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ISTEP+ Preparation and Practice

Grade 8 Mathematics Teacher's Guide

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Table of Contents

Test Preparation and Practice for the ISTEP+

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Correlations of Indiana's Standards for Assessment to Practice Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Test 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Scoring Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Class Recording Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

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Grade 8

Test Preparation and Practice for the ISTEP+

iii

Correlation Chart

Indiana's Academic Standards for Mathematics

8.2.5 Find the slope of a linear function given the equation and write the equation of a line given the slope and any point on the line. 8.2.6 Translate among tables, equations, verbal expressions and graphs of linear functions and recognize that in (y = mx + b) that m is the rate of change and b is the vertical intercept of the graph. 8.2.7 Identify functions as linear or nonlinear and contrast their characteristics from tables, graphs and equations. 8.2.8. Use linear functions and linear equations to represent, analyze and solve problems.

Test(s)/Item Number(s)

Test 3: Items 8, 16; Test 4: Items 4, 11; Test 5: Item 10; Test 6: Item 16 Test 3: Item 7, 10; Test 4: Item 3, 14; Test 5: Item 14; Test 6: Item 7 Test 6: Item 5

Test 3: Item 20

Standard 3: Geometry and Measurement

8.3.1 Perform basic compass and straight edge constructions: angle and segment bisectors, copies of segments and angles, and perpendicular segments. Describe and justify the constructions. 8.3.2 Identify, define, and describe properties of three-dimensional geometric objects, describe how two or more figures intersect in a plane or in space, and visualize or describe the cross section of a solid.

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Test 1: Item 10

Test 2: Item 4; Test 3: Item 6; Test 4: Item 13; Test 5: Item 5; Test 6: Item 6 Test 1: Items 2, 11, 20; Test 2: Item 11; Test 3: Item 12; Test 4: Item 8; Test 5: Item 13; Test 6: Item 18 continued

8.3.3 Explain why the Pythagorean Theorem is valid using a variety of methods and use the Pythagorean Theorem and its converse to calculate lengths of the line segments.

Grade 8

Test Preparation and Practice for the ISTEP+

ix

Overview

Test Preparation and Practice for the ISTEP+

In the spring, your students will be taking the Indiana Statewide Testing for Educational Progress-Plus (ISTEP+). The test items provided in this booklet for test preparation and practice will cover the state-assessed content standards, which are organized into the following subdomains: number sense and computation, algebra and functions, geometry and measurement, and data analysis and probability. The purposes of the six tests in this booklet are to: · familiarize students with the ISTEP+ question and test page formats; · allow students to practice math skills that are taught in the classroom; and · allow students to practice math skills that will be covered on the ISTEP+. Each test item is correlated to an Indiana content standard. Test Question Format The tests in this booklet contain multiple-choice, gridded-response, and open-ended items that mirror the format of the ISTEP+. Each test has twenty items. For each multiple-choice item, students choose the best answer from the four possible answers given and circle the letter in front of the correct answer choice. For each gridded-response item, students will fill in the answer to the problem on a response grid. Gridded-response answers may be whole numbers, decimals, or fractions. When recording their answers, students should not insert spaces between the digits or symbols but should include a decimal point or a fraction bar if it is part of the answer. For each open-ended item, students will need to show their work and/or explain their answer to each item completely and accurately, demonstrating an understanding of the content. Students will write their answers to the open-ended items in the space provided. The answers should be written so that they can be easily read and understood by another person. Students may use drawings, words, and/or numbers in answering the open-ended items. Students must write the answer within the space provided on the page; any answer written outside the boxed area will not be scored. Materials Students may use a ruler or protractor on some problems while taking the tests provided in this booklet. An icon will appear at the top of a test item to let the student know when a manipulative can be used to solve the problem.

