1. science
2. mathematics
3. algebra

GLENCOE
MATHEMATICS
Grade
Includes:
• West Virginia Content Standards
and Objectives, Tenth Grade,
Correlated to Glencoe Algebra 1
and Glencoe Geometry
• Student Recording Chart
• Diagnostic Test
• Numerous Practice Questions
for Each Objective
• Full-Size Sample Test
10
Test-Taking Tips
• Go to bed early the night before the test. You will think more clearly
after a good night’s rest.
• Read each problem carefully and think about ways to solve the
problem before you try to answer the question.
• Relax. Most people get nervous when taking a test. It’s natural. Just
do your best.
• Answer questions you are sure about first. If you do not know the
answer to a question, skip it and go back to that question later.
• Think positively. Some problems may seem hard to you, but you may
be able to figure out what to do if you read each question carefully.
• If no figure is provided, draw one. If one is furnished, mark it up to
help you solve the problem.
• When you have finished each problem, reread it to make sure your
answer is reasonable.
• Become familiar with a variety of formulas and when they should
be used.
• Make sure that the number of the question on the answer sheet
matches the number of the question on which you are working in
your test booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States
of America. Except as permitted under the United States Copyright Act, no part of this book may
be reproduced in any form, electronic or mechanical, including photocopy, recording, or any
information storage or retrieval system, without prior written permission of the publisher.
Send all inquiries to:
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8787 Orion Place
Columbus, OH 43240-4027
ISBN: 0-07-868587-7
WESTEST Grade 10
Practice and Sample Test Workbook
1 2 3 4 5 6 7 8 9 10 079 13 12 11 10 09 08 07 06 05 04
Contents
Student Recording Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
West Virginia Content Standards and Objectives, Tenth Grade,
Correlated to Glencoe Algebra 1 and Glencoe Geometry . . . . . . . . . . v
Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Test Practice
Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Standards Practice
10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
10.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
10.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Test Practice
Sample Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
How to Use This Workbook
The material in this booklet is designed to help you prepare for the
West Virginia Educational Standards Test (WESTEST), Grade 10.
Copyright © Glencoe/McGraw-Hill
Diagnostic Test This test will help you identify any weaknesses you
may have as you prepare to take the WESTEST 10. Once you’ve taken the
test and it’s been graded, complete the Student Recording Chart that is
found on page iv. Mark an × in the square for each question that they
answered incorrectly.
Practice If you missed one or two of the questions for a particular
objective, you could probably use some extra practice with that objective.
The Student Recording Chart lists practice pages for each objective.
Complete the appropriate practice pages. If you are unsure about how to do
some of the problems, you may want to refer to your mathematics book.
Sample Test After you have completed your practice worksheet(s), take
the Sample Test on pages 46 to 55.
WESTEST, Grade 10
iii
Student Recording Chart
Directions Mark an × by each question from the Diagnostic Test that you
answered incorrectly. If there are one or two ×s marked for a SOL, write Yes in
the Need Practice? box. Then complete the practice pages for that standard.
Standard
10.1.1
10.1.2
10.1.3
10.2.1
10.2.2
11 ■ 19 ■
4 ■ 33 ■
41 ■ 33 ■
18 ■
1 ■ 23 ■
31 ■ 44 ■
11, 14–15
12, 14–15
13–15
16, 25–26
17, 25–26
10.2.3
10.2.4
10.2.5
10.2.6
10.2.7
7 ■ 39 ■
14 ■
16 ■
13 ■ 29 ■
27 ■ 36 ■
18, 25–26
19, 25–26
20, 25–26
21, 25–26
22, 25–26
10.2.8
10.2.9
10.3.2
10.3.3
10.3.4
24 ■
10 ■ 21 ■
6 ■ 26 ■
20 ■ 34 ■
15 ■ 40 ■
42 ■ 33 ■
23, 25–26
24–26
27, 32–33
28, 32–33
29, 32–33
10.3.5
10.4.1
10.4.2
10.4.4
3 ■ 30 ■
42 ■ 33 ■
8 ■ 38 ■
25 ■ 43 ■
2 ■ 12 ■
28 ■ 32 ■
43 ■ 48 ■
Practice Pages
30–33
34, 38–39
35, 38–39
36–39
Standard
10.5.1
10.5.2
10.5.3
10.5.4
17 ■ 22 ■
45 ■ 33 ■
5■
35 ■ 45 ■
9 ■ 37 ■
45 ■ 33 ■
40, 44–45
41, 44–45
42, 44–45
43–45
Test Questions
Need Practice?
Practice Pages
Standard
Test Questions
Need Practice?
Practice Pages
Standard
Test Questions
Need Practice?
Practice Pages
Standard
Test Questions
Test Questions
Need Practice?
Practice Pages
iv
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
Need Practice?
West Virginia Content Standards and Objectives,
Tenth Grade, Correlated to Glencoe Algebra 1
and Glencoe Geometry
Lessons in which the standards are a primary focus are indicated in bold.
Algebra 1
Lesson(s)
Objectives
Geometry
Lesson(s)
Standard 1: Number and Operations
Students will:
• demonstrate understanding of numbers, ways of representing numbers, and relationships among
numbers and number systems;
• demonstrate meanings of operations and how they relate to one another; and
• compute fluently and make reasonable estimates through communication, representation, reasoning
and proof, problem solving, and making connections within and beyond the field of mathematics.
10.1.1 Solve computational and practical problems using 1-2, 1-5, 1-6, 2-1, 2-2, 1-2, 1-3, 1-6, 3-3, 3-5,
properties of numbers, order of operation,
2-3, 2-4, 2-7, 10-6,
computation, and estimation with decimals,
11-1, 11-2
fractions, integers, and mixed numbers, including
ratio, proportion, and percents. (AM1.1, AGP.1,
AGP.2, AGP.17)
10.1.2 Write numbers involving scientific notation and
4-1, 4-3, 4-4, 4-7, 6-1,
6-2, 6-3, 6-4, 7-2, 8-2,
11-1
8-3
combine numbers written in scientific notation to
solve practical problems. (AM1.2)
10.1.3 Estimate and simplify square roots into both
2-7, 11-1, 11-2
exact and approximate forms. (AM1.14, A1.16)
PS10, 1-3, 7-2, 7-3,
15-3
Standard 2: Algebra (MA.S.2)
Students will:
• demonstrate understanding of patterns, relations, and functions;
• represent and analyze mathematical situations and structures using algebraic symbols;
• use mathematical models to represent and understand quantitative relationships; and
• analyze change in various contexts through communication, representation, reasoning and proof,
problem solving, and making connections within and beyond the field of mathematics.
Copyright © Glencoe/McGraw-Hill
10.2.1 Define variables and solve multi-step linear
equations and one-variable inequalities, interpret
results on a number line and apply the skills
toward solving practical problems. (AM1.10,
AM1.11, AGP.18, A1.2, A1.3)
10.2.2 Solve literal equations for a given variable and
1-3, 3-4P, 3-4, 3-5,
1-2, 1-3, 1-4, 1-5, 1-6,
3-6, 3-7, 3-8, 6-1, 6-2, 3-2, 3-6, 4-6, 5-1, 5-4,
6-3, 6-4, 6-5
5-5, 6-1, 6-3, 7-4, 8-1,
8-4, 10-3, 10-4, 10-6,
PS6, PS7
3-8
1-2
apply the skills toward solving practical problems.
(AM1.8, A1.4)
10.2.3 Solve practical problems using a four-step problem 3-1, 3-4P, 3-4, 3-5,
solving approach, justifying steps based on the
properties of real numbers. (AM1.9, AM1.7)
2-5, 2-6
3-6
P = Preview Lesson, F = Follow-Up Lesson, PS = Prerequisite Skill Lesson, RM = Reading Math
WESTEST, Grade 10
v
Algebra 1
Lesson(s)
Objectives
10.2.4 Evaluate and simplify algebraic expressions using
1-1, 1-2, 1-4, 1-5,
grouping symbols, order of operations, properties of 1-6, 8-1, 8-2, 8-3,
real numbers with justification of steps, and the laws 8-6, 8-7, 8-8
of exponents. (AGP.17, AM1.5, AM1.15, A1.7)
10.2.5 Solve absolute value equations in one variable and
6-5
Geometry
Lesson(s)
PS5, PS10, PS11,
PS12
1-3
interpret the results on a number line. (AM1.12, A1.6)
10.2.6 Analyze a given set of data for the existence of a
pattern numerically, algebraically and graphically.
(AM2.1, A1.6)
10.2.7 Determine the slope of a line given an equation of a
line, the graph of a line and two points to be
identified. (AM2.2, A1.8)
10.2.8 Write and graph linear equations. (AM2.3, AM2.4,
A1.9, A1.10)
4-7P, 4-7, 4-8, RM4, 2-1
10-7
5-1, 5-2, 5-3, 5-3F,
5-4, 5-5, 5-6
3-3, 3-4, 3-5, 3-6
4-5, 4-5F, 4-8, 5-2, 3-4, 3-5, 3-6
5-3P, 5-3, 5-3F, 5-4,
5-5, 5-6
10.2.9 Factor and perform basic operations on simple
8-5P, 8-5, 8-6, 8-7P, 10-8, PS10, PS11,
polynomials. (AM2.7, AM2.8, AM2.9, A1.13, A1.14, 8-7, 8-8, 9-2P, 9-2, PS12, PS13
A1.15)
9-3P, 9-3, 9-4, 9-5,
RM9, 9-6, 12-3,
12-4, 12-5
10.3.1 Use appropriate tools to make geometric
1-2, 1-3, 1-4, 1-5P,
3-5, 4-4, 4-5, 5-1P,
6-4, 8-4, 8-5, 8-6,
10-3, 10-5P, 10-5,
10-8
constructions. (AGP.9)
10.3.2 Identify angle relationships and apply in solving
1-5, 2-8, 3-1, 3-2,
3-5, 6-3, 6-4
problems (complementary, supplementary, vertical
and adjacent as well as relationships formed by
parallel lines cut by a transversal). (AGP.13, AGP.14)
10.3.3 Investigate similar figures and apply proportions
in problem solving situations. (AGP.15)
vi
WESTEST, Grade 10
11-3, 11-7P, 11-7
6-2, 6-3, 6-4, 6-5,
6-6, 7-1, 9-5, 13-4
Copyright © Glencoe/McGraw-Hill
Standard 3: Geometry
Students will:
• analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships;
• specify locations and describe spatial relationships using coordinate geometry and other
representational systems;
• apply transformations and use symmetry to analyze mathematical situations; and
• solve problems using visualization, spatial reasoning, and geometric modeling through communication,
representation, reasoning and proof, problem solving, and making connections within and beyond
the field of mathematics.
Algebra 1
Lesson(s)
Objectives
10.3.4 Explore circle relationships, emphasizing the
vocabulary of circles. (AGP.16)
10.3.5 Solve right triangle problems using the
Geometry
Lesson(s)
1-1, 3-8, 8-2, 11-3,
PS
10-2, 10-3, 10-4, 10-5,
10-6
11-4
1-3, 7-2, 7-3, 9-6
Pythagorean Theorem. (MA8.4.4)
Standard 4: Measurement
Students will:
• demonstrate understanding of measurable attributes of objects and the units, systems, and processes
of measurement; and
• apply appropriate techniques, tools and formulas to determine measurements through communication,
representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics.
10.4.1 Calculate the missing measures of angles and
8-5, 11-7P, 11-7, 14-3 1-6, 8-1, 11-3
lengths of sides of a polygon from given data,
using formulas.
