Transcript FCAT Mathematics Sample Items for Grade 8

FCAT Mathematics Sample
Items for Grade 8
All questions are from the FCAT Mathematics Item
Specification for Grades 6 - 8
Table of Content
Strand A
Slides 3 – 16
Strand B
Slides 17 – 36
Strand C
Slides 37 – 56
Strand D
Slides 57 – 74
Strand E
Slides 75 - 89
understands the
relative size of
integers, fractions, and
decimals; numbers
expressed as
percents; numbers
with exponents;
numbers in scientific
notation; radicals;
absolute value; and
ratios.
MC
1) The coldest temperatures on record for four
southern states are -2ºF, -27ºF, -34ºF, and -17º F.
Which of the following shows these temperatures
in order from least to greatest?
A.
B.
C.
D.
-2º, -17º, -34º, -27º
-2º, -27º, -34º, -17º
-34º, -27º, -17º, -2º
-34º, -17º, -27º, -2º
understands that
numbers can be
represented in a
variety of equivalent
forms,
including integers,
fractions, decimals,
percents, scientific
notation, exponents,
radicals, and absolute
value.
(Also assesses
A.1.3.1 and A.1.3.3)
MC, GR
2) Mr. Link has harvested 27 acres of his 36-acre
orange grove, or 27/36 of the grove. What is another
way to express this number?
3/ 4
Other Correct Responses: 9/12,
0.75
understands that
numbers can be
represented in a
variety of equivalent
forms,
including integers,
fractions, decimals,
percents, scientific
notation, exponents,
radicals, and absolute
value.
(Also assesses
A.1.3.1 and A.1.3.3)
MC, GR
3) In 1992, the Orlando International Airport served
approximately 21,000,000 passengers. Which of
the following is NOT another way of expressing the
number 21,000,000?
A.
B.
C.
D.
2.1 × 107
21 × 106
21 million
2.1 million
understands that
numbers can be
represented in a
variety of equivalent
forms,
including integers,
fractions, decimals,
percents, scientific
notation, exponents,
radicals, and absolute
value.
(Also assesses
A.1.3.1 and A.1.3.3)
MC, GR
4) Steve’s friend wants to know how many students are in
Steve’s poetry club. Steve used the expression below to
represent the number of students in the club.
How many students are in Steve’s poetry club?
21
understands and uses
exponential and
scientific notation.
MC, GR
5) A space shuttle can travel at a speed of 3 × 107
meters per hour. At this speed, how far will it travel in
24 hours?
A. 3.0 × 107 meters
B. B. 3.0 × 108 meters
C. 7.2 × 107 meters
D. 7.2 × 108 meters
understands and uses
exponential and
scientific notation.
MC, GR
6) What is the value of the following expression?
93 – 54
104
understands and
explains the
effects of addition,
subtraction,
multiplication, and
division on whole
numbers, fractions,
including mixed
numbers, and
decimals, including the
inverse relationships
of positive and
negative numbers.
MC
7) When multiplying a whole number greater than 1
by a positive fraction less than 1, the product is
which of the following?
A. greater than the whole number
B. less than the whole number
C. less than the fraction
D. equal to 1
selects the appropriate
operation to solve
problems involving
addition, subtraction,
multiplication, and
division of rational
numbers, ratios,
proportions, and
percents, including the
appropriate application
of the algebraic order
of operations.
MC, GR
8) In what order should the operations be
performed in the expression below?
4+8÷2×3–1
A.
B.
C.
D.
÷, +, –, ×
÷, ×, +, –
×, +, ÷, –
+, ÷, ×, –
selects the appropriate
operation to solve
problems involving
addition, subtraction,
multiplication, and
division of rational
numbers, ratios,
proportions, and
percents, including the
appropriate application
of the algebraic order
of operations.
MC, GR
9) What is the value of the expression below?
3 −1
4+8÷2×3
1/ 8
Other Correct Responses: 2/16,
0.125
adds, subtracts,
multiplies, and
divides whole
numbers, decimals,
and fractions,
including mixed
numbers, to solve realworld problems, using
appropriate methods
of computing, such as
mental mathematics,
paper and pencil, and
calculator.
MC, GR
10) Todd bought a pair of sneakers, originally priced
at $64.95 and marked down 15%. The sale price
was then further reduced by 10%. How much did
Todd pay for the sneakers, including 6% sales
tax?
A.
B.
C.
D.
