Writing Mathematics Practice Test Book
Grade 10 SBA–HSGQE
HSGQE Retest
10P01WM
Alaska Department of Education
& Early Development
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Comprehensive System of Student Assessment
Grade 10 Standards Based Assessments
Mathematics
FORM 10P01WM
PAGE 21
For an item that is not multiple-choice, you must respond to what
is requested, write in English (and/or mathematics symbols when
appropriate), and make sure that your responses are readable. No
credit will be given to any response that
•
•
•
•
•
•
•
is too short to score
consists of “I don’t know”
indicates refusal to respond to the item
consists of copying the item
does not address the item or topic
is not legible
is written in a language other than English. (If part of the response
is in English, that part will be scored.)
PAGE 22
MATHEMATICS PRACTICE TEST
SAMPLE QUESTIONS
Sample A
The coordinates on a grid of the location of 2 trees in a park are (3, 9) and
(5, 3). What are the coordinates of the midpoint of the line segment joining
the 2 trees?
A (2, 6)
B (4, 6)
C (4, 12)
D (8, 12)
Sample B
The table below shows Kelly’s telephone bill.
TELEPHONE BILL
Number of
Minutes Used
Total Bill
500
$30.00
600
$35.00
700
$40.00
The pattern continues. Kelly uses 1,000 minutes. What will be Kelly’s total bill?
A
$45.00
B
$50.00
C
$55.00
D
$60.00
GO ON
PAGE 23
MATHEMATICS PRACTICE TEST
Sample C
Jim is making a similar, large rectangle from a small rectangle as shown below.
Small
Rectangle
2 inches
Large
Rectangle
6 inches
height
12 inches
What is the height of the large rectangle? This item is worth 2 points.
Show the work.
Answer: ______________________________ inches
STOP
PAGE 24
MATHEMATICS PRACTICE TEST
You may use the Mathematics Reference Sheet any time during the test.
1
2
Travis found the area of a circle using the formula A = π r2. What type of number is π?
A
integer
B
irrational
C
natural
D
rational
The 3 shapes below are the same size and are regular pentagons.
A
C
B
What is the measure of /ABC?
A
18°
B
36°
C
45°
D
72°
GO ON
PAGE 25
MATHEMATICS PRACTICE TEST
The bar graph below compares the percent of students in Alaska to the percent of students
in the U.S. who played on 1 or more sports teams in a year.
SPORTS-TEAM PLAYERS
Percent of Students
3
70
60
50
40
30
20
10
0
total
male
female
Students
Key
U.S.
Alaska
Which table shows the data in the graph?
A
SPORTS-TEAM PLAYERS
Students
total
female
male
C
Percent in Percent in
Alaska
U.S.
57
63
51
60
64
65
SPORTS-TEAM PLAYERS
Students
total
female
male
B
Percent in Percent in
Alaska
U.S.
67
52
60
56
69
68
SPORTS-TEAM PLAYERS
Students
total
female
male
D
Percent in Percent in
Alaska
U.S.
65
55
60
55
65
65
SPORTS-TEAM PLAYERS
Students
total
female
male
Percent in Percent in
Alaska
U.S.
63
57
60
51
65
64
GO ON
PAGE 26
MATHEMATICS PRACTICE TEST
4
5
Randy bought a pen on sale. The sale price of the pen was $2.34. The original price of the
pen was $3.25. What percent did Randy save by buying the pen on sale?
A
28
B
39
C
72
D
91
The table below shows the value of a car during its first 3 years.
VALUE OF CAR
Year
Value
0
$21,000
1
$18,500
2
$16,000
3
$13,500
The pattern continues. What will be the value of the car in year 6?
A
$1,000
B
$3,500
C
$6,000
D
$8,500
GO ON
PAGE 27
MATHEMATICS PRACTICE TEST
6
The spinner shown below is used in a game.
GAME SPINNER
8
1
7
2
6
3
5
4
Esther spins the spinner 8 times and gets an even number 5 times. Which statement correctly
compares the experimental and theoretical probability of getting an even number?
A The experimental probability is the same as the theoretical probability.
B The experimental probability is greater than the theoretical probability by }18.
C The experimental probability is less than the theoretical probability by }18.
D The experimental probability is greater than the theoretical probability by }12.
GO ON
PAGE 28
MATHEMATICS PRACTICE TEST
7
Jenny incorrectly simplified 42 × 43 and got an answer of 166. Explain what Jenny did wrong,
and write the correct answer on the line below. This item is worth 2 points.