10.4.2 Estimate, measure, and perform operations
1-2, 13-1, 13-2, 13-3,
13-4, PS22
involving length, mass, and capacity using
customary and metric units. (AGP.7)
10.4.3 Use appropriate tools to measure geometric
1-2
figures. (AGP.8)
10.4.4 Develop and apply formulas for area, perimeter, 3-1, 8-1, 8-1F, 8-7,
surface area, and volume and apply them in
solving practical problems. (AGP.10, AGP.11,
AGP.12)
12-5, PS
6-2, 6-5, 11-1, 11-2,
11-3, 11-5, 12-3, 12-4,
12-5, 12-6, 12-7, 13-1,
13-2, 13-3, 13-4, PS14
Copyright © Glencoe/McGraw-Hill
Standard 5: Data Analysis and Probability
Students will:
• formulate questions that can be addressed with data, and collect, organize, and display relevant data
to answer them.
• select and use appropriate statistical methods to analyze data; develop and evaluate inferences and
predictions that are based on models; and
• apply and demonstrate an understanding of basic concepts of probability through communication,
representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics.
10.5.1 Collect, organize, interpret data, and predict
1-9, 2-5, RM2, 13-1,
outcomes using the mean, mode, median, range, 13-3, 13-4, 13-5,
and standard deviation. (AM1.13, AGP.5)
13-5F
10.5.2 Find the probability of conditional events and
14-3, 14-4
10-1
2-6, 2-6F
1-2F, 11-5, 13-2, 13-3
13-3, 13-5, PS
3-4, 10-8, PS1
mutually exclusive events. (AGP.6)
10.5.3 Predict the outcomes of simple events using
the rules of probability. (AM1.16)
10.5.4 Read, interpret and construct graphs to solve
problems. (AGP.4)
WESTEST, Grade 10
vii
Formulas
Triangle
Rectangular Prism
h
A 1–2bh
h
V wh
w
b
Rectangle
Pythagorean theorem
w
A w
c
b
a2 b2 c 2
a
Parallelogram
h
A bh
(n 2)
n 180
Measure of each interior
angle of regular polygon
(n number of sides)
b
Circle
r
A r 2 180
distance rate time
V 4–3 r 3 180
y mx b
V r 3h
y x2 x1
2
1
r
Slope-intercept form of
linear equation
Cylinder
r
h
viii WESTEST, Grade 10
y y
Slope of line
Copyright © Glencoe/McGraw-Hill
Sphere
Name
Date
Diagnostic Test
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
1 Jeremy is a salesman at an audio-video store. He is paid a base salary of
$220 a week, plus a commission of 4% on the items he sells. If he earned
a total of $650 one week, what was the total value of the items he sold
that week? 10.2.1
A $1,720
B $8,600
C $10,750
D $16,250
1
C
2 The figure shows the running track at Gita’s high school. The ends of the
track are semicircles. To the nearest meter, how much distance will Gita
cover if she jogs 10 laps around the outer edge of this track? 10.4.4
2
B
3
C
4 Which gives the number 0.00004056 in scientific notation? 10.1.2
A 40.56 106
B 4.056 105
C 4.056 104
D 4.056 105
4
B
5 The table gives West Virginia population data from the 2000 U.S. Census.
In 2000, which was closest to the probability that a resident of West
Virginia lived in Huntington or Parkersburg? 10.5.2
5
C
5m
48 m
A 1,160 m
C 1,745 m
B 1,274 m
D 4,800 m
3 Which is closest to the height of this ramp? 10.3.5
12.3 m
11.9 m
Copyright © Glencoe/McGraw-Hill
A 9.7 m
C 3.1 m
B 6.9 m
D 0.4 m
West Virginia Huntington Morgantown Parkersburg
1,808,344
51,475
26,809
33,099
A 1.8%
C 4.7%
B 2.8%
D 6.2%
Go on
WESTEST, Grade 10
1
Name
Diagnostic Test
Date
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
6
D
7
D
8
B
9 The circle graph shows how Adam
and Lauren Strauss have budgeted
Housing
Food
their after-tax income. If their
35%
20%
monthly after-tax income is
Entertainment
$2,450, how much is their monthly
5%
10%
Other
Clothing
budget for transportation and
25%
Transportation
entertainment? 10.5.4
A $122.50
B $245.00
C $367.50
D $612.50
9
C
10 Which polynomial represents the product (z 2)(z2 2z 4)? 10.2.9
A z3 4z2 4z 8
B z3 8
C z3 2z2 4z
D z3 8
10
B
6 Lines p and q are parallel. Which is a
pair of corresponding angles? 10.3.2
A 4 and 8
B 2 and 6
C 3 and 5
D 5 and 7
2
3
4
6
5
1
7
8
p
7 Marla and Jesse are raking the leaves in their grandmother’s backyard. It
would take Marla 221 hours to do this job working alone, while it would
take Jesse 3 hours working alone. If x represents the number of hours it
will take them to rake the leaves working together, which equation can
be solved to find x? 10.2.3
2.5 3
A x
2
B
1
x
13 21.5
1
C x
2.5 3
D
1
x
13 21.5
8 The figure shows the shape of the Schneider
family’s dining room. If mB 142°, what
is mD? 10.4.1
A 152°
B 128°
C 120°
D 76°
2
WESTEST, Grade 10
C
D
B
E
A
F
Go on
Copyright © Glencoe/McGraw-Hill
q
Name
Date
Diagnostic Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
11 What is the value of
5(8) (4)2
? 10.1.1
2 3 6 24
A 14
B 6
C 172
D 6
12 Sam is planning to replace the floor molding in the living room of his
house. The figure shows the dimensions of this room and the size of the
opening to the kitchen, where there is no wall. How many feet of molding
will Sam need to purchase if the home improvement store where he buys
it will only sell him a whole number of feet? 10.4.4
11
D
12
B
13
C
14
D
15
A
7 ft 6 in.
10 ft 2 in.
18 ft 10 in.
A 47 ft
C 58 ft
B 51 ft
D 192 ft
13 The table shows the monthly rents that Sean and Mary Simonds paid for
the first four years they rented their apartment. If Sean and Mary keep
this apartment and this pattern of annual rent increases continues, what
will be the total amount of rent they will pay during the 6th year? 10.2.6
Year
1
2
3
4
Monthly Rent $475 $505 $535 $565
Copyright © Glencoe/McGraw-Hill
A $3,300
C $7,500
B $6,250
D $7,860
14 What is the value of 5x3y0z2 if x 2, y 5, and z 4? 10.2.4
A 640
B 52
C 0
D
5
2
15 Which term describes a chord that passes through the center of a circle?
A diameter
10.3.4
B radius
C secant
D tangent
Go on
WESTEST, Grade 10
3
Name
Date
Diagnostic Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
16
D
17
A
18
C
19 Kara drove from Huntington to Wheeling, a distance of 230 miles, on
9.2 gallons of gas. If she gets the same gas mileage, how much gas will
she need to drive from Wheeling to Charleston, a distance of 179 miles?
(Round your answer to the nearest tenth of a gallon.) 10.1.1
A 6.9 gal
B 7.2 gal
C 8.5 gal
D 11.8 gal
19
B
20 Which statement is true? 10.3.3
A All squares are similar.
C All hexagons are similar.
20
A
21
B
16 Which graph shows all solutions of | 5 2x | 3? 10.2.5
A
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
B
C
D
17 The table shows Mark’s test scores in his English and biology classes.
Which statement is true about these scores? 10.5.1
English
Biology
78
86
84
91
67
75
89
82
75
74
A In English, his mean score is higher than his median score, but in
biology, his median score is higher than his mean score.
B His median score is the same in both classes.
C His median score is higher in English than in biology.
D The range of his scores is higher in biology than in English.
27
? 10.1.3
18 Which is equivalent to 300
B 37
D 273
B All rectangles are similar.
D All parallelograms are similar.
21 Which is a factor of 6x2 x 35? 10.2.9
A 3x 5
B 3x 7
C 2x 5
D 3x 7
4
WESTEST, Grade 10
Go on
Copyright © Glencoe/McGraw-Hill
A 310
27
C 73
Name
Date
Diagnostic Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
22
A
23
D
24 Which is an equation of the line with slope 13 and passing through the
point at (4, 5)? 10.2.8
A x 3y 11
B 3x y 7
C 3x y 17
D x 3y 19
24
D
25 Justin cut the rope into 3 equal pieces. What is the length of each piece?
25
C
26
B
22 Jonathan is a student who works part-time as a cashier in a coffee shop.
He earns $5.75 an hour, but the number of hours he works varies from
week to week. The table shows the number of hours he worked each
week over a four-week period. How many hours would Jonathan need to
work during the following week in order to earn an average (mean) of
$115 per week for 5 weeks? 10.5.1
Week
Hours Worked
1
20
2
19
3
22
4
25
A 14
C 20
B 17
D 21.5
23 Which graph shows the solution set of 6 2x 4(x 3)? 10.2.1
A
5 4 3 2 1
0
1
2
3
4
5
B
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
C
D
Copyright © Glencoe/McGraw-Hill
5 4 3 2 1
0
1
2
3
4
5
10.4.2
14 ft 3 in.
A 4 ft 1 in.
C 4 ft 9 in.
26 What is the value of y? 10.3.2
A 70
B 65
C 50
D 25
B 4 ft 8 in.
D 4 ft 10 in.
x
y
(3x 10)
Go on
WESTEST, Grade 10
5
Name
Date
Diagnostic Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
27 Which could be the slope of this line? 10.2.7
y
27
D
28
C
29
A
30
C
A 53
B 35
C
3
5
D
5
3
O
x
28 To the nearest square inch, how much gift wrap will Tiffany need to wrap
a gift that is placed in this container? (Assume that each surface is covered
with no overlap.) 10.4.4
8 in.
15 in.
377 in2
427 in2
478 in2
1,156 in2
29 How many dots are needed to draw the 12th figure in this pattern? 10.2.6
Figure 1
A
B
C
D
Figure 2
Figure 3
Figure 4
45
49
144
145
30 Anna and Jim went hiking at Cedar Creek State Park. From the parking lot,
they hiked 2.6 miles west and 1.8 miles north, and then stopped at a picnic
table for lunch. What is the shortest distance between the picnic table and
the parking lot? (Round your answer to the nearest tenth of a mile.) 10.3.5
A 4.4 mi
B 3.5 mi
C 3.2 mi
D 2.1 mi
6
WESTEST, Grade 10
Go on
Copyright © Glencoe/McGraw-Hill
A
B
C
D
Name
Date
Diagnostic Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
31
A
32
A
33 When Saturn is farthest from the Sun, its distance from the Sun is about
936.2 million miles. Which of the following gives the approximate
distance from Saturn to the Sun and back to Saturn? 10.1.2
A 1.8724 109 mi
B 4.681 108 mi
C 9.362 108 mi
D 18.724 1016 mi
33
A
34 Haley, who is a 4th grader, is standing in her school playground on a sunny
day. She is 4 feet 3 inches tall, and her shadow is 2 feet 6 inches long. If
the shadow of the school flagpole at the same time is 30 feet 6 inches,
which is closest to the height of the flagpole? 10.3.3
34
B
31 The formula P 2L 2W can be used to find
the perimeter of a rectangle with length L and
width W. How can this formula be rewritten to
find the length of a rectangle if its perimeter
and width are known? 10.2.2
P 2W
A L
2
B L P2 2W
C L 12 (P W)
D L 2P 2W
W
L
32 A sporting goods store sells exercise balls in two sizes, large and jumbo.
Which is closest to the amount of air needed to fully inflate one ball of
each size for a store display? 10.4.4
20 in.
24 in.
Copyright © Glencoe/McGraw-Hill
A 11,400 in3
C 6,400 in3
B 8,600 in3
D 4,100 in3
h
4 ft 3 in.
2 ft 6 in.
30 ft 6 in.
