Release of Spring 2022

MCAS Test Items

from the

Grade 10 Mathematics
Paper-Based Test
June 2022
Massachusetts Department of
Elementary and Secondary Education
 This document was prepared by the
Massachusetts Department of Elementary and Secondary Education
Jeffrey C. Riley
Commissioner

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Please credit the “Massachusetts Department of Elementary and Secondary Education.”

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Phone 781-338-3000 TTY: N.E.T. Relay 800-439-2370
www.doe.mass.edu
 Overview of Grade 10 Mathematics Test
The spring 2022 grade 10 Mathematics test was a next-generation assessment that was administered in two primary formats: a
computer-based version and a paper-based version. The vast majority of students took the computer-based test. The paper-based
test was offered as an accommodation for students with disabilities who are unable to use a computer, as well as for English
learners who are new to the country and are unfamiliar with technology.

Most of the operational items on the grade 10 Mathematics test were the same, regardless of whether a student took the computer-
based version or the paper-based version. In places where a technology-enhanced item was used on the computer-based test,
an adapted version of the item was created for use on the paper test. These adapted paper items were multiple-choice, multiple-
select, or short-answer items that tested the same Mathematics content and assessed the same standard as the technology-
enhanced item.

This document displays released items from the paper-based test. Released items from the computer-based test are
available on the MCAS Resource Center website at mcas.pearsonsupport.com/released-items.

Test Sessions and Content Overview

The grade 10 Mathematics test was made up of two separate test sessions. Each session included selected-response, short-answer,
and constructed-response questions. On the paper-based test, the selected-response questions were multiple-choice items and
multiple-select items, in which students select the correct answer(s) from among several answer options.

Standards and Reporting Categories

The grade 10 Mathematics test was based on high school standards in the Massachusetts Curriculum Framework for
Mathematics (2017). The standards in the 2017 framework are organized under the five major conceptual categories listed
below.

• Number and Quantity

• Algebra

• Functions

• Geometry

• Statistics and Probability

The grade 10 test assessed standards that overlap between the Model Algebra I/Model Geometry and Model Mathematics I/Model
Mathematics II courses. The Massachusetts Curriculum Framework for Mathematics is available on the Department website at
www.doe.mass.edu/frameworks/current.html.

Mathematics test results for grade 10 are reported under four MCAS reporting categories, which are based on the five framework
conceptual categories listed above.

The table at the conclusion of this document provides the following information about each released operational item:
reporting category, standard covered, item type, and item description. The correct answers for selected-response and short-
answer questions are also displayed in the table.

Reference Materials and Tools

Each student taking the grade 10 Mathematics test was provided with a grade 10 Mathematics Reference Sheet. A copy of the
reference sheet follows the final question in this chapter.

During Session 2, each student had sole access to a calculator. Calculator use was not allowed during Session 1.

During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowed for current and former
English learner students only. No other reference tools or materials were allowed.

1
 Grade 10 Mathematics
SESSION 1
This session contains 21 questions.

You may use your reference sheet during this session.

You may not use a calculator during this session.

Directions
Read each question carefully and then answer it as well as you can. You must record
all answers in this Test & Answer Booklet.

For some questions, you will mark your answers by filling in the circles in your
Test & Answer Booklet. Make sure you darken the circles completely. Do not make
any marks outside of the circles. If you need to change an answer, be sure to erase
your first answer completely.

For other questions, you will need to fill in an answer grid. Directions for completing
questions with answer grids are provided on the next page.

If a question asks you to show or explain your work, you must do so to receive full
credit. Write your response in the space provided. Only responses written within the
provided space will be scored.

2
Mathematics Session 1

Directions for Completing Questions with Answer Grids

1. Work the question and find an answer.
2. Enter your answer in the answer boxes at the top of the answer grid.
3. Print only one number or symbol in each box. Do not leave a blank box in
the middle of an answer.
4. Under each answer box, fill in the circle that matches the number or
symbol you wrote above. Make a solid mark that completely fills the
circle.
5. Do not fill in a circle under an unused answer box.
6. Fractions cannot be entered into an answer grid and will not be scored.
Enter fractions as decimals.
7. If you need to change an answer, be sure to erase your first answer
completely.
8. See below for examples of how to correctly complete an answer grid.

EXAMPLES

– 1 4 4 8 3 1 6 65 . 3 9 . 5 5 5 5
\
– \
– \
– \
–
• \
\ • \
• \\ • \
• • \ • • \
\ • \
• \\ • \
• • \ • • \
\ • \
• \\ • \
• • \ • • \
\ • \
• \\ • \
• • \ •

\\\\\\
0 0 0 0 0 0 \
0 \
0 \
0 \
0 \
0 \ 0 \
0 \ 0 \
0 \
0 \
0 \
0 \ 0 \
0 \ 0 \\\\\\
0 0 0 0 0 0 \
0

\
1 \
1 \
1 \
1 \ 1 \
1 \ 1 \
1 \
1 \
1 \
1 \ 1 \
1 \ 1 \
1 \
1 \
1 \
1 \ 1 \
1 \ 1 \
1 \
1 \
1 \
1 \ 1 \
1 \ 1