Answer:
8
A cylinder has a volume of 150 cubic yards. How many cubic feet is this?
A
150 × 3
B
150 × 9
C
150 × 12
D
150 × 27
GO ON
PAGE 29
MATHEMATICS PRACTICE TEST
9
Alyssa made the design shown below.
y
A
B
x
Which transformation could be used to show that figure A is congruent to figure B?
10
A
add 5 to each x-coordinate
B
multiply each y-coordinate by {1
C
multiply each x-coordinate by {1
D
rotate the figure 90 degrees about the origin
3 }
Which shows how to find the value of x in the equation Ïx = 8?
A
83
B
8×3
C
3 }
D
8÷3
Ï8
GO ON
PAGE 30
MATHEMATICS PRACTICE TEST
11
12
Which property of multiplication shows that 25 × (4 × 83) = (25 × 4) × 83?
A
associative
B
commutative
C
distributive
D
identity
The stem and leaf plot below displays information about the number of people who
attended the Saturday matinees at Oak Woods Theater for 14 weeks.
SATURDAY MATINEES
AT OAK WOODS THEATER
3
4
5
6
7
9
5
1
2
5
7 8
1 3 5 9
2
9 9
KEY
7 4 = 74
How many Saturdays had more than 50 people in attendance?
A
5
B
7
C
10
D
13
GO ON
PAGE 31
MATHEMATICS PRACTICE TEST
13
A company logo contains the shape represented by the figure below.
y
x
Which shape is congruent to the figure above?
A
B
y
y
x
C
x
D y
y
x
x
GO ON
PAGE 32
MATHEMATICS PRACTICE TEST
14
The table shows the production of chairs at a furniture factory with respect to the number of
weeks from the beginning of the year. This item is worth 4 points.
CHAIR PRODUCTION
Number of
Weeks
Chairs Produced
3
450
6
900
9
1,350
12
1,800
15
2,250
Write an equation in slope-intercept form ( y = mx + b) that models the situation.
Show the work.
The pattern continues. How many weeks will it take the factory to make 5,250 chairs?
Show the work.
Answer:
weeks
GO ON
PAGE 33
MATHEMATICS PRACTICE TEST
15
3
__
Which is equivalent to 32 × 3?
9
__
A 36
5
__
B 32
6
__
C 32
9
__
D 32
16
What number of square meters is the same as 125 square centimeters?
A
0.00125
B
0.0125
C
0.125
D
1.25
GO ON
PAGE 34
MATHEMATICS PRACTICE TEST
17
Which graph represents the inequality y < 2x?
A
B
y
y
x
C
x
D
y
x
y
x
GO ON
PAGE 35
MATHEMATICS PRACTICE TEST
A group of friends recorded the time it took to ride their bikes around the park. The scatter
plot below shows their results with the line of best fit.
y
BICYCLING AROUND THE PARK
10
9
8
Time (minutes)
18
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9 10
x
Number of Laps
Using the line of best fit, which is closest to the number of minutes it would take to
complete 9 laps?
A
4
B
5
C
6
D
7
GO ON
PAGE 36
MATHEMATICS PRACTICE TEST
19
20
A gumball machine contains 45 gumballs and 5 prizes. Vanessa puts in a coin and receives
an item. She then puts in a second coin and receives another item. What is the probability
that she will first get 1 gumball and then get 1 prize?
1
225
A
}
B
}
C
}
D
}
9
100
9
98
2
9
The cost of materials needed to make a sail is represented by the equation below where C is
the cost and b is the length of the base of the sail.
C = }b2 + 10
Which shows the equation solved for b?
A
b = C + 12
B
b = C − 12
C
b = 2C − 10
D
b = 2C − 20
STOP
PAGE 37
DO NOT
MARK
ON THIS
PAGE
PAGE 38
Name
Alaska Mathematics Standards Reference Sheet
Shape
Circle
A = r2
Triangle
A=
Rectangle
A = lw
1
2
C= d =2 r
bh
Key
1
2 h(b 1 +
Trapezoid
A=
Parallelogram
A = bh
Shape
Circumference
Area
b2 )
b = base
h = height
l = length
w = width
= slant height
d = diameter
r = radius
B = area of base
Use 3.14 or 22
7 for
Volume
1
3
Total Surface Area
SA = 12 ( 2 r) +
Right Circular Cone
V=
Square Pyramid
V = 13 lwh
Sphere
V=
Right Circular Cylinder
V = r 2h
SA = 2 rh + 2 r 2
Rectangular Solid
V = lwh
SA = 2(lw) + 2(hw) + 2(lh)
Triangular Prism
V = Bh
4
3
r 2h
r3
.
r2 = r +
SA = 4 ( 12 l ) + l 2 = 2 l + l 2
SA = 4 r2
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).
