XIV.
Mathematics, Grade 8
Grade 8 Mathematics Test
The spring 2010 grade 8 MCAS Mathematics test was based on learning standards in the Massachusetts
Mathematics Curriculum Framework (2000). The Framework identifies five major content strands, listed
below.
■ Number Sense and Operations
■ Patterns, Relations, and Algebra
■ Geometry
■ Measurement
■ Data Analysis, Statistics, and Probability
The grades 7–8 learning standards for each of these strands appear on pages 62–66 of the Mathematics
Curriculum Framework, which is available on the Department website at www.doe.mass.edu/frameworks/
current.html.
In test item analysis reports and on the Subject Area Subscore pages of the MCAS School Reports and
District Reports, Mathematics test results are reported under five MCAS reporting categories, which are
identical to the five Mathematics Curriculum Framework content strands listed above.
Test Sessions
The MCAS grade 8 Mathematics test included two separate test sessions. Each session included
multiple-choice, short-answer, and open-response questions. Approximately half of the common test
items are shown on the following pages as they appeared in test booklets.
Reference Materials and Tools
Each student taking the grade 8 Mathematics test was provided with a plastic ruler and a grade 8
Mathematics Reference Sheet. A copy of the reference sheet follows the final question in this chapter.
An image of the ruler is not reproduced in this publication.
During session 2, each student had sole access to a calculator with at least four functions and a square root
key. Calculator use was not allowed during session 1.
The use of bilingual word-to-word dictionaries was allowed for current and former limited English
proficient students only, during both Mathematics test sessions. No other reference tools or materials were
allowed.
Cross-Reference Information
The tables at the conclusion of this chapter indicate each released and unreleased common item’s
reporting category and the framework learning standard it assesses. The correct answers for released
multiple-choice and short-answer questions are also displayed in the released item table.
214
Mathematics
Session 1
You may use your reference sheet and MCAS ruler during this session.
You may not use a calculator during this session.
DIRECTIONS
This session contains eight multiple-choice questions and two short-answer questions. Mark your
answers to these questions in the spaces provided in your Student Answer Booklet.
ID:228687 B Common EQ ID:263834 C Common
●
1 The list below shows the number of ●
3 Which of the following inequalities
is true?
pages Marian read in her library book
each day for one week.
A. 3 p
B. 9 p
11, 13, 11, 15, 20, 17, 11
C. 5 2
D. 6 3
What is the mode of the number of
pages that Marian read each day?
A. 9 ID:265339 B Common
B. 11 ●
4 The table below shows a linear pattern.
C. 13
Term 1 2 3 … n
D. 14
Value 5 7 9 … ?
Which of the following expressions
ID:219576 A Common represents the value of the nth term in
●
2 Dan earned some money working for
1
the pattern?
his uncle. He spent of the money on
3 A. n 2
1
magazines and of the money on a
4
B. 2 n 3
snack. Which of the following fractions
represents the part of Dan’s money he C. 3 n 2
did not spend? D. 4 n 1
5
A.
12
1
B.
2
2
C.
3
5
D.
7
215
Mathematics Session 1
Question 5 is a short-answer question. Write your answer to this question in the box provided in your
Student Answer Booklet. Do not write your answer in this test booklet. You may do your figuring in
the test booklet.
ID:253766 Common EQ
●
5 What is the solution to the equation below?
3x 9 6
216
Mathematics Session 1
Mark your answers to multiple-choice questions 6 and 7 in the spaces provided in your Student
Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test
booklet.
ID:264515 A Common ID:263850 C Common
●
6 The students in an eighth-grade class
had a dance. They spent $500 for a
●
7 What is the value of the expression
below?
local band. The equation below can be 2
used to find the total profit, y, if the ( 16 )
students sold x tickets to the dance.
A. 4
y 4x 500
B. 8
What does the 4 represent in the equation?
