Answer - B
Spring 2003 #3
(8.7) Geometry and spatial
reasoning. The student uses
geometry to model and describe the
physical world. The student is
expected to
(B) use geometric concepts and
properties to solve problems in fields
such as art and architecture;
An artist painted a mural from the photograph
shown below. If the artist used a scale of ½ inch to
represent 1 foot, which of the
following best represents the
dimensions in feet of the mural?
Correct Answer - H
April 2006 #8
The blueprint dimensions for a newly
constructed house are proportional to the
house’s actual dimensions. On the blueprints
the house’s foundation measures 75 centimeters
long by 40 centimeters wide. If the house’s
foundation measures 15 meters long, what is the
foundation’s actual width?
A
8m
B
28.1 m
C
50 m
D
200 m
Correct Answer - A
April 2004 #9
Near the downtown area of a city, there is a vacant
triangular plot of land with sides that measure 22
feet, 27 feet, and 17 feet. If the city council decides
to plant an oak tree in the corner with the smallest
angle, where should the tree be planted?
A
In the corner opposite the side that is 17 feet
B
In the corner opposite the side that is 22 feet
C
In the corner opposite the side that is 27 feet
D
In the center of the triangular plot
Correct Answer - A
April 2004 #41
Mr. Harrison wants to calculate the cost of
buying a carpet to cover his rectangular living
room floor. He knows the cost per square foot of
carpet, and he knows the length, width, and
height of the living room. Which geometric
formula should Mr. Harrison use to determine the
cost of the carpet he needs?
F
c2 = a2 + b2
G
V = Bh
H
A = lw
J
P = 2l + 2w
Correct Answer - H
April 2004 #50
A blueprint of a house plan uses a scale in which
¼ inch equals 1 foot. If the length of one side of
the house is 65 feet, how many inches will the
length be on the blueprint?
F
4 in.
G
16¼ in.
H
65¼ in.
J
260 in.
Correct Answer - G
Spring 2003 #12
A regular hexagon is drawn in a circle as a design
on a window. Opposite vertices are connected by
line segments.
What is the measure of angle Y in degrees?
Record your answer and fill in the bubbles on your
answer document. Be sure to use the
correct place value.
Correct Answer - 60
Spring 2003 #21
(8.7) Geometry and spatial
reasoning. The student uses
geometry to model and describe the
physical world. The student is
expected to
(C) use pictures or models to
demonstrate the Pythagorean
Theorem.
The drawing below shows how 3 squares can be joined
at their vertices to form a right triangle.
Which is closest to the area in square
inches of the largest square?
A
1914 in.2
B
233 in.2
C
210 in.2
D
1073 in.2
Correct Answer - D
April 2006 #15
Look at the right triangle shown below. Which of the
following could be the triangle’s dimensions?
F
12, 16.8, 18.2
G
5.4, 10.6, 16
H
1.2, 1.6, 2
J
8, 10, 12.5
Correct Answer - H
April 2004 #36
The sides of squares can be used to form triangles. The areas of
the squares that form right triangles have a special relationship.
Using the dimensions of the squares shown below, determine
which set of squares will form a right triangle.
Correct
Answer
C
Spring 2003 #13
Use the Pythagorean theorem to find the figure that
is a right triangle.
Correct Answer - J
Spring 2003 #56
Objective 8:
The student will demonstrate an
understanding of the concepts and
uses of measurement and similarity.
(8.8) Measurement. The student
uses procedures to determine
measures of solids. The student is
expected to
(A) find surface area of prisms and
cylinders using [concrete] models
and nets (two-dimensional models);
The net of a right triangular prism is shown below. Use the ruler
on the Mathematics Chart to measure the dimensions of the right
triangular prism to the nearest centimeter. Which is closest to the
total surface area of this right triangular prism?