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Grade 8

Test Preparation and Practice for the ISTEP+

v

Overview

Scoring Answers are provided on the Scoring Guide. Students will receive 1 point for each correctly answered multiple-choice item. Each open-ended item will carry a point value of 2 or 3. A problem with a value of 3 points will have two components. Use the following rubrics and scoring guides to score student responses. 2-Point Rubric 2 Points 1 Point 0 Points Exemplary response Correct process; error in computation Other 3 Points 2 Points 1 Point 0 Points 3-Point Rubric Exemplary response Two correct components One correct component Other

Test-Taking Hints Before administering each test, you may find it helpful to review these basic test-taking strategies with your students. 1. Read each question carefully. Think about how you could solve the problem. 2. On the multiple-choice questions, answer the easy questions first. If the question seems too hard, skip it and go back to it later. Eliminate any answers you know are wrong. If you're still stuck, make an educated guess. 3. Write neatly and proofread your open-ended answers. Be sure that you have shown all of your work and have explained how you got your answer within the space provided. 4. When you are finished, if you have time left, look over your test and make sure that you have answered all the questions. 5. Be sure that each answer choice is circled clearly and completely, and that there are no stray marks. 6. Relax. Give each test your best effort. If you start to feel nervous, take a few deep breaths.

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vi Test Preparation and Practice for the ISTEP+

Grade 8

Correlation Chart

Correlations of Indiana's Academic Standards for Mathematics to Practice Tests

Indiana's Academic Standards for Mathematics

Test(s)/Item Number(s)

Standard 1: Number Sense and Computation

8.1.1 Interpret calculator or computer displays of numbers given in scientific notation and read, write, compare and solve problems using decimals in scientific notation. 8.1.2 Recognize positive integer powers as repeated multiplication and negative integer powers as repeated division or multiplication by the multiplicative inverse. Test 2: Items 1, 15; Test 3: Item 3; Test 4: Item 9; Test 5: Item 11 Test 1: Items 6, 13; Test 2; Item 10; Test 3: Item 2; Test 4: Item 12 Test 1: Item 1; Test 2: Item 3; Test 3: Item 1; Test 4: Item 1; Test 6: Item 12 Test 1: Items 14, 19; Test 2: Item 18; Test 3: Item 17; Test 4: Item 17; Test 6: Item 8 Test 1: Item 3; Test 2: Item 16; Test 4: Items 2, 16; Test 5: Items 1, 2; Test 6: Item 1 continued

8.1.3 Use the laws of exponents for integer exponents and evaluate expressions with negative integer exponents.

8.1.4 Identify, compare and order irrational numbers.

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8.1.5 Calculate square roots of perfect squares, estimate square roots of numbers less than 1,000, and use the inverse relationship between squares and square roots.

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Test Preparation and Practice for the ISTEP+

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Correlation Chart

Indiana's Academic Standards for Mathematics

8.1.6 Solve percent, ratio and proportion problems. · Find average rates. · Express one quantity as a percentage of another. · Compare two quantities by percentage. · Use percentages greater than 100%. · Increase or decrease a quantity by a given percentage. · Find the original amount of a given percentage increase or decrease. · Solve problems involving percents, ratios and proportions. · Solve problems involving simple and compound interest.

Test(s)/Item Number(s)

Test 5: Item 7; Test 6: Item 16

Standard 2: Algebra and Functions

8.2.1 Write and solve linear equations and inequalities, interpret the solution or solutions in their context, and verify the reasonableness of the results. Test 1: Items 9, 16; Test 2: Item 9; Test 3: Items 4, 20; Test 4: Item 7; Test 5: Item 15; Test 6: Items 11, 19 Test 1: Item 4; Test 3: Item 20; Test 5: Item 1 Test 1: Items 12, 15; Test 2: Item 2; Test 3: Items 5, 11; Test 4: Item 10; Test 5: Item 3; Test 6: Item 10 Test 3: Item 14; Test 5: Item 20; Test 6: Item 7

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8.2.2 Solve equations and formulas for a specified variable.

8.2.3 Simplify algebraic expressions involving powers.

8.2.4 Identify and graph linear functions and identify lines with positive and negative slope.

viii Test Preparation and Practice for the ISTEP+

Grade 8

Correlation Chart

Indiana's Academic Standards for Mathematics

8.3.4 Solve simple problems involving rates and other derived measurements, including problems involving speed, uniform speed, average speed and density, by applying the concept of proportionality to measurement in different contexts. Express measurements in a given unit or in terms of other units of the same types. 8.3.5 Use scale factors to find the area and volume of similar figures. 8.3.6 Find and use the surface area and volume of cones, spheres and pyramids. 8.3.7 Estimate and compute the area of irregular two-dimensional shapes and the volume of irregular three-dimensional objects by breaking them down into more basic geometric objects. 8.3.8 Solve problems involving conversions within the same measurement system and estimate the measure of an object in one system given the measure of that object in another system and the approximate conversion factor.