PAGE
41 angle is equal to 180(n -- 2)
In a regular polygon, the measure of an
interior
n.
r2
Alaska Mathematics Standards Reference Sheet
Formulas
Slope-intercept form of an equation
of a line, where m = slope and
b = the y-intercept:
Distance between two points
P 1 (x1, y1) and P2 (x2 , y2 ):
(x 2 -- x1 ) 2 + (y2-- y 1 ) 2
y = mx + b
Midpoint between two points
P 1 (x 1, y 1) and P 2 (x 2 , y 2 ):
Distance, rate, time formula,
where d = distance, r = rate, t = time:
(x +2 x
2
d = rt
1,
y2 + y1
2
)
Quadratic formula,
if ax 2 + bx + c = 0:
Simple Interest = prt
where p = principal, r = rate, t = time
x=
-- b +
--
b 2 -- 4ac
2a
Conversions
1
1
1
1
1
yard = 3 feet = 36 inches
mile = 1,760 yards = 5,280 feet
acre = 43,560 square feet
hour = 60 minutes
minute = 60 seconds
1
1
1
1
1
liter = 1,000 milliliters = 1,000 cubic centimeters
meter = 100 centimeters = 1,000 millimeters
kilometer = 1,000 meters
gram = 1,000 milligrams
kilogram = 1,000 grams
1
1
1
1
cup = 8 fluid ounces
pint = 2 cups
quart = 2 pints
gallon = 4 quarts
1 pound = 16 ounces
1 ton = 2,000 pounds
1 meter = 3.28 feet
1 kilogram = 2.20 pounds
DO NOT
MARK
ON THIS
PAGE
PAGE 39
Writing Mathematics Practice Test Book
Grade 10 SBA–HSGQE
HSGQE Retest
Form 10P01WM
Copyright © 2007 by Alaska Department of Education & Early
Development. No part of this publication may be reproduced or
distributed in any form or by any means, or stored in a database or
retrieval system, without the prior written permission of the publisher.
COMPREHENSIVE SYSTEM OF STUDENT ASSESSMENT
(CSSA)
Mathematics Practice Test Scoring Guide
Grade 10 SBA–HSGQE
HSGQE Retest
Alaska Department of Education & Early Development
Mathematics Practice Test Scoring Guide
with Answer Keys, Scoring Guidelines, and Sample Papers
General Introduction
The Alaska Department of Education and Early Development (EED), in cooperation with Data Recognition
Corporation, designed and produced the Alaska Practice Test to support students in doing their best on the Alaska
Comprehensive System of Student Assessment, Standards Based Assessments in grade 10. A scoring guide, with
answer keys, scoring guidelines, sample student papers, and a test map, provides the teacher with information and
tools to score each practice test.
Content
A Practice Test Scoring Guide for each grade level and subject area is posted on the EED Website
(http://www.eed.state.ak.us/tls/assessment). To access this website, follow these instructions.
Directions to access the AK EED Website
1. Type or copy and paste the link to the Alaska EED Website into your browser.
http://www.eed.state.ak.us/tls/assessment
2. Select Standards Based Assessments.
3. Select Item Samplers / Practice Tests.
4. Select the grade-level assessment (or other document) you wish to download.
5. At this point you may save the file to your computer or print the file directly from the website. Printing
from the website can be very time consuming. It is likely you will want to save the file(s) to your computer,
then print.
This guide is divided into two sections. Section I includes the answer keys and scoring guidelines (with detailed
item-specific scoring rubrics for scoring short and extended constructed-response questions) and sample student
papers with annotations for each score point. Section II presents a grade-level test map that lists item sequence,
corresponding Grade Level Expectation and/or Performance Standard, and an answer key.
Purpose
The passages, stimuli, prompts, graphs, charts, and items included for each content-area practice test were created
for use in Alaska classrooms. These materials may be copied and used as part of a local instructional program.*
Alaska educators may use the reading, writing, and mathematics practice tests, the Practice Test Administration
Directions, and the Practice Test Scoring Guides to support daily instruction in the classroom and to prepare their
students for the operational assessments.
