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This booklet contains the answers to the FCAT 2.0 Mathematics sample questions, as well as
explanations for the answers. It also gives the Next Generation Sunshine State Standards
(NGSSS) benchmark assessed by each item. Although the Florida State Board of Education
adopted the Common Core State Standards in the summer of 2010, these standards have not
yet been implemented. For this reason, the FCAT 2.0 tests and sample questions and
answers are based on the 2007 NGSSS. The benchmarks included in this booklet provide
teachers with additional information. For more detailed information, follow this link to the
Florida NGSSS website: http://www.floridastandards.org/index.aspx, or follow this link to
the current benchmark language in the FCAT 2.0 Mathematics Test Item Specifications:
http://fcat.fldoe.org/fcat2/itemspecs.asp.
In addition, one or more possible approaches to solving the questions are provided.
Students may use approaches other than these and still receive credit if they also obtain a
correct answer.
Multiple-choice and gridded-response items in FCAT 2.0 Mathematics tests are scored by
awarding one point for each correct answer.
The intent of these sample test materials is to orient teachers and students to the types of
questions on FCAT 2.0 tests. By using these materials, students will become familiar with the
types of items and response formats they will see on the actual test. The sample questions
and answers 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 2.0 Test Item Specifications
at http://fcat.fldoe.org/fcat2/itemspecs.asp.
The sample questions for students and the sample answers for teachers will only be
available online, at http://fcat.fldoe.org/fcat2/fcatitem.asp.
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
To solve the problem, determine how many students are represented by each
milk carton.
If 6 students drink milk at lunch on Monday and 3 milk cartons are shown, then
If 10 students drink milk at lunch on Wednesday and 5 milk cartons are
shown, then 10 ÷ 5 = 2. Each milk carton represents 2 students who drink milk
at lunch.
Next, determine the number of students who drink milk at lunch on Friday. Count the
6 whole milk cartons shown for Friday. Using the information that 1 milk carton
represents 2 students, multiply 6 × 2 to get 12 students. If 1 milk carton represents
2 students, then half of a milk carton represents 1 student. 12 + 1 = 13.
Thirteen students drink milk at lunch on Friday, option D.
To solve this problem, use the strategy of making an easier problem. First, change the
number 8 to (5 + 3). Then, multiply both digits by 9.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
3 The correct answer is B (2).
To solve this problem, imagine folding the picture of the scallop in half so that the two
halves match. Draw a line on the picture where it can be folded so the two halves match.
The picture can be folded vertically and horizontally, giving it 2 lines of symmetry.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
To solve this problem, recognize that a complete iteration of the pattern consists of four
figures (triangle, square, rotated triangle, circle). There are three complete iterations of
this pattern shown. Repeating the pattern, extend the pattern to identify the next figure,
which is the third figure (rotated triangle) of a full iteration.
To solve this problem, list all the factors of 6 and 8. Identify 2 as a factor of 6 and 8.
3
Divide both 6 and 8 by 2; therefore, 4
is the equivalent fraction.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
6 The correct answer is H (32 ÷ 4).
To solve this problem, recognize that the 32 pieces of candy must be shared equally
among the 4 friends (partitive model of division). The only expression that can be used is
H, 32 ÷ 4.
To solve this problem, recognize that each whole flower has 10 petals. On Flower A,
5 5 1 4
10
of the petals are shaded; 10
is equivalent to 2 . On Flower B, 10 of the petals are
4 2 5 4
shaded; 10
is equivalent to 5
. Because 10 is greater than 10 , option A, 21 is greater than
2
5
, is the correct answer.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
To solve this problem, write the multiplication equation that could be used to find the
total number of beach balls, 8 × 2 = b. Of the equations shown, b ÷ 8 = 2 is the only
equation that could also be used to find the total number of beach balls, as it is the
inverse equation of 8 × 2 = b.
First Strategy:
1
To solve the problem, make the last figure one whole by moving 4
of the second figure to
1
it. That results in 2 4
of the figures being shaded.
