Grade K-Algebra 2...0–17 Use Math Triumphs to accelerate the achievement of students who are two or more years below grade level. Students should follow a personalized remediation

ISBN: 978-0-07-662454-6MHID: 0-07-662454-4

Diagnostic Chart

suggestions for intervention and remediation suggested materials

Diagnostic and Placement Tests

Grade K-Algebra 2simplify placement

decisions

Scoring Guide

simplify placement

Sco ide

Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2

Grade K-Algebra 2

ContentsUsing the Diagnostic and Placement Tests

Placement Options

When to Use the Placement Tests

Interpreting Scores

Scoring Guide Masters

Using Placement Tests for Diagnostic Purposes

Learning Objectives Masters

Answer Keys

Inte

rvention/Remediation

connectED.mcgraw-hill.com

M_S_DPT_CV_662454.indd 1M_S_DPT_CV_662454.indd 1 9/21/11 3:08 PM9/21/11 3:08 PM

99 Diagnostic and Placement Tests

Program: DPT Component: Test WorkbookPDF Proof

Vendor: Aptara Grade: Grade 8

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.Placement

TestScoringGuide

Student Name

Key: Consider this student for…

8

Math Triumphs

Grade 8 Strategic Intervention —See page 103 for materials list.

Glencoe Math, Course 3

For each part, mark the box under the number of correctly answered questions.

Total

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Mark the total number correct below.

0 1 2 3 4 5 6 7 8 9 10

The Number System

Expressions and Equations

Functions

Geometry

Statistics and Probability

099_113_DPT_G8_662454.indd 99099_113_DPT_G8_662454.indd 99 9/21/11 11:45 AM9/21/11 11:45 AM

Diagnostic and Placement Tests 100



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use.Placement

TestLearningObjectives 8

Student Name

In the column on the left, mark the questions that the student answered incorrectly.

Domain

Question

Number Objective

The Number System

1Use rational approximations of irrational numbers to compare the size of irrational numbers.

2Use rational approximations of irrational numbers to estimate the value of expressions

3 Know that numbers that are not rational are called irrational.

Expressions and Equations

4 Graph proportional relationships.

5 Solve linear equations in one variable.

6 Solve linear equations in one variable.

7Perform operations with numbers expressed in scientific notation.

8Perform operations with numbers expressed in scientific notation.

9Know and apply the properties of integer exponents to generate equivalent numerical expressions.

10 Analyze and solve pairs of simultaneous linear equations.

11Solve linear equations with rational number coefficients, including equations whose solutions require using the distributive property.

Functions

12Construct a function to model a linear relationship between two quantities.

13Understand that a function is a rule that assigns to each input exactly one output.

14Understand that a function is a rule that assigns to each input exactly one output.

15Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.

16Describe qualitatively the functional relationship between two quantities by analyzing a graph.

17Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).





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.Domain

Question

Number Objective

Geometry

18Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

19Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

20Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.


22Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

23Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

24Use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal.

25Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.


27Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Statistics and Probability

28Construct and interpret scatter plots for bivariate measure-ment data to investigate patterns of association between two quantities.

29Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

30Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.





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A Special Note About Intervention

When using diagnostic tests, teachers should always question the reason behind the students’ scores. Students can struggle with mathematics concepts for a variety of reasons. Personalized instruction is recommended for English language learners, students with specific learning disabilities, students with certain medical conditions, or for those who struggle with traditional instructional practice. Teachers should always consider the needs of the individual student when determining the best approach for instruction and program placement.

Student

Performance

Level

Number of

Questions

Correct

Suggestions for Intervention and Remediation

Intensive

Intervention

0–17 Use Math Triumphs to accelerate the achievement of students who are two or more years below grade level. Students should follow a personalized remediation plan. A variety of materials and instructional methods are recommended. For example, instruction and practice should be provided in print, technology, and hands-on lessons.

Strategic

Intervention

18–23 Use the additional Intervention and Remediation materials listed on the next page. This list of materials can provide helpful resources for students who struggle in the traditional mathematics program. Strategic intervention allows students to continue to remain in the Glencoe Math program, while receiving the differentiated instruction they need. Teaching Tips and other resources are also listed in the Teacher Edition.