Go on
A 18 ft
B 52 ft
C 55 ft
D 76 ft
WESTEST, Grade 10
7
Name
Date
Diagnostic Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
35 If the probability that it will rain tomorrow is 0.32, what is the probability
that it will not rain? 10.5.3
A 0.18
B 0.32
C 0.64
D 0.68
35
D
36 What is the slope of the line 7x 4y 28? 10.2.7
36
A
37
C
38 Which could be the lengths of the three sides of a triangle? 10.4.1
A 1 cm, 3 cm, 5 cm
B 12 cm, 12 cm, 24 cm
C 15 cm, 17 cm, 32 cm
D 16 cm, 25 cm, 32 cm
38
D
39 Andrea wants to rent a car for a holiday weekend in order to visit her
friend Kaitlyn in Martinsburg. Andrea can rent the car she wants from
Rent-for-Less for $20 a day plus 24 cents a mile, or she can rent the
same car from Car-4-U for $35 a day with unlimited mileage. If she
plans to rent the car for 3 days, how many miles will she need to drive
for Car-4-U to be the better deal? 10.2.3
A at least 188 mi
B at most 187 mi
C at least 64 mi
D at most 63 mi
39
A
40
B
A 74
B 47
C
4
7
D
7
4
10.5.4
60
50
40
30
20
10
0
42
35
28
18
21–30
31–40 41–50
Age
A 21–30
C 41–50
51–60
B 31–40
D 51–60
40 In circle O, if mSOT 71° and mRQ 57°,
what is mRUQ? 10.3.4
A 57°
B 64°
C 71°
D 85°
8
WESTEST, Grade 10
S
R
Q
U
O
T
Go on
Copyright © Glencoe/McGraw-Hill
Number of Employees
37 The histogram shows the age distribution of the employees of a small
company. Which interval contains the median age of the employees?
Name
Date
Diagnostic Test
(continued)
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
41 The diameter of a red blood cell is 0.0000084 meter. Write a paragraph
to explain how to rewrite this number in scientific notation. Then use the
process that you have described to write the number in scientific notation.
10.1.2
Sample answer: In scientific notation, the decimal place goes directly to the
right of the first nonzero digit, which is 8. I need to move the decimal point
6 places to the right. Because I have to move the decimal point to the right,
the exponent will be negative, and because I need to move it 6 places, I know
that the exponent on the 10 will be 6.
0.0000084 8.4 106
42 Find the radius of circle O. Explain your
reasoning. 10.3.4, 10.3.5
A
12 cm
B
Sample answer: B is an inscribed angle
5 cm
in the circle. I know it is a right angle
O
C
because it intercepts a semicircle, so its
1
measure is 2 (180°) 90°. Since B is a
right angle, ABC is a right triangle with
hypotenuse AC
. By the Pythagorean Theorem (or using a Pythagorean triple),
122 52 169
13 cm. Since AC
is a diameter and OA
is a radius,
AC 1
1
13
OA 2 (AC) 2 (13) 2 or 6.5 cm.
The radius of circle O is 6.5 cm.
Copyright © Glencoe/McGraw-Hill
43 What is the volume of this cylindrical drum? (Round your answer to the
nearest tenth of a cubic foot.) 10.4.2, 10.4.4
32 in.
21–2 yd
Sample answer: All of the measurements need to be in the same units, and
I need to give my answer in cubic feet, so I changed the given measurements
to feet. The diameter of the cylinder is 32 in., so the radius is
4
1
5
15
16 in. 1 ft 4 in. 3 ft. The height of the cylinder is 22 yd 2 (3 ft) 2 ft.
The formula for the volume of a cylinder is V r2h, so the
4 2 15
Go on
volume of the drum is 3 2 41.9 ft3.
WESTEST, Grade 10
9
Name
Date
Diagnostic Test
(continued)
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
44 The formula F 95C 32 can be used to convert temperatures from
degrees Celsius to degrees Fahrenheit. 10.2.2
Part A Solve this equation for C to obtain a formula that can be used to
convert temperatures from degrees Fahrenheit to degrees Celsius.
Sample answer:
9
F 5C 32
9
F 32 5C
5(F 32) 9C
5(F 32)
9
C or C 5(F 32)
9
Part B The highest temperature ever recorded in West Virginia was
112°F on July 10, 1935 in Martinsburg. Use your formula from
Part A to convert this temperature to degrees Celsius.
Sample answer: C 5(F 32)
9
5(112 32)
9
44
The record high temperature is about 44°C.
45 The stem-and-leaf plot shows the scores for the
students in Mr. Roland’s 1st period biology class
on a 100-point chapter test. 10.5.1, 10.5.3, 10.5.4
Part A For these data, place these measures of
central tendency in increasing order: the
median, the mode, and the mean.
Stem
3
4
5
6
7
8
9
10
| Leaf
|2
|14
|578
|122
|023
|235
|358
|0
5 8
6 9 9
5 5 7
9
Copyright © Glencoe/McGraw-Hill
Sample answer: There are 28 scores, so
3 | 2 32
the median is the average of the 14th
73 76
and 15th scores, which is 2 74.5.
The mode is the most common score, which is 85, the only
score that appears 3 times. To find the mean, I added up all the
2,046
scores and divided by 28: 28 73.1. In increasing order, the
measures are mean, median, mode.
Part B What is the probability that a randomly chosen student who took
this test got an A or B (a score of 80 or above) on the test?
Sample answer: There are 11 scores of 80 or above, so the
11
probability is 28 0.393.
STOP
10
WESTEST, Grade 10
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.1.1 Solve computational and practical problems using
properties of numbers, order of operation, computation, and estimation
with decimals, fractions, integers, and mixed numbers, including ratio,
proportion, and percents.
D
2 Megan bought 3 CDs for $11.99 each and 4 DVDs for $14.99 each. How
much did she spend, not including sales tax?
A $118.86
B $95.93
C $94.43
D $92.93
2
B
3 Dylan and Rachel Lincoln are spending a long weekend at Kanawha State
Forest, which is near Charleston. They want to hike a total of 30 miles on
Saturday, Sunday, and Monday. If they hike 814 miles on Saturday and
1112 miles on Sunday, how far will they have to hike on Monday to make
their goal?
3
A
4 Pedro drove from Beckley to Parkersburg, a distance of 135 miles, on
5.8 gallons of gas. If he gets the same gas mileage, how much gas will
he need to drive from Wheeling to White Sulphur Springs, a distance of
260 miles? (Round your answer to the nearest tenth of a gallon.)
A 9.6 gal
B 10.6 gal
C 11.2 gal
D 22.3 gal
4
C
5 Kayla bought a dress from a rack that displayed
the sign at the right. If the original price of the
dress she chose was $65, how much did Kayla
pay for it, not including sales tax?
A $52.00
B $46.80
C $45.50
D $35.00
5
B
A 2
C
Copyright © Glencoe/McGraw-Hill
(8)(4) (2)4
?
5 4 7 32
1
1 What is the value of
2
3
B
48
131
D 2
A 1014 mi
B 11 mi
C 1434 mi
D 1934 mi
SPRING CLEARANCE
Price on tag is 20%
off original price.
Additional 10% markdown
taken at register.
WESTEST, Grade 10
11
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.1.2 Write numbers involving scientific notation and
combine numbers written in scientific notation to solve practical problems.
1 The population of West Virginia in 2000, according to the U.S. Census,
was about 1,808,000. Which gives this number in scientific notation?
B 18.08 105
A 1,808 103
C 1.808 106
D 1.808 107
1
C
2 Which is another way to write the number 3.45 106 ?
A 3,450,000
B 0.000345
C 0.00000345
D 0.000000345
2
C
3 When Jupiter is closest to the Sun, its distance from the Sun is about
460.3 million miles. Which of the following gives the approximate
distance from Jupiter to the Sun and back to Jupiter when Jupiter is
closest to the Sun?
B 9.206 108 mi
A 4.603 106 mi
C 9.206 109 mi
D 4.603 1012 mi
3
B
4
D
5 The speed of light is approximately 1.86 105 miles per second, and
the average distance between Earth and the Sun is approximately
9.3 107 miles. About how long does it take sunlight to reach Earth?
A 8 hr 20 min
B 1 hr 23 min 20 sec
C 8 min 20 sec
D 18 sec
5
C
6 The diameter of a single human hair is approximately 2.0 105 meter.
What is the approximate width of 5,000 hairs if they are placed side by
side with no space between them?
A 1m
B 10 cm
C 1 cm
D 1 mm
6
B
A 1.6 109
12
C 1.6 10 5
12
WESTEST, Grade 10
(4.0 106)(1.2 102)
?
3.0 105
B 1.6 101
D 1.6 109
Copyright © Glencoe/McGraw-Hill
4 Which is equivalent to
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.1.3 Estimate and simplify square roots into both exact
and approximate forms.
1
B
2 If 52 is placed on a number line, between which two points will it be
located?
A 8 and 7
B 7 and 6
C 6 and 5
D 5 and 4
2
A
3 Which is closest to the length of the diagonal
of this square?
A 11 cm
B 12 cm
C 14 cm
D 20 cm
3
C
4
D
5
C
6
B
7
B
?
1 Which is closest to 130
A 11.3
C 12.0
B 11.4
D 13.0
10
2 cm
10 cm
10 cm
?
4 Which is equivalent to 98
A 27
C 9.8
B 7.2
D 72
5 Which is equivalent to 125
45
?
A 55 53
B 52
D 80
Copyright © Glencoe/McGraw-Hill
C 25
6 Which is the reciprocal of 5?
A
5
5
5
C 25
7 What is another way to write
5
B 5
D 5
2
?
5 3
A 2(5 3 )
B 5 3
C 5 3
5 3
D 2
WESTEST, Grade 10
13
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.1.1, 10.1.2, 10.1.3
1 A cookie recipe calls for 221 cups of flour to make 4 dozen cookies. For
her sister’s graduation party, Elizabeth wants to make 14 dozen cookies
from this recipe. How much flour will she need? 10.1.1
Sample answer: I wrote a proportion and solved it using cross multiplication
to get the answer.
Let x the number of cups of flour needed to make 14 dozen cookies.
1
22 cups
4 dozen
x cups
14 dozen
1
22
x
14
4
1
22 (14) 4x
35 4x
x
35
4
3
84
3
She will need 84 cups of flour.
2 The land area of West Virginia is 15,410,560 acres. Write a paragraph to
explain how to rewrite this number in scientific notation. Then use the
process that you have described to express this area in scientific notation.
Sample answer: The way the number is written now, the decimal point is at the
end of the number, even though it isn’t shown. Place a decimal point there. In
scientific notation, the decimal point has to go right after the first nonzero digit,
so mark the spot between the 1 and the 5 at the beginning of the number.
Move the decimal point to this spot and count how many places you moved it.
Count that you moved it 7 places to the left. This gives the exponent on the 10.
15,410,560 15,410,560. 1.541056 107
3 Write 98
200
288
as a single term involving a simplified
radical. Show each step of your work. 10.1.3
Sample answer:
98
200
288
49
2
100
2
144
2
72
102
122
(7 10 12)2
52
14
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
10.1.2
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.1.1, 10.1.2, 10.1.3 (continued)
4 An electronics store marks up all laptop computers 20% above cost. The
cost to the store for one of their most popular models is $1,450. 10.1.1
Part A Mark works at this store and is responsible for putting price tags
on all the items before they go on the floor. What price should he
put on the tag for this computer? Explain in words how you
figured this out and show all your work.
Sample answer:
Marking up a price by 20% means adding 20% of the cost of the item to its cost.
The markup is 20% of $1,450 0.20($1,450) $290.
The price should be $1,450 $290 $1,740.
Part B Store records showed that this computer wasn’t selling well, so the
manager decided to put it on sale at 20% off. What will be the
sale price? Explain in words how you figured this out and show
all your work.
Sample answer:
Reducing or marking down a price by 20% means subtracting 20% of the
price of the item from its price.
The markdown is 20% of $1,740 0.20($1,740) $348.
The sale price should be $1,740 $348 $1,392.