$48.71
$49.69
$51.64
$52.67
adds, subtracts,
multiplies, and
divides whole
numbers, decimals,
and fractions,
including mixed
numbers, to solve realworld problems, using
appropriate methods
of computing, such as
mental mathematics,
paper and pencil, and
calculator.
MC, GR
11) Kirk and his father are on a 200-mile bicycle trip
across Florida. They plan to ride for five days. During
the first four days, they traveled the following distances:
45.8 miles, 42 miles, 41.5 miles, and 38.4 miles. How
many more miles do Kirk and his father have to travel to
reach their 200-mile goal?
32 .3
adds, subtracts,
multiplies, and
divides whole
numbers, decimals,
and fractions,
including mixed
numbers, to solve realworld problems, using
appropriate methods
of computing, such as
mental mathematics,
paper and pencil, and
calculator.
MC, GR
12) Ramón is purchasing 2 pairs of pants priced at $21
per pair, 3 shirts priced at $10 each, and 1 pair of shoes
priced at $36. All of these prices are before tax. The
price of every item Ramón is purchasing will be reduced
by 20% when his total purchase is being calculated,
before tax is added. What dollar amount will be
subtracted from Ramón’s total purchase, before tax?
21 .6
uses estimation
strategies to
predict results and to
check the
reasonableness
of results.
(Also assesses
A.4.2.1, B.2.3.1,
and B.3.3.1)
MC
13) Margo wants to cover the top of her table with a
mosaic pattern made of different-colored tiles. The tiles
come in boxes that each contain 125 tiles. Margo has
determined that Section 1 of the table top, shown in the
drawing below, will require approximately 57 tiles to
complete the pattern.
uses estimation
strategies to
predict results and to
check the
reasonableness
of results.
(Also assesses
A.4.2.1, B.2.3.1,
and B.3.3.1)
MC
Which is closest to the whole number of boxes of
tiles Margo should purchase to complete the mosaic
design for the entire table top?
A.
B.
C.
D.
6
10
200
600
uses concrete and
graphic models
to derive formulas for
finding perimeter,
area, surface area,
circumference, and
volume of two- and
three-dimensional
shapes, including
rectangular solids and
cylinders.
(Also assesses
B.1.2.2 and B.2.3.1)
Grades 6–7 MC, GR
Grade 8 GR, SR
14) Sachi is building a brick patio and needs to determine
its total area. The dimensions of the patio are shown in the
diagram below.
11 feet
13 feet
9 feet
16 feet
uses concrete and
graphic models
to derive formulas for
finding perimeter,
area, surface area,
circumference, and
volume of two- and
three-dimensional
shapes, including
rectangular solids and
cylinders.
(Also assesses
B.1.2.2 and B.2.3.1)
Grades 6–7 MC, GR
Grade 8 GR, SR
What is the total area, in square feet, of the patio?
154
uses concrete and
graphic models
to derive formulas for
finding perimeter,
area, surface area,
circumference, and
volume of two- and
three-dimensional
shapes, including
rectangular solids and
cylinders.
(Also assesses
B.1.2.2 and B.2.3.1)
Grades 6–7 MC, GR
Grade 8 GR, SR
15) A cylindrical column 12 centimeters in diameter is
strengthened by wrapping one steel band around the
base of the column, with no overlap. What should be the
length of the steel band in centimeters (cm)?
264 / 7
Other Correct Responses: 37.68,
37.71
uses concrete and
graphic models
to derive formulas for
finding perimeter,
area, surface area,
circumference, and
volume of two- and
three-dimensional
shapes, including
rectangular solids and
cylinders.
(Also assesses
B.1.2.2 and B.2.3.1)
Grades 6–7 MC, GR
Grade 8 GR, SR
16) Calvin is preparing a training schedule and needs to
determine the distance around the school track. The
track coach gave him the drawing below and told him
that the track is composed of two straight segments with
the ends of the track in the shape of semicircles with a
radius of 35 meters.
90 meters
35 meters
35 meters
What is the distance around the track? In the Answer
Book, show your work or explain in words how you
determined the distance.
uses concrete and
graphic models
to derive formulas for
finding perimeter,
area, surface area,
circumference, and
volume of two- and
three-dimensional
shapes, including
rectangular solids and
cylinders.
(Also assesses
B.1.2.2 and B.2.3.1)
Grades 6–7 MC, GR
Grade 8 GR, SR
In the Answer Book Show your work or explain in words
how you determined the distance.
Distance __________________
A correct and complete response includes the distance
and valid work or explanation as shown below.