Grade 8 24 or more Use Glencoe Math. This student does not require overall intervention. However, based on the student’s performance on the different sections, intervention may be required. For example, a student who missed 1 or more questions in the Function section may require extra assistance as you cover these skills throughout the year.

8





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.Grade 8

Get ConnectGet ConnectED Find these materials at www.connectED.mcgraw-hill.com.

Reteach Masters A brief explanation, along with examples and exercises, for every lesson in the Student Edition (Two pages for Problem-Solving Lessons and one page per lesson for all other lessons) and included in the Chapter Resource Masters

Skills Practice Masters

Additional practice in computational and application exercises for each lesson in the Student Edition and included in the Chapter Resource Masters

Homework Practice Masters

Additional practice in computational and spiral review exercises for each lesson in the Student Edition and included in the Chapter Resource Masters

Self-Check Quizzes

Students can check their understanding for each lesson and email their results to the teacher

Chapter Readiness Quizzes

Online assessment to use at the beginning of each chapter in the Student Edition

Personal Tutor Online instructions for step-by-step solutions for the examples of each lesson in the student textbook

Quick Review Skills Workbook

Additional computational practice in basic skills

Additional TechnologyExamView® Assessment Suite

Networkable software includes a Worksheet Builder to make worksheets and tests, a Student Module to take tests on-screen, and a Management System to keep student records





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LENGTH

Metric

1 kilometer = 1,000 meters

1 meter = 100 centimeters

1 centimeter = 10 millimeters

Customary

1 mile = 1,760 yards

1 mile = 5,280 feet

1 yard = 3 feet

1 foot = 12 inches

CAPACITY AND VOLUME

Metric

1 liter = 1,000 milliliters

Customary

1 gallon = 4 quarts

1 gallon = 128 ounces

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 ounces

MASS AND WEIGHT

Metric

1 kilogram = 1,000 grams

1 gram = 1000 milligrams

Customary

1 ton = 2,000 pounds

1 pound = 16 ounces

TIME

1 year = 365 days

1 year = 12 months

1 year = 52 weeks

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Mathematics Chart1

23

45

67

89

1011

1213

1415

1617

1819

20C

entim

eter

s0





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.

PERIMETER

square P = 4s

rectangle P = 2� + 2w or

P = 2(� + w)

AREA

square A = s2

rectangle A = �w or A = bh

triangle A = 1 _ 2 bh or A = bh

__ 2

trapezoid A = 1 _ 2 (b

1 + b

2)h or

A = (b

1 + b

2)h

_______ 2

circle A = πr2

CIRCUMFERENCE

circle C = 2πr or

C = πd

VOLUME

cube V = s3

retangular prism V = �wh or

V = Bh*

triangular prism V = Bh*

cylinder V = πr2h or

V = Bh*

cone V = 1 _ 3 πr2h or

V = 1 _ 3 Bh*

sphere V = 4 _ 3 πr3

*B represents the area of the base of a solid fi gure.

PI

π ≈ 3.14 or π ≈ 22

__ 7

PYTHAGOREAN THEOREM

a2 + b2 = c2

Mathematics Chart1

23

45

60Inches





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1 Which set of numbers is ordered from least to greatest? 1

A 3 __ 8 ; 1 __ 2 ; 1; √

__

2 ; 4

B 3 __ 8 ; 1 __ 2 ; √

__

2 ; 1; 4

C 4; √

__

2 ; 1; 1 __ 2 ; 3 __ 8

D 1 __ 2 ; 3 __ 8 ; 1; 4; √

__

2

2 The area of a square is 8 square meters. Which of these is 2 closest to the length of one side of the square?

F 2 meters

G 2.8 meters

J 4 meters

H 3.5 meters

3 Which of the following sets of numbers does √

___

49 NOT belong? 3

A integer

B real number

C rational number

D irrational number

Diagnostic and

Placement

Grade 8

Name

Date

This test contains 30 multiple-choice questions. Work each problem in the space on this page. Select the best answer. Write the letter of the answer on the blank at the right.





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4 The table shows circles and 4 their corresponding diameters. Which of the following graphs show the correct relationship between the radius and the area of each circle?