\\\\\\ 2
2 2 2 2 2 2 \ \
2 \
2 \
2 \
2 \ 2 \
2 \ 2 \
2 \
2 \
2 \
2 \ 2 \
2 \ 2 \\\\\\ 2
2 2 2 2 2 2 \
\
3 \
3 \
3 \
3 \ 3 \
3 \ 3 \
3 \
3 \
3 \
3 \ 3 \
3 \ 3 \
3 \
3 \
3 \
3 \ 3 \
3 \ 3 \
3 \
3 \
3 \
3 \ 3 \
3 \ 3

\\\\\\ 4
4 4 4 4 4 4 \ \
4 \
4 \
4 \
4 \ 4 \
4 \ 4 \
4 \
4 \
4 \
4 \ 4 \
4 \ 4 \\\\\\ 4
4 4 4 4 4 4 \
\
5 \
5 \
5 \
5 \ 5 \
5 \ 5 \
5 \
5 \
5 \
5 \ 5 \
5 \ 5 \
5 \
5 \
5 \
5 \ 5 \
5 \ 5 \
5 \
5 \
5 \
5 \ 5 \
5 \ 5

\\\\\\ 6
6 6 6 6 6 6 \ \
6 \
6 \
6 \
6 \ 6 \
6 \ 6 \
6 \
6 \
6 \
6 \ 6 \
6 \ 6 \\\\\\ 6
6 6 6 6 6 6 \
\
7 \
7 \
7 \
7 \ 7 \
7 \ 7 \
7 \
7 \
7 \
7 \ 7 \
7 \ 7 \
7 \
7 \
7 \
7 \ 7 \
7 \ 7 \
7 \
7 \
7 \
7 \ 7 \
7 \ 7

\\\\\\ 8
8 8 8 8 8 8 \ \
8 \
8 \
8 \
8 \ 8 \
8 \ 8 \
8 \
8 \
8 \
8 \ 8 \
8 \ 8 \\\\\\ 8
8 8 8 8 8 8 \
\
9 \
9 \
9 \
9 \ 9 \
9 \ 9 \
9 \
9 \
9 \
9 \ 9 \
9 \ 9 \
9 \
9 \
9 \
9 \ 9 \
9 \ 9 \
9 \
9 \
9 \
9 \ 9 \
9 \ 9

3
Mathematics Session 1
MA315404 OP D

q What is the solution of this equation?

3(x + 5) = 5x − 7

A x = −1

B x=4

C x=6

D x = 11

MA713335046_PA OP B

w Two car rental companies each charge a fixed fee for renting a car, plus an
additional amount for each mile the car is driven.

• Company A charges a fixed fee of $25 plus $0.10 per mile.

• Company B charges a fixed fee of $15 plus $0.20 per mile.
Which pair of equations can be used to determine y, the total amount, in
dollars, a customer will be charged for renting a car from Company A or
Company B and driving it x miles?

A Company A: y = 0.25x + 10
Company B: y = 0.15x + 20

B Company A: y = 0.10x + 25
Company B: y = 0.20x + 15

C Company A: y = 10x + 0.25

Company B: y = 20x + 0.15

D Company A: y = 25x + 0.10

Company B: y = 15x + 0.20

4
Mathematics Session 1
MA311237 OP C

e Triangle LMN is similar to triangle PQR. The triangles and some of their
dimensions are shown in this diagram.

11.2 cm
z

L N

Q
5.6 cm
2.9 cm

P R

Based on the dimensions in the diagram, what is the value of z?

A 2.7 cm

B 4.8 cm

C 5.8 cm

D 8.3 cm

5
Mathematics Session 1
MA287432 OP C

 Consider this expression.

8x2 + 16x + 24

Which of the following is equivalent to the expression?

A 8(x2 + 16x + 24)

B 8(x2 + 2x) + 3

C 8(x2 + 2x + 3)

D 8(x2 + 5x)

MA311209 OP D

 The first five terms of an arithmetic sequence are shown.

2, 6, 10, 14, 18,...

Which of the following expressions represents the nth term of the sequence?

A 3n

B 4n

C 3n − 1

D 4n − 2

6
Mathematics Session 1

This question has four parts. Be sure to label each part of your response.
MA901364620 OP X

 This graph models the linear relationship between the distance a car traveled
and time.

y
Distance Traveled

500
450
400
Distance (miles)

350
(6, 300)
300
250
200
150
100
50
x
0 1 2 3 4 5 6 7 8 9 10
Time (hours)

A. What does the point (6, 300) represent in this situation?

B. Based on the graph, what was the average speed of the car? Show or
explain how you got your answer.

C. A second car traveled a distance of 209 miles in 5 hours and 6 minutes.

Estimate the average speed of the second car. Show or explain how you
got your answer.

D. A third car traveled at an average speed of 61 miles per hour for 8 hours
and 28 minutes. Estimate the total distance the third car traveled. Show
or explain how you got your answer.

7
Mathematics Session 1

8
Mathematics Session 1
MA901372985_PA OP A

 A student performed a demonstration to illustrate a property of triangles.

First, the student created a paper triangle with angles 1, 2, and 3, as shown
in this diagram.

2 3
Paper Triangle

Then the student folded the triangle along the dotted lines, shown in the
diagram above, to create the rectangle below.

2 1 3
Rectangle

What property of triangles is best illustrated by the student’s demonstration?

A The sum of the interior angle measures of a triangle is equal to 180°.

B The sum of the exterior angle measures of a triangle is equal to 180°.

C The sum of the exterior angle measures of a triangle is equal to 360°.