•A distance ≈ 400 meters or 399.8 meters or 70π+ 180
meters (using 3.14 for π)
AND
Valid work that leads to a correct response (using22/7 for
π): 90 m + 90 m = 180 m,22/7 × 70 = 220 m,220 m + 180
m = 400 m
OR an explanation similar to the following:
The length of the two straight segments of the track is 90
m + 90 m = 180 m. The distance around one end of the
track is half the distance around a circle. The distance
around both ends of the track is the circumference of a
circle.
uses concrete and
graphic models
to derive formulas for
finding rates, distance,
time, and angle
measures.
(Also assesses
B.1.2.2 and B.2.3.1)
Grade 6 (Assessed
with C.1.3.1)
Grades 7–8 MC, GR
17) Under water, a sound wave travels 73,920 feet in 14
seconds. What is the speed of a sound wave in feet per
second?
5280
uses concrete and
graphic models
to derive formulas for
finding rates, distance,
time, and angle
measures.
(Also assesses
B.1.2.2 and B.2.3.1)
Grade 6 (Assessed
with C.1.3.1)
Grades 7–8 MC, GR
18) Dominic drove from Salt Lake City, Utah, to Bryce
Canyon National Park in 6 hours and 45 minutes at an
average speed of 48 miles per hour. What is his driving
distance, in miles?
A.
B.
C.
D.
208
302.4
309.6
324
19) The drawing below shows the distances, in miles,
between some Florida cities.
uses concrete and
graphic models
to derive formulas for
finding rates, distance,
time, and angle
measures.
(Also assesses
B.1.2.2 and B.2.3.1)
Grade 6 (Assessed
with C.1.3.1)
Grades 7–8 MC, GR
uses concrete and
graphic models
to derive formulas for
finding rates, distance,
time, and angle
measures.
(Also assesses
B.1.2.2 and B.2.3.1)
Grade 6 (Assessed
with C.1.3.1)
Grades 7–8 MC, GR
Henry will drive from Ft. Myers to Naples and then will drive
along the Tamiami Trail to Miami at an average rate of 60
miles per hour. How many hours should it take Henry to drive
nonstop from Ft. Myers to Miami using this route?
2. 4
understands and
describes how the
change of a figure in
such dimensions as
length, width, height,
or radius affects its
other measurements
such as perimeter,
area, surface
area, and volume.
(Also assesses
C.2.3.1)
MC, GR
20) A park sculpture has a base in the shape of a
rectangular prism. The sculpture’s base has a volume of
960 cubic inches. An artist is making a model of the
sculpture with dimensions half the size of the actual
sculpture. What is the volume of the base on the artist’s
model?
A.
B.
C.
D.
120 cubic inches
240 cubic inches
480 cubic inches
960 cubic inches
understands and
describes how the
change of a figure in
such dimensions as
length, width, height,
or radius affects its
other measurements
such as perimeter,
area, surface
area, and volume.
(Also assesses
C.2.3.1)
MC, GR
21) A rectangular lot on wildlife preserve land has
dimensions of 5 miles by 8 miles. If the dimensions of the
lot are doubled, by how many times will the area
increase?
4
understands and
describes how the
change of a figure in
such dimensions as
length, width, height,
or radius affects its
other measurements
such as perimeter,
area, surface
area, and volume.
(Also assesses
C.2.3.1)
MC, GR
22) Meri will increase the length of her rectangular patio
and rectangular driveway by 5 feet, as shown in the
diagram below.
understands and
describes how the
change of a figure in
such dimensions as
length, width, height,
or radius affects its
other measurements
such as perimeter,
area, surface
area, and volume.
(Also assesses
C.2.3.1)
MC, GR
By how many square feet will the total area of the patio
and driveway increase when the length of each is
increased as shown?
150
constructs, interprets,
and uses scale
drawings such as
those based on
number lines and
maps to solve realworld problems.
(Also assesses
B.2.3.1)
MC, GR
23) Hector is going to visit relatives in Bellville this summer.
He wants to know how far Bellville is from his home in
Aimsworth. He found the map below.
On the map, Hector
measured a total of 3
inches from Aimsworth to
Bellville. Based on the map
scale above, how many
miles is it from Aimsworth to
Bellville?
A.15 miles
B.30 miles
C.50 miles
D.60 miles
constructs, interprets,
and uses scale
drawings such as
those based on
number lines and
maps to solve realworld problems.
