1. science
2. mathematics

2010
Grade 9
FCAT Mathematics
Sample Questions
The intent of these sample test materials is to orient teachers and students to the types of
questions on FCAT tests. By using these materials, students will become familiar with the types
of items and response formats that they will see on the actual test. The sample test materials are
not intended to demonstrate the length of the actual test, nor should student responses be used
as an indicator of student performance on the actual test. Additional information about test
items can be found in the FCAT Test Item Specifications at http://fcat.fldoe.org/fcatis01.asp and
previously released FCAT tests at http://fcat.fldoe.org/fcatrelease.asp.
When the 2010 FCAT Mathematics tests and associated sample test materials were developed,
the State of Florida was in the process of revising the Sunshine State Standards in mathematics.
These newer standards were not yet approved for use in Florida’s schools, so it was not feasible
to incorporate these new standards into the 2010 FCAT Mathematics tests. The portion of the
2010 FCAT Mathematics tests that will be used to calculate student results and school grades in
2010 will be composed of items that assess mastery of the 1996 Sunshine State Standards. The
2010 FCAT Mathematics tests will contain field test items that assess mastery of the 2007
Sunshine State Standards. Student performance on these items will not be used to calculate
student results or school grades, but data will be gathered and examined so these items can be
considered for use on future tests, including those assessing the newer standards.
Directions for Answering the Mathematics Sample Questions
Mark your answers on the Mathematics Sample Answer Sheet, which begins on page 13 of this
book. If you don’t know how to work a problem, ask your teacher to explain it to you. Your
teacher has the answers to the sample questions. Beginning in 2010, the sample questions will be
distributed to students in print and will be available online, but the sample answers for teachers
will only be available online at http://fcat.fldoe.org/fcatsmpl.asp.
You may need formulas and conversions to help you solve some of the problems. You may refer
to the Reference Sheets on pages 5 and 6 as often as you like.
Rulers are NOT to be used with the Grade 9 FCAT Mathematics Sample Questions.
Use the space in your Mathematics Sample Questions Book to do your work on the multiplechoice and gridded-response questions, but be sure to put your answers on the Sample
Answer Sheet.
Helpful Hints for Taking the FCAT Mathematics Test
1) When starting a new problem, always clear your calculator by pressing the On/Clear key.
2) If you see an E in the display, clear the error before you begin.
3) If you see an M in the display, clear the memory and the calculator before you begin.
4) Remember, your calculator will NOT automatically perform the algebraic order of operations.
5) The negative sign may appear either to the left or to the right of the number.
6) When solving any mathematics item, do not round decimal equivalents and/or approximations until the final
step of the item or task. Focus on whether the item specifies the decimal place, equivalent fraction, and/or pi
approximation needed for the answer. In most cases, front-end estimation and truncation are not accurate
processes for estimation.
Solar Cell
Memory Indication
Negative Sign
Display
Error Indication
Memory Keys
On/Clear
CALCULATOR MODEL
Sign Change
Percent
ON/C MRC
+
M–
OFF
Off
–
7
8
9
÷
Division
%
4
5
6
×
Multiplication
1
2
3
–
Subtraction
0
•
=
+
Addition
Square Root
Clear Entry
M+
CE
Equal Sign
Decimal Point
Page 2
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
How to Complete the Grade 9 Response Grids
Mathematics test questions with this symbol require that you fill in a grid on your
answer sheet. There may be more than one correct way to fill in a response grid.
This section shows you different ways the response grids may be completed.
Grade 9 response grids have the following parts:
answer boxes
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fraction bar
decimal point
number bubbles
Directions
1. Work the problem and find an answer.
2. Write your answer in the answer boxes at the top of the grid.
• Print your answer with the first digit in the left answer box OR with the last digit in the right
answer box.
• Print only one digit or symbol in each answer box. Do NOT leave a blank answer box in the
middle of an answer.
• Be sure to write a decimal point or fraction bar in the answer box if it is a part of the answer.
3. Fill in a bubble under each box in which you wrote your answer.
• Fill in one and ONLY one bubble for each answer box. Do NOT fill in a bubble under an
unused answer box.
• Fill in each bubble by making a solid black mark that completely fills the circle.
• You MUST fill in the bubbles accurately to receive credit for your answer.
Whole Number
60 + 10 =
70
70
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Decimal
Show the decimal
6
equivalent of 5 100 .
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FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
5 . 06
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Decimal or Fraction
You may NOT write a mixed number such as 13 14 in the answer grid. If your
answer is a mixed number, you must convert the answer to an improper fraction,
such as
53
4
, or to a decimal number, such as 13.25. If you tried to fill in 13 14 , it
would be read as
131
4
and would be counted wrong.