A
18 cm2
B
60 cm2
0
C
48 cm2
1
D
36 cm2
0
1
2
3
2
3
2
1
0
5
3
4
Correct
Answer
C
April 2006 #25
The net of a cylinder is shown below. Use the ruler on the
Mathematics Chart to measure the dimensions of the cylinder
to the nearest tenth of a centimeter. Which of the following
best represents the total surface area of this cylinder?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
137 cm2
G
93 cm2
H
23 cm2
J
14 cm2
Correct
Answer
F
0 1 2 3 4 5 6 7 8 9 10 11 12 13 1
F
0 1 2 3 4
April 2004 #38
(8.8) Measurement. The student
uses procedures to determine
measures of solids. The student is
expected to
(B) connect models to formulas for
volume of prisms, cylinders,
pyramids, and cones;
Look at the cylinder shown below. Which
equation best represents the volume, V, of this
cylinder in terms of π?
A
V = 16πr2
B
V = 8πr2
C
V = 4πr2
D
V = 4πr3
Correct Answer - D
April 2006 #31
A triangular prism is shown below. What is the
volume of this triangular prism?
A
192 in.3
B
240 in.3
C
384 in.3
D
480 in.3
Correct Answer - A
April 2004 #27
Steven has a cylindrical fish tank with a diameter of 8
inches and a height of 14 inches. He placed some rocks
that took up 50 cubic inches at the bottom of the tank.
Then he filled the tank with springwater to 2 inches from
the top. Which is the best strategy for determining the
volume of water the fish has for swimming?
F
π(8)2(14) – 50
G
π(8)2(14 – 2) – 50
H
π(4)2(14 – 2) – 50
J
π(14 – 2)2(4) – 50
Correct Answer - H
April 2004 #30
The net of a cube is shown below. Use the ruler on the
Mathematics Chart to measure the dimensions of the cube
to the nearest quarter inch. Which best represents the
volume of this cube to the nearest cubic inch?
A
2 in.3
B
9 in.3
C
12 in.3
D
18 in.3
0
Correct Answer - A
1
2
Spring 2003 #33
(8.8) Measurement. The student
uses procedures to determine
measures of solids. The student is
expected to
(C) estimate answers and use
formulas to solve application
problems involving surface area and
volume.
Mr. Bergman built a rectangular sandbox for his
children, as shown below. If each 50-pound bag contains
approximately 0.70 cubic foot of sand, which is closest
to the number of bags of sand that Mr. Bergman used to
completely fill this sandbox?
A 81
B 19
C 972
D 116
Correct Answer - D
April 2006 #27
The owners of Neatly Packaged Company make a
cylindrical container that has the dimensions shown
below. What is the approximate lateral surface area
available for the package label?
A
131.95 in.2
B
151.19 in.2
C
263.89 in.2
D
115.45 in.2
Correct Answer - A
April 2004 #13
Ginny made a cylindrical clay vase for her art
project. If the vase has a volume of 339 cubic
inches and a diameter of 6 inches, which is
closest to the height of the vase?
F
36 in.
G
18 in.
H
12 in.
J
3 in.
Correct Answer - H
Spring 2003 #30
(8.9) Measurement. The student
uses indirect measurement to solve
problems. The student is expected
to
(A) use the Pythagorean Theorem to
solve real-life problems;
A slide was installed at the local swimming pool, as
shown below. Which is closest to the length of the
slide?
A
29 ft
B
16 ft
C
21 ft
D
81 ft
Correct Answer - C
April 2006 #53
Mrs. Cheung hired a landscaping service to plant a row
of bushes around her triangular backyard. If the bushes
must be planted 3 feet apart, approximately how many
bushes are needed for Mrs. Cheung’s backyard?
A
23
B
25
C
28
D
32
Correct Answer - A
April 2004 #15
The drawing shows part of the plan for a new
underground lawn-sprinkler system. Which is
closest to the length of the section of plastic pipe
from point A to point C?
A
4.7 ft
B
5.7 ft
C
6.7 ft
D
7.7 ft
Correct Answer - B
Spring 2003 #11
(8.9) Measurement. The student
uses indirect measurement to solve
problems. The student is expected
to
(B) use proportional relationships in
similar shapes to find missing
measurements.