24) Carmello is making a model of our solar system. He
wants his model to look like the one shown below.
(Also assesses
B.2.3.1)
MC, GR
The average distance between the orbital paths of
Mercury and Venus is approximately 31.2 million miles.
According to the scale above, how far apart, in
centimeters, should the orbital paths be on the model?
constructs, interprets,
and uses scale
drawings such as
those based on
number lines and
maps to solve realworld problems.
(Also assesses
B.2.3.1)
MC, GR
The average distance between the orbital paths of
Mercury and Venus is approximately 31.2 million miles.
According to the scale above, how far apart, in
centimeters, should the orbital paths be on the model?
5 .2
constructs, interprets,
and uses scale
drawings such as
those based on
number lines and
maps to solve realworld problems.
(Also assesses
B.2.3.1)
MC, GR
25) Mr. Ogimachi will travel from Holt City to Valley View for
a business trip. He plans to leave Holt City at 6:45 a.m. He
used the map below to estimate the distance from Holt City
to Valley View, and determined the distance on the map to
be 9 centimeters (cm).
constructs, interprets,
and uses scale
drawings such as
those based on
number lines and
maps to solve realworld problems.
(Also assesses
B.2.3.1)
MC, GR
If Mr. Ogimachi drives at an average rate of 60
kilometers (km) per hour without stopping, which of the
following is closest to the time he should arrive in Valley
View?
A.
B.
C.
D.
8:20 a.m.
8:25 a.m.
9:00 a.m.
10:45 a.m.
solves problems
involving units of
measure and converts
answers to a larger or
smaller unit within
either the metric or
customary system.
MC, GR
26) The round steel rod shown below is 5.75 feet long. If a
steelworker cuts the steel rod into 10 equal pieces,
approximately how many inches long will each piece be?
A.
B.
C.
D.
0.479 inches
0.575 inches
5.75 inches
6.9 inches
solves problems
involving units of
measure and converts
answers to a larger or
smaller unit within
either the metric or
customary system.
MC, GR
27) The distance from Robert’s house to a boat dock is 425
meters. Robert walks to the dock and back to his house each
day. After 3 days, how far, in kilometers, will Robert have
walked?
2 .55
28) Triangle ABC is an isosceles triangle.
understands the basic
properties of,
and relationships
pertaining to, regular
and irregular
geometric shapes in
two and three
dimensions.
(Also assesses
C.1.2.1)
What is the measure of Angle A?
MC
A. 44°
B. 68°
C. 112°
D. 136°
29) The figure below is composed of several triangles.
understands the basic
properties of,
and relationships
pertaining to, regular
and irregular
geometric shapes in
two and three
dimensions.
(Also assesses
C.1.2.1)
MC
Which of the following pairs of line segments in the figure
must be parallel?
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
30) Before she can enter a race, Jasmine needs to know
the height of her sailboat. Jasmine is 5 feet tall and casts a
shadow 6 feet long, as shown below.
If the lengths of the sailboat’s shadow and Jasmine’s
shadow at the same time of day are known, which of
the following properties could be used to find the height
(h), in feet, of the sailboat?
A. congruency
B. parallelism
C. symmetry
D. similarity
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
31) Look at the figures below showing a floor tile design.
Figure 1 was transformed to make the new design in Figure 2
using only two steps.
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
Complete the following in the Answer Book:
Part A
Explain in words how Figure 1 can be transformed to
Figure 2 in only two steps. Use mathematical terms to
describe the transformation.
Part B
On the grid, draw Figure 3 by making the following
transformations to Figure 2: Rotate Figure 2 ninety
degrees clockwise around point D and reflect the rotated
figure over vertical line n. Be sure to label this new figure
as Figure 3, and also label points A, B, C, and D.
Part C
Explain in words whether Figures 1, 2, and 3 are
congruent or not, and why.
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
A correct and complete response includes appropriate
Response explanations and an appropriate drawing.
Part A
• An explanation similar to the following:
First I reflected Figure 1 over line n. Then I rotated it
clockwise 90° about point C1.
• OR
I rotated Figure 1 90° counterclockwise about point C and
reflected it over line n.
• OR other valid explanation
AND
Part B
• Correctly drawn and labeled figure, as shown on the grid.
AND
Part C
• An explanation similar to the following:
All three figures are congruent because their size and shape
are exactly the same; only their positions are different.
• OR other valid explanation.
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
32) The diagram below shows a side view of a bridge. In
the diagram, ABC is congruent to DEF.