Circles

Circle Diameter (feet)

R 2

S 4

T 8

U 12

F Ar

ea (

feet

)

Circle Sizes

Circle Radius (feet)

y

xO 1 2 3 4 5 6 7 8

2468

101214

22201816

R (1, 3.14)

T (4, 12.56)

U (6, 18.84)

S (2, 6.28)

H

Area

(fe

et)

Circle Sizes


y

xO 2 4 6 8 10 12 14 16

50100150200250300350

500450400

R (2, 12.56)

T (8, 200.96)

U (12, 452.12)

S (4, 50.24)

G

Area

(fe

et)

Circle Sizes


y

xO 1 2 3 4 5 6 7 8R (1, 3.14)

T (4, 50.24)

U (6, 113.04)

S (2, 12.56)10203040506070

1101201009080

J

Area

(fe

et)

Circle Sizes


y

xO 2 4 6 8 10 12 14 16

5101520253035

504540

R (2, 6.28)

T (8, 25.12)

U (12, 37.68)

S (4, 12.68)

5 The picture models the equation 5x 1 2 5 3x 1 6. 5

=xx

x

x x 1

1x

x

x1 1

1 11

1=xx

x

x x 1

1xxxx

xx

xx xx 11

11x

x

x1 1

1 11

1xx

xx

xx11 11

11 1111

11

What value of x makes the equation true?

A x 51 C x 54

B x 52 D x 56

6 In �ABC, the measure of ∠A is 33° and the measure of ∠C is 90°. 6 What is the measure of ∠B?

F 17° G 57° H 137° J 147°





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use.7 Light travels at a speed of about 2.998 3 10 8 meters per second. 7

Express this number in standard notation.

A 299,800,000 C 0.0000002998

B 0.00002998 D 29,980,000

8 A thunderstorm cloud holds about 6,200,000,000 raindrops. 8 Which of the following shows this number in scientific notation?

F 0.62 3 10 10 H 6.2 3 10 8

G 6.2 3 10 9 J 62.0 3 10 8

9 Which of the following is equivalent to the expression 4 4 3 4 –6 ? 9

A 1 ___ 4 2

B 1 ___

4 10 C 4 10 D 4 2

10 What is true concerning the lines graphed by the system of 10 equations shown below?

⎧

⎫

8x 1 6 5 2y

12x 2 3 5 3y

F The lines intersect. H The lines are parallel.

G The lines are perpendicular. J The lines are the same.

11 What is the solution of the equation? 11

1 __ 3 (x 1 15) 5 7

A x 5 2 __ 3 B x 5 2 C x 5 6 D x 5 36

12 What function is represented in the table? 12

n f(n)

1 3

2 7

3 11

4 15

5 19

n

F f(n) 5 n 1 3 H f(n) 5 4n 1 2

G f(n) 5 4n 2 1 J f(n) 5 3n 2 2





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13 Mr. Wilson wrote the function f(x) 5 7x 2 15 on the 13 chalkboard. What is the value of this function for f(6)?

A 27 B 37 C 42 D 57

14 On average, a dog runs 5.5 times faster than a child. 14 Which function can be used to find the speed of a

dog, given the speed of the child?

F f(c) 5 5.5c H f(c) 5 c 1 5.5

G f(c) 5 5.5 ___ c J f(c) 5 c

___ 5.5

15 What is the slope and y-intercept of the equation 15 6x 2 1 5 3y 2 10?

A m 5 2, b 5 3 C m 5 3, b 5 4

B m 5 2, b 5 23 D m 5 6, b 5 9

16 Which best describes the graph of the function f(x) 5 4x? 16

F A straight line through the origin with a steep slope upward to the right.

G A straight line through the origin with a steep slope downward to the right.

H A straight line through 4 on the x-axis with a slope downward to the right.

J A straight line through 4 on the y-axis with a slope upward to the right.

17 Which function described below has the greatest rate of change? 17

I f(x) 5 4x 2 3

II f(x) 5 1 __ 2 x 1 5

III x f(x)

1 6

2 12

3 18

4 24

A I

B II

C III

D They all have the same rate of change.

18 The delivery ramp at the Corner Café is a right triangle. 18 The hypotenuse is 4 meters long. One leg is 3 meters long. What is the length of the other leg?