Trapezoid KMPR is similar to trapezoid LNQS. Which
is closest to the perimeter of trapezoid LNQS?
A
23 units
B
31 units
C
25 units
D
63 units
Correct Answer - A
April 2006 #7
Jeremy’s house is 45 feet wide. In a photograph
the width of the house was 2.5 inches, and its
height was 2 inches. What is the actual height of
Jeremy’s house?
A
18 ft
B
26 ft
C
32 ft
D
36 ft
Correct Answer - D
April 2006 #41
To estimate the height of her school’s gym, Nicole
sights the top of the gym wall in a mirror that she
has placed on the ground. The mirror is 3.6 meters
from the base of the gym wall.
Nicole is standing 0.5 meter
from the mirror, and her
height is about 1.8 meters.
What is the height of the
gym wall?
F
1m
G
5.9 m
H
7.2 m
J
12.96 m
Correct Answer - J
April 2004 #42
A certain parallelogram has the dimensions shown. Which
set of dimensions would produce a similar figure?
F
17.6 cm, 88 cm
G
70.4 cm, 176 cm
H
105.6 cm, 132 cm
J
140.8 cm, 220 cm
Correct Answer - H
Spring 2003 #16
(8.10) Measurement. The student
describes how changes in
dimensions affect linear, area, and
volume measures. The student is
expected to
(A) describe the resulting effects on
perimeter and area when
dimensions of a shape are changed
proportionally;
The owner of an amusement park created a circular maze
that has a diameter of 50 feet. If the owner doubles the
radius of the maze, which statement describes what will
happen to the circumference and area of the maze?
A The circumference and the area will double.
B The circumference and the area will quadruple.
C The circumference will double, and the area will quadruple.
D The circumference will quadruple, and the area will double.
Correct Answer - C
April 2006 #23
If the dimensions of a rectangle with a perimeter
of 24 inches are tripled, what will be the
perimeter in inches of the new rectangle?
Record your answer and fill in the bubbles on
your answer document. Be sure to use the
correct place value.
Correct Answer - 72
April 2004 #21
The scale of two similar quadrilaterals is 1:2.
The perimeter of the smaller quadrilateral is 80
centimeters. What is the perimeter of the larger
quadrilateral?
A
40 cm
B
80 cm
C
160 cm
D
320 cm
Correct Answer - C
Spring 2003 #55
(8.10) Measurement. The student
describes how changes in
dimensions affect linear, area, and
volume measures. The student is
expected to
(B) describe the resulting effect on
volume when dimensions of a solid
are changed proportionally.
The edges of a large cube are 4 times longer than
the edges of a small cube. How many times
greater is the volume of the large cube?
F
4 times
G
12 time
H
16 times
J
64 times
Correct Answer - J
Spring 2003 #28
Objective 9:
The student will demonstrate an
understanding of percents, proportional
relationships, probability, and statistics
in application problems.
(8.3) Patterns, relationships, and
algebraic thinking. The student
identifies proportional relationships in
problem situations and solves
problems. The student is expected to
(B) estimate and find solutions to
application problems involving
percents and proportional relationships
such as similarity and rates.
Bruce went to a barbershop for a haircut. The price
for a haircut at this barbershop is $15, tax included. If
Bruce tipped the barber 15% of the cost of the haircut
and the tax, how much change in dollars and cents
should he have received if he paid with a $20 bill?
Record your answer and fill in the bubbles on your answer
document. Be sure to use the correct place value.
Correct Answer – 2.75
April 2006 #21
Of the 32 students in Mrs. Zane’s class, 25% have
brown hair. Of the remaining students, 12.5%
have red hair. How many students in Mrs. Zane’s
class have red hair?
A
3
B
4
C
21
D
Not here
Correct Answer - A
April 2004 #29
The world’s fastest flying insect is the dragonfly.