Which statement about BAC and DEF must be true?
A. They must have equal measures
B. They must each measure at least 45 degrees
C. Their measures must have a sum of 90 degrees
D. Their measures must have a sum of 180 degrees
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
33) The Wilford Outdoor Advertising Agency sought a building
whose side was tall enough to accommodate an 18-meter high
rectangular billboard. The advertising artist found a building he
thought might work. He is 2 meters tall and on the morning he
examined the building, he cast a shadow 0.5 meter long, while
the building cast a shadow 4 meters long.
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
Part A
Write a proportion which could be used to find the height of the
side of the building. Let x represent the height of the side of
the building in meters.
Part B
Use your proportion in Part A to find the
height of the building. Show all work
necessary to justify your answer.
Part C
The advertising artist came back to the
building at 4:00 in the afternoon to recheck
the building. At that time, his shadow was
1.5 meters long. How long, in meters, should
the building’s shadow have been at that
time? Show all work necessary to justify
your answer.
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
understands the
geometric concepts
of symmetry,
reflections,
congruency, similarity,
perpendicularity,
parallelism, and
transformations,
including flips
(reflections),
slides (translations),
turns (rotations), and
enlargements.
(Also assesses
B.1.3.3, C.1.2.1,
C.1.3.1, and C.3.3.1)
Grades 6–7 MC
Grade 8 MC, ER
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
34) Jack wants to make ΔLMN similar to ΔPQR. He has
plotted points L and M on the grid below and needs to
place point N. Which of the following coordinates of point N
would make ΔLMN similar to ΔPQR?
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
A. ( 0, -1)
B. (-3, -1)
C. (-1, -1)
D. (-6, -1)
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
35) You are designing a camping tent with an octagonshaped base and have drawn a diagram of the base on the
coordinate grid below.
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
Complete the following in the Answer Book:
Part A
How many lines of symmetry does this diagram have?
Part B
Draw all the lines of symmetry on the diagram and
determine the coordinates for the point at which the
lines intersect.
A correct and complete response includes the correct
Response number of lines of symmetry, a correct drawing of
the lines of symmetry on the grid, and the correct coordinates
for the point of intersection as shown below.
Part A
• Lines of symmetry = 4
AND
Part B
• Four lines of symmetry correctly drawn on the diagram
• AND Coordinates = (4, 3)
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
36) In architecture, coordinate planes are used to help
make design layouts for buildings. The grid below
represents a building layout with several points plotted.
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
Part A
On the coordinate plane above, plot and label points C
(-5, -2) and F (6, 9).—– —– —– —– Then draw the
following line segments: AC, BC, DF, and EF.
Part B
The distance between points C and F is the widest part
of the building. What is the width, in feet, of the widest
part of the building? Show all work necessary to justify
your answer.
Top-Score Response
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
Top-Score Response
represents and applies
geometric properties
and relationships to
solve real-world
and mathematical
problems.
(Also assesses
C.2.3.1, C.2.3.2, and
C.3.2.2)
Grades 6 MC
Grades 7 MC, GR
Grade 8 MC, SR
37) What are the coordinates of the y-intercept of line QR?
identifies and plots
ordered pairs in
all four quadrants of a
rectangular coordinate
system (graph) and
applies simple
properties of lines.
MC
A. (2, 0)
B. (0, 2)
C. (-1, 0)
D. (0, -1)
38) A graphic artist has drawn the pattern shown below.
describes a wide
variety of patterns,
relationships, and
functions through
models, such as
manipulatives, tables,
graphs, expressions,
equations, and
inequalities.
(Also assesses
A.5.3.1)
MC, GR
If the artist continues the pattern, what will Row 15 look like?
39) Use the function table to find the value of y when x = 5.
describes a wide
variety of patterns,
relationships, and
functions through
models, such as
manipulatives, tables,
graphs, expressions,
equations, and
inequalities.
(Also assesses
A.5.3.1)
MC, GR
16
40) The diagram below shows some rows of Pascal’s triangle.
describes a wide
variety of patterns,
relationships, and
functions through
models, such as
manipulatives, tables,
graphs, expressions,
equations, and
inequalities.
(Also assesses
A.5.3.1)
MC, GR
Which of the following should be in row 5 of Pascal’s triangle?
describes a wide
variety of patterns,
relationships, and
functions through
models, such as
manipulatives, tables,
graphs, expressions,
equations, and
inequalities.