F √

__

7 meters H 3.5 meters

G √

___

12 meters J 5 meters





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use.19 The map below shows where four of Nahimana’s friends live. 19 Each unit on the map represents 1 mile.

y

xO

Josh

Carter

AeshaJenny

About how far apart do Aesha and Josh live?

A about 5 mi B about 6 mi C about 7.5 mi D about 8.5 mi

20 What is the volume of the cylinder shown below? 20

11 ft

2 ft

F 44 ft 3 H 138.16 ft 3

G 69.08 ft 3 J 276.32 ft 3

21 What is the difference in the volume of the two triangular 21 prisms shown below?

15 cm

8 cm

32 cm

5 cm

7 cm14 cm

A 32 cm 3 C 1,675 cm 3

B 158 cm 3 D 3,350 cm 3

22 A photo with a length of 3 inches and a width of 5 inches is 22 enlarged to poster size. The poster and the photo are similar. The length of the poster is 21 inches. What is the width of the poster?

F 7.2 inches H 19 inches

G 12.6 inches J 35 inches





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23 Rectangle ABCD is shown on the coordinate grid below. 23 Which of the following graphs represent the translation of Rectangle ABCD over the following: (x, y) → (x11, y22)?

y

xO 1 2 3 4

765432

-2

-7-6-5-4-3-2

A

D C

B

A

y

xO 2 3 4

7654421

-2

-7-6-5-4-3-2

A

D C

B

C y

xO 1 2 3 4

7654321

-2

-7-6-5-4-3-2

A

D C

B

B y

xO 2 3 4

7654321

-2

-8-7-6-5-4-3-2

A

D C

B D y

xO 1 2 3 4

7654321

-2

-7-6-5-4-3-2

A

D C

B

24 A rectangle is cut along its diagonal. The measure of ∠A is 55°. 24 What is the measure of ∠B?

A

B

F 125° G 105° H 45° J 35°

25 A 26-foot rope is used to brace a tent pole at the county fair. 25 The rope is anchored 10 feet from the box of the pole.

10 ft

Tent

pol

e 26 ft

How tall is the tent pole?

A 21.8ft B 24ft C 28ft D 30ft





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use. 26 A cylindrical water tower is 24 feet high and has a diameter 26

of 20 feet. Approximately how many cubic feet of water could the tower hold?

F 2,400 cubic feet H 9,600 cubic feet

G 7,500 cubic feet J 30,200 cubic feet

27 The triangles below are similar triangles. Find the value of 27 x and y.

3 cm

5 cm

4 cm

10 cm x

y

A x 5 6, y 5 8 C x 5 1.5, y 5 2

B x 5 3, y 5 4 D x 5 12, y 5 16

28 The scatter plot below shows the yearly advertising 28 expenditures and the relative sales for a small company. What can be concluded from this data?

Sale

s (i

n t

ho

usa

nd

s o

f d

olla

rs)

250225200175150125100755025

Advertising Expenditures (in dollars)

1500500 1000 2000

F As advertising increases, sales tend to decrease.

G As advertising increases, sales tend to increase.

H As advertising increases, sales remain the same.

J As advertising increases, sales always increase.





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. 29 The box plot shows a set of test scores. 29

Which statement is correct?

0 10 20 30 40 50 60 70 80 90 100

A More students scored between 40 and 60 points than between 88 and 96 points.

B An equal number of students scored from 40 to 60 as from 88 to 96.

C The lowest score was 60.

D The highest score was 88.

30 A survey is taken to determine which type of vehicle is 30 most popular. The data is shown in the bar graph below.

05

1015

2025

30

SUV Minivan Sports Mid-Size

MenWomen

Type of Vehicle

Nu

mb

er o

f Pe

op

le

What can you conclude about the survey?

F The survey is biased because most men do not favor sports vehicles.

G The survey is biased because there are more men surveyed than women.

H The survey is not biased because sports cars are most popular among both men and women.

J The survey is not biased because all car types are favored by both men and women.