It can fly 36 miles per hour. If a dragonfly flew in
a straight path at this rate, what distance would it
fly in 15 minutes?
F
2 mi
G
9 mi
H
25 mi
J
540 mi
Correct Answer - G
April 2004 #6
Mr. Salinas, a real estate agent, received a 5%
commission on the selling price of a house. If
his commission was $6,975, what was the
selling price of the house?
F
$7,342
G
$34,875
H
$139,500
J
$662,625
Correct Answer - H
April 2004 #42
(8.11) Probability and statistics. The
student applies concepts of theoretical
and experimental probability to make
predictions. The student is expected to
(A) find the probabilities of compound
events (dependent and independent);
Jerry has a CD case that contains 4
country music CDs, 1 rock-and-roll
CD, 2 rap CDs, and 3 Tejano CDs.
What is the probability of Jerry
randomly selecting a Tejano CD and
then, without replacing it, randomly
selecting a rap CD from his case?
Correct Answer - B
April 2006 #17
Jared has a white cube and a red
cube. The surfaces of each cube are
numbered with a unique number
from 1 to 6. If Jared tosses the
cubes, what is the probability he will
get a 4 on the white cube and an odd
number on the red cube?
Correct Answer - A
April 2004 #15
(8.11) Probability and statistics. The
student applies concepts of theoretical
and experimental probability to make
predictions. The student is expected to
(B) use theoretical probabilities and
experimental results to make
predictions and decisions.
The table below shows the results of rolling a fair number
cube 50 times during a classroom activity. What is the
difference between the theoretical probability of rolling a
number less than 4 and the experimental results recorded
in the table?
F
8%
G
79%
H
58%
J
29%
Correct Answer - F
April 2006 #44
The table shows the results of a number cube
being rolled. Based on the results, what is the
experimental probability of rolling a 1?
Correct Answer - C
April 2004 #43
(8.12) Probability and statistics. The
student uses statistical procedures to
describe data. The student is expected
to
(A) select the appropriate measure of
central tendency to describe a set of
data for a particular purpose;
Nicholas earned the following grades on his
science exams: 83, 88, 87, and 83. If Nicholas
scores a 90 on his last exam, which measure of
central tendency will give him the highest score?
F
Mode
G
Median
H
Range
J
Mean
Correct Answer - G
April 2004 #34
Given the set of data {20, 15, 10, 20, 15, 10, 20, 20, 50},
which statement best interprets the data?
F
Only the mean is 20.
G
The range of the set of data is 20.
H
The mean, median, and mode are all 20.
J
The mode and median are not the same.
Correct Answer - H
April 2004 #18
(8.12) Probability and statistics. The
student uses statistical procedures to
describe data. The student is expected
to
(C) construct circle graphs, bar graphs,
and histograms, with and without
technology.
The table shows a math department’s budget for the
upcoming school year. Which bar graph best
represents the data given in the table?
Correct Answer - J
April 2006 #56
Of the 800 students at a local high school, 200 students have no
siblings, 318 students have one sibling, 160 students have two
siblings, and the rest of the students have three or more siblings.
Use the key below to find the circle graph that best represents this
information.
Correct Answer - B
April 2004 #3
The student election committee at Chesterfield High School recorded
the number of votes that each of 4 presidential candidates received
in the student council election. A total of 240 students voted.
Charlene received 12.5% of the votes, Jimmy received 33.3%,
Stephen received 16.7%, and Lupe received 37.5%. Which bar
graph best represents the number of votes each presidential
candidate received in the student council election?
Correct Answer - D
April 2004 #39
(8.13) Probability and statistics. The
student evaluates predictions and
conclusions based on statistical data.
The student is expected to
(B) recognize misuses of graphical or
numerical information and evaluate
predictions and conclusions based on
data analysis.
Richard budgets $1200 of his
job earnings on a monthly
basis. The graph below shows
his monthly budget. Which
conclusion can be drawn from
the information given?