C. 16
A. the price per ticket D. 32
B. the cost of the band
C. the number of tickets sold
D. the profit made from selling x tickets
217
Mathematics Session 1
Question 8 is a short-answer question. Write your answer to this question in the box provided in your
Student Answer Booklet. Do not write your answer in this test booklet. You may do your figuring in
the test booklet.
ID:268713 Common EQ
●
8 Mr. Jamison is the principal at a new school with an enrollment of 430 students. He surveyed
10% of the students at his school to find out which colors they would like as the school colors.
What is the number of students in the sample size of the principal’s survey?
218
Mathematics Session 1
Mark your answers to multiple-choice questions 9 and 10 in the spaces provided in your Student
Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test
booklet.
ID:252989 B Common ID:219566 C Common
●
9 The rate of interest paid on savings ●
10 What is the value of the expression below?
accounts at a bank increased by 1 %.
2 8 3 7
Which of the following shows
1
% written as a decimal? A. 12
2
A. 0.0012 B. 2
B. 0.005 C. 4
C. 0.12 D. 18
D. 0.5
219
Mathematics
Session 2
You may use your reference sheet and MCAS ruler during this session.
You may use a calculator during this session.
DIRECTIONS
This session contains eight multiple-choice questions, one short-answer question, and two open-response
questions. Mark your answers to these questions in the spaces provided in your Student Answer
Booklet.
ID:289725 CMH034_area_table.eps B Common ID:229552 B Common EQ
●
11 The table below shows the area of a
trapezoid when the lengths of the bases
●
12 A box of identically shaped light bulbs
contains the following:
stay the same but the height is changed. • 11 red light bulbs
• 13 blue light bulbs
Area of Trapezoid
• 10 green light bulbs
Height Area • 16 orange light bulbs
(in meters) (in square meters)
If 1 light bulb is chosen at random from
3 7.5 the box, what is the probability that it will
5 12.5 be green?
7 17.5 1
A.
9 22.5 4
1
B.
What is the area of the trapezoid when 5
the height is 17 meters? 1
C.
10
A. 47.5 square meters
1
D.
B. 42.5 square meters 50
C. 39.5 square meters
D. 37.5 square meters
220
Mathematics Session 2
ID:253755 CMH058_salary_table.eps C Common
●
13 Elena and Kristen started new jobs at
the same time. The table below shows
their annual salaries for the first 4 years.
Annual Salaries
Number of Elena’s Kristen’s
Years Salary Salary
1 $ 15,000 $ 22,000
2 $ 17,500 $ 23,000
3 $ 20,000 $ 24,000
4 $ 22,500 $ 25,000
5
6
Elena’s salary continued to increase
by the same amount each year, and
Kristen’s salary continued to increase by
the same amount each year. Which of
the following statements is true for
year 6?
A. Elena’s salary was $30,000.
B. Kristen’s salary was $26,000.
C. Elena’s salary was $500 more than
Kristen’s salary.
D. Kristen’s salary was $500 more than
Elena’s salary.
221
Mathematics Session 2
Question 14 is a short-answer question. Write your answer to this question in the box provided in
your Student Answer Booklet. Do not write your answer in this test booklet. You may do your figuring
in the test booklet.
ID:219703 LW8316_Triangle.eps Common EQ
●
14 David drew ABC on a coordinate plane, as shown below.
6
5
4
3
A
2
1
C B
x
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
–1
–2
–3
–4
–5
–6
David reflected ABC over the x-axis. What are the coordinates of the image of point A?
222
Mathematics Session 2
Mark your answers to multiple-choice questions 15 through 17 in the spaces provided in your Student
Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test
booklet.
ID:229637 C Common
●
15 The chart below shows the number of goals scored by the Sharks soccer team and their opponents
for 5 games.
Goals Scored by Sharks and Opponents
Number of Goals Number of Goals
Game Scored by the Sharks Scored by Opponents
1st 5 3
2nd 4 0
3rd 3 2
4th 4 6
5th 5 1
In what percent of the games did the Sharks score more goals than their opponents?