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Program: DPT Component: Test Workbook (AK)PDF Proof

Vendor: Aptara Grade: Grade K–Algebra 2

Answers (Grade 8)

Dia

gnos

tic a

nd P

lace

men

t Tes

ts

10

6

1 W

hich

set

of n

umbe

rs is

ord

ered

from

leas

t to

grea

test

? 1

A

A

3 __

8 ;

1 __

2 ;

1; √

__

2 ; 4

B

3 __

8 ;

1 __

2 ;

√ __

2

; 1; 4

C

4

; √

__

2 ; 1

; 1 __

2 ;

3 __

8

D

1 __

2 ;

3 __

8 ;

1; 4

; √

__

2

2 T

he a

rea

of a

squ

are

is 8

squ

are

met

ers.

Whi

ch o

f the

se is

2

G

cl

oses

t to

the

leng

th o

f one

sid

e of

the

squa

re?

F

2

met

ers

G

2.

8 m

eter

s

J

4

met

ers

H

3.

5 m

eter

s

3 W

hich

of t

he fo

llow

ing

sets

of n

umbe

rs d

oes

√ __

_ 49

NO

T be

long

? 3

D

A

in

tege

r

B

re

al n

umbe

r

C

ra

tion

al n

umbe

r

D

ir

rati

onal

num

ber

Dia

gn

os

tic a

nd

Pla

cem

en

t

Gra

de

8

Nam

e

Dat

e

This

test

con

tain

s 30

mul

tipl

e-ch

oice

que

stio

ns. W

ork

each

pro

blem

in th

e sp

ace

on th

is p

age.

Sel

ect t

he b

est a

nsw

er. W

rite

the

lett

er o

f the

ans

wer

on

the

blan

k at

the

righ

t.

099_

113_

DPT

_G8_

6624

54.in

dd

106

9/21

/11

11:

45 A

M

1

07

D

iagn

ostic

and

Pla

cem

ent T

ests

4 T

he ta

ble

show

s ci

rcle

s an

d

4

Gth

eir c

orre

spon

ding

dia

met

ers.

W

hich

of t

he fo

llow

ing

grap

hs s

how

th

e co

rrec

t rel

atio

nshi

p be

twee

n th

e ra

dius

and

the

area

of e

ach

circ

le?

Circ

les

Circ

leDi

amet

er (f

eet)

R2

S4

T8

U12

F

Area (feet)

Circ

le S

izes

Circ

le R

adiu

s (fe

et)

y

xO

12

34

56

78

246810121422 20 18 16

R ( 1

, 3.1

4)T ( 4

, 12.

56)

U ( 6

, 18.

84)

S ( 2

, 6.2

8)

H

Area (feet)

Circ

le S

izes

Circ

le R

adiu

s (fe

et)

y

xO

24

68

1012

1416

50100

150

200

250

300

350

500

450

400

R ( 2

, 12.

56)

T ( 8

, 200

.96)

U ( 1

2, 4

52.1

2)

S ( 4

, 50.

24)

G

Area (feet)

Circ

le S

izes

Circ

le R

adiu

s (fe

et)

y

xO

12

34

56

78

R ( 1

, 3.1

4)T ( 4

, 50.

24)

U ( 6

, 113

.04)

S ( 2

, 12.

56)

10203040506070110

120

100 90 80

J

Area (feet)

Circ

le S

izes

Circ

le R

adiu

s (fe

et)

y

xO

24

68

1012

1416

510152025303550 45 40

R ( 2

, 6.2

8)T ( 8

, 25.

12)

U ( 1

2, 3

7.68

)

S ( 4

, 12.

68)

5 T

he p

ictu

re m

odel

s th

e eq

uati

on 5

x 1

2 5

3x

1 6

. 5

B

=x

x

xxx

1 1x

xx1

1

11

1

1=

xx

xxx

1 1xx

xx

xxxxxx

11 11x

xx1

1

11

1

1xx

xxxx11

11

1111

11

11

W

hat v

alue

of x

mak

es th

e eq

uati

on tr

ue?

A

x

51

C

x 5

4

B

x

52

D

x 5

6

6 I

n �

ABC,

the

mea

sure

of ∠

A is

33°

and

the

mea

sure

of ∠

C is

90°

. 6

G

W

hat i

s th

e m

easu

re o

f ∠B

?