Test(s)/Item Number(s)

Test 1: Items 5, 17; Test 2: Item 12; Test 3: Item 18; Test 4: Item 5; Test 6: Item 2 Test 2: Item 5; Test 5: Item 6 Test 5: Items 8, 9, 18; Test 6: Items 13, 17 Test 1: Item 7; Test 2: Item 19; Test 3: Item 19; Test 4: Item 18; Test 6: Item 3

Test 2: Item 6

Standard 4: Data Analysis and Probability

8.4.1 Identify claims based on statistical data and, in simple cases, evaluate the Test 6: Item 14 reasonableness of the claims. Design a study to investigate the claim. 8.4.2 Identify different methods of selecting samples, analyzing the strengths and weaknesses of each method and the possible bias in a sample or display. Test 3: Item 15; Test 5: Item 17

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x Test Preparation and Practice for the ISTEP+

Grade 8

Correlation Chart

Indiana's Academic Standards for Mathematics

8.4.3 Use mean, median, mode, upper and lower quartiles and range to compare data sets. Organize and display data to highlight important features such as the range and how the data is spread around a central value. Investigate what happens to the display when some of the data values are changed. 8.4.4 Analyze, interpret and display data in box-and-whisker plots. 8.4.5 Display two-variable data in scatter plots and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data and write the equation of that line. 8.4.6 Describe and apply the addition rule for probabilities for simple events that are mutually exclusive and for simple events that are not. 8.4.7 Compute probabilities of events from simple experiments with equally probable outcomes, using such methods as organized list, tree diagrams and area models.

Test(s)/Item Number(s)

Test 1: Item 18; Test 2: Items 13, 20; Test 3: Item 9; Test 5: Item 16

Test 6: Item 9

Test 4: Item 20; Test 6: Item 20

Test 2: Item 8; Test 4: Item 19 Test 2: Items 14, 17; Test 3: Item 13; Test 4: Item 6; Test 5: Item 19

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Grade 8

Test Preparation and Practice for the ISTEP+

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Test 1

Grade 8 Mathematics

1

Which of the following is equivalent to the expression below? 16xyzxyzxyz A 16xyz B 16x2y2z2 C 16x3y3z3 D 16x4y4z4

2

Look at the triangle below.

/ / /

15

c

0 1 2 3

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

20 Using the Pythagorean theorem, what is the length of c? Mark your answer in the answer grid.

4 5 6 7 8 9

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Grade 8 · Test 1

1

Test Preparation and Practice for the ISTEP+

Test 1

Grade 8 Mathematics

3

Which of these numbers is between 4 and 5 on the number line? A 12 B 16 C 17 D 27

___ ___ ___ ___

4

Given that y = kx with k = 2.5, which equation can be used to find x when y = 4? A x = 2.5(4) B 4 = ___ y

2.5

C y = ___ 4

2.5

D 4 = 2.5x

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Test Preparation and Practice for the ISTEP+

2

Grade 8 · Test 1

Test 1

Grade 8 Mathematics

5

A plane flew 2400 miles in 6 hours. What was the plane's average speed in miles per hour? A 40 miles per hour B 300 miles per hour C 400 miles per hour D 404 miles per hour

6

Which equation shows 83 simplified? A 8·1=8 B 8 · 3 = 24 C 8 + 8 + 8 = 24 D 8 · 8 · 8 = 512

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Grade 8 · Test 1

3

Test Preparation and Practice for the ISTEP+

Test 1

Grade 8 Mathematics

7

Mario made the drawing of his room shown below. 18 ft 3 ft 10 ft 12 ft What is the area, in square feet, of Mario's room? Show All Work

Answer _______________ square feet

8

Carrie measured the height, in inches, of 12 of her classmates. Her results are shown below. 57 58 59 60 56 62 68 64 65 58 64 61

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What is the MEAN height, in inches, of these students? A 58 B 60 C 61 D 64