A. 40%
B. 50%
C. 80%
D. 100%
223
Mathematics Session 2
ID:253747 CMH053_hexagon.eps D Common ID:229635 B Common
●
16 The relationship between the perimeter
and side length of a regular hexagon is
●
17 The formula below can be used to find S,
the sum of all integers from 1 to n, where
shown on the graph below. n is any positive integer.
Relationship between n ( n 1)
S
Perimeter and Side Length 2
of a Regular Hexagon What is the value of S when n = 50?
y
30 A. 1250
27 B. 1275
Perimeter (in inches)
24
C. 2500
21
18 D. 2550
15
12
9
6
3
x
0 1 2 3 4 5
Side Length (in inches)
What happens to the perimeter of
a regular hexagon as its side length
increases by 1?
A. The perimeter increases by 1.
B. The perimeter increases by 2.
C. The perimeter increases by 3.
D. The perimeter increases by 6.
224
Mathematics Session 2
Question 18 is an open-response question.
• BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
• Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
• If you do the work in your head, explain in writing how you did the work.
Write your answer to question 18 in the space provided in your Student Answer Booklet.
ID:253894 CMH107_recycling.eps Common EQ
●
18 A cafeteria has a recycling container for cans. The recycling container has a lid that is in the
shape of a circle with an opening in the center that is also in the shape of a circle. The lid
and some of its dimensions are shown in the diagram below.
Recycling Container Lid
6 inches
30 inches
The shaded part of the diagram represents the opening in the lid.
a. What is the circumference, in inches, of the lid of the recycling container? Show or explain
how you got your answer. (Use 3.14 for p.)
b. What is the area, in square inches, of the lid, including the opening? Show or explain how
you got your answer. (Use 3.14 for p.)
c. What is the area, in square inches, of the lid, not including the opening? Show or explain
how you got your answer. (Use 3.14 for p.)
225
Mathematics Session 2
Mark your answers to multiple-choice questions 19 and 20 in the spaces provided in your Student
Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test
booklet.
ID:219645 A Common ID:263851 A Common EQ
●
19 The mean height, in inches, of 5 girls
on the middle school basketball team is
●
20 What is 150% of 48?
exactly 66 inches. The table below lists A. 72
the heights of 4 of the girls. B. 32
Girls’ Heights C. 7.2
D. 3.2
Height
Name (in inches)
Jessica 65
Ali 65
Sina 70
Amanda 66
Becky ?
Which of the following is the height
of Becky?
A. 64 inches
B. 65.5 inches
C. 66 inches
D. 66.5 inches
226
Mathematics Session 2
Question 21 is an open-response question.
• BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.
• Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
• If you do the work in your head, explain in writing how you did the work.
Write your answer to question 21 in the space provided in your Student Answer Booklet.
ID:265583 CMH319_similar_rectangles Common EQ
●
21 Danielle measured two of the computer screens in her school’s computer lab. The two screens
and some of their dimensions are shown below.
hes
x 9 inches inc 8.2 inches
.4
15
12 inches y
Screen 1 Screen 2
a. What is the area, in square inches, of Screen 1? Show or explain how you got your answer.
b. What is x, the diagonal length in inches of Screen 1? Show or explain how you got your
answer.
c. Which computer screen, Screen 1 or Screen 2, has the greater area? Show your work or
explain how you got your answer.