D The sum of any two side lengths of a triangle is greater than the length of
its third side.

9
Mathematics Session 1
MA287734 OP A

 Which of the following graphs represents the solution set of this system of
inequalities?

y ≥ 1x + 3
2
y ≥ −x + 5

A y B y

6 6
5 5
4 4
3 3
2 2
1 1
x x
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6

C y D y

6 6
5 5
4 4
3 3
2 2
1 1
x x
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6

10
Mathematics Session 1
MA294292 OP D

 Parallel lines g and h are intersected by line j. Lines g, h, j, and expressions

representing angle measurements are shown in this diagram.

(4x + 40)°
g

(x + 10)°
h
(3x + 66)°

Based on the diagram, which of the following equations is not always true?

A (x + 10) + (3x + 66) = 180

B (4x + 40) + (x + 10) = 180

C (3x + 66) = (4x + 40)

D (x + 10) = (4x + 40)

MA314948 OP A

 Which of the following is equivalent to this expression?

7 − 2(4x − 3y)

A 7 − 8x + 6y

B 7 − 8x + 3y

C 7 − 8x − 3y

D 7 − 8x − 6y

11
Mathematics Session 1

This question has two parts.

MA713346383_PA OP D; B

 The volume, V, of a cylinder with radius r and height h can be found using
this equation.

V = r2h

Part A

Which of the following equations has been correctly rearranged to solve for h?

A h = V + r2

B h = V − r2

h= r
2
C V

V
D h = r2

Part B

Which of the following equations has been correctly rearranged to solve for r?

A r= h
V

V
B r=
h

h
C r=
2V

V
D r=
2 h

12
Mathematics Session 1
MA713829689_PA OP C

 Consider this expression.

4 2
(x3y5) (x3y2)¯

Which of the following is equivalent to the expression?

A xy5

B x12y

C x6y16

D x18y24

This question has four parts. Be sure to label each part of your response.
MA311223 OP X

 A student received a gift card to use at a coffee shop. The student used the
gift card to spend the same amount of money at the coffee shop every day
until the remaining value of the card was $0. This function represents f(n),
the value, in dollars, of the gift card after n days.

f(n) = −2.5n + 75

A. Based on the function, what was the original value, in dollars, of the gift
card? Show or explain how you got your answer.

B. Based on the function, how much money, in dollars, did the student spend
each day at the coffee shop? Show or explain how you got your answer.

C. What was the remaining value, in dollars, of the gift card after 20 days?
Show or explain how you got your answer.

D. How many days in total did it take until the remaining value of the gift
card was $0? Show or explain how you got your answer.

13
Mathematics Session 1

14
Mathematics Session 1

This question has two parts.

MA903658309 OP X; A

 This function models retail sales data in the United States from 2000 to 2017.

R(t) = 263.3 + 11.6t

In the model,

• t represents the number of years since 2000, and

• R represents the amount, in billions of dollars, of retail sales for the

year.

Part A

Based on the model, what was the amount, in billions of dollars, of retail
sales in the United States for the year 2000?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

\
–
• \
\ • \ • \
• • \
• \\ •

\\\\\\ \
0 0 0 0 0 0 0

\ 1 \
1 \ 1 \
1 \ 1 \
1 \ 1

\\\\\\ \
2 2 2 2 2 2 2

\\\\\\ \
3 3 3 3 3 3 3

\\\\\\ \
4 4 4 4 4 4 4

\\\\\\ \
5 5 5 5 5 5 5

\\\\\\ \
6 6 6 6 6 6 6

\\\\\\ \
7 7 7 7 7 7 7

\\\\\\ \
8 8 8 8 8 8 8

\\\\\\ \
9 9 9 9 9 9 9

15
Mathematics Session 1

Part B

Based on the model, which of the following statements about retail sales in
the United States from 2000 to 2017 is true?

A Retail sales increased by an average of $11.6 billion each year.

B Retail sales increased by an average of $22.7 billion each year.

C Retail sales increased by an average of $263.3 billion each year.

D Retail sales increased by an average of $274.9 billion each year.

16
Mathematics Session 1
MA901762643_PA OP D

 Segment GJ is shown on this coordinate plane.

7
J 6
5
4
G 3
2
1
x
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
-2
-3

Which of the following best describes a transformation of the segment that

will result in an image that is parallel to segment GJ?

A a reflection over the x-axis

B a reflection over the y-axis

C a 90° clockwise rotation about the origin

D a 180° clockwise rotation about the origin

17
Mathematics Session 1
MA900779724 _PA OP D

 Consider this function.

f(x) = 3x2 − 7

The graph of f(x) is translated 4 units down to create the graph of g(x).

Which of the following functions represents g(x)?

A g(x) = −x2 − 3

B g(x) = −x2 − 11

C g(x) = 3x2 − 3

D g(x) = 3x2 − 11

MA281578 OP C

 The area of a square is represented by this expression.

g2 + 8g + 16

Which of the following expressions represents the length of one side of the
square?

A g + 16

B g+8

C g+4

D g+2

18
Mathematics Session 1

This question has two parts.

MA901375276_PA OP B; C

 Part A

Consider this expression.

4
n3)

Which of the following is equivalent to the expression for all positive values
of n?

A n3

B n6

C n7

D n12

Part B

Consider this expression.