(Also assesses
A.5.3.1)
MC, GR
41) The femur, or thighbone, is the longest bone in the
human body. Scientists can calculate a person’s approximate
height by measuring the length of the person’s femur. The
table below shows the linear relationship between femur
length (f) and a person’s height (h).
describes a wide
variety of patterns,
relationships, and
functions through
models, such as
manipulatives, tables,
graphs, expressions,
equations, and
inequalities.
(Also assesses
A.5.3.1)
MC, GR
A scientist measures a human femur bone that is 40
centimeters long. What is the value of h when f has a
value of 40?
169
creates and interprets
tables, graphs,
equations, and verbal
descriptions to
explain cause-andeffect relationships.
(Also assesses
A.5.3.1)
Grades 6–7 MC, GR
Grade 8 MC, GR, SR
42) A holiday shop buys a box of ornaments for $51.00
and resells them for $7.00 per ornament. If x represents
the number of ornaments in a box, which of the following
expressions could be used to find the difference
between the selling price and the cost of one box of
ornaments?
A. 7x + 51
B. 7x − 51
C. 51x + 7
D. 51x − 7
43) What is the value of the expression -3x + 7, when x = -6?
creates and interprets
tables, graphs,
equations, and verbal
descriptions to
explain cause-andeffect relationships.
(Also assesses
A.5.3.1)
Grades 6–7 MC, GR
Grade 8 MC, GR, SR
25
creates and interprets
tables, graphs,
equations, and verbal
descriptions to
explain cause-andeffect relationships.
44) Lyndsey is designing a border using a row of hexagonal
tiles with each side measuring 1 foot. She made the following
table to determine the perimeter of the border as the number
of tiles used increases.
(Also assesses
A.5.3.1)
Grades 6–7 MC, GR
Grade 8 MC, GR, SR
Part A
Write a rule or expression that could be used to determine
the perimeter of the border using any number of tiles (n).
Part B
Based on the rule or expression you wrote in Part A, what
will be the perimeter if Lyndsey uses 25 tiles in her
border?
Top-Score Response
A correct and complete response includes a correct
rule or expression and the correct answer for 25 tiles.
creates and interprets
tables, graphs,
equations, and verbal
descriptions to
explain cause-andeffect relationships.
(Also assesses
A.5.3.1)
Grades 6–7 MC, GR
Grade 8 MC, GR, SR
Valid expression equivalent to the following: 4n + 2
OR
Valid rule similar to the following:
Multiply the number of tiles by four
and then add two.
OR
other valid rule or expression written in words or
symbols
AND
Valid answer equivalent to the following:
4(25) + 2 100 + 2
Perimeter = 102 feet
45) The equation below is used to find C, the total charge in
dollars, not including tax, for a purchase of company jackets
( j) that have a specific design and color.
creates and interprets
tables, graphs,
equations, and verbal
descriptions to
explain cause-andeffect relationships.
(Also assesses
A.5.3.1)
Grades 6–7 MC, GR
Grade 8 MC, GR, SR
100
C  j (20 
)
j
What is the total charge, not including tax, for a purchase of
300 jackets?
A. $120
B. $200
C. $6100
D. $36,000
represents and solves
real-world problems
graphically, with
algebraic expressions,
equations, and
inequalities.
(Also assesses
A.1.3.3)
Grades 6–7 MC
Grade 8 MC, SR
46) In professional ice hockey, a team earns 2 points
for a win, 1 point for a tie, and 0 points for a loss.
During the first half of the 1996-1997 season, one
team had 8 losses and 10 ties, and had earned 62
points. Which of the following equations could be
used to determine the number of wins (w) this
team had?
A.
B.
C.
D.
62 = w + 8
62 = w + 10
62 = 2w + 10
62 = 2w + 8
represents and solves
real-world problems
graphically, with
algebraic expressions,
equations, and
inequalities.
(Also assesses
A.1.3.3)
Grades 6–7 MC
Grade 8 MC, SR
47) The average yearly rainfall for a town in California is 14
inches. For the past 10 years, the yearly rainfall has been not
more than 6 inches above or below that average. Which
number line below shows the range of the yearly rainfall for
the past 10 years?
represents and solves
real-world problems
graphically, with
algebraic expressions,
equations, and
inequalities.
(Also assesses
A.1.3.3)
Grades 6–7 MC
Grade 8 MC, SR
48) A shop owner buys a box of identical photo albums
for $51.00 and sells them for $7.00 per photo album. If
x represents the number of photo albums in a box,
which of the following expressions could be used to
find the difference between the total selling price and
the cost of 1 box of photo albums?