Copyright © Glencoe/McGraw-Hill
5 The diameter of Mercury at its equator is about 4.8794 million meters,
while the diameter of Jupiter at its equator is about 142.98 million
meters. 10.1.1, 10.1.2
Part A Write each of these numbers in scientific notation. Explain your
reasoning.
Sample answer:
One million 1,000,000 106, so 4.8794 million 4.8794 106.
142.98 million 142.98 106 1.4298 108.
Part B Find the ratio of the diameter of Jupiter at its equator to the
diameter of Mercury. About how many times as great is the
diameter of Jupiter as the diameter of Mercury? Show all your
calculations.
Sample answer:
1.4298 108
4.8794 106
1.4298
4.8794
108 6 0.293 102 29.3.
The diameter of Jupiter is about 29.3 times the diameter of Mercury.
WESTEST, Grade 10
15
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.1 Define variables and solve multi-step linear
equations and one-variable inequalities, interpret results on a number
line, and apply the skills toward solving practical problems.
1 If Heather has x quarters, y dimes, z nickels, and w pennies in her wallet,
how much money does she have in dollars?
A 0.25x 0.10y 0.05z 0.01w
B 25x 10y 5z w
C xyzw
D 0.025x 0.010y 0.005z 0.001w
1
A
2 Which equation has no solution?
A x55x
C 5x 2 8x 2
2
D
3
C
4
B
5
A
6
D
B 3(x 7) 3x 21
D 4(x 5) 2x (6x 12)
3 What are all solutions of 32x 56 x 13?
A 12
B 12, 12
C
1
2
D 2
4 Rita has 15 coins, of which q are quarters and the rest are nickels. How
many nickels does she have?
A q 15
B 15 q
C 15 q
D
15
q
5 Which graph shows the solution of 5 3x 14?
A
5 4 3 2 1
0
1
2
3
4
5
B
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
D
5 4 3 2 1
0
1
2
3
4
5
6 Nicole is trying to choose a long-distance telephone plan. She is
considering two plans: Plan M has a monthly fee of $3.95 and charges
6 cents per minute. Plan R charges a flat rate of $25.95 a month for
unlimited long-distance calling. How many minutes of long-distance
calls would Nicole need to make during an average month for Plan R to
be the better choice?
A under 498 min
B over 498 min
C under 366 min
D over 366 min
16
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
C
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.2 Solve literal equations for a given variable and
apply the skills toward solving practical problems.
1
A
2
B
3 The formula A P Prt gives the amount A, in dollars, in a savings
account paying simple interest if a principal of P dollars is invested at an
annual interest rate of r% for t years. How much must Amanda deposit in
an account paying 4% simple interest in order to have $900 in her account
five years after she opens it? (Assume that she makes no further deposits
and withdrawals during the five-year period.)
A $865.39
B $820
C $750
D $720
3
C
4 In physics, the formula 1f p1 q1 describes the relationship between the
focal length of a lens f, the distance between the object and the lens p, and
the distance between the lens and the image q. How can Luis rewrite this
formula to give the distance between the lens and its image if he knows
the focal length of the lens and the distance between the object and the lens?
A qfp
B q fp p
4
D
1 The formula A 12 (B b)h can be used
to find the area of a trapezoid with bases
of lengths B and b and height h. How can
this formula be rewritten to give B in
terms of A, b, and h?
b
h
B
2A bh
A B
h
2A b
B B
h
Ab
C B
2h
D B 12(A b)h
Copyright © Glencoe/McGraw-Hill
2 Sean is planning to drive from his home in Huntington to Kevin’s house
in Wheeling, a distance d of 230 miles. In order to tell Kevin when to
expect him, Sean wants to estimate the time t it will take him to get to
Wheeling. He knows the formula d rt. How should he rewrite this
formula so that he can use it to find how long the trip will take him at a
specific average speed?
A t rd
B t dr
C t dr
D tdr
pf
C q fp
fp
D q
pf
WESTEST, Grade 10
17
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
1 Brandon is 8 years less than twice the age of his brother Steven. The sum
of their ages is 28. If s represents Steven’s age, which equation describes
this situation?
A (2s 8) s 28
B (2s 8) s 28
C 2s 8 28
D (2s 8) s 28
1
D
2 Kelsey and Allison went shopping together at the Martinsburg Mall.
They decided to buy some clothes at a store that was running a special
sale in which all shorts were sold at one price and all jeans at another
price. Kelsey spent $92 for 2 pairs of jeans and 3 pairs of shorts, while
Allison spent $81 for 1 pair of jeans and 4 pairs of shorts. What was the
sale price for a pair of shorts? (Ignore sales tax.)
A $14
B $15.75
C $19.50
D $25
2
A
3 In a chemistry lab, Letisha must mix 10 liters of 15% alcohol solution
with a 25% alcohol solution to get an 18% solution. If x represents the
amount of 25% solution she will need, which equation can she solve to
find this amount?
A 0.15x 0.25(10) 0.18(10 x)
B 0.15(10) 0.18x 0.25(10 x)
C 0.15(10) 0.25x 0.18(10 x)
D x 0.15(10) 0.25x
3
C
4 Craig received scores of 72, 85, and 79 on his first 3 biology tests. To
figure out what score he would need on his 4th test to give him a test
average of at least 80, he wrote the inequality
4
D
72 85 79 x
4
80. (1)
Then, as his first step in solving this inequality, he wrote
72 85 79 x 320. (2)
What property of real numbers did he use to get from inequality (1) to
inequality (2)?
A Addition Property of Inequality
B Associative Property of Multiplication
C Distributive Property
D Multiplication Property of Inequality
18
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
OBJECTIVE 10.2.3 Solve practical problems using a four-step problem
solving approach, justifying steps based on the properties of real numbers.
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.4 Evaluate and simplify algebraic expressions using
grouping symbols, order of operations, properties of real numbers, and
laws of exponents.
1 What is the value of 3(x y) 5(x y) if x 12 and y 8?
A 88
B 40
C 40
D 88
1
A
2 What is the value of 5mn 2m2p 3p3 if m 4, n 3, and p 2?
A 100
B 20
C 20
D 28
2
B
3 Which property of real numbers allows you to rewrite 5(a2 2ab b2)
as 5a2 10ab 5b2?
A Associative Property of Addition
B Associative Property of Multiplication
C Commutative Property of Multiplication
D Distributive Property
3
D
4 Which expression is equivalent to (4x2y)3?
A 64x6y3
B 64x5y4
C 12x6y3
D 64x5y3
4
A
5 What is the value of 3p0r3s2 if p 5, r 2, and s 3?
5
B
6
D
7
B
A
135
8
Copyright © Glencoe/McGraw-Hill
C 216
6 What is another way to write
27
8
B
D 1,080
2x2y3 4
3x y 5 2
A
2x12y 20
3
B
C
81
1
16x 2y20
D
?
16y 20
81x12
81x12y 20
16
7 Which expression is equivalent to (3r 2s4)(2r 3s4)2?
A 12r 5
C
6r 8
s4
B
12r 8
s4
D 12r 8s4
WESTEST, Grade 10
19
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.5 Solve absolute value equations in one variable and
interpret the results on a number line.
1 What are all solutions of | 2x 5 | 7?
A 6 and 1
B 1 and 6
C 6
D No solutions
1
B
2 What are all numbers on the real number line that are 5 units from 3.5?
A 8.5 and 1.5
B 8 and 2
C 6 and 1
D 1.5
2
A
3 Which graph shows all solutions of | 5 x | 3?
A
3
D
4
D
5
B
6
C
7
D
10 8 6 4 2
0
2
4
6
8 10
10 8 6 4 2
0
2
4
6
8 10
10 8 6 4 2
0
2
4
6
8 10
10 8 6 4 2
0
2
4
6
8 10
B
C
D
4 Which equation has exactly one solution?
A | 3x 5 | 5
B | 3x 5 | 5
C | 3x 5 | 0.1
D | 3x 5 | 0
A
7
6
B 1
C
1
9
7
D 36
6 For which of the following equations does the graph show all solutions?
5 4 3 2 1
0
1
2
3
4
5
A | 2x 7 | 3
C | 2x 7 | 3
7 Which equation has no solutions?
A |5 4x| 6
C |5 4x| 0
20
WESTEST, Grade 10
B | 2x 7 | 3
D | x 3.5 | 1
B |5 4x| 0.6
D |5 4x| 6
Copyright © Glencoe/McGraw-Hill
5 What is the sum of the solutions of x 12 23?
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.6 Analyze a given set of data for the existence of a
pattern numerically, algebraically, and graphically.
1
C
2 What is the 8th term of the sequence 1, 2, 4, 8, …?
A 128
B 64
C 64
D 128
2
A
3 The table shows the number of bacteria in a colony at several times on
one day. If the population of the colony continues to follow this pattern of
growth, which is the best estimate of the number of bacteria at 8:00 P.M.
on the same day?
3
D
4
B
1 The table shows Trevor’s hourly wage during his first four years on his
job. If Trevor stays on this job and this pattern of annual raises continues,
what will be his hourly wage during his 7th year on the job?
Year
1
Hourly Wage $5.50
2
$5.80
3
$6.10
A $7.60
C $7.30
4
$6.40
B $7.40
D $7.00
Copyright © Glencoe/McGraw-Hill
Time
Number of Bacteria
8:00 A.M.
0,500
10:00 A.M.
0,750
Noon
1,125
2:00 P.M.
1,688
A
B
C
D
2,400
2,900
3,800
5,700
4 How many dots are needed to draw the 10th figure in the pattern?
Figure 1
A
B
C
D
Figure 2
Figure 3
110
55
45
21
WESTEST, Grade 10
21
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.7 Determine the slope of a line given an equation of
a line, the graph of a line, or two points.
1 What is the slope of the line y 4x 5?
A 5
B 4
C 4
8
3
B
5
3
C
3
5
2
C
3
A
4
B
5
D
6
A
7
C
D 85
3 Which of the following is an equation of a line with slope 27?
A 2x 7y 14
C 2x 7y 14
B
D 5
2 What is the slope of the line 3x 5y 8?
A
1
B 7x 2y 14
D 7x 2y 14
4 Which is the slope of this line?
A 2
y
B 12
C
O
1
2
x
D 2
5 What is the slope of the line that contains the points at (4, 6) and
(6, 2)?
5
4
B
C 12
1
2
D 45
6 The points shown in this table lie on a line. What is the slope of this line?
x
y
4 2
20 15
6
5
A 2.5
C 0.4
7 Which line has slope 0?
A xy
C y0
22
WESTEST, Grade 10
B 0.4
D 2.5
B xy0
D x0
Copyright © Glencoe/McGraw-Hill
A
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.8 Write and graph linear equations.
1 Which is an equation of the line that passes through the points at (4, 0)
and (0, 3)?
A 3x 4y 12
B 3x 4y 12
C 4x 3y 12
D 4x 3y 12
1
B
2 Which is an equation of the line with slope 35 and passing through the
point at (2, 6)?
A 3x 5y 24
B 5x 3y 8
C 5x 3y 28
D 3x 5y 36
2
D
3 Which is an equation of the horizontal line through the point at (4, 7)?
A x4
B x y 3 C y 7
D x y 11
3
C
4 Which could be an equation for this graph?
4
A
5
D
6
A
y
A y 32 x 32
B y 23 x 23
x
O
C y 23 x 23
D y 32 x 32
Copyright © Glencoe/McGraw-Hill
5 Which could be the graph of the equation y 2x 3?
A
B
y
y
x
O
C
D
y
x
O
y
x
O
O
x
6 Which is an equation of the vertical line through the point at (6, 3)?
A x60
B x60
C y30
D xy3
WESTEST, Grade 10
23
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.2.9 Factor and perform basic operations on simple
polynomials.