(x 5
x4)

Which of the following is equivalent to the expression for all positive values
of x?
2
—
A x 10
4
—
B x9
9
—
C x5
5
—
D x2

19
Mathematics Session 1
MA274106 _PA OP A

 Line segment PR is shown on this coordinate plane.

9
8
7
6
5
4
3
2 P(5, 1) R(8, 1)
1
x
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
-1
-2

Point R is rotated 180° clockwise about point P.

Which of the following are the coordinates of its image, R′?

A (2, 1)

B (5, −2)

C (8, −2)

D (11, 1)

20
Mathematics Session 1
MA250982 OP A

2 What is the y-value in the solution of this system of equations?

3x + y = 3

−2x + y = −12

A y = −6

B y = −3

C y=3

D y=6

MA307124 OP X

2 In right triangle QRS, the length of side QR is equal to one-half the length of
hypotenuse QS .

What is the measure, in degrees, of /S?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

\
–
• \
\ • \ • \
• • \
• \\ •

\ 0 \
0 \ 0 \
0 \ 0 \
0 \
0

\ 1 \
1 \ 1 \
1 \ 1 \
1 \
1

\ 2 \
2 \ 2 \
2 \ 2 \
2 \
2

\ 3 \
3 \ 3 \
3 \ 3 \
3 \
3

\ 4 \
4 \ 4 \
4 \ 4 \
4 \
4

\ 5 \
5 \ 5 \
5 \ 5 \
5 \
5

\ 6 \
6 \ 6 \
6 \ 6 \
6 \
6

\ 7 \
7 \ 7 \
7 \ 7 \
7 \
7

\ 8 \
8 \ 8 \
8 \ 8 \
8 \
8

\ 9 \
9 \ 9 \
9 \ 9 \
9 \
9

21
 Grade 10 Mathematics
SESSION 2
This session contains 21 questions.

You may use your reference sheet during this session.

You may use a calculator during this session.

Directions
Read each question carefully and then answer it as well as you can. You must record
all answers in this Test & Answer Booklet.

For some questions, you will mark your answers by filling in the circles in your
Test & Answer Booklet. Make sure you darken the circles completely. Do not make
any marks outside of the circles. If you need to change an answer, be sure to erase
your first answer completely.

For other questions, you will need to fill in an answer grid. Directions for completing
questions with answer grids are provided on the next page.

If a question asks you to show or explain your work, you must do so to receive full
credit. Write your response in the space provided. Only responses written within the
provided space will be scored.

22
Mathematics Session 2

Directions for Completing Questions with Answer Grids

1. Work the question and find an answer.
2. Enter your answer in the answer boxes at the top of the answer grid.
3. Print only one number or symbol in each box. Do not leave a blank box in
the middle of an answer.
4. Under each answer box, fill in the circle that matches the number or
symbol you wrote above. Make a solid mark that completely fills the
circle.
5. Do not fill in a circle under an unused answer box.
6. Fractions cannot be entered into an answer grid and will not be scored.
Enter fractions as decimals.
7. If you need to change an answer, be sure to erase your first answer
completely.
8. See below for examples of how to correctly complete an answer grid.

EXAMPLES

– 1 4 4 8 3 1 6 65 . 3 9 . 5 5 5 5
\
– \
– \
– \
–
• \
\ • \
• \\ • \
• • \ • • \
\ • \
• \\ • \
• • \ • • \
\ • \
• \\ • \
• • \ • • \
\ • \
• \\ • \
• • \ •

\\\\\\
0 0 0 0 0 0 \
0 \
0 \
0 \
0 \
0 \ 0 \
0 \ 0 \
0 \
0 \
0 \
0 \ 0 \
0 \ 0 \\\\\\
0 0 0 0 0 0 \
0

\
1 \
1 \
1 \
1 \ 1 \
1 \ 1 \
1 \
1 \
1 \
1 \ 1 \
1 \ 1 \
1 \
1 \
1 \
1 \ 1 \
1 \ 1 \
1 \
1 \
1 \
1 \ 1 \
1 \ 1

\\\\\\ 2
2 2 2 2 2 2 \ \
2 \
2 \
2 \
2 \ 2 \
2 \ 2 \
2 \
2 \
2 \
2 \ 2 \
2 \ 2 \\\\\\ 2
2 2 2 2 2 2 \
\
3 \
3 \
3 \
3 \ 3 \
3 \ 3 \
3 \
3 \
3 \
3 \ 3 \
3 \ 3 \
3 \
3 \
3 \
3 \ 3 \
3 \ 3 \
3 \
3 \
3 \
3 \ 3 \
3 \ 3

\\\\\\ 4
4 4 4 4 4 4 \ \
4 \
4 \
4 \
4 \ 4 \
4 \ 4 \
4 \
4 \
4 \
4 \ 4 \
4 \ 4 \\\\\\ 4
4 4 4 4 4 4 \
\
5 \
5 \
5 \
5 \ 5 \
5 \ 5 \
5 \
5 \
5 \
5 \ 5 \
5 \ 5 \
5 \
5 \
5 \
5 \ 5 \
5 \ 5 \
5 \
5 \
5 \
5 \ 5 \
5 \ 5