A.
B.
C.
D.
7x + 51
7x - 51
51x + 7
51x - 7
represents and solves
real-world problems
graphically, with
algebraic expressions,
equations, and
inequalities.
(Also assesses
A.1.3.3)
Grades 6–7 MC
Grade 8 MC, SR
49) Samuel went with his family to Alligator Park. While
they were waiting for the alligator show to start, a park
employee told their group that if there were 3 more
alligators in the pond, there would be a total of 140 legs
on the alligators in the water.
Part A
Write an equation that could be used to determine the
number of alligators (a) in the pond. (Assume that each
alligator has 4 legs).
Part B
Solve your equation from Part A to determine the number
of alligators in the pond.
Top-Score Response
represents and solves
real-world problems
graphically, with
algebraic expressions,
equations, and
inequalities.
A correct and complete response includes
the correct equation and the correct
answer as shown below.
(Also assesses
A.1.3.3)
• OR other valid equation
•An equation equivalent to the following:
4n + 12 = 140
AND
Grades 6–7 MC
Grade 8 MC, SR
• The number of alligators = 32
uses algebraic
problem-solving
strategies to solve
real-world problems
involving linear
equations and
inequalities.
MC, GR
50) Miko is flying her plane within its safety limit at
an altitude of 35,000 feet. To avoid a storm, she
ascends 5,500 feet without going past the plane's
safety limit. Based on the inequality of a + 5,500 ≤
35,000, where a represents the original altitude in
feet, which of the following could be the original
altitude of the plane?
A.
B.
C.
D.
40,000 feet
30,000 feet
29,750 feet
27,750 feet
uses algebraic
problem-solving
strategies to solve
real-world problems
involving linear
equations and
inequalities.
51) The Chatham County Water Department charges a
monthly administrative fee of $9.40 and $0.0049 for each
gallon of water used up to 5,000 gallons. The equation to
figure the total cost, C, for use of up to 5,000 gallons is
C = 9.4 + (g × 0.0049),
where g is the number of gallons up to 5,000. What will be
the monthly charge for a customer who used 4,100 gallons
of water in one month?
29. 4 9
MC, GR
uses algebraic
problem-solving
strategies to solve
real-world problems
involving linear
equations and
inequalities.
52) The Chatham County Water Department charges a
monthly administrative fee of $9.40 and $0.0049 for each
gallon of water used up to 5,000 gallons. The equation to
figure the total cost, C, for use of up to 5,000 gallons is
C = 9.4 + (g × 0.0049),
where g is the number of gallons up to 5,000. If a
customer’s total cost was $29.49 for one month, what was
the total number of gallons of water used that month?
4100
MC, GR
collects, organizes,
and displays data in a
variety of forms,
including tables, line
graphs, charts, bar
graphs, to determine
how different ways of
presenting data can
lead to different
interpretations.
(Also assesses
E.1.3.3)
Grades 6–7 MC, GR
Grade 8 MC, GR, ER
53) Each water molecule is made up of one oxygen atom that
weighs approximately 16 atomic mass units (amu) and two
hydrogen atoms that each weigh approximately 1 amu. Which
of the displays below best shows the weight of an oxygen
atom in proportion to the weight of the whole water molecule?
54) The plot below shows the heart rate for Micah’s
students halfway through a kickboxing exercise class.
collects, organizes,
and displays data in a
variety of forms,
including tables, line
graphs, charts, bar
graphs, to determine
how different ways of
presenting data can
lead to different
interpretations.
(Also assesses
E.1.3.3)
Grades 6–7 MC, GR
Grade 8 MC, GR, ER
collects, organizes,
and displays data in a
variety of forms,
including tables, line
graphs, charts, bar
graphs, to determine
how different ways of
presenting data can
lead to different
interpretations.
(Also assesses
E.1.3.3)
Grades 6–7 MC, GR
Grade 8 MC, GR, ER
Micah said the optimum heart rate should be between
110 and 140 beats per minute. How many of the
students’ heart rates shown on the plot are between
110 and 140 beats per minute?
14
collects, organizes,
and displays data in a
variety of forms,
including tables, line
graphs, charts, bar
graphs, to determine
how different ways of
presenting data can
lead to different
interpretations.