Test Preparation and Practice for the ISTEP+

4

Grade 8 · Test 1

Test 1

Grade 8 Mathematics

9

Brittany has a job walking 3 dogs for a family in her apartment building. She charges a certain price per dog plus a total of $9 for treats and leashes for each walk. Brittany is paid $24 per walk. The equation below can be used to find how much she charges per dog. 3x + 9 = 24 How much does Brittany charge per dog? A $2 B $3 C $4 D $5

10

Use your protractor to solve this problem. What is the measure of ABC? A

B A 45°

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C

B 48° C 50° D 51°

Grade 8 · Test 1

5

Test Preparation and Practice for the ISTEP+

Test 1

Grade 8 Mathematics

11

Which of the following is NOT a Pythagorean triple? A 2, 3, 4 B 3, 4, 5 C 5, 12, 13 D 8, 15, 17

12

Simplify the expression below.

4 81

/ / /

Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

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Test Preparation and Practice for the ISTEP+

6

Grade 8 · Test 1

Test 1

Grade 8 Mathematics

13

Which shows the prime factorization of 48 using exponents? A 23 · 3 B 22 · 32 C 24 · 3 D 23 · 32

14

Look at the numbers below. 1, 2, 3 , 4, 5 , 6, 7 , 9

__ __ __ __

Arrange the numbers in order from LEAST to GREATEST. Show All Work

Answer __________________________________________

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Grade 8 · Test 1

7

Test Preparation and Practice for the ISTEP+

Test 1

Grade 8 Mathematics

15

Look at the square below.

14x in.

14x in. What is the AREA, in square inches, of the square? Show All Work

Answer ____________________ square inches

16

Chen's parents pay him $3 per hour to weed their garden. For every job, Chen gives his brother $4 to carry all the weeds away in a wheelbarrow. For one job, Chen made $8. The equation below can be used to find how many hours Chen spent weeding the garden. 3a ­ 4 = 8 How many hours did Chen spend weeding the garden? A 2 hours B 3 hours C 4 hours D 5 hours

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Test Preparation and Practice for the ISTEP+

8

Grade 8 · Test 1

Test 1

Grade 8 Mathematics

17

Keisha is driving at an average speed of 65 miles per hour. How far will Keisha drive in 5 hours? A 13 miles B 70 miles C 300 miles D 325 miles

18

Prices for the same DVD sold at different stores are shown below. $14.99 $9.99 $8.75 $18.99 $11.50 $10.00

What is the MEAN price of the DVD? Show All Work

Answer $________________ What is the MEDIAN price of the DVD?

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Show All Work

Answer $________________

Grade 8 · Test 1

9

Test Preparation and Practice for the ISTEP+

Test 1

Grade 8 Mathematics

Estimate 8 . Then graph 8 on the number line below.

__ __

19

0

1

2

3

20

Look at the triangle below. Follow these directions. · Draw squares on all three sides of the triangle. · Find the length of the hypotenuse. · Find the area of each square.

8 in.

15 in.

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Test Preparation and Practice for the ISTEP+

10

Grade 8 · Test 1

Test 2

Grade 8 Mathematics

1

A scientist measured the distance between earth and a star to be 950,000,000 miles. Which shows this number in scientific notation? A 950 × 106 B 9.5 × 107 C 9.5 × 108 D 95 × 108

2

Simplify the expression below. (34)2

0 / / /

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

Mark your answer in the answer grid.

1 2 3 4 5 6 7 8 9

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Grade 8 · Test 2

11

Test Preparation and Practice for the ISTEP+

Test 2

Grade 8 Mathematics

3

Which shows the simplified form of the expression below? 24 · 23 A 48 B 64 C 128 D 256

4

Look at the cube below.

How many vertices and edges does the cube have? A 4 vertices and 6 edges B 5 vertices and 8 edges C 6 vertices and 9 edges

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D 8 vertices and 12 edges

Test Preparation and Practice for the ISTEP+

12

Grade 8 · Test 2

Test 2

Grade 8 Mathematics

5

Look at the rectangles below. B' B 2 cm A D A' D' 5 cm C C'

Rectangle ABCD has been dilated to rectangle A'B'C'D' by a scale factor of 3. What is the area of rectangle A'B'C'D'? A 20 square centimeters B 30 square centimeters C 60 square centimeters D 90 square centimeters

6

The number of degrees Celsius is about half of 30 less than the equivalent number of degrees Fahrenheit. A comfortable indoor temperature is 72°F. About what temperature is this in degrees Celsius? A about 6°C

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B about 22°C C about 84°C D about 114°C

Grade 8 · Test 2

13

Test Preparation and Practice for the ISTEP+

Test 2

Grade 8 Mathematics

7

On the lines below, describe a central angle of a circle.