\\\\\\ 6
6 6 6 6 6 6 \ \
6 \
6 \
6 \
6 \ 6 \
6 \ 6 \
6 \
6 \
6 \
6 \ 6 \
6 \ 6 \\\\\\ 6
6 6 6 6 6 6 \
\
7 \
7 \
7 \
7 \ 7 \
7 \ 7 \
7 \
7 \
7 \
7 \ 7 \
7 \ 7 \
7 \
7 \
7 \
7 \ 7 \
7 \ 7 \
7 \
7 \
7 \
7 \ 7 \
7 \ 7

\\\\\\ 8
8 8 8 8 8 8 \ \
8 \
8 \
8 \
8 \ 8 \
8 \ 8 \
8 \
8 \
8 \
8 \ 8 \
8 \ 8 \\\\\\ 8
8 8 8 8 8 8 \
\
9 \
9 \
9 \
9 \ 9 \
9 \ 9 \
9 \
9 \
9 \
9 \ 9 \
9 \ 9 \
9 \
9 \
9 \
9 \ 9 \
9 \ 9 \
9 \
9 \
9 \
9 \ 9 \
9 \ 9

23
Mathematics Session 2
MA315696 OP B

2 In this diagram, JKL  STU.

U
J
60° S
L 2 cm

4 cm
K
T

Based on the measurements in the diagram, what is the measure of K?

A 15°

B 30°

C 45°

D 60°

24
Mathematics Session 2
MA717348780_PA OP A

2 Which list shows the rates, which relate distance and time, in order from
least to greatest?

A 100,000 yards per hour

1 mile per minute
100 feet per second

B 100 feet per second

1 mile per minute
100,000 yards per hour

C 1 mile per minute

100 feet per second
100,000 yards per hour

D 100 feet per second

100,000 yards per hour
1 mile per minute

MA903579407 OP A

 A bag contains 21 red marbles and 4 blue marbles, all of the same size and
shape. Two marbles will be randomly selected from the bag. The first marble
will not be returned to the bag before the second marble is selected.

Given that the first marble selected is blue, what is the probability that the
second marble selected will also be blue?

3
A 24

3
B 25

4
C 24

4
D 25

25
Mathematics Session 2
MA900784138 OP B

 A ball is dropped from the top of a ladder and bounces on the ground several
times. A student measures the maximum height of each bounce.

This function models h(n), the maximum height, in inches above the ground,
of the ball during its nth bounce.

h(n) = 96(0.55)n

What does the value 96 represent in the function?

A the number of times the ball bounces

B the initial height of the ball before it is dropped

C the decrease in the height of the ball per bounce

D the factor by which the height of each bounce is multiplied

26
Mathematics Session 2
MA903681943 OP B

 A circle with a diameter of 10 centimeters is divided into 24 equal sectors.

The sectors are separated and rearranged to create the figures shown in the
steps of this diagram.

10 cm
x cm

Step 1 Step 2 Step 3 Step 4

The length of the figure in Step 4 of the diagram is x centimeters. Which of

the following is closest to the value of x?

A 12

B 16

C 24

D 32

27
Mathematics Session 2

This question has four parts. Be sure to label each part of your response.
MA713808299 OP X

 All juniors and seniors at a high school were surveyed about whether they
had ever had a summer job. This graph shows the data from the survey.

Summer Jobs
for Students
250
200
150 Key
100
Summer job
50
No summer job
0
Juniors Seniors

A. Based on the graph, what is the total number of students who were
surveyed?

B. Based on the graph, what is the probability that a randomly selected

student had a summer job and is a junior? Show or explain how you got
your answer.

C. Based on the graph, what is the probability that a randomly selected

student had a summer job given that the student is a junior? Show or
explain how you got your answer.

D. Based on the graph, are juniors or seniors more likely to have had a
summer job? Explain your answer using conditional probabilities.

28
Mathematics Session 2



29
Mathematics Session 2
MA901767462_PA OP A

 A triangle is shown on this coordinate plane. The triangle will be dilated by a

scale factor of 2.5 with respect to the origin.

10
9
8
7
6
5
4
3
2
1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
x
1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

30
Mathematics Session 2

Which of the following graphs correctly shows the triangle and its image after
the dilation?

A y B y
10 10
9 9
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
x x
1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6
-7 -7
-8 -8
-9 -9
-10 -10

C y y
D
10 10
9 9
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
x
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
-6 -6
-7 -7
-8 -8
-9 -9
-10 -10

31
Mathematics Session 2
MA315448 OP C

 A restaurant serves iced tea in small glasses and large glasses.

• 1 small glass and 2 large glasses contain a total of 48 fluid ounces of

iced tea.
• 2 small glasses and 3 large glasses contain a total of 76 fluid ounces of
iced tea.
What is the total number of fluid ounces contained in 1 large glass of iced
tea?

A 8

B 14

C 20

D 28

32
Mathematics Session 2
MA308751 OP B

 This diagram shows a circle and an inscribed quadrilateral, with angle

measures represented by expressions.

T
(5x – 1)°

(3x + 5)°
W V

Based on the diagram, what is mV?

A 68°

B 71°

C 109°

D 136°

33
Mathematics Session 2
MA901700241_PA OP A

 It takes a barber between 20 and 30 minutes to give a customer a haircut.

• The barber will give haircuts for a total of 8 hours today.

• He has already spent 96 minutes cutting hair today.

What is a reasonable estimate of the number of additional haircuts the

barber can give today?

A 16

B 24

C 32

D 40

34
Mathematics Session 2

This question has two parts.