F

17

°

G

57°

H

137°

J

147°

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161_207_DPT_AK_662454.indd 188161_207_DPT_AK_662454.indd 188 21/09/11 5:02 PM21/09/11 5:02 PM

Cop

yrig

ht ©

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-Hill

Com

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es, I

nc. P

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issi

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rant

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rep

rodu

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lass

room

use

.




Answers (Grade 8)

Dia

gnos

tic a

nd P

lace

men

t Tes

ts

10

8

7 L

ight

trav

els

at a

spe

ed o

f abo

ut 2

.998

3 1

0 8 m

eter

s pe

r sec

ond.

7

A

Ex

pres

s th

is n

umbe

r in

stan

dard

not

atio

n.

A

29

9,80

0,00

0

C

0.

0000

0029

98

B

0.

0000

2998

D

29

,980

,000

8 A

thun

ders

torm

clo

ud h

olds

abo

ut 6

,200

,000

,000

rain

drop

s.

8

G

Whi

ch o

f the

follo

win

g sh

ows

this

num

ber i

n sc

ient

ific

nota

tion

?

F

0.

62 3

10

10

H

6.2

3 1

0 8

G

6.

2 3

10

9

J

62.0

3 1

0 8

9 W

hich

of t

he fo

llow

ing

is e

quiv

alen

t to

the

expr

essi

on 4

4 3 4

–6 ?

9

A

A

1 __

_ 4

2 B

1 __

_ 4

10

C

4 10

D

4

2

10

Wha

t is

true

con

cern

ing

the

lines

gra

phed

by

the

syst

em o

f 1

0

H

equa

tion

s sh

own

belo

w?

⎧ ⎫

8x 1

6 5

2y

12x

2 3

5 3

y

F

Th

e lin

es in

ters

ect.

H

Th

e lin

es a

re p

aral

lel.

G

Th

e lin

es a

re p

erpe

ndic

ular

. J

Th

e lin

es a

re th

e sa

me.

11

Wha

t is

the

solu

tion

of t

he e

quat

ion?

11

C

1 __

3 (x

1 1

5) 5

7

A

x

5 2 __

3

B

x 5

2

C

x 5

6

D

x 5

36

12

Wha

t fun

ctio

n is

repr

esen

ted

in th

e ta

ble?

12

G

nf(n

)

13

27

311

415

519

n

F

f(

n) 5

n 1

3

H

f(n)

5 4

n 1

2

G

f(

n) 5

4n

2 1

J f(

n) 5

3n

2 2

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1

09

D

iagn

ostic

and

Pla

cem

ent T

ests

13

Mr.

Wils

on w

rote

the

func

tion

f(x)

5 7

x 2

15

on th

e

13

A

ch

alkb

oard

. Wha

t is

the

valu

e of

this

func

tion

for f

(6)?

A

27

B

37

C

42

D

57

14

On

aver

age,

a d

og ru

ns 5

.5 ti

mes

fast

er th

an a

chi

ld.

14

F

W

hich

func

tion

can

be

used

to fi

nd th

e sp

eed

of a

do

g, g

iven

the

spee

d of

the

child

?

F

f(

c) 5

5.5

c

H

f(

c) 5

c 1

5.5

G

f(

c) 5

5.5

___

c

J

f(c)

5

c __

_ 5.

5

15

Wha

t is

the

slop

e an

d y-

inte

rcep

t of t

he e

quat

ion

1

5

A

6x 2

1 5

3y

2 1

0?

A

m

5 2

, b 5

3

C

m

5 3

, b 5

4

B

m

5 2

, b 5

23

D

m

5 6

, b 5

9

16

Whi

ch b

est d

escr

ibes

the

grap

h of

the

func

tion

f(x)

5 4

x?

16

F

F

A

str

aigh

t lin

e th

roug

h th

e or

igin

wit

h a

stee

p sl

ope

upw

ard

to th

e ri

ght.

G

A

str

aigh

t lin

e th

roug

h th

e or

igin

wit

h a

stee

p sl

ope

dow

nwar

d to

the

righ

t.

H

A

str

aigh

t lin

e th

roug

h 4

on th

e x-

axis

wit

h a

slop

e do

wnw

ard

to th

e ri

ght.