In the space below, draw a diagram of a central angle.

8

The spinner shown below is spun once.

8 7 6 5

1 2 3 4

What is the probability that the spinner will stop in sectors 1 or 3?

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1 A __ 8 1 B __ 4 1 C __ 2 3 D __ 4

Test Preparation and Practice for the ISTEP+

14

Grade 8 · Test 2

Test 2

Grade 8 Mathematics

9

Kendra has $8 in her savings account. Every week, she puts another $4 in the account. The equation below shows that she has $20 after n weeks. 4n + 8 = 20 After how many weeks does Kendra have $20? A 2 weeks B 3 weeks C 4 weeks D 7 weeks

10

Which of the following is the simplified form of the expression below? (y · y · y · y)(y · y · y) A 4y + 3y = 12y B 4y · 3y = 12y2 C y4 + y3 = y7 D y4 · y3 = y7

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Grade 8 · Test 2

15

Test Preparation and Practice for the ISTEP+

Test 2

Grade 8 Mathematics

11

Look at the triangle below. c 12 mm Using the Pythagorean Theorem, what is the length of c? A c = 17 mm B c = 34 mm C c = 11 mm D c = 13 mm

___ ___

5 mm

12

Nicholas is driving at an average speed of 55 miles per hour. How many miles will Nicholas drive in 5 hours? Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9

/

/

/

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7

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8 9

Test Preparation and Practice for the ISTEP+

16

Grade 8 · Test 2

Test 2

Grade 8 Mathematics

13

The heights of six basketball players are shown below. 6 feet 2 inches 6 feet 3 inches 6 feet 1 inch 6 feet 6 inches 6 feet 5 inches 6 feet 6 inches

What is the MEDIAN height of the six players? A 6 feet 2 inches B 6 feet 3 inches C 6 feet 4 inches D 6 feet 6 inches

14

Julio flips a coin three times. Use a tree diagram to find the sample space. Show All Work

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What is the probability of getting HEADS on all three tosses? Answer __________________________________________

Grade 8 · Test 2

17

Test Preparation and Practice for the ISTEP+

Test 2

Grade 8 Mathematics

15

Jupiter's distance from the sun is four hundred eighty-three million miles. Write this distance in standard form and in scientific notation. standard form ________________________________ scientific notation ________________________________

16

Which of the following numbers is between 3 and 4 on the number line? A 4 B 9

__ __ ___ ___

C 12 D 16

17

Carmen and Jack are playing a game with a number cube. Jack rolls the number cube. What is the probability of Jack rolling an odd number?

1 A __ 5 1 B __ 4 1 C __ 2 5 D __ 6

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Test Preparation and Practice for the ISTEP+

18

Grade 8 · Test 2

Test 2

Grade 8 Mathematics

18

Look at the numbers below.

1 1 __, 0.__, __, 0.7, 0.0__, 7 7 7 3

Arrange the numbers in order from LEAST to GREATEST. Show All Work

Answer________________________________________________

19

Look at the figure below.

15 ft

17 ft

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6 ft What is the area, in square feet, of the figure? Show All Work

Answer___________________________ square feet

Grade 8 · Test 2

19

Test Preparation and Practice for the ISTEP+

Test 2

Grade 8 Mathematics

20

The amounts for Diane's monthly telephone bills for last year are shown below. $35.47 $30.31 $39.26 $44.45 $42.01 $36.07 $47.54 $49.64 $37.41 $42.01 $29.86 $33.36

To the nearest cent, what is the MEAN cost of the monthly telephone bills? Show All Work

Answer $________________________________ To the nearest cent, what is the MEDIAN cost of the monthly telephone bills? Show All Work

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Answer $________________________________ What is the MODE for this set of data? Answer $________________________________

Test Preparation and Practice for the ISTEP+

20

Grade 8 · Test 2

Test 3

Grade 8 Mathematics

1

Which of the following shows the simplified form of the expression below? 3x­2y­1xyz A 3x­3yz