MA903452431 OP B; X

 A pentagon is graphed on this coordinate plane.

1 unit
y
1 unit
7
6
5 (3, 4)
(0, 4) 4
3
(–4, 1) 2
1 (3, 0)
x
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-1
-2
-3
(–1, –3) -4
-5
-6
-7

Part A

What is the perimeter, in units, of the pentagon?

A 17.8 units

B 22 units

C 23.2 units

D 27 units

35
Mathematics Session 2

Part B

What is the area, in square units, of the pentagon?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

\
–
• \
\ • \ • \
• • \
• \\ •

\ 0 \
0 \ 0 \
0 \ 0 \
0 \
0

\ 1 \
1 \ 1 \
1 \ 1 \
1 \
1

\ 2 \
2 \ 2 \
2 \ 2 \
2 \
2

\ 3 \
3 \ 3 \
3 \ 3 \
3 \
3

\ 4 \
4 \ 4 \
4 \ 4 \
4 \
4

\ 5 \
5 \ 5 \
5 \ 5 \
5 \
5

\ 6 \
6 \ 6 \
6 \ 6 \
6 \
6

\ 7 \
7 \ 7 \
7 \ 7 \
7 \
7

\ 8 \
8 \ 8 \
8 \ 8 \
8 \
8

\ 9 \
9 \ 9 \
9 \ 9 \
9 \
9

36
Mathematics Session 2
MA903566809 OP D

 This histogram shows the populations, in thousands, of different age groups

in a city.

Population of a City
22
20
Population (thousands)
18
16
14
12
10
8
6
4
2
0
19

de d
ol an
–3

–5

–7
0–

r
20

40

60

80
Age (years)

Based on the histogram, what fraction of the total population of the city is
between the ages of 20 and 59?

17
A 65

18
B 65

30
C 65

35
D 65

37
Mathematics Session 2

This question has four parts. Be sure to label each part of your response.
MA302066 OP X

 A vase in the shape of a right circular cylinder has a diameter of

22 centimeters.

A. What is the area, in square centimeters, of the base of the vase? Show or
explain how you got your answer.

B. The vase is partially filled with water to a depth of 10 centimeters.

What is the volume, in cubic centimeters, of the water in the vase? Show
or explain how you got your answer.

C. A solid sphere with a diameter of 12 centimeters is placed into the vase.

What is the volume, in cubic centimeters, of the sphere? Show or explain

how you got your answer.

D. The sphere sinks to the bottom of the vase. As a result, the water level
rises, but the water does not overflow.

What is the total number of centimeters the water level in the vase rises
when the sphere sinks to the bottom? Show or explain how you got your
answer.

38
Mathematics Session 2



39
Mathematics Session 2

This question has two parts.

MA901378123_PA OP B; B

 A student has an after-school job. This function models the amount of money,
in dollars, the student earns for working h hours in a week.

M(h) = 12.5h

The student can work a maximum of 20 hours in a week.

Part A

Which of the following is the domain of the function?

A 0 ≤ h ≤ 12.5

B 0 ≤ h ≤ 20

C 12.5 ≤ h ≤ 20

D 12.5 ≤ h ≤ 32.5

Part B

Which of the following is the range of the function?

A 0 ≤ M(h) ≤ 650

B 0 ≤ M(h) ≤ 250

C 125 ≤ M(h) ≤ 250

D 250 ≤ M(h) ≤ 650

40
Mathematics Session 2
MA311240 OP B

 Triangle EFG is similar to triangle JKL.

• The measure of E is 32°.

• The measure of K is 49°.

What is the measure of F ?

A 32°

B 49°

C 81°

D 99°

41
Mathematics Session 2
MA903470727 OP X

 A marketing company surveyed random customers from two age groups

about their favorite type of juice. The results of the survey are shown in this
table.

Favorite Juice

Type of Juice

Apple Orange Grape Total

Less
Age of Customer

80 120 50 250
Than 30

30 or
140 70 40 250
Greater

Total 220 190 90 500

Based on the table, what percentage of the customers surveyed chose apple
juice as their favorite type of juice?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

\
–
• \
\ • \ • \
• • \
• \\ •

\ 0 \
0 \ 0 \
0 \ 0 \
0 \
0

\ 1 \
1 \ 1 \
1 \ 1 \
1 \
1

\ 2 \
2 \ 2 \
2 \ 2 \
2 \
2

\ 3 \
3 \ 3 \
3 \ 3 \
3 \
3

\ 4 \
4 \ 4 \
4 \ 4 \
4 \
4

\ 5 \
5 \ 5 \
5 \ 5 \
5 \
5

\ 6 \
6 \ 6 \
6 \ 6 \
6 \
6

\ 7 \
7 \ 7 \
7 \ 7 \
7 \
7

\ 8 \
8 \ 8 \
8 \ 8 \
8 \
8

\ 9 \
9 \ 9 \
9 \ 9 \
9 \
9

42
Mathematics Session 2
MA901373728 OP B

 Consider Y.

A compass and a straightedge were used to perform a construction given Y.

This diagram shows the completed construction.

X
P

Y Z

These steps were followed to complete the construction.

• An arc was drawn, with the compass, from point Y through the sides of
the angle to create point X and point Z.
• Two arcs were drawn, each with the same compass setting, one from
point X and one from point Z. The arcs intersect to create point P.
• A ray was drawn, with the straightedge, from point Y through point P.