A More than 30% of Richard’s budget is for credit
card payments, insurance, and food combined.
B Richard budgets $384 for utilities, insurance, and
his car payment combined.
C Less than 50% of Richard’s budget is for rent,
food, and utilities combined.
D Richard budgets $228 for savings, entertainment,
and clothes combined.
Correct Answer - B
April 2006 #19
The table shows the population and the area in square miles of
some U.S. states. Which statement best describes the
relationship between the population and the area of the state?
A The larger a state’s area, the
larger its population is.
B No relationship can be
determined from the data
in the table.
C New Jersey has the smallest
population of the states in the
table because it has the smallest area.
D Texas is the largest U.S. state.
Correct Answer - B
April 2004 #39
Objective 10:
The student will demonstrate an
understanding of the mathematical
processes and tools used in problem
solving.
(8.14) Underlying processes and
mathematical tools. The student applies
Grade 8 mathematics to solve problems
connected to everyday experiences,
investigations in other disciplines, and
activities in and outside of school. The student
is expected to
(A) identify and apply mathematics to
everyday experiences, to activities in and
outside of school, with other disciplines, and
with other mathematical topics;
Mr. Harmon is planning to sell his house and
wants to paint all the rooms. A can of paint costs
$12.95 plus 7.75% sales tax and covers about 476
square feet. What other information is needed to
determine the number of cans of paint Mr.
Harmon needs to purchase?
F
The number of rooms in the house
G
The area in square feet to be painted
H
The total cost of each can of paint
J
The name of the store where Mr. Harmon
will buy the paint
Correct Answer - G
April 2004 #2
Jerry and Dan are recycling newspaper for a school
project. Together they made 21 stacks of newspaper.
Each stack is 4 feet tall. Dan can load a stack in 15
minutes, and Jerry can load a stack in 10 minutes. What
information is NOT needed to find whether they can
load all the newspaper in 2 hours if they work together?
F
The time it takes to load the newspaper.
G
The rate at which each boy loads the newspaper.
H
The height of each stack of newspaper.
J
The number of stacks of newspaper.
Correct Answer - H
Spring 2003 #48
Greta and her friends are having lunch at Joe’s
Diner. The total cost of their lunch, including tax,
is $54.63. Greta and her friends have $65.00
altogether and want to leave a tip equal to 15% of
the total bill. Is $65.00 enough to cover the cost of
their lunch and the 15% tip for the server?
F
No, they need $0.56 more.
G
No, they need $3.29 more.
H
Yes, and they have $2.18 left over.
J
Yes, they have the exact amount.
Correct Answer - H
Spring 2003 #52
(8.14) Underlying processes and
mathematical tools. The student applies
Grade 8 mathematics to solve problems
connected to everyday experiences,
investigations in other disciplines, and
activities in and outside of school. The student
is expected to
(B) use a problem-solving model that
incorporates understanding the problem,
making a plan, carrying out the plan, and
evaluating the solution for reasonableness;
The price for this year’s season tickets to a city hockey
team’s games was reduced by 15% from last year’s ticket
price, x. As a result, there was a 22% increase in the
number of season-tickets sold this year. If a total of 4000
season tickets were sold last year and each season ticket is
equally priced, which expression could be used to
determine the total sales from this year’s season tickets?
A
4000(1 + 0.22)(1 + 0.15)x
B
4000(1 + 0.22)(1 – 0.15)x
C
4000(1 – 0.22)(1 – 0.15)x
D
4000(1 – 0.22)(1 + 0.15)x
Correct Answer - B
April 2006 #9
For a spring break special, an amusement park charged
$10 per person for admission with unlimited rides. The
regular admission price is $5 per person plus $0.50 per
ride. Which of the following statements is true?
A
If a person plans to get on 10 rides, the spring
break special costs less.
B
If a person plans to get on 10 rides, the regular
admission price costs less.
C
If a person plans to get on fewer than 10 rides, the
regular admission price costs less.
D
The spring break special costs less no matter how
many rides a person plans to get on.