1
D
2 Which is the completely factored form of 2x2 18x 36?
A (2x 6)(x 6)
B (2x 12)(x 3)
C 2(x 9)(x 2)
D 2(x 3)(x 6)
2
D
3 Which is the completely factored form of 9x2 30xy 25y 2?
A (3x 5y)2
B (3x 5y)2
C (3x 5y)(3x 5y)
D (3x)2 (5y)2
3
A
4 Which expression gives the difference (8y2 5y 6) (8y2 5y 9)?
A 16y2 10y 15
B 15
C 10y 15
D 10y 3
4
C
5 Which expression is equivalent to 3(2z2 4z 5) 2(4z2 z 1)?
A 14z2 10z 13
B 2z2 10z 13
2
C 2z 10z 13
D 2z2 10z 13
5
D
6 Which polynomial represents the product (3r 2s) (9r 5s)?
A 27r 2 3rs 10s2
B 27r 2 3rs 10s2
C 27r 2 33rs 10s2
D 27r 2 3rs 10s2
6
A
7 What is the quotient when 6x2 11x 4 is divided by 2x 1?
A 3x 4
B 3x 4
C 3x 2
D 4x2 10x 5
7
A
8
C
8 What is another way to write
A
B
C
D
24
3x2 5xy
10x2 20xy
3x2 5xy 1
3x2 5xy 1
WESTEST, Grade 10
B x8
D x1
15x3y 25x2y 2 5xy
?
5xy
Copyright © Glencoe/McGraw-Hill
1 Which is a factor of x2 7x 8?
A x4
C x2
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.2.1, 10.2.2, 10.2.3, 10.2.5, 10.2.6, 10.2.8
1 Chris bought a jacket on sale for $48. The jacket was on sale at 25% off
the original price. What was the original price of the jacket? Write an
equation that you can use to solve this problem and show all your work
to solve it. 10.2.1, 10.2.3
Sample answer: Let x the original price of the jacket. 25% is 0.25, so the
sale price can be written as x 0.25x, so my equation is x 0.25x 48.
x 0.25x 48
0.75x 48
x
48
0.75
x 64
The original price of the jacket was $64.
2 Solve | 2x 1 | | 4x 3 |. Show all your steps. Explain properties you
use that are special properties of absolute value. 10.2.5
Sample answer:
| 2x 1 | | 4x 3 |, so 2x 1 4x 3 or 2x 1 (4x 3) 4x 3
because 2 numbers or expressions can only have the same absolute value if
they are equal or opposites. This gave me 2 linear equations that I solved to
get the two solutions of the equation.
2x 1 4x 3
2x 1 4x 3
2x 4
6x 2
1
x 2
x Copyright © Glencoe/McGraw-Hill
3
3 Graph 2x y 4. Explain how you chose the points you used to draw
the line. Identify the points you used on the graph. 10.2.8
y
O
x
Sample answer:
I used the x- and y-intercepts. If x 0, the equation
becomes y 4, or y 4, so the line goes through
the point (0, 4). If y 0, the equation becomes 2x 4,
or x 2, so the line goes through the point (2, 0).
As a check, I found a third point (3, 2). I plotted these
3 points and drew the line through them.
WESTEST, Grade 10
25
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.2.1, 10.2.2, 10.2.3, 10.2.5, 10.2.6, 10.2.8 (continued)
4 The relationship between the time it takes two people to complete a job
working together and the times it takes them to do the same job working
separately can be described by the equation 1t 1a 1b, where t is the
time required working together, and a and b are the times required
working separately. 10.2.2
Part A Solve this equation for t in terms of a and b. Show all your steps.
1
t
1
t
Sample answer:
tab
1
a
1
b
1
1
a
b
tab
ab tb ta
ab t(b a)
t
ab
ba
Part B Ryan and Tyler are students at West Liberty State College. Their
dorm room needs cleaning. If Ryan can clean the room in 3 hours
working alone, and Tyler can clean the room in 4 hours working
alone, how long will it take them to clean the room working
together? Use your equation from Part A to solve this problem.
Sample answer: t t
h
5
7
4
60 min 43 min
Working together, it will take them about 1 h 43 min.
5 The table shows the first 4 terms
Term Number 1
2
3
of a certain sequence of numbers.
2
3
4
10.2.6
Term
3
5
7
4
5
9
Part A Explain in words any patterns you see in the terms of the
sequence and how each term is related to the term number.
Sample answer: To get from one term to the next, add 1 to the numerator and
add 2 to the denominator. All the denominators are odd numbers. The
numerator is always 1 more than the term number. To get the denominator,
double the term number and add 1.
Part B Use the patterns you found in Part A to write an expression for
the nth term (or general term) of the sequence.
Sample answer: The nth term is
26
WESTEST, Grade 10
n1
.
2n 1
Copyright © Glencoe/McGraw-Hill
5
7
ab
; a 3, b ba
12
5
34
1
7
7
34
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.3.2 Identify angle relationships and apply in solving
problems (complementary, supplementary, vertical, and adjacent, as well
as relationships formed by parallel lines cut by a transversal).
1 What is the measure of the complement of a 39° angle?
A 141°
B 129°
C 61°
D 51°
1
D
2 Which angles in the figure are both adjacent
and supplementary?
A 2 and 3
B 2, 3, and 4
C 1 and 2, 1 and 5
D 4 and 5
2
C
3
C
4
A
5
B
1
2
Copyright © Glencoe/McGraw-Hill
3 What is the value of y?
A 45
B 120
C 135
D 150
4 Lines s and t are parallel. Which is a pair
of alternate exterior angles?
A 2 and 8
B 1 and 8
C 3 and 5
D 4 and 7
5 If line m is parallel to line n , what is the
value of x?
A 135
B 125
C 55
D 35
x
1
2
4
5
4
3
3x y
s
3
5
6
8
t
7
55
x
m
n
WESTEST, Grade 10
27
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.3.3 Investigate similar figures and apply proportions
in problem solving situations.
1
C
2 Which statement is true?
A All right triangles are similar.
B All isosceles triangles are similar.
C All obtuse triangles are similar
D All equilateral triangles are similar.
2
D
3 Kristi is using a road map of West Virginia on which 1 inch represents
20 miles. She measures a straight-line distance of 734 inches between
Charleston and Morgantown. Which is closest to the actual distance
between these cities?
A 140 mi
B 145 mi
C 155 mi
D 160 mi
3
C
4 Kyle is standing in a park on a sunny
day. He is 5 feet 6 inches tall, and his
shadow is 3 feet 3 inches long. If a nearby
tree has a shadow that is 10 feet 9 inches
long at the same time, which is closest to
the height of the tree?
5 ft 6 in.
A 18 ft 2 in.
3 ft 3 in.
B 17 ft 10 in.
C 13 ft 0 in.
D 6 ft 4 in.
4
A
5
B
1 In the figure, LMN PQR. What are the values of x and y?
M
Q
14.4
y
L
8
N
A x 6.4, y 11
C x 9.6, y 9
R
5
6
P
B x 9, y 11.4
D x 10, y 8
5 If HJK RST, which of the following must be true?
A HJ RS
B mK mT
C
28
HK
RT
JRKS
WESTEST, Grade 10
D mJ mR
Copyright © Glencoe/McGraw-Hill
x
10 ft 9 in.
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.3.4 Explore circle relationships, emphasizing the
vocabulary of circles.
Q
in circle O?
1 Which term describes P
A chord
B diameter
C radius
D tangent
P
O
A
2
B
3
D
4
D
5
C
Q
2 R, S, and T are points on circle O. If mRTU 56°, what is mRST ?
R
S
O
T
U
A 124°
C 292°
B 248°
D 304°
3 Which could be the measure of a minor arc of a circle?
A 350°
B 200°
C 180°
D 90°
is tangent to circle O at R. If
is tangent to circle O at Q, and PR
4 PQ
mQSR 215°, what is mP?
Copyright © Glencoe/McGraw-Hill
1
Q
S
O
P
R
A 70°
C 40°
B 55°
D 35°
5 Which term describes a line that intersects a circle in 2 different points?
A chord
B radius
C secant
D tangent
WESTEST, Grade 10
29
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.3.5 Solve right triangle problems using the
Pythagorean Theorem.
1
B
2
C
3 Which could be the lengths of the three sides of a right triangle?
A 1 in., 1 in., 2 in.
B 8 ft, 9 ft, 10 ft
C 12 m, 12 m, 12 m
D 10 cm, 26 cm, 24 cm
3
D
4 Miriam and Ed Rose spent Labor Day weekend hiking, swimming, and
boating at Blackwater Falls State Park in the Potomac Highlands. On
Sunday, they hiked 1.5 miles east, then 1.9 miles south, then 1.2 miles
east, and then stopped for a picnic lunch. To the nearest tenth of a mile,
what was the distance between their starting point and their picnic spot?
A 4.6 mi
B 3.3 mi
C 3.1 mi
D 2.7 mi
4
B
5 The advertised size of a television set is the length of the diagonal of the
screen. Natalie bought a 13-inch TV for her dorm room at Fairmont State
College. If the screen is 11 inches across, which is closest to its height?
A 7 in.
B 8 in.
C 10 in.
D 12 in.
5
A
1 What is the length of the longer leg of this right triangle?
17 cm
8 cm
A 17 cm
C 12.5 cm
B 15 cm
D 9 cm
2 Benjamin is using a 10-foot ladder to paint his bedroom. If he places the
ladder 5 feet from the base of a wall, about how far up the wall will the
ladder reach?
10 ft
5 ft
30
WESTEST, Grade 10
B 7 ft 9 in.
D 11 ft 2 in.
Copyright © Glencoe/McGraw-Hill
A 5 ft
C 8 ft 8 in.
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.3.5 (continued)
6 Which is closest to the length of the diagonal of
this square?
A 12 cm
B 10 cm
C 8.5 cm
D 8.0 cm
Forest St.
7
D
8
C
9
A
School
50 yd
Stone Park
Home
C
6 cm
7 Danielle can walk from her apartment to her school either by walking
north on Forest Street and then east on Linden Street, or by cutting
diagonally across Stone Park. Which is closest to the distance she will
save by walking through the park?
Linden St.
6
100 yd
A 150 yd
C 50 yd
B 119 yd
D 38 yd
8 Allison, who lives in Buckhannon, is planning to ship a birthday present to
her cousin Maria, who lives in Knoxville, Tennessee. In order to know if
the gift she has bought will fit in the carton shown in the figure or if she
will need to use a larger one, Allison needs to know the length RS, which
is the length of the body diagonal of the carton. Which is closest to this
length?
Copyright © Glencoe/McGraw-Hill
S
6 in.
R
8 in.
12 in.
A 13.5 in.
C 15.6 in.
B 14.4 in.
D 26.0 in.
9 Which could be the lengths of the sides of an isosceles right triangle?
A 5 cm, 52 cm, 5 cm
C 1 cm, 2 cm, 3 cm
B 5 cm, 5 cm, 5 cm
D 5 cm, 5 cm, 53 cm
WESTEST, Grade 10
31
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.3.2, 10.3.3, 10.3.4, 10.3.5
1 On a school field trip, Samantha visited West Virginia Independence Hall
in Wheeling and bought a postcard of this building. On the postcard, the
building is 10 centimeters wide and 8 centimeters tall. She decided to
use the postcard to make a scale model of Independence Hall for a class
project. If her model is 36 centimeters wide, how tall should it be?
(Round your answer to the nearest centimeter.) 10.3.3
Sample answer: Let x the height of the model.
36 cm
10 cm
x cm
8 cm
10x 8 36 288
x 28.8 29
Samantha’s model should be about 29 cm tall.
9.2
RU 84
The length of RU is 84
cm, which is approximately 9.2 cm.
3 The ratio of the measures of two supplementary angles is 8:7. What are
the measures of these angles? 10.3.2
Sample answer: Let 8x and 7x be the angle measures. Since the measures of
supplementary angles add up to 180°, my equation is 8x 7x 180.
8x 7x 180
15x 180
x
180
15
12
8x 8(12) 96, and 7x 7(12) 84, so the angle measures are 96° and 84°.