43
Mathematics Session 2

Based on the construction, which of the following is not true?

A mPYX = mPYZ

B mXYZ = 1 (mPYZ)
2
C ray YP is an angle bisector of XYZ

D point P is equidistant from points X and Z

44
Mathematics Session 2

This question has two parts.

MA903457147 OP D; X

 This diagram shows circle L, central angle XLY, and some of their
measurements.

6 in.

L 120°

Part A

Which of the following is closest to the area, in square inches, of the shaded
sector of circle L?

A 9.4

B 18.8

C 28.3

D 37.7

45
Mathematics Session 2

Part B

What is the length, to the nearest tenth of an inch, of ?

Enter your answer in the answer boxes at the top of the answer grid and
completely fill the matching circles.

\
–
• \
\ • \ • \
• • \
• \\ •

\ 0 \
0 \ 0 \
0 \ 0 \
0 \
0

\ 1 \
1 \ 1 \
1 \ 1 \
1 \
1

\ 2 \
2 \ 2 \
2 \ 2 \
2 \
2

\ 3 \
3 \ 3 \
3 \ 3 \
3 \
3

\ 4 \
4 \ 4 \
4 \ 4 \
4 \
4

\ 5 \
5 \ 5 \
5 \ 5 \
5 \
5

\ 6 \
6 \ 6 \
6 \ 6 \
6 \
6

\ 7 \
7 \ 7 \
7 \ 7 \
7 \
7

\ 8 \
8 \ 8 \
8 \ 8 \
8 \
8

\ 9 \
9 \ 9 \
9 \ 9 \
9 \
9

MA805405196_PA OP C

 Which of the following can not be modeled by a linear function?

A The total cost of purchasing apples that cost 60 cents each.

B As 5-pound bricks are added to a cart, the total weight increases.

C The number of people registered on a website doubles every month.

D The total distance traveled by a turtle walking at a constant speed

increases over time.

46
Mathematics Session 2
MA281661 OP C

 The coordinates of each vertex of quadrilateral LMNP are listed.

• L(x, y)
• M(2x, −y)
• N(−2x, −y)
• P(−x, y)

In quadrilateral LMNP, x = y, and x ≠ 0. What type of quadrilateral is LMNP?

A square

B rhombus

C trapezoid

D rectangle

MA315444 OP D

 All the students in Mr. Greene’s class are either 17 years old or 18 years old.

• There are a total of 20 students in Mr. Greene’s class.

• The sum of the ages of the 20 students is 345 years.

What is the total number of 17-year-old students in Mr. Greene’s class?

A 5

B 8

C 12

D 15

47
 Massachusetts Comprehensive Assessment System
Grade 10 Mathematics Reference Sheet

CONVERSIONS
1 cup = 8 fluid ounces 1 inch = 2.54 centimeters 1 pound = 16 ounces
1 pint = 2 cups 1 meter 39.37 inches 1 pound 0.454 kilogram
1 quart = 2 pints 1 mile = 5280 feet 1 kilogram 2.2 pounds
1 gallon = 4 quarts 1 mile = 1760 yards 1 ton = 2000 pounds
1 gallon 3.785 liters 1 mile 1.609 kilometers
1 liter 0.264 gallon 1 kilometer 0.62 mile
1 liter = 1000 cubic centimeters

AREA (A) FORMULAS CIRCLE FORMULAS

square . . . . . . . . . . . A = s 2 pi . . . . . . . . . . . . . 3.14
rectangle . . . . . . . . . A = lw
circumference . . . . C = 2 r OR C = d
parallelogram . . . . . . A = bh
area . . . . . . . . . . . A = r2
triangle . . . . . . . . . . A = 1 bh
2

trapezoid . . . . . . . . . A = 1 h(b + b2) RIGHT TRIANGLES

2 1

circle . . . . . . . . . . . . A = r 2 Pythagorean Theorem

c a2 + b2 = c2
a
TOTAL SURFACE AREA (SA) FORMULAS
Trigonometric Ratios
cube . . . . . . . . . . . . . . . SA = 6s 2 sin = a
b c
right square pyramid . . . . SA = s 2 + 2s cos = b
c
( = slant height)
tan = a
right rectangular prism . . SA = 2(lw) + 2(hw) + 2(lh) b

SPECIAL RIGHT TRIANGLES

VOLUME (V) FORMULAS

cube . . . . . . . . . . . . V = s 3
x 45° x 2
(s = length of an edge)
prism . . . . . . . . . . . . V = Bh 45°
x
cylinder . . . . . . . . . . V = r 2 h