Correct Answer - C
April 2006 #13
A triangle is inscribed in a
square, as shown below. What
is the area of the shaded triangle
inscribed in the square?
Correct Answer - C
April 2006 #43
The school drama club plans to attend a Shakespeare
festival in 6 weeks. The total cost per person is $185.75.
The club has $296 in its account and will divide the
money equally among the 8 members who attend the
festival. Troy is planning to attend the festival and has
already saved $55. How much more money does Troy
need in order to cover his cost to attend the festival?
A
$93.75
B
$110.25
C
$148.75
D
Not here
Correct Answer - A
April 2004 #7
In the system of equations 4x + 2y = 10
and 3x + 7y = -18, which expression can
be correctly substituted for y in the
equation 3x + 7y = -18?
A
10 – 2x
B
10 + 2x
C
5 – 2x
D
5 + 2x
Correct Answer - C
April 2004 #31
What is the perimeter to the nearest centimeter of
the regular octagon drawn below?
F
41 cm
G
36 cm
H
27 cm
J
18 cm
Correct Answer - G
Spring 2003 #8
Mitch wants to use 40 feet of fencing to enclose a
flower garden. Which of these shapes would use
all the fencing and enclose the largest area?
F
A rectangle with a length of 8 feet and a
width of 12 feet
G
An isosceles right triangle with a side length
of about 12 feet
H
A circle with a radius of about 5.6 feet.
J
A square with a side length of 10 feet
Correct Answer - J
Spring 2003 #38
(8.14) Underlying processes and mathematical
tools. The student applies Grade 8 mathematics to
solve problems connected to everyday experiences,
investigations in other disciplines, and activities in
and outside of school. The student is expected to
(C) select or develop an appropriate problemsolving strategy from a variety of different types,
including drawing a picture, looking for a pattern,
systematic guessing and checking, acting it out,
making a table, working a simpler problem, or
working backwards to solve a problem.
A toad is 25 feet north of a bullfrog. Every time the
toad jumps 1 foot, the bullfrog jumps 3 feet. If both
the toad and the bullfrog jump due north, how many
jumps will it take for the bullfrog to pass the toad?
A
12
B
9
C
13
D
7
Correct Answer - C
April 2006 #29
A rectangle has an area of 144 square inches
and a perimeter of 50 inches. What are the
dimensions of the rectangle?
A
10 in. by 15 in.
B
9 in. by 16 in.
C
8 in. by 18 in.
D
4 in. by 36 in.
Correct Answer - B
April 2004 #5
Manuel has 5 more CDs than Pedro has. Bob has
twice as many CDs as Manuel has. Altogether the
boys have 63 CDs. Which equation can be used to
find how many CDs each person has?
A
5x + 2x + x = 63
B
x + (x + 5) + 2x = 63
C
x + (x + 5) + 2(x + 5) = 63
D
x + 2(5x) + 5x = 63
Correct Answer - C
Spring 2003 #35
(8.15) Underlying processes and
mathematical tools. The student
communicates about Grade 8 mathematics
through informal and mathematical language,
representations, and models. The student is
expected to
(A) communicate mathematical ideas using
language, efficient tools, appropriate units,
and graphical, numerical, physical, or
algebraic mathematical models.
Mrs. Aman asked her students to look at the
drawing shown below to determine the length of
d. Which of the following student responses best
represents the length of d?
A
8 units
B
11 units
C
14 units
D
3 units
Correct Answer - A
April 2006 #33
A circle and its diameter are shown
below. The value of π is the result of
which of the following ratios comparing
a circle’s circumference to its diameter?
Correct Answer - D
April 2004 #19
Shannon has spent $850 on gasoline and repairs for
her car in the last 6 months. Of this total, she spent
$300 on repairs. The gasoline she purchased cost
$1.29 per gallon. Which of the following can be
used to determine how many gallons of gas, g,
Shannon has bought within the last 6 months?