OR
Second Strategy:
9 1
Count the total number of fourths that are shaded, 4
. Of the fractions given, 2 4
is the
9
only one that is equivalent to 4
.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
10 The correct answer is H ( ).
29
9
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
First Strategy:
Add all 4 estimates to get a total of 7,000. About 7,000 calendars should be ordered for
the students in the 4 schools.
OR
Second Strategy:
, , is about 3,000
, , is about 4,000
Add the two estimates together (3, 000 + 4, 000 = 7 ,000). About 7,000 calendars should
be ordered for the students in the 4 schools.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
12 The correct answer is G (6).
Charles—Erin
Charles—Gayle
Charles—Paco
Erin—Gayle
Erin—Paco
Gayle—Paco
The ordering of the pairs is not important (i.e., Charles—Erin is the same pair as
Erin—Charles). There are 6 different possible pairs of students.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
To solve this problem, analyze each option and eliminate all false statements.
Option A is false because the square is the only shape that has exactly two pairs of
parallel sides.
Option B is false because the pentagon is the only shape that has exactly
five vertices.
Option C is the correct answer because all shapes given (square, triangle, hexagon, and
pentagon) are regular polygons. A regular polygon is both equilateral (all sides
congruent) and equiangular (all angles congruent).
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
14 The correct answer is G (picture of 3 rhombi and 3 triangles).
To solve this problem, draw in the shapes that would be used to compose the figure. The
shapes from each option are shaded in the composed figures.
F. H.
G. I.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
First Strategy:
To solve this problem, apply the definition of perimeter (the distance around a figure)
by using the centimeter ruler to measure all 8 sides of the picture. Then add the
8 measurements together.
OR
Second Strategy:
To solve this problem, recognize that the figure is composed of 2 rectangles (opposite
sides have equal measure). Using this information, recognize that there are 2 pairs of
congruent segments. After measuring one segment, double that measurement to
compensate for the congruent segment.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
16 The correct answer is H 2 4 inches .( 1
)
Reporting Category: Geometry and Measurement
To solve this problem, use the inch side of the ruler to measure the stone arrowhead. To
measure, align the beginning of the figure with the zero indicated on the ruler.
Interpret the markings on the ruler as fractions of an inch.
1
The stone arrowhead has a length of 2 4
inches.
Benchmark: MA.3.G.5.3 Tell time to the nearest minute and to the nearest
quarter hour, and determine the amount of time elapsed.
To solve this problem, identify the time displayed as 7:50. Add 25 minutes to 7:50, or
count clockwise in 5-minute intervals. 8:15 is twenty-five minutes later than 7:50.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
SAMPLE
3 FCAT 2.0 Mathematics Sample Answers
First Strategy:
To solve this problem, use the combination model for multiplication. Each shirt is
paired with each pair of shorts to find that 2 (shirts) multiplied by 3 (pairs of shorts)
equals 6 uniform combinations.
OR
Second Strategy:
To solve this problem, match the red shirt with each of the 3 colors of shorts to get
3 uniform combinations. Match the white shirt with each of the 3 colors of shorts to
get 3 more uniform combinations. Calculate 3 + 3 to get a total of 6 possible
uniform combinations.
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FCAT 2.0 Mathematics Sample Answers Florida Department of Education
FCAT 2.0 Mathematics Sample Answers
SAMPLE
3
19 The correct answer is D (correct bar graph).
To solve this problem, determine the correct graph by comparing each graph to the
given data.
In Graph A, the data for votes for the flip-flops and sneakers are displayed incorrectly.
There should be 8 votes for flip-flops and 10 votes for sneakers displayed.
In Graph B, the data for the votes for sandals are displayed incorrectly. There should only
be 4 votes indicated, not 8.
In Graph C, the data for the votes for flip-flops, sandals, and sneakers are displayed
incorrectly. In this graph, the data have been incorrectly doubled.
Graph D is the correct answer. All the data have been displayed accurately.
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FCAT 2.0 Mathematics Sample Answers 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
Copyright © 2012
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 2.0 materials. The Department encourages
schools and districts to recycle nonsecure FCAT 2.0 interpretive publications after use.