32
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
S
2 In RST, what is the length of R
U
, the altitude
10 cm
? (Write your answer in exact radical form
to ST
R
8 cm U
and then as a decimal rounded to the nearest
tenth of a centimeter.) 10.3.2, 10.3.5
T
Sample answer:
Because S T, I know that RST is isosceles with legs R
S and R
T, and base
S
T. In an isosceles triangle, the altitude to the base is also the median, so
SU UT 4 cm. Since R
U
⊥
ST
, I can use the Pythagorean Theorem in RSU
to find RU.
(RU)2 (SU)2 (RS)2
(RU)2 (RS)2 (SU)2 102 42 100 16 84
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.3.2, 10.3.3, 10.3.4, 10.3.5 (continued)
and RU
are chords of circle O. 10.3.3, 10.3.4
4 SV
Part A Complete this similarity statement for the
two triangles in the figure.
RST ______
Explain how you know that the triangles
are similar.
S
5
8
R
3
U
T
x
O
V
Sample answer: RST VUT
S U because they are inscribed angles that intercept the same arc.
R V for the same reason, so the triangles are similar by the AA Similarity
Postulate. (I could also use the vertical angles as one of the angle pairs.)
Part B Use the similar triangles to find x.
Sample answer: I can write a proportion that involves corresponding sides of
the triangles.
RT
VT
8
x
ST
UT
5
3
5x 24
24
4
x 5 or 45
is tangent to circle O
5 In the figure, QS
at Q and to circle P at S. 10.3.4, 10.3.5
S
6
Copyright © Glencoe/McGraw-Hill
O
R
P
Part A Look at OQR and PSR. What
3
4
kind of triangles are these? What
Q
is the relationship between the two
triangles? Explain how you know.
Sample answer: They are both right triangles and they are similar. I know they
are right triangles because a radius of a circle is perpendicular to a tangent at
the point of tangency, which tells me that OQR and PSR are both right
angles. Using these right angles and the vertical angles, ORQ and PRS,
I know the triangles are similar by the AA Similarity Postulate.
Part B Find the distance between the centers of the circles.
R and P
R are the hypotenuses of the right triangles. I can use
Sample answer: O
the Pythagorean Theorem or the 3-4-5 Pythagorean triple to find that OR 5.
PS
6
2, PR 2(OR) 10, so the
Since the triangles are similar, and OQ
3
distance between the centers is OR PR 5 10 15.
WESTEST, Grade 10
33
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.4.1 Calculate the missing measures of angles and
lengths of sides of a polygon from given data, using formulas.
1
D
2
A
3 What is the measure of each interior angle of a regular pentagon?
A 72°
B 108°
C 120°
D 144°
3
B
4 Which could not be the lengths of the 3 sides of a triangle?
A 5 cm, 5 cm, 5 cm
B 12 cm, 18 cm, 15 cm
C 7 cm, 24 cm, 25 cm
D 12 cm, 20 cm, 7 cm
4
D
5 Sonja is a student at Mountain State University in Beckley. She hung
this college pennant in her dorm room. If m3 38°, what is m1?
5
C
1 What is the measure of the largest angle in this triangle?
(3x 16)
(x 8)
(4x 20)
A 72°
C 108°
B 92°
D 112°
2 The figure shows the shape of Melissa’s flower garden. What is the
measure of the largest angle?
x
(4x )
B 135°
D 90°
12 in.
1
MSU
2
3
12 in.
A 52°
C 71°
34
WESTEST, Grade 10
B 62°
D 104°
Copyright © Glencoe/McGraw-Hill
A 144°
C 120°
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.4.2 Estimate, measure, and perform operations
involving length, mass, and capacity using customary units and metric
units.
1 Which is the most appropriate unit for measuring the distance between
2 cities?
A millimeter
B centimeter
C meter
D kilometer
1
D
2 Which is the most appropriate unit for measuring the capacity of a car’s
gas tank?
A milliliter
B centiliter
C liter
D kiloliter
2
C
3 Joshua cut a piece off this log that was 3 feet 5 inches long. What is the
length of the remaining portion of the log?
3
B
4 Zachary’s doctor prescribed an antibiotic that he must take for 10 days
to treat an infection. The prescription specifies that he is to take a
250-milligram tablet 3 times a day. How many grams of medication will
he take over the full course of treatment?
A 7.5 g
B 75 g
C 750 g
D 7,500 g
4
A
5 Briana is making punch for a party. She is using a recipe that calls for
5 cups of lemonade when making punch to serve 8 people. How many
quarts of lemonade will she need to make this recipe for 56 people?
5
D
6
A
9 ft 2 in.
8 in.
Copyright © Glencoe/McGraw-Hill
A 5 ft 1 in.
C 6 ft 3 in.
A 1712 qt
B 5 ft 9 in.
D 6 ft 9 in.
B 14 qt
C 10 qt
D 834 qt
6 Emma Jaynes weighed 7 pounds 13 ounces at birth. If she exactly tripled
her birth weight during her first year, how much did she weigh on her
first birthday?
A 23 lb 7 oz
B 22 lb 3 oz
C 21 lb 13 oz
D 15 lb 10 oz
WESTEST, Grade 10
35
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.4.4 Develop and apply formulas for area, perimeter,
surface area, and volume and apply them in solving practical problems.
1
C
2 The Grave Creek Mound at Moundsville, West Virginia, is the largest
conical-type burial mound in the United States. It was built by the
Adena people, who were Native Americans who lived in this area over
2,000 years ago. The mound is 62 feet in height and 240 feet in
diameter. Which is closest to the area of its base?
B 45,240 ft2
A 750 ft2
C 46,750 ft2
D 892,800 ft2
2
B
3 Which is closest to the amount of air needed to
inflate this beach ball?
A 201 in3
B 1,206 in3
C 1,608 in3
D 2,145 in3
3
D
4
B
1 How much cardboard is needed to construct this carton?
10 cm
36 cm
25 cm
B 9,000 cm2
D 1,510 cm2
16 in.
4 Mr. and Mrs. Myers plan to fence a portion of their backyard as a play
area for their children. One side of the play area will be directly behind
the house, so it will not need to be fenced. How much fencing will they
need to buy?
House
15 ft
37 ft
A 52 ft
C 107 ft
36
WESTEST, Grade 10
B 67 ft
D 555 ft
Copyright © Glencoe/McGraw-Hill
A 18,000 cm2
C 3,020 cm2
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.4.4 (continued)
5 About how much water will be needed to fill this wading pool 34 of the
way full?
5
A
6
B
7
D
8
A
31–2 ft
20 in.
A 48 ft3
C 72 ft3
B 69 ft3
D 96 ft3
6 Claudia has chosen a portion of her backyard for planting a vegetable
garden. To the nearest square foot, what is the area that she will have
available for planting?
10.6 ft
5.4 ft
5.9 ft
8.2 ft
Copyright © Glencoe/McGraw-Hill
A 30 ft2
C 53 ft2
B 51 ft2
D 60 ft2
7 The soup can and the ice cream cone have the
same height, and their bases have the same
radius. What is the ratio of the volume of the
ice cream cone to the volume of the soup can?
A 3:1
B 2:1
C 1:2
D 1:3
8 Tom Ross is a landscaper who is designing
a garden to surround a circular fountain in
a park in Monongalia County. To the nearest
square foot, what is the area Tom will have
available for planting?
A 302 ft2
B 384 ft2
C 452 ft2
D 1,206 ft2
r
r
h
Garden
Fountain
10 ft
22 ft
WESTEST, Grade 10
37
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.4.1, 10.4.2, 10.4.4
1 The measures of the four angles of a quadrilateral are in the ratio
6:5:4:3. What are these angle measures? Your solution should include an
equation and a check of your answer. 10.4.1
Sample answer: Let 6x, 5x, 4x, and 3x be the angle measures. Since the sum
of the measures of the angles of any quadrilateral is 360°, my equation is
6x 5x 4x 3x 360.
6x 5x 4x 3x 360
18x 360
x 20
6x 6(20) 120, 5x 5(20) 100, 4x 4(20) 80, and 3x 3(20) 60, so
the angle measures are 120°, 100°, 80°, and 60°.
Check: 120° 100° 80° 60° 360°
2 What is the area of this isosceles trapezoid?
14 in.
10.4.2, 10.4.4
Sample answer: All of the measurements
need to be in the same units, so I changed
the measurements that are given in yards
and feet to inches.
2
5
13 ft 3 (12 in.) 20 in.;
1
4
A
1
(B b)h
2
1
(14 20)(9)
2
yd
12–3 ft
1
yd 4 (36 in.) 9 in.
Now I can use the formula A A
1–
4
1
(B
2
b)h to find the area of the trapezoid.
153
3 A ball has a radius of 10 centimeters.
A cylindrical container has a radius
of 10 centimeters and a height of
10 centimeters. Will the ball or the
container hold more water? 10.4.4
10 cm
10 cm
10 cm
Sample answer: Ball: The formula for the volume of a sphere is
4
4
4,000
V 3 r 3 3 (10)3 3 in3. Container: The formula for the volume of a
4,000
1
cylinder is V r 2h (10)2(10) 1,000 in3. Since 3 1,3333,
4,000
4,000
1,000, so in3 1,000 in3. The ball has the greater volume,
3
3
so it will hold more water.
38
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
The area of the trapezoid is 153 in2.
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.4.1, 10.4.2, 10.4.4 (continued)
4 The figures show an equilateral triangle
and a square, each with one exterior angle
drawn at each vertex. In each part, explain
your reasoning and show any formulas
you used to get your answers. 10.4.1
1
1
2
4
3
2
3
Part A Find the measure of each exterior angle of the triangle and the sum
of the measures of these angles. Then do the same for the square.
Sample answer: The measure of each (interior) angle of an equilateral triangle
180°
is 3 60°. Each exterior angle and its adjacent interior angle form a linear
pair, so they are supplementary. Therefore, each exterior angle measures
180° 60° 120°, and the sum of the three exterior angles is 3(120°) 360°.
The measure of each (interior) angle of a square is 90°. Each exterior angle
measures 180° 90° 90°, and the sum of the four exterior angles is
4(90°) 360°.
Part B In a certain regular polygon, the measure of each exterior angle
is 18°. How many sides does this polygon have?
Sample answer: The sum of the exterior angles (1 at each vertex) of any
polygon is 360°, and in a regular polygon, each of these angles has the same
360°
360°
measure, so the measure of each exterior angle is n. If n 18°, then
n 20, so the polygon has 20 sides.
Copyright © Glencoe/McGraw-Hill
5 The Lots-a-Fun Toy Company makes hollow blocks and balls. Their
most popular products are a block that is 12 centimeters on each side
and a ball with a diameter of 16 centimeters. 10.4.4
Part A Find the volume and surface area of the block and the ball. Show
all formulas that you use.
Sample answer: The block is a cube. V s3 123 1,728 cm3;
SA 6s2 6(12)2 864 cm2
4
4
The ball is a sphere. V 3 r3 3 (8)3 2,145 cm3;
SA 4r2 4(8)2 804 cm2
Part B Which takes more material to make, the block or the ball?
Explain your reasoning.
Sample answer: Both objects are hollow, so the material needed to make
them is measured by the surface area. Even though the sphere has the greater
volume, the block has the greater surface area, so the block requires more
material.
WESTEST, Grade 10
39
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.5.1 Collect, organize, interpret data, and predict
outcomes using the mean, mode, median, range, and standard deviation.
1 Mr. Martinez gave his 5th period Spanish class
a five-point vocabulary quiz. The tally shows
the students’ scores. What is the mode for these
scores?
A 3
B 3.13
C 4
D 5
Score Number of
Students
||
0
|||
1
||||
2
|||| ||
3
|||| |||
4
|||| |
5
2 The table shows Veronica’s test scores in her math and history classes.
Which statement is true about these scores?