J

A

str

aigh

t lin

e th

roug

h 4

on th

e y-

axis

wit

h a

slop

e up

war

d to

the

righ

t.

17

Whi

ch fu

nctio

n de

scri

bed

belo

w h

as th

e gr

eate

st ra

te o

f cha

nge?

1

7

C

I

f(

x) 5

4x

2 3

II

f(

x) 5

1 __

2 x

1 5

II

I x

f(x)

16

212

318

424

A

I

B

II

C

III

D

Th

ey a

ll ha

ve th

e sa

me

rate

of c

hang

e.

18

The

del

iver

y ra

mp

at th

e Co

rner

Caf

é is

a ri

ght t

rian

gle.

1

8

FTh

e hy

pote

nuse

is 4

met

ers

long

. One

leg

is 3

met

ers

long

. W

hat i

s th

e le

ngth

of t

he o

ther

leg?

F

√

__

7 m

eter

s

H

3.

5 m

eter

s

G

√

___

12 m

eter

s

J 5

met

ers

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Copyright ©

The M

cGraw

-Hill C

ompanies, Inc. Perm


use.



Answers (Grade 8)

Dia

gnos

tic a

nd P

lace

men

t Tes

ts

11

0

19

The

map

bel

ow s

how

s w

here

four

of N

ahim

ana’

s fr

iend

s liv

e.

19

D

Ea

ch u

nit o

n th

e m

ap re

pres

ents

1 m

ile.

y

xO

Josh

Carte

r

Aesh

aJe

nny

A

bout

how

far a

part

do

Aes

ha a

nd Jo

sh li

ve?

A

ab

out 5

mi

B

abou

t 6 m

i C

ab

out 7

.5 m

i D

ab

out 8

.5 m

i

20

Wha

t is

the

volu

me

of th

e cy

linde

r sho

wn

belo

w?

20

H

11 ft

2 ft

F

44

ft 3

H

138.

16 ft

3

G

69

.08

ft 3

J

276.

32 ft

3

21

Wha

t is

the

diff

eren

ce in

the

volu

me

of th

e tw

o tr

iang

ular

2

1

C

pris

ms

show

n be

low

?

15 c

m

8 cm

32 c

m

5 cm

7 cm

14 c

m

A

32

cm

3

C

1,

675

cm 3

B

15

8 cm

3

D

3,

350

cm 3

22

A p

hoto

wit

h a

leng

th o

f 3 in

ches

and

a w

idth

of 5

inch

es is

2

2

Jen

larg

ed to

pos

ter s

ize.

The

pos

ter a

nd th

e ph

oto

are

sim

ilar.

Th

e le

ngth

of t

he p

oste

r is

21 in

ches

. Wha

t is

the

wid

th o

f th

e po

ster

?

F

7

.2 in

ches

H

19

inch

es

G

12

.6 in

ches

J

35

inch

es

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11

D

iagn

ostic

and

Pla

cem

ent T

ests

23

Rec

tang

le A

BCD

is s

how

n on

the

coor

dina

te g

rid

belo

w.

23

C

Whi

ch o

f the

follo

win

g gr

aphs

repr

esen

t the

tran

slat

ion

of R

ecta

ngle

AB

CD o

ver t

he fo

llow

ing:

(x, y

) → (x

11,

y2

2)?

y

xO

12

34

7 6 5 4 3 2

-2

-7-

6-5-

4-3-

2

A DCB

A

y

xO

23

4

7 6 5 4 4 2 1

-2

-7-

6-5-

4-3-

2

A DCB

C

y

xO

12

34

7 6 5 4 3 2 1

-2

-7-

6-5-

4-3-

2

A DCB

B

y

xO

23

4

7 6 5 4 3 2 1

-2

-8-

7-6-

5-4-

3-2

A DCB

D

y

xO

12

34

7 6 5 4 3 2 1

-2

-7-

6-5-

4-3-

2

A DCB

24

A re

ctan

gle

is c

ut a

long

its

diag

onal

. The

mea

sure

of ∠

A is

55°

. 2

4

J

Wha

t is

the

mea

sure

of ∠

B?

A

B

F

12

5°

G

105°

H

45

° J

35°

25

A 2

6-fo

ot ro

pe is

use

d to

bra

ce a

tent

pol

e at

the

coun

ty fa

ir.