A
1.29g – 300 = 850
B
1.29g + 300 = 850
C
1.29 – 300g = 850
D
1.29 + 300g = 850
Correct Answer - B
April 2004 #53
Rinaldo’s school sold all of the tickets to a band concert.
The tickets cost $8 each. The auditorium where the
concert was held had 39 rows, with 56 seats in each row.
Which of the following is a correct method for Rinaldo
to calculate the total amount of ticket sales?
F Rinaldo can multiply 56 by $8 and then add $39.
G Rinaldo can add 39 and 56 and then multiply by $8.
H Rinaldo can multiply 39 and 56 and then multiply by $8.
J Rinaldo can add 56 and $8 and then multiply by 39.
Correct Answer - H
Spring 2003 #2
Which of the following is best
represented by the data in the
graph below?
F Comparing the length of a side of a
square to the square’s area.
G Comparing the length of the radius
of a circle to the circle’s
circumference.
H Comparing the length of a side of a
cube to the cube’s volume.
J Comparing the length of the diameter
of a circle to the circle’s area.
Correct Answer - H
Spring 2003 #32
(8.16) Underlying processes and
mathematical tools. The student
uses logical reasoning to make
conjectures and verify conclusions.
The student is expected to
(A) make conjectures from patterns or
sets of examples and nonexamples;
Lee, Kelly, Linda, and Madison all took the same
math test. Linda earned a lower score than Kelly,
but she did not earn the lowest score. The highest
test-scorer’s name does not begin with an L.
Madison earned a higher score than Kelly. Which
person earned the lowest score on the math test?
A
Kelly
B
Lee
C
Linda
D
Madison
Correct Answer - B
April 2006 #3
A pattern exists for digits in the ones place of the value
that results from raising 7 to the power of n, where n is
an integer greater than or equal to 1. Which digit is in
the ones place of the value of 750?
F
7
G
9
H
3
J
1
Correct Answer - G
April 2006 #30
The table shows the first-class postage rates for different
years. Which conclusion is true for the data given?
A The rate for first-class postage was
above $0.18 during the 1970s.
B The rate for first-class postage
remained below $0.32 during the 1990s.
C The rate for first-class postage remained
below $0.29 during the 1980s.
D The rate for first-class postage increased
by 4% between 1971 and 1995.
Correct Answer - C
April 2006 #51
Linda owns a set of seven wrenches. The
wrenches come in consecutive increments of 1/8
inch. Linda has misplaced a wrench. The sizes
she has are 1/8 inch, 1/4 inch, 1/2 inch, 5/8 inch,
3/4 inch, and 7/8 inch. Which size wrench is
missing from Linda’s set?
A
3/16 in.
B
3/8 in.
C
11/16 in.
D
Not here
Correct Answer - B
April 2004 #11
A pattern exists as a result of raising i, an imaginary
number, to n, an integer greater than or equal to 1.
Based on the table, which of the following best
represents i raised to the 16th power?
Correct Answer - D
April 2004 #47
A pattern exists among
the digits in the ones place
when 2 is raised to
different powers, as
shown in the table below.
For example, in 24 = 16
the number in the ones
place is 6. Which digit is
in the ones place in 238?
A
2
B
4
C
6
D
8
Correct Answer - B
Spring 2003 #23
(8.16) Underlying processes and
mathematical tools. The student
uses logical reasoning to make
conjectures and verify conclusions.
The student is expected to
(B) validate his/her conclusions using
mathematical properties and
relationships.
Stephen claims that the exterior angle for any
regular polygon is either an acute angle or an obtuse
angle. If each of the following polygons is regular,
which one could disprove Stephen’s theory?
F
Triangle
G
Quadrilateral
H
Pentagon
J
Hexagon
Correct Answer - G
April 2006 #24
Which statement about the triangles below is true?
F
All the triangles are scalene.
G
All the triangles are equiangular.
H
All the triangles are equilateral.
J
All the triangles are isosceles.
Correct Answer - J
April 2004 #22