Important: The practice tests were developed for usability purposes only, and in no way should the tests
or scores students receive be considered a predictor of a student’s ability to perform on the operational
assessments. Passages, prompts, stimuli, and items provide samples of what students will see on the
operational tests. Items are not necessarily the same in terms of measurement, rigor, or the length of time it
takes a student to respond.
*The permission to copy and/or use these materials does not extend to commercial purposes.
Mathematics Practice Test Scoring Guide: Grade 10
2
Item Format
The mathematics practice test includes two types of mathematics items: multiple choice and constructed
response. Practice test multiple-choice items have four answer options. The correct response to each
multiple-choice item is worth one point.
Two types of constructed-response items are presented in the mathematics practice test: short
constructed response (SCR) are 2-point items; extended constructed response (ECR) are 4-point items.
Item-specific scoring guidelines and examples of responses for each score point are presented with each
constructed-response item.
Measurement items are not included in the mathematics practice test because teachers will
download the practice tests from the Alaska Education and Early Development Website
(http://www.eed.state.ak.us/tls/assessment) and print them on local computers. When printing occurs
using local computers, measurement items (that require a ruler) may be scaled differently from the
actual figure that appears on the PDF, and true measurement cannot be achieved. Teachers are
encouraged, however, to include measurement items on their regular classroom tests.
Scoring Guidelines
Following the multiple-choice answer key are general scoring rubrics for 2-point and 4-point constructedresponse items. The general scoring rubric includes item-specific guidelines to assist the teacher with
scoring constructed-response items.
Sample student papers are included for each short and extended constructed-response score point. An itemspecific annotation follows each sample student response. The annotations are designed to provide the teacher
with the explanation of why the score point was awarded.
Test Maps
The test map presents the sequence of the items, the Grade Level Expectation and/or Performance Standard
to which each item is aligned, and the answer key. This at-a-glance chart is designed to assist the teacher with
scoring the practice test.
3
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
1.
2.
3.
4.
5.
6.
7.
B
B
D
A
C
B
Jenny incorrectly simplified 42 × 43 and got an answer of 166. Explain what Jenny did
wrong, and write the correct answer on the line below. This item is worth 2 points.
Answer:
Mathematics Practice Test Scoring Guide: Grade 10
4
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
7.
Short Constructed Response
Score
Rubric
2
3 of 3 parts correct
1
1 or 2 of 3 parts correct
OR
Some correct and relevant work or explanation
0
Response is incorrect or irrelevant
Explanation of error in bases
Explanation of error in exponents
Correct answer
Problem Solution:
Jenny multiplied the bases. (When multiplying two exponential terms that have
the same bases, the base remains the same and not 4 × 4 = 16) or equivalent
Jenny multiplied the exponents. (When multiplying two exponential terms that
have the same bases, one adds the exponents [2 + 3 = 5], not multiplies them) or
equivalent
45 or 210 or 1024 or equivalent
5
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #7
Response Score: 2
Short Constructed Response:
Annotation for score point: 2
Three of 3 parts correct:
1. Correct explanation of error in bases (“She multiplied the two 4s” . . . “the 4 should
remain [unchanged]”)
2. Correct explanation of error in exponents (“. . . multiplied the exponents . . . should be
added”)
3. Correct answer of 45
Mathematics Practice Test Scoring Guide: Grade 10
6
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #7
Response Score: 1
Short Constructed Response:
Annotation for score point: 1
Two of 3 parts correct:
1. Correct explanation of error in bases (“She multiplied 4 ● 4 . . . and got [base] 16 . . .”)
2. Correct explanation of error in exponents (“She multiplied 2 ● 3 . . . and got
[exponent] 6”)
3. Incorrect answer of 306
7
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #7
Response Score: 0
Short Constructed Response:
Annotation for score point: 0
No parts correct:
1. Incorrect answer of 46
2. No correct explanation
Mathematics Practice Test Scoring Guide: Grade 10
8
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
8.
9.
10.
11.
12.
13.
14.
D
C
A
A
C
D
The table shows the production of chairs at a furniture factory with respect to the
number of weeks from the beginning of the year. This item is worth 4 points.