3yz B ___ x2 3z C ___ x2y 3z D __ x

2

What is the simplified form of the expression below? 2­5 Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9 / / /

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

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Grade 8 · Test 3

21

Test Preparation and Practice for the ISTEP+

Test 3

Grade 8 Mathematics

3

What is 0.000294 in scientific notation? A 29.4 × 10­5 B 2.94 × 10­4 C 0.294 × 10­3 D 2.94 × 104

4

A container has a small leak. It started with 32 milliliters of liquid and loses 4 milliliters of liquid every hour. The equation below can be used to find how many hours it will take for the container to have 26 milliliters of liquid remaining. ­4x + 32 = 26 After how many hours does the container have 26 milliliters of water remaining? A x = ­14.5 B x = ­1.5 C x = 1.5 D x = 14.5

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Test Preparation and Practice for the ISTEP+

22

Grade 8 · Test 3

Test 3

Grade 8 Mathematics

5

Which of the following is the simplified form of the expression below? 10­5 × 103 A 10­8 B 10­2 C 102 D 108

6

Look at the pyramid below.

A triangular pyramid has how many vertices and edges? A 8 vertices and 12 edges B 6 vertices and 9 edges C 5 vertices and 8 edges D 4 vertices and 6 edges

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Grade 8 · Test 3

23

Test Preparation and Practice for the ISTEP+

Test 3

Grade 8 Mathematics

7

Look at the coordinate plane below. 4 2 0

-4 -2 -2 -4

y

b

a

x 2 4

Write the equation of each line in slope-intercept form. line a ____________________________________________ line b ____________________________________________ At what point do lines a and b intersect? Answer __________________________

8

What is the slope of the line y = ­ __x + 3? 3

2

A ­3

2 B ­ __ 3 2 C __ 3

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D 3

Test Preparation and Practice for the ISTEP+

24

Grade 8 · Test 3

Test 3

Grade 8 Mathematics

9

A dog trainer was interested in the ages of the dogs that she trains. One day she collected the data, in months, of the ages of the dogs. 12 27 24 60 16 65 20 18 25 15

Which measure best represents the typical age of the dogs? A mean B median C mode D range

10

Kevin is playing a game with his brother. In the game, x is the number a player rolls on the number cube, and y is the number of points the player gets for each roll. The table of values below shows the points for each roll. x 1 2 3 4 5 6 y 0 1 2 3 4 5

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What rule determines how many points a player gets? A y=x­2 B y=x­1 C y=x+1 D y=x+2

Grade 8 · Test 3

25

Test Preparation and Practice for the ISTEP+

Test 3

Grade 8 Mathematics

11

Which of the following is NOT equal to 10­5? A ­100,000

1 B ___ 105 1 C ______ 100,000

D 0.00001

12

Shanice made a triangular sail for her sailboat. 25 in. s 24 in. What is the length, in inches, of s? Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9 / / /

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

26

Grade 8 · Test 3

Test 3

Grade 8 Mathematics

13

Two number cubes labeled 1 through 6 are rolled. What is the probability of rolling doubles (the same number on each cube)?

1 A __ 6 1 B __ 3 17 C __ 36 1 D __ 2

14

4 3 2 inc h 1

5

Use your ruler as a straightedge. On the coordinate plane below, graph the line that passes through (0, ­2) and (2, 4). 4 2 0

-4 -2 -2 -4

y

x 2 4

Does your line have a positive slope or a negative slope? Answer _______________________ slope

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 3

27

Test Preparation and Practice for the ISTEP+

Test 3

Grade 8 Mathematics

15

Julia wants to know how much time students in her school spend doing homework each day. She asks 10 of her friends how much time they spend on their homework each day. On the lines below, give three examples of how bias may occur in Julia's sample.

16

What is the slope of the line y = 3? A undefined B 0 C 1 D 3

17

Which list is NOT in order from LEAST to GREATEST?

__

© Houghton Mifflin Harcourt All rights reserved.

A 0.5, 0.55, 0. 5

__ 5 1 B __, 0. 4, __ 3 8 __ 2 C __, 0.6, 0. 7 3 __ __ 4 D __, 0. 8, 1. 8 5

Test Preparation and Practice for the ISTEP+

28

Grade 8 · Test 3

Test 3

Grade 8 Mathematics

18

Antonio can run 4 miles in 24 minutes. At that rate, how long will it take him to run 8 miles? Solve the problem by writing and solving a proportion. Show All Work

Answer________________________________________________

19

The figure below is the model of a building that has two towers connected by a walkway.