CORRECT
12 34 +
1
2
=
53 / 4
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INCORRECT
1 3 . 25
OR
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FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
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Grade 9 and Retake FCAT Mathematics Reference Sheet
Area
Triangle
KEY
1
A = 2 bh
Rectangle
A = lw
Trapezoid
A = 2 h (b1 + b2)
1
b
h
l
w
S.A.
=
=
=
=
=
=
base
height
length
width
slant height
surface area
d
r
A
C
V
=
=
=
=
=
diameter
radius
area
circumference
volume
Use 3.14 or 22
for π.
7
Parallelogram
A = bh
A = π r2
Circle
Volume/Capacity
Circumference
C = πd or C = 2πr
Total Surface Area
1
1
S.A. = 2 (2πr) + πr2 or S.A. = πr + πr2
1
S.A. = 4( 12 l ) + l 2 or S.A. = 2l + l 2
V = 3 πr3
4
S.A. = 4πr2
V = πr2 h
S.A. = 2πrh + 2πr2
Right Circular
Cone
V = 3 πr2 h
Right Square
Pyramid
V = 3 l wh
Sphere
Right Circular
Cylinder
Rectangular Prism V = l wh
S.A. = 2(l w) + 2(hw) + 2(l h)
In the following formulas, n represents the number of sides.
• In a polygon, the sum of the measures of the interior angles is equal to 180(n − 2).
• In a regular polygon, the measure of an interior angle is equal to 180(n − 2) . n
Page 5
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
Grade 9 and Retake FCAT Mathematics Reference Sheet Distance between two points
Pythagorean theorem:
P1 (x1, y1) and P2 (x2, y2):
c
a
a2 + b 2 = c2
b
(x2 − x1)2 + (y2 − y1)2
Midpoint between two points
P1 (x1, y1) and P2 (x2, y2):
Slope-intercept form of an equation
of a line:
( x +2 x , y +2 y )
2
1
2
1
y = mx + b
where m = slope and b = the y-intercept.
Distance, rate, time formula:
Simple interest formula:
I = prt
d = rt
where d = distance, r = rate, t = time.
where p = principal, r = rate,
t = time.
Conversions
1 yard = 3 feet = 36 inches
1 mile = 1,760 yards = 5,280 feet
1 acre = 43,560 square feet
1 hour = 60 minutes
1 minute = 60 seconds
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 liter = 1000 milliliters = 1000 cubic centimeters
1 meter = 100 centimeters = 1000 millimeters
1 kilometer = 1000 meters
1 gram = 1000 milligrams
1 kilogram = 1000 grams
1 pound = 16 ounces
1 ton = 2,000 pounds
Metric numbers with four digits are presented without a comma (e.g., 9960 kilometers).
For metric numbers greater than four digits, a space is used instead of a comma
(e.g., 12 500 liters).
Page 6
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
SAMPLE
FCAT Mathematics Sample Questions
1
In this drawing, line l is parallel to line m and line s is perpendicular to PR. The
measure of ∠ 1 is 110°.
s
l
1
m
P
2
R
What is the measure of ∠ 2?
2
A.
110°
B.
70°
C.
40°
D.
20°
Which expression is equivalent to the perimeter of the shaded portion of
the rectangle?
4
F.
2 x + 10
G.
2 x + 12
H.
4 x + 14
I.
8 x + 28
Page 7
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
9
9
SAMPLE
3
FCAT Mathematics Sample Questions
Weekly attendance figures for a movie shown at a theater are given in the table
below. The movie will no longer be shown when the weekly attendance drops
below 200.
WEEKLY ATTENDANCE FIGURES
Week
Attendance
1
6,160
2
3,080
3
1,540
4
770
If this attendance pattern continues, during which week will attendance first drop
below 200?
4
A.
5
B.
6
C.
7
D.
8
Jim, Ben, and Mark played in a four-day golf tournament. The four scores for each
golfer are shown in the Venn diagram below.
GOLF SCORES
Mark
Ben
99
84
86
94
87
96
102
Jim
What is the lowest score that Mark and Jim have in common?
F.
84
G.
87
H.
94
I.
96
Page 8
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
SAMPLE
FCAT Mathematics Sample Questions
5
9
As a diver swims deeper under the water, the water pressure increases on the diver.
WATER PRESSURE
Depth (in feet)
Pressure (in square inches)
10
4.3
20
8.6
30
12.9
40
17.2
50
21.5
Which equation represents p, the water pressure in square inches, as a function of d,
the depth in feet?