cone . . . . . . . . . . . . V = 1 r 2h
3
60° 2y
y
pyramid . . . . . . . . . . V = 1 Bh
3
30°
sphere . . . . . . . . . . . V = 4 r 3
3 y 3
48
 Grade 10 Mathematics
Spring 2022 Released Operational Items
PBT
Page Reporting Item Correct
Item Standard Item Description
No. Category Type* Answer**
No.
Algebra and Determine the solution of a linear equation in one
1 4 A-REI.B.3 SR D
Functions variable.
Algebra and Identify linear equations in two variables that represent a
2 4 A-CED.A.2 SR B
Functions real-world situation.
Given two similar triangles, use a proportional
3 5 Geometry G-SRT.B.5 SR C
relationship to determine an unknown side length.
Algebra and Factor a trinomial expression to identify an equivalent
4 6 A-SSE.A.2 SR C
Functions expression.
Algebra and Determine an expression that represents an arithmetic
5 6 F-BF.A.2 SR D
Functions sequence, given its first five terms.
Number and Interpret the units in a graph that represents a real-world
6 7–8 N-Q.A.2 CR
Quantity situation and estimate solutions of associated problems.
Identify the triangle theorem that is illustrated by a folded
7 9 Geometry G-CO.C.10 SR A
paper demonstration.
Algebra and Identify the graph of the solution set of a system of linear
8 10 A-REI.D.12 SR A
Functions inequalities in two variables.
Identify an equation that may not be true based on a
9 11 Geometry G-CO.C.9 SR D
diagram featuring parallel lines and a transversal.
Algebra and Expand a polynomial expression to create an equivalent
10 11 A-APR.A.1 SR A
Functions expression.
Algebra and Rearrange an equation to solve for different aspects of the
11 12 A-CED.A.4 SR D;B
Functions formula it represents.
Number and Given an exponential expression, use properties of
12 13 N-RN.A.2 SR C
Quantity exponents to identify an equivalent expression.
Evaluate a linear function over specific values of its
Algebra and
13 13–14 F-IF.A.2 CR domain and interpret given values of the function in terms
Functions
of a real-world context.
Statistics and Interpret the slope and the y-intercept of a linear model
14 15–16 S-ID.C.7 SA 263.3;A
Probability based on real-world data.
Describe a transformation of a line segment that will
15 17 Geometry G-CO.A.4 SR D
result in a parallel image.
Algebra and Identify an equation that represents the graph of a
16 18 F-BF.B.3 SR D
Functions function after it has been translated.
Algebra and Factor a quadratic expression to solve a real-world
17 18 A-SSE.B.3 SR C
Functions problem.
Number and Identify equivalent radical expressions using rational
18 19 N-RN.A.1 SR B;C
Quantity exponents.
Determine the coordinates of an end point of a line
19 20 Geometry G-CO.A.2 SR A
segment, graphed on a coordinate plane, after a rotation.
Algebra and Determine the y-value of the solution of a system of linear
20 21 A-REI.C.6 SR A
Functions equations.
Determine an angle measure in a right triangle based on
21 21 Geometry G-SRT.C.6 SA 30
the relationship of two of the triangle's side lengths.
Determine an unknown angle measure based on a diagram
22 24 Geometry G-SRT.B.5 SR B
of two similar triangles.
Number and Compare rates that relate distance and time, given in
23 25 N-Q.A.1 SR A
Quantity different units.

49
 PBT
Page Reporting Item Correct
Item Standard Item Description
No. Category Type* Answer**
No.
Statistics and Compute a conditional probability based on dependent
24 25 S-CP.A.3 SR A
Probability events in a real-world situation.
Algebra and Interpret the parameters of an exponential function based
25 26 F-LE.B.5 SR B
Functions on a real-world context.
26 27 Geometry G-GMD.A.1 SR Use dissections to find the partial circumference of a circle. B
Calculate compound and conditional probabilities from
Statistics and
27 28–29 S-CP.B.6 CR data displayed in a graph and interpret the graph in terms of
Probability
the probabilities.
Identify the graph of a triangle on a coordinate plane after
28 30–31 Geometry G-SRT.A.1 SR A
a dilation.
Algebra and Create two-variable linear equations and use them to solve
29 32 A-CED.A.2 SR C
Functions a real-world problem.
Determine the measure of an angle of a quadrilateral
30 33 Geometry G-C.A.3 SR B
inscribed in a circle.
Number and Use estimation and rounding strategies to solve a real-
31 34 N-Q.A.3 SR A
Quantity world problem.
Calculate the perimeter and the area of a pentagon graphed
32 35–36 Geometry G-GPE.B.7 SA B;31
on a coordinate plane.
Statistics and
33 37 S-ID.A.1 SR Interpret a histogram based on a set of real-world data. D
Probability
Use volume formulas for cylinders and spheres to solve
34 38–39 Geometry G-GMD.A.3 CR
real-world problems.
Algebra and Determine the domain and range of a linear function based
35 40 F-IF.B.5 SR B;B
Functions on a real-world context.
Determine the measure of an angle in one of a pair of
36 41 Geometry G-SRT.A.3 SR B
similar triangles.
Statistics and Calculate a marginal relative frequency from data in a two-
37 42 S-ID.B.5 SA 44
Probability way table.
38 43–44 Geometry G-CO.D.12 SR Interpret the results of the construction of an angle bisector. B
Determine the area of a sector of a circle and its arc length
39 45–46 Geometry G-C.B.5 SA D;12.5
given the radius of the circle and a central angle measure.
Algebra and Identify a situation which can not be modeled by a linear
40 46 F-LE.A.1 SR C
Functions function.
Determine the nature of a quadrilateral given its
41 47 Geometry G-GPE.B.4 SR C
coordinates represented by expressions.
Algebra and Create a one-variable equation, based on a real-world
42 47 A-CED.A.1 SR D
Functions context, and use the equation to solve a problem.

  * Mathematics item types are: selected-response (SR), short-answer (SA), and constructed-response (CR).
** Answers are provided here for selected-response and short-answer items only. Sample responses and scoring guidelines for constructed-
response items will be posted to the Department’s website later this year.

50