227
Massachusetts Department of Massachusetts Comprehensive Assessment System
ELEMENTAR
ELEMENTARY
TARY
RY & SECONDAR
SECONDARY
RY Grade 8 Mathematics Reference Sheet
PERIMETER FORMULAS VOLUME FORMULAS
square . . . . . . . . . . . P 4s rectangular prism . . . . . . V lwh
OR
rectangle. . . . . . . . . P 2b 2h V Bh
OR (B = area of a base)
P 2l 2w
cube . . . . . . . . . . . . . . . . . V s3
(s length of an edge)
triangle . . . . . . . . . . P a b c
cylinder . . . . . . . . . . . . V πr 2 h
AREA FORMULAS 4 3
sphere . . . . . . . . . . . . . V
3
πr
square . . . . . . . . . . . A s2
rectangle. . . . . . . . . A bh CIRCLE FORMULAS
OR C 2πr
A lw OR
C πd
parallelogram . . . . . A bh
1
A πr 2
triangle . . . . . . . . . . A 2
bh
1
trapezoid. . . . . . . . . A 2
h ( b1 b2) PYTHAGOREAN THEOREM
circle. . . . . . . . . . . . A πr 2
TOTAL SURFACE AREA FORMULAS c
a
rectangular prism . . SA 2 ( lw ) 2 ( hw ) 2 ( lh )
b
cylinder . . . . . . . . . SA 2 πr 2 2 πrh
a2 b2 c2
sphere . . . . . . . . . . . SA 4 πr 2
228
Grade 8 Mathematics
Spring 2010 Released Items:
Reporting Categories, Standards, and Correct Answers*
Correct Answer
Item No. Page No. Reporting Category Standard
(MC/SA)*
1 215 Data Analysis, Statistics, and Probability 8.D.3 B
2 215 Number Sense and Operations 8.N.12 A
3 215 Number Sense and Operations 8.N.2 C
4 215 Patterns, Relations, and Algebra 8.P.4 B
5 216 Patterns, Relations, and Algebra 8.P.7 x = –5
6 217 Patterns, Relations, and Algebra 8.P.6 A
7 217 Number Sense and Operations 8.N.9 C
8 218 Data Analysis, Statistics, and Probability 8.D.1 43
9 219 Number Sense and Operations 8.N.1 B
10 219 Number Sense and Operations 8.N.6 C
11 220 Patterns, Relations, and Algebra 8.P.1 B
12 220 Data Analysis, Statistics, and Probability 8.D.4 B
13 221 Patterns, Relations, and Algebra 8.P.10 C
14 222 Geometry 8.G.6 (1, –2)
15 223 Data Analysis, Statistics, and Probability 8.D.2 C
16 224 Patterns, Relations, and Algebra 8.P.8 D
17 224 Patterns, Relations, and Algebra 8.P.2 B
18 225 Measurement 8.M.3
19 226 Data Analysis, Statistics, and Probability 8.D.3 A
20 226 Number Sense and Operations 8.N.10 A
21 227 Geometry 8.G.4
*Answers are provided here for multiple-choice items and short-answer items only. Sample responses and scoring guidelines for
open-response items, which are indicated by shaded cells, will be posted to the Department’s website later this year.
229
Grade 8 Mathematics
Spring 2010 Unreleased Common Items:
Reporting Categories and Standards
Item No. Reporting Category Standard
22 Number Sense and Operations 8.N.1
23 Measurement 8.M.5
24 Data Analysis, Statistics, and Probability 8.D.1
25 Data Analysis, Statistics, and Probability 8.D.4
26 Number Sense and Operations 8.N.8
27 Geometry 8.G.2
28 Measurement 8.M.1
29 Patterns, Relations, and Algebra 8.P.5
30 Number Sense and Operations 8.N.7
31 Geometry 8.G.8
32 Number Sense and Operations 8.N.3
33 Data Analysis, Statistics, and Probability 8.D.2
34 Patterns, Relations, and Algebra 8.P.7
35 Number Sense and Operations 8.N.5
36 Measurement 8.M.4
37 Patterns, Relations, and Algebra 8.P.3
38 Data Analysis, Statistics, and Probability 8.D.3
39 Patterns, Relations, and Algebra 8.P.10
40 Data Analysis, Statistics, and Probability 8.D.3
41 Patterns, Relations, and Algebra 8.P.4
42 Data Analysis, Statistics, and Probability 8.D.4
230