6
A.
p = 0.43d
B.
p = 4.3d
C.
p = 23.3d
D.
p = 2.33d
The number of portable buildings produced by Chambers Manufacturing last week
was 70 on Monday, 60 on Tuesday, 80 on Wednesday, and 50 on Thursday. After
production on Friday, the mean number of buildings produced for the week was 67.
What is the median number of buildings produced last week by Chambers
Manufacturing?
F.
67
G.
68
H.
70
I.
75
Page 9
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
SAMPLE
7
FCAT Mathematics Sample Questions
David and Terri drove a small motorboat down a river with the current. The rate the
boat traveled in still water was r miles per hour, and the current’s average speed was
c miles per hour. It took them 1.5 hours to travel 4 miles downstream. Which of the
following equations can be used to represent this information?
B.
1.5 = (r + c)4
1.5 = (r − c)4
C.
4 = (r + c)1.5
D.
4 = (r − c)1.5
A.
8
9
A wholesaler is offering two different package deals of roses and carnations to
florists. One package contains 20 dozen roses and 34 dozen carnations for $504.00.
The other package contains 15 dozen roses and 17 dozen carnations for $327.00. This
information can be represented by the system of equations below, where r represents
the cost of one dozen roses and c represents the cost of one dozen carnations.
20r + 34c = 504
15r + 17c = 327
Solve the system of equations to find the cost, in dollars, of a dozen roses.
9
Charlie needs to simplify the expression below before he substitutes values for x
and y.
x18 y12 + x9 y 8
x3 y 4
If x ≠ 0 and y ≠ 0, which of the following is a simplified version of the
expression above?
F.
x 9y 5
G.
x 24 y 16
H.
x 6y 3 + x 3y 2
I.
x 15 y 8 + x 6 y 4
Page 10
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
SAMPLE
FCAT Mathematics Sample Questions
10
9
A triangle can be formed on a map by drawing lines that connect the cities of
Orlando, Melbourne, and Fort Myers, as shown below. On the map, the distance
between Orlando and Melbourne is 2.1 cm, the distance between Orlando and Fort
Myers is 5.6 cm, and the distance between Melbourne and Fort Myers is 5.4 cm.
y
Orlando
2.1 cm
Melbourne
5.6 cm
5.4 cm
Fort Myers
x
If the distance between Orlando and Fort Myers is 140 miles, what is the distance, in
miles, between Orlando and Melbourne?
Page 11
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
SAMPLE
11
9
FCAT Mathematics Sample Questions
In a technical drawing class, students are analyzing the side view of a house that has
been positioned on a coordinate grid, as shown below.
y
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
P (6, 12)
Q (11, 10)
(1, 7)
1 2 3 4 5 6 7 8 9 10 11 12
x
Which of the following equations best represents the line that contains PQ?
A.
y = - 25 x + 14.4
B.
y =
C.
y = - 25 x + 14.4
D.
y =
5
2
2
5
x + 27
x + 27
Page 12
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
SAMPLE
FCAT Mathematics Sample Answer Sheet
9
Name
Answer all the Mathematics Sample Questions on this Sample Answer Sheet.
1
A
B
C
D
2
F
G
H
I
3
A
B
C
D
4
F
G
H
I
5
A
B
C
D
6
F
G
H
I
7
A
B
C
D
8
9
F
G
H
I
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Page 13
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
D
Notes
Page 14
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
Notes
Page 15
FCAT 2010 Sample Test Materials © 2009 Florida Department of Education
Copyright Statement for This Office of Assessment Publication
Authorization for reproduction of this document is hereby granted to persons acting in an official capacity within the
Uniform System of Public K–12 Schools as defined in Section 1000.01(4), Florida Statutes. The copyright notice at the bottom
of this page must be included in all copies.
All trademarks and trade names found in this publication are the property of their respective owners and are not associated
with the publishers of this publication.
This publication is provided by the Florida Department of Education to Florida public schools free of charge and is not
intended for resale.
Permission is NOT granted for distribution or reproduction outside of the Uniform System of Public K–12 Schools or for
commercial distribution of the copyrighted materials without written authorization from the Florida Department of
Education. Questions regarding use of these copyrighted materials should be sent to the following:
The Administrator
Office of Assessment
Florida Department of Education
Tallahassee, Florida 32399-0400
FL00001829
Copyright © 2009
State of Florida
Department of State
The Florida Department of Education and its test contractors currently employ strategies to protect the
environment in the production and destruction of FCAT materials. The Department encourages schools
and districts to recycle non-secure FCAT interpretive publications after use.
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