Math
83
History 75
A
B
C
D
77
81
86
78
73
90
C
2
D
3
A
91
86
Her median score is higher in history than in math.
The range of her scores is greater in history than in math.
In math, her mean and median scores are the same.
Her mean scores are the same in both classes.
3 The graphs show the distributions of 10th grade standardized math test
scores for two high schools. The highest possible scores on both tests is
200, and the scores for both schools are normally distributed. Which
conclusion can you draw by comparing these graphs?
50
100 150 200
Score
0
50
100 150 200
Score
A The mean score is the same for both schools, but the standard
deviation is greater for Southeast High School.
B The mean score is the same for both schools, but the standard
deviation is greater for Northwest High School
C The standard deviation is the same for both schools, but the mean is
greater for Southeast High School.
D The standard deviation is the same for both schools, but the mean is
greater for Northwest High School.
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
0
Southeast High School
Frequency
Frequency
Northwest High School
40
1
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.5.2 Find the probability of conditional events and
mutually exclusive events.
1 The table gives population data from the 2000 U.S. Census. In 2000,
which is closest to the probability that a resident of West Virginia lived
in Wheeling?
1
B
2
D
3
C
4
B
United States West Virginia Charleston, WV Wheeling, WV
284,796,887
1,808,344
53,421
31,419
A 0.17%
C 3.0%
B 1.7%
D 17%
2 The table shows the enrollment at Fox Ridge High School at the
beginning of the 2003–2004 school year by grade level and gender.
Which is closest to the probability that a randomly chosen female
student is a junior or senior?
Freshman Sophomore
Female
175
183
Male
162
179
Junior
169
182
A 0.531
C 0.482
Senior
147
154
B 0.499
D 0.469
Copyright © Glencoe/McGraw-Hill
3 If Jason draws a marble at random from a bag containing 5 red marbles,
4 blue marbles, 3 yellow marbles, and 6 white marbles, what is the
probability that he will draw a marble that is either blue or white?
A
4
9
B
1
2
C
5
9
D
2
3
4 The table shows the probability of each sum that can be obtained when a
pair of standard 6-sided dice is rolled. On a random throw of a pair of
dice, what is the probability that Alexis will roll a sum that is at least 9?
Sum
Probability
2
3
4
5
6
7
8
9
10
11
12
1
36
1
18
1
12
1
9
5
36
1
6
5
36
1
9
1
12
1
18
1
36
A
1
6
B
5
18
C
4
11
D
5
6
WESTEST, Grade 10
41
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.5.3 Predict the outcomes of simple events using the
rules of probability.
1
C
2 Which of the following cannot be the probability of an event?
A 1.001
B 1
C 0.001
D 0
2
A
3 Cameron is a college basketball player who made 35 of his last 48 free
throws. Which is closest to the probability that he will miss the basket
on his next free throw?
A 27%
B 39%
C 50%
D 73%
3
A
4 River Branch High School has a total enrollment of 1,265 students. In the
Venn diagram, B represents the event, “plays in the band,” and C represents
the event, “sings in the chorus.” Which is closest to the probability that a
randomly selected River Branch student is a member of the chorus, but
not a member of the band?
4
B
5
C
1 Amber tossed a fair penny 4 times, and it landed heads up each time. If
she tosses this penny a 5th time, what is the probability that she will get
heads again?
A 0
B
B
178
1
5
C
1
2
D
4
5
C
35
A 14.1%
C 20.6%
B 17.9%
D 27.4%
5 In a standard deck of 52 playing cards, there are 4 suits (spades, hearts,
clubs, and diamonds), with the same number of cards in each suit. Within
each suit, the jack, king, and queen are called “face cards.” If Erin draws
a card at random from a standard deck, what is the probability that she
will get a face card?
42
A
10
13
B
4
13
C
3
13
D
3
52
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
826
Name
Date
Standards Practice
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
OBJECTIVE 10.5.4 Read, interpret, and construct graphs to solve
problems.
1 The students in Mr. Schmidt’s 5th
Number of
Flavor
period class are learning how to
Students
gather and organize data and to
Chocolate
10
display the data in various types of
Vanilla
05
graphs. The table shows the results
Chocolate Chunk
08
of a class survey of the students’
Other
07
favorite ice cream flavors. If the
students make a circle graph to display the data, how many degrees of
the circle should they use for the Chocolate Chunk section?
A 120°
B 96°
C 84°
D 48°
1
B
2 The table shows the population of West Virginia
every 10 years from 1950 through 2000 according
to the U.S. Census. Which type of display would
be most appropriate to show how the state
population changed over this time period?
A circle graph
B double bar graph
C line graph
D stem-and-leaf plot
2
C
3
D
Year Population
1950 2,005,552
1960 1,860,421
1970 1,744,237
1980 1,949,644
1990 1,793,477
2000 1,808,344
2,000
1,600
1,200
800
400
0
20
19
99
–2
0
00 00
–2
20
0
01 01
–2
20
0
02 02
–2
20
0
03 03
–2
00
4
First Day
Enrollment
Copyright © Glencoe/McGraw-Hill
3 The bar graph shows first-day enrollment at West Valley High School for
several recent school years. Between which two school years did
enrollment at this school change the most?
School Year
A
B
C
D
1999–2000 to 2000–2001
2000–2001 to 2001–2002
2001–2002 to 2002–2003
2002–2003 to 2003–2004
WESTEST, Grade 10
43
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.5.1, 10.5.2, 10.5.3, 10.5.4
1 The stem-and-leaf plot shows the scores for the
students in Mrs. Olsen’s fifth-period geometry
class on a 100-point chapter test. For these scores,
which is greater, the mean or the median? By
how many points do these measures of central
tendency differ? 10.5.1, 10.5.4
Stem
3
4
5
6
7
8
9
10
| Leaf
|5
|27
|368
|122
|025
|244
|358
5
7 9 9
5 6
Sample answer: There are 25 test scores.
|0
3 | 5 35
I listed them in increasing order:
35, 42, 47, 53, 56, 58, 61, 62, 62, 65, 70, 72, 75, 77, 79, 79, 82, 84, 84, 85, 86, 93,
95, 98, and 100. To find the mean, I added all these numbers on my calculator
1,800
and divided by 25: 25 72. Since there are 25 scores, the median will be the
13th score from either the lowest or highest score, which is 75. The median
test score is 3 points greater than the mean.
2 The following list gives the ages of the people who attended the Watkins
family reunion at Beech Fork State Park in southwestern West Virginia:
25, 32, 14, 6, 35, 42, 48, 63, 44, 67, 2, 11, 21, 19, 41, 68. Make a
histogram for this data, using 10-year age intervals starting with 0–9.
3 For an annual report, the financial officer of a company made a list of the
salaries of all of the employees of the company. Do you think the mean or
median would best represent this data? Explain your reasoning. 10.5.1
Sample answer: I think the median is best because half of the people earn
above that amount and half of the people below, so it gives me a good idea
of how much money the average employee is making. The mean isn’t good
because a few high salaries, like that of the president of the company, would
affect it too much.
44
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
10.5.4
Name
Date
Standards Practice
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
OBJECTIVES 10.5.1, 10.5.2, 10.5.3, 10.5.4 (continued)
4 Eric tossed a penny 3 times and recorded whether he got heads or tails
each time. 10.5.2, 10.5.3
Sample answer:
Part A Draw a tree diagram that shows the equally
likely outcomes of this experiment. Show
the probability of each outcome on your
diagram.
Part B What is the probability that Eric will get heads on exactly 2 of
the tosses? Use your tree diagram to answer this question.
Sample answer: I see that 3 of the 8 possible outcomes on my tree diagram
have 2 heads: HHT, HTH, and THH. Since the 8 outcomes are equally likely, the
3
probability of getting exactly 2 heads is 8.
Part C If the 1st penny lands heads up, what is the probability that Eric
will get heads on exactly 2 of the 3 tosses? If your answers for
Parts B and C are different, explain why.
Copyright © Glencoe/McGraw-Hill
Sample answer: I only need to look at the outcomes that list H first. There are
4 of these, and 2 of them, HHT and HTH, have 2 heads, so I know that the
probability of getting exactly 2 heads if I know the first coin landed heads up
2
1
is 4 2. This answer is different from my answer in Part B because Part C
involves conditional probability and uses a reduced sample space.
5 There are 480 students at West River Middle School.
The circle graph shows the results of a survey in which
all students at the school were asked their favorite
sport to watch on television. 10.5.2, 10.5.3, 10.5.4
Basketball
136
Other
80
Football
144
48
72
Hockey
Baseball
Part A What is the probability that a randomly
selected student chose hockey?
Sample answer: Since 72 out of 480 students chose hockey, the probability is
72
3
or 0.15 or 15%.
480
20
Part B If you know that a certain student chose either baseball or
football, what is the probability that this student chose baseball?
Sample answer: There were 48 144 192 students who picked either
baseball or football, and 48 of those students chose baseball, so the
48
1
or 0.25 or 25%.
probability is 192
4
WESTEST, Grade 10
45
Name
Date
Sample Test
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
1 Mike is using a road map of West Virginia on which 1 inch represents
22 miles. He measures a straight-line distance of 8.9 inches between
Parkersburg and White Sulphur Springs. Which is closest to the actual
distance between these cities? 10.3.3
A 205 mi
B 196 mi
C 190 mi
D 180 mi
1
B
2 Which is the solution of 25 34x 58x 13? 10.2.1
2
D
3
B
95 is placed on a number line, between which two points will it be
4 If located? 10.1.3
A 10 and 9
B 9 and 8
C 8 and 9
D 9 and 10
4
A
5 The table shows the enrollment in a high
school on the first day of school for several
recent years. If enrollment at this school
continues to follow this pattern of growth,
which is the best estimate of the enrollment
on the first day of school of the 2005–2006
school year? 10.2.6
A 1,095
B 1,110
C 1,150
D 1,205
5
C
96
11
A 24
B
C 32
D 96
3 All sides of this stop sign are the same length. What is the measure of
each interior angle of this polygon? 10.4.1
STOP
46
WESTEST, Grade 10
B 135°
D 100°
Year
Enrollment
2000–2001
0,900
2001–2002
0,945
2002–2003
0,992
2003–2004
1,042
Go on
Copyright © Glencoe/McGraw-Hill
A 144°
C 120°
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
6 What is the value of 4r 2s 10st 6t 3 if r 3, s 6, and t 2?
A 288
B 144
10.2.4
C 48
D 288
6
B
7 Mrs. Stevens gave her third-period Geometry class a ten-point quiz. The
tally shows the students’ scores on this quiz. What was the mean quiz
score? 10.5.1
7
A
8 If two vertical angles are complementary, what are their measures?
A 30° and 60°
B 45° and 45°
10.3.2
C 60° and 120°
D 90° and 90°
8
B
9 Which is closest to the amount of paper needed to
make the label for this soup can? 10.4.4
A 86 cm2
B 128 cm2
C 256 cm2
D 299 cm2
9
C
10
D
Score Number of Score Number of
Students
Students
|
||||
0
06
||||
||
1
07
|
|||| |||
2
08
||
||||
3
09
||
4
10
|||
5
A 6.75
B 7.0
C 7.5
D 8.0
7.4 cm
11 cm
Copyright © Glencoe/McGraw-Hill
10 Which could be the graph of the equation 3x 4y 12? 10.2.8
A
B
y
y
x
x
O
C
O
D
y
y
x
O
O
x
Go on
WESTEST, Grade 10
47
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
11 Austin spent $42 (not including sales tax) for a jacket that was on sale
for 25% off. What was the original price of the jacket? 10.1.1
A $168
B $67
C $56
D $33.60
11
C
12 What is the slope of the line that passes through the points at (6, 5)
and (3, 11)? 10.2.7
12
B
13
A
14 Geoff and Chris went mountain biking on the North Bend Rail Trail in
north central West Virginia. Chris started on the trail at noon and rode at
an average speed of 16 miles per hour. Geoff started from the same spot
half an hour later and rode at an average speed of 20 miles per hour. If
neither of them stopped before they met, at what time did Geoff catch up
with Chris? 10.2.3
A 12:54 P.M.