CHAIR PRODUCTION
Number of
Weeks
Chairs Produced
3
450
6
900
9
1,350
12
1,800
15
2,250
Write an equation in slope-intercept form ( y = mx + b) that models the situation.
Show the work.
The pattern continues. How many weeks will it take the factory to make 5,250
chairs?
Show the work.
Answer:
weeks
9
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
14. Extended Constructed Response
Score
Rubric
4
4 of 4 parts correct
3
3 of 4 parts correct
2
2 of 4 parts correct
1
1 of 4 parts correct
OR
Some correct and relevant work or explanation (e.g., correct value of
slope without support and with no work)
0
Response is incorrect or irrelevant
Correct equation
Correct work shown for obtaining the equation
Correct number of weeks or number of weeks based on student’s equation (error
carried through if incorrect)
Correct work shown for calculating the number of weeks
Problem Solution:
y = 150x or equivalent (variables may be different but must be an equation)
900 – 450 450
}
slope = }
6 – 3 = 3 = 150 and 450 = 150 ● 3 + b and 450 – 450 = b = 0
thus, y-intercept = 0 and does not need to be in the equation
35 (weeks) or answer based on an incorrect equation in Part A
5250
} = 35 or equivalent (may see repeated subtractions that account for blocks of
150
weeks—e.g., 5250 – 2250 = 3000 for 15 weeks, etc.)
Mathematics Practice Test Scoring Guide: Grade 10
10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #14
Response Score: 4
Extended Constructed Response:
Annotation for score point: 4
Four of 4 parts correct:
1. Correct equation (y = 150x + 0)
∆y
2. Correct work shown for equation (uses }
∆x = m to find slope & substitutes in number of
weeks and chairs to find y-intercept)
3. Correct number of weeks (35)
4. Correct work shown for number of weeks (5,250 = 150x)
11
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #14
Response Score: 3
Extended Constructed Response:
Annotation for score point: 3
Three of 4 parts correct:
1. Correct equation (y = 150x)
2. Insufficient work shown for equation (does not address y-intercept)
3. Correct number of weeks (35)
5250 150x
}
4. Correct work shown for number of weeks (}
150 = 150 )
Mathematics Practice Test Scoring Guide: Grade 10
12
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #14
Response Score: 2
Extended Constructed Response:
Annotation for score point: 2
Two of 4 parts correct:
1. Incorrect equation (y/450 = x)
2. No correct work shown for equation
3. Correct number of weeks (35)
}
4. Correct work shown for number of weeks (5250 × 3 = 15750 and 450 + 15750 )
13
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #14
Response Score: 1
Extended Constructed Response:
Annotation for score point: 1
One of 4 parts correct:
1. Incorrect equation (150 = m + b)
2. Incorrect work shown for equation
2
3. Incorrect number of weeks (35}3 ) due to calculation error
4. Correct work shown for number of weeks
Mathematics Practice Test Scoring Guide: Grade 10
14
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
Item #14
Response Score: 0
Extended Constructed Response:
Annotation for score point: 0
No parts correct:
Response is incorrect or irrelevant
15
Mathematics Practice Test Scoring Guide: Grade 10
SECTION I: Grade 10 Mathematics Practice Test Answer Keys,
Scoring Guidelines, and Sample Student Papers
15.
16.
17.
18.
19.
20.
B
B
A
B
C
D
Mathematics Practice Test Scoring Guide: Grade 10
16
SECTION II: Grade 10 Mathematics Test Map
Mathematics
Sequence
GLE
HSGQE
Key
1
N-1
NA
B
2
G-1
NA
B
3
S&P-1
M6.2.1
D
4
E&C-3
M3.3.4
A
5
F&R-1
M4.3.2
C
6
S&P-5
NA
B
7
N-2
M1.4.4
Short Constructed Response
8
MEA-1
NA
D
9
G-4
NA
C
10
N-5
NA
A
11
N-7
M1.4.7
A
12
S&P-2
M6.3.2
C
13
G-3
M5.2.3
D
14
F&R-2/F&R-1
M4.4.2
M4.3.1
Extended Constructed Response
15
E&C-2
NA
B
16
MEA-1
NA
B
17
F&R-2
NA
A
18
S&P-4
NA
B
19
S&P-6
NA
C
20
F&R-7
NA
D
17
Mathematics Practice Test Scoring Guide: Grade 10
Mathematics Practice Test Scoring Guide
Grade 10 SBA–HSGQE
HSGQE Retest
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