2 cm 12 cm 3 cm 8 cm 2 cm 5 cm

© Houghton Mifflin Harcourt All rights reserved.

12 cm

2 cm 5 cm

The front of the model will be painted a different color than the rest of the model. How many square centimeters will the paint for the front of the building need to cover? Show All Work

Answer___________________________ square centimeters

Grade 8 · Test 3

29

Test Preparation and Practice for the ISTEP+

Test 3

Grade 8 Mathematics

20

Corey is planning a party. The cost to rent a party room is $400. A meal for each person is $12. Write an equation to represent the situation. Equation___________________________ What is the total cost of the party if Corey invites 45 friends? (Hint: Remember to include Corey.) Show All Work

Answer $___________________________ About how much will Corey be spending per person? (Hint: Remember to include Corey.) Show All Work

© Houghton Mifflin Harcourt All rights reserved.

Answer $___________________________

Test Preparation and Practice for the ISTEP+

30

Grade 8 · Test 3

Test 4

Grade 8 Mathematics

1

Which of the following shows the simplified form of the expression below?

2 (__) 3 4 A __ 9 3 B __ 2 9 C __ 4

2

D 3

2

What is the simplified form of 9 · 36 ? Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9

__

___

/

/

/

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 4

31

Test Preparation and Practice for the ISTEP+

Test 4

Grade 8 Mathematics

3

Eric earns $9 an hour. He created a table below to show his pay for 1, 2, 3, and 4 hours of work. h 1 2 3 4 p 9 18 27 36

What equation should Eric write to show the relationship in his table? A h = 9p B p = 9h C p = __ h

9 p

D h = __ 9

4

Which of the following is the equation of a line that has slope __ and passes through 3 point (0, ­4)?

2

A y = __x + 4 2

3 2 3 2

B y = __x + 4 3 C y = __x ­ 4 2 D y = __x ­ 4 3

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

32

Grade 8 · Test 4

Test 4

Grade 8 Mathematics

5

Cooper rode his bike 1 mile in 5 minutes. What is Cooper's average rate in MILES PER HOUR?

1 A __ mph 5

B 5 mph C 12 mph D 20 mph

6

Diego tosses a coin and spins a spinner with sections 1, 2, 3, and 4. What is the probability that he will toss tails and spin an even number?

1 A __ 8 1 B __ 4 1 C __ 2

D 1

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 4

33

Test Preparation and Practice for the ISTEP+

Test 4

Grade 8 Mathematics

7

LaToya is thinking of a number. If she triples the number and adds 8, the result is greater than 14. On the line below, write an inequality to describe the possible choices for LaToya's number. Inequality __________________________ Solve the inequality. Then graph the solution on the number line below. Show All Work

-2

-1

0

1

2

3

4

8

Bridget lives directly 16 blocks east of the school. Jason lives directly 16 blocks south of the school. School 16 blocks

© Houghton Mifflin Harcourt All rights reserved.

16 blocks

How far apart do Bridget and Jason live from each other? A 2

__ __ __ __

B 4 2

C 16 2

D 256 2

Test Preparation and Practice for the ISTEP+

34

Grade 8 · Test 4

Test 4

Grade 8 Mathematics

9

Simplify: (1.5 × 10­6) (3 × 10­8) A 4.5 × 10­14 B 4.5 × 10­2 C 4.5 × 1014 D 4.5 × 1048

10

Simplify: _______ 4yz

2xy z A _____ yz xz 2y3 C ___ x2z3 2y4 D ____ x2yz4 2y B ___ 2 4

3 3 3

8x 2y4z

3

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 4

35

Test Preparation and Practice for the ISTEP+

Test 4

Grade 8 Mathematics

11

What is the slope of the line in the equation below? y = ­3x ­ 2 A ­5 B ­3 C ­2 D ­1

12

1 -3 What is the simplified form of __ ? 4 Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9

()

/

/

/

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

36

Grade 8 · Test 4

Test 4

Grade 8 Mathematics

13

Look at the pyramid below.