B 2:00 P.M.
C 2:30 P.M.
D 3:00 P.M.
14
C
15 How much water would be needed to fill this fish tank 23 of the way to
the top? 10.4.4
15
B
A 32
C
B 23
2
3
D
is
13 If mQS 138°, mQR 148° and PS
tangent to circle O at S, what is mP?
3
2
Q
10.3.4
O
32°
37°
46°
69°
S
R
P
12 in.
9 in.
20 in.
A
B
C
D
48
2,160 in3
1,440 in3
1,056 in3
704 in3
WESTEST, Grade 10
Go on
Copyright © Glencoe/McGraw-Hill
A
B
C
D
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
16
D
17
A
18
A
19 The thickness of a red blood cell is approximately 2.4 106 meters.
Which is closest to the thickness of 8,000 red blood cells stacked on top of
each other, if they could be placed so that there is no space between them?
10.1.2
A 0.000192 m
B 0.00192 m
C 0.0192 m
D 0.192 m
19
C
20 Which is the completely factored form of x4 16? 10.2.9
A (x 2)4
B (x 2)2(x 2)2
C (x2 4)(x2 4)
D (x 2)(x 2) (x2 4)
20
D
16 Which graph shows the solution of 3(4 x) 7x 4? 10.2.1
A
5 4 3 2 1
0
1
2
3
4
5
B
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
C
D
5 4 3 2 1
0
1
2
3
4
5
17 Jasmine took a survey of 50 students
in her middle school in which she asked
them to name their favorite class. The
table shows the results of her survey. If
Jasmine makes a circle graph to display
this data, how many degrees of the circle
should she use for the Math section?
10.5.4
A 64.8°
B 40.0°
C 32.4°
D 18.0°
Number of
Students
Art
5
English
7
Math
9
Music
8
Science
7
Social Studies
8
Other
6
Class
18 If LMN QTR, which of the following must be true? 10.3.3
A mM mT
B L R
Copyright © Glencoe/McGraw-Hill
C
LM
QT
MN
QR
D LN QR
Go on
WESTEST, Grade 10
49
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
21
D
22 Mrs. Fox takes a 600-milligram calcium tablet every morning. How
many grams of calcium does she take each week? 10.4.2
A 0.42 g
B 4.2 g
C 42 g
D 420 g
22
B
23 The formula y mx b gives the equation of a line with slope m and
y-intercept b. How can this formula be rewritten to give the x-coordinate
of a specific point (x, y) on the line if the y-coordinate of the point, the
slope, and the y-intercept are known? 10.2.2
23
A
24
C
25
C
21 Which graph shows all solutions of |x 6| |3x 3|? 10.2.5
A
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
5 4 3 2 1
0
1
2
3
4
5
B
C
D
yb
yb
A x m
B x m
ym
by
D x m
24 The table shows the probability of each sum that can be obtained when a
pair of standard 6-sided dice is rolled. On a random throw of a pair of
dice, what is the probability that Lindsay will get a sum that is a multiple
of 3? 10.5.2
Sum
Probability
2
3
4
5
6
7
8
9
10
11
12
1
36
1
18
1
12
1
9
5
36
1
6
5
36
1
9
1
12
1
18
1
36
A
1
4
B
5
18
C
1
3
D
4
11
25 If line m is parallel to line n, what is the
value of x? 10.3.2
A 132
B 42
C 33
D 12
50
WESTEST, Grade 10
48
m
4x n
Go on
Copyright © Glencoe/McGraw-Hill
C x b
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
Temperature (F)
26 The line graph shows the average daily high temperature in Charleston.
In which month is the average daily high temperature closest to that in
April? 10.5.4
90
80
70
60
50
40
0
26
C
27
C
28
A
29
C
30
A
J F M A M J J A S O N D J
Month
A May
C October
B September
D November
27 P and Q are points on circle O. Which term
describes PQ? 10.3.4
A chord
B diameter
C secant
D tangent
28 What is another way to write
P
O
Q
4
? 10.1.3
10 6
A 10
6
B 10 6
10
6
C 4
Copyright © Glencoe/McGraw-Hill
D 1
29 Which is closest to h, the length of the altitude
to the base of this isosceles triangle? 10.3.5
A 6.6 cm
B 7.0 cm
C 10.9 cm
D 11.0 cm
30 Which expression is equivalent to
A
y12z4
x6
B
x6
1
y 2z4
12 cm
h
10 cm
x2y3z0 2
? 10.2.4
xy3z2
C
z4
2
x
D
y36z4
x8
Go on
WESTEST, Grade 10
51
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
31 What are the quotient and remainder when 8x2 6x 36 is divided by
2x 5? 10.2.9
A quotient: 4x 7; remainder: 1
B quotient: 4x 7; remainder: 1
C quotient: 4x 7; remainder: 1
D quotient: 4x 7; remainder: 1
31
C
32 If the circumference of a fully inflated beach ball is 46
centimeters,
which is closest to the amount of air that was needed to inflate it? 10.4.4
A 305,700 cm3
B 50,950 cm3
C 38,200 cm3
D 6,650 cm3
32
B
33 The table shows the enrollment at Fairways Middle School on the 1st day
of the 2003–2004 school year by grade level and gender. Which is closest
to the probability that a randomly chosen boy enrolled in this school on
that day was a 7th grader? 10.5.2
33
D
34 Danielle spent $17.34 at the Philippi Post Office for a combination of
37-cent and 23-cent stamps. If x represents the number of 23-cent stamps
and she bought a total of 62 stamps, which equation describes this
situation? 10.2.3
A 0.23x 0.37(x 62) 17.34
B 23x 37(62 x) 17.34
C 23x 37(x 62) 17.34
D 0.23x 0.37(62 x) 17.34
34
D
35 In parallelogram PQRS, what is mS? 10.4.1
35
B
Grade 6th Grade 7th Grade 8th Grade
Boys
106
112
095
Girls
098
108
103
B 0.333
D 0.358
Q (3
x 23)
P
(x 15)
A 108°
C 128°
52
WESTEST, Grade 10
R
S
B 118°
D 135°
Go on
Copyright © Glencoe/McGraw-Hill
A 0.180
C 0.350
Name
Date
Sample Test
(continued)
Read each question and choose the best answer. Then write the letter for
the answer you have chosen in the blank at the right of each question.
(2)5 4(3)
5254
36
A
37
D
38
A
39 Which is an equation of the line that passes through the point at (3, 7)
and is parallel to the x-axis? 10.2.8
A x 3
B y7
C xy4
D x y 10
39
B
40 Lisette Tompkins is a landscaper who is
designing a garden for a park in Monroe
County. She has decided that the garden
will have decorative stones in the center,
surrounded by plants. To the nearest square
foot, what is the area that Lisette will have
available for planting? 10.4.4
A 763 ft2
B 243 ft2
C 191 ft2
D 127 ft2
40
C
36 What is the value of 2 ? 10.1.1
44
19
A 20
B
C 290
D 20
37 What is the probability that a randomly chosen two-digit positive integer
will be a multiple of both 3 and 5? 10.5.3
8
15
B
1
3
C
1
8
D
1
15
Copyright © Glencoe/McGraw-Hill
38 To walk from his home to his school,
Frank can either walk south on Elm
Street and then west on Second Avenue,
or he can cut diagonally across an
empty lot. How much distance will
School
he save by walking across the empty
lot? 10.3.5
A 440 ft
B 660 ft
C 770 ft
D 1,100 ft
Home
660 ft
Elm St.
A
880 ft
Second Ave.
Plants
Stones
9 ft
18 ft
Go on
WESTEST, Grade 10
53
Name
Date
Sample Test
(continued)
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
4
as a single term involving a simplified radical. 10.1.3
41 Write 75
3
Sample answer:
4
25
75
3
3
3
15
3
23
3
4
3
53
2
3
53
2
3
3
3
23
53
3
13
3
3
42 On an algebra quiz, Maria had to solve 4 2x 3(x 2). Here is what
she wrote on her quiz paper.
4 2x 3(x 2)
4 2x 3x 6
2x 3x 10
5x 10
x2
Maria’s teacher did not give her credit for this problem. Explain Maria’s
error and show how to complete the solution correctly. 10.2.1
Sample answer: Maria’s work was correct until the last step, but then she
forgot that when you multiply or divide both sides of an inequality by a
negative number, you have to reverse the inequality symbol. Since she divided
both sides by 5 in the last step, the final inequality should be x 2.
2–
3
ft
14 in.
13–4
ft
Sample answer: To find the amount of cardboard needed to construct this
carton, I need to find its surface area. To do this, all of the measurements must
be in the same units, and I need to first give my answer in square inches, so
I convert the measurements that are given in feet to inches.
2
3
ft 2
(12
3
3
in.) 8 in., and 14 ft 1.75(12 in.) 21 in.
The carton is a rectangular prism, so its surface area is given by the formula
S 2LW 2LH 2WH 2(21 in.)(14 in.) 2(21 in.)(8 in.) 2(14 in.)(8 in.) 1,148 in2. There are 122 144 in2 in a square foot, so the number of square
1,148
8.
feet is 144
Go on
It would take 1,148 in2 or about 8 ft2 of cardboard to construct
the carton.
54
WESTEST, Grade 10
Copyright © Glencoe/McGraw-Hill
43 How much cardboard is needed to construct
this carton? First give your answer in square
inches and then give it to the nearest square
foot. 10.4.2, 10.4.4
Name
Sample Test
Date
(continued)
Read each problem carefully and write your answer in the space provided.
Show all your work and use complete sentences to answer all questions.
is
44 PR is tangent to circle O at R, and PS
tangent to circle O at S. 10.3.4, 10.3.5
R
O
P
Part A Look at PRO and PSO. What
kind of triangles are these? What is
the relationship between the two
S
triangles? Explain how you know.
Sample answer: They are both right triangles and they are congruent. I know
they are right triangles because a radius of a circle is perpendicular to a tangent
at the point of tangency, which tells me that PRO and PSO are both right
O and S
O are radii, and all radii of the same circle are congruent,
angles. Since R
I know that RO
SO
. Also, O
P
is common to both triangles and is the
hypotenuse for both of them. So I know that PRO PSO by the
Hypotenuse-Leg congruence theorem.
Part B If the radius of circle O is 8 centimeters and OP 17
centimeters, what is the length of the tangent segment PS ?
is the hypotenuse. I used the
Sample answer: In right triangle PSO, OP
Copyright © Glencoe/McGraw-Hill
10
8
6
4
2
0
0–
10 9
–1
20 9
–2
30 9
–3
40 9
–4
50 9
–5
60 9
–6
70 9
–7
80 9
–8
9
45 The histogram shows the age
distribution of the people who attended
the Fox family reunion that was held at
Watoga State Park in the mountains of
Pocahontas County. 10.5.2, 10.5.3, 10.5.4
Number of People
172 82 225
15 cm.
Pythagorean Theorem to find PS: PS Part A What is the probability that a
Age
randomly selected person who
attended the reunion was 40–49 years old?
Sample answer: Since 8 out of 50 people were ages 40 to 49, the probability is
8
4
or 0.16 or 16%.
50
25
Part B If you know that a certain person at the reunion is under age 50,
what is the probability that this person is at least 40 years old?
Sample answer: A man who is aged at least 40, but less than 50, must be
40–49 years old. There were 4 7 5 10 8 34 people under age 50,
8
4
and 8 of these people were in the 40s, the probability is 3
1
or about
4
7
0.235 or 23.5%.
Part C If your answers in Parts A and B are different, explain why.
Sample answer: Part B involves conditional probability and
uses a reduced sample space.
STOP
WESTEST, Grade 10
55