(Also assesses
E.1.3.3)
Grades 6–7 MC, GR
Grade 8 MC, GR, ER
55) Some students were asked in which room of the home
they prefer to do homework. The table below shows the
number of students who prefer to study in one of four different
rooms.
Part A
On the grid, construct a bar graph to show the number of
students who study in each room.
Part B
Complete the circle graph using the percent of students who
prefer to study in each room.
Part C
Determine which graph most clearly shows that more than half
of the students prefer to study in the bedroom or the kitchen.
Top-Score Response
A correct bar graph similar to the following:
collects, organizes,
and displays data in a
variety of forms,
including tables, line
graphs, charts, bar
graphs, to determine
how different ways of
presenting data can
lead to different
interpretations.
(Also assesses
E.1.3.3)
Grades 6–7 MC, GR
Grade 8 MC, GR, ER
· OR other valid bar graph
AND
• A correct circle graph similar to the following:
collects, organizes,
and displays data in a
variety of forms,
including tables, line
graphs, charts, bar
graphs, to determine
how different ways of
presenting data can
lead to different
interpretations.
(Also assesses
E.1.3.3)
Grades 6–7 MC, GR
Grade 8 MC, GR, ER
• OR other valid circle graph
AND
• An explanation similar to the following:
The circle graph is better because it clearly shows that more
than half of the students prefer to study in the bedroom or the
kitchen.
OR
The bar graph is better because it shows that more than 500
students prefer to study in the bedroom or the kitchen.
• OR other valid explanation.
56) The land areas of the seven continents are listed in the
table below.
understands and
applies the concepts
of range and central
tendency (mean,
median, and mode).
(Also assesses
E.1.3.3)
MC, GR
What is the approximate mean land area of
the seven continents?
A.
B.
C.
D.
17.3 million square miles
14.0 million square miles
8.3 million square miles
6.9 million square miles
understands and
applies the concepts
of range and central
tendency (mean,
median, and mode).
57) Julio is doing a report about the quality of life in various
countries. He found the following information about life
expectancy.
(Also assesses
E.1.3.3)
MC, GR
What is the median life expectancy of people living in the
countries listed above?
understands and
applies the concepts
of range and central
tendency (mean,
median, and mode).
(Also assesses
E.1.3.3)
MC, GR
66
compares
experimental results
with mathematical
expectations of
probabilities.
58) Pat is taking a vacation to a health spa. She has
decided to participate in 1 sporting activity and 2
cooking activities while at the spa. Her choices in
each category are shown below.
MC
How many combinations of 1 sporting activity and 2
cooking activities could Pat choose from while at the spa?
A.
B.
C.
D.
32
24
18
12
compares
experimental results
with mathematical
expectations of
probabilities.
MC
59) A national ice cream company conducted a survey
with a random sample of 100 people to find out which
flavors of ice cream people like best. The results are
shown below.
compares
experimental results
with mathematical
expectations of
probabilities.
Beth and Stuart conducted the same survey during lunch
with a sample of 25 students and got the results shown
below.
MC
If the results of Beth and Stuart’s survey had been like the
national results, how many more students would have
picked vanilla as their favorite ice cream?
A.
B.
C.
D.
7 students
11 students
28 students
43 students
determines odds for
and odds against a
given situation.
(Also assesses
E.2.2.2)
MC
60) While playing for a local baseball team, Jamal hit the
ball 20 out of 30 times at bat. Based on this record, what
would be the odds in favor of Jamal hitting the ball the
next time he comes up to bat?
A.
B.
C.
D.
3 to 2
2 to 3
2 to 1
1 to 2
determines odds for
and odds against a
given situation.
(Also assesses
E.2.2.2)
MC
61) In a group of 30 people, 27 are right-handed and the
others are left-handed. If one person is selected at
random from this group, what is the probability that the
person selected will be left-handed?
formulates
hypotheses, designs
experiments, collects
and interprets data,
and evaluates
hypotheses by making
inferences and
drawing conclusions
based on statistics
(range, mean, median,
and mode) and tables,
graphs, and charts.
(Also assesses
E.3.3.2)
MC
62) As a tree ages, the trunk of the tree gets bigger.
Scientists can estimate the age of a tree by measuring
the distance around, or the circumference of, the tree
trunk. A team of scientists believe that the trees in Florida
are older than the trees in Georgia, Alabama, and
Mississippi. In which of the following geographic areas
should the scientists measure the circumference of 200
trees to best test their hypothesis?
A.
B.
C.
D.
one area of each state
one area of Florida
various areas of each state
various areas of Florida