How many faces does a square pyramid have? A 3 B 4 C 5 D 6

14

Look at the coordinate plane below. b 4 2 0

-4 -2 -2

y

a

x 2 4

© Houghton Mifflin Harcourt All rights reserved.

-4

Write the equation of each line in slope-intercept form. line a ____________________________________________ line b ____________________________________________ At what point do lines a and b intersect? Answer __________________________

Grade 8 · Test 4

37

Test Preparation and Practice for the ISTEP+

Test 4

Grade 8 Mathematics

15

Look at the circle below. B

A

O

C

Identify each part of the circle. Segment AC ___________________________ Angle BOC ___________________________ Segments AO, BO, CO ___________________________

16

Which of these numbers is between 10 and 11 on the number line? A 100 B 115 C 121 D 144

____ ____ ____ ____

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

38

Grade 8 · Test 4

Test 4

Grade 8 Mathematics

17

Use your protractor to solve this problem. Look at the angle below. A

B What is the measure of ABC? A 125° B 130° C 132° D 135°

C

18

Eva's backyard has an irregular shape. A diagram of her backyard is shown below. 45 ft

12 ft 22 ft 12 ft

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12 ft What is the area, in square feet, of Eva's backyard? Show All Work

Answer________________________ square feet

Grade 8 · Test 4

39

Test Preparation and Practice for the ISTEP+

Test 4

Grade 8 Mathematics

19

Scott flips a coin three times. On the lines below, explain which is more likely, that Scott will toss tails at least once or that he will not toss tails at least once.

20

The table below shows the relationship between test scores and hours of study. Test Score 40 50 60 65 70 80 75 80 90 Hours of Study 1.0 1.5 2.0 2.5 3.0 3.0 4.5 5.0 5.0

Plot the data on the grid below. Then draw a line of best fit. Find the equation of the line.

© Houghton Mifflin Harcourt All rights reserved.

100 90 80 70 60 50 40 30 20 10 1 2 3 4 5 Number of Hours

Equation________________________________

Test Preparation and Practice for the ISTEP+

Score

40

Grade 8 · Test 4

Test 5

Grade 8 Mathematics

1

Which of the following is the solution of the equation below? 3x2 = 48 A x = ±2 B x = ±4 C x = ±8 D x = ±12

2

Maggie drew the diagram below of her rectangular garden.

/ / /

0

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

8 3

1 2 3 4 5

3 16

6 7

What is the AREA, in square feet, of Maggie's garden? Mark your answer in the answer grid.

8 9

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 5

41

Test Preparation and Practice for the ISTEP+

Test 5

Grade 8 Mathematics

3

The two rectangles below are similar.

x 4 cm x 16 cm

Find x. A x = ±64 cm B x = ±8 cm C x = 4 cm D x = 8 cm

4

Monica divided a circle into sixths to make a spinner.

© Houghton Mifflin Harcourt All rights reserved.

What is the measure of each central angle? A 30° B 60° C 90° D 360°

Test Preparation and Practice for the ISTEP+

42

Grade 8 · Test 5

Test 5

Grade 8 Mathematics

5

A vertical cross-section of a cone at the apex is what type of figure?

h

A a circle B a right triangle C an isosceles triangle D a scalene triangle

6

Marco wants to enlarge the photograph below by a scale factor of 4. 7 inches

5 inches

© Houghton Mifflin Harcourt All rights reserved.

What is the AREA of the enlarged photo? A 140 square inches B 280 square inches C 384 square inches D 560 square inches

Grade 8 · Test 5

43

Test Preparation and Practice for the ISTEP+

Test 5

Grade 8 Mathematics

7

Tien has $1,000 in an account at Bank A and $1,000 in an account at Bank B. Bank A pays 4% simple interest. Bank B pays 4% interest compounded annually. How much money does Tien have in each account after 3 years? Show All Work

Bank A $ Bank B $

8

Look at the diagram of the cone shown below. 8 cm

12 cm

© Houghton Mifflin Harcourt All rights reserved.

What is the total surface area of the cone? Use 3.14 for . A 50.24 cm2 B 96.00 cm2 C 150.72 cm2 D 200.96 cm2

Test Preparation and Practice for the ISTEP+

44

Grade 8 · Test 5

Test 5

Grade 8 Mathematics

9

Look at the pyramid below, with its square base of