25

B

The

rope

is a

ncho

red

10 fe

et fr

om th

e bo

x of

the

pole

.

10

ft

Tent pole

26 ft

H

ow ta

ll is

the

tent

pol

e?

A

21

.8ft

B

24

ft

C

28ft

D

30

ft

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Cop

yrig

ht ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on

is g

rant

ed to

rep

rodu

ce f

or c

lass

room

use

.




Answers (Grade 8)

Dia

gnos

tic a

nd P

lace

men

t Tes

ts

11

2

26

A c

ylin

dric

al w

ater

tow

er is

24

feet

hig

h an

d ha

s a

diam

eter

2

6

Gof

20

feet

. App

roxi

mat

ely

how

man

y cu

bic

feet

of w

ater

cou

ld

the

tow

er h

old?

F

2,

400

cubi

c fe

et

H

9,

600

cubi

c fe

et

G

7,

500

cubi

c fe

et

J

30,2

00 c

ubic

feet

27

The

tria

ngle

s be

low

are

sim

ilar t

rian

gles

. Fin

d th

e va

lue

of

27

A

x

and

y.

3

cm

5

cm

4 c

m

10

cm

x

y

A

x

5 6

, y 5

8

C

x 5

1.5

, y 5

2

B

x

5 3

, y 5

4

D

x 5

12,

y 5

16

28

The

sca

tter

plo

t bel

ow s

how

s th

e ye

arly

adv

ertis

ing

28

G

expe

nditu

res

and

the

rela

tive

sal

es fo

r a s

mal

l co

mpa

ny. W

hat c

an b

e co

nclu

ded

from

this

dat

a?

Sales (in thousands of dollars)

250

225

200

175

150

125

100 75 50 25

Ad

vert

isin

g E

xpen

dit

ure

s (i

n d

olla

rs)

1500

500

1000

2000

F

A

s ad

vert

isin

g in

crea

ses,

sal

es te

nd to

dec

reas

e.

G

A

s ad

vert

isin

g in

crea

ses,

sal

es te

nd to

incr

ease

.

H

A

s ad

vert

isin

g in

crea

ses,

sal

es re

mai

n th

e sa

me.

J

A

s ad

vert

isin

g in

crea

ses,

sal

es a

lway

s in

crea

se.

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1

13

D

iagn

ostic

and

Pla

cem

ent T

ests

29

The

box

plo

t sho

ws

a se

t of t

est s

core

s.

2

9

BW

hich

sta

tem

ent i

s co

rrec

t?

010

2030

4050

6070

8090

100

A

M

ore

stud

ents

sco

red

betw

een

40 a

nd 6

0 po

ints

than

bet

wee

n 88

and

96

poin

ts.

B

A

n eq

ual n

umbe

r of s

tude

nts

scor

ed fr

om 4

0 to

60

as fr

om 8

8 to

96.

C

Th

e lo

wes

t sco

re w

as 6

0.

D

Th

e hi

ghes

t sco

re w

as 8

8.

30

A s

urve

y is

take

n to

det

erm

ine

whi

ch ty

pe o

f veh

icle

is

30

G

mos

t pop

ular

. The

dat

a is

sho

wn

in th

e ba

r gra

ph b

elow

.

051015202530

SUV

Min

ivan

Spor

tsM

id-S

ize

Men

Wom

en

Typ

e o

f V

ehic

le

Number of People

W

hat c

an y

ou c

oncl

ude

abou

t the

sur

vey?

F

Th

e su

rvey

is b

iase

d be

caus

e m

ost m

en d

o no

t fav

or s

port

s ve

hicl

es.

G

Th

e su

rvey

is b

iase

d be

caus

e th

ere

are

mor

e m

en s

urve

yed

than

wom

en.

H

Th

e su

rvey

is n

ot b

iase

d be

caus

e sp

orts

car

s ar

e m

ost p

opul

ar a

mon

g bo

th m

en

and

wom

en.

J

Th

e su

rvey

is n

ot b

iase

d be

caus

e al

l car

type

s ar

e fa

vore

d by

bot

h m

en a

nd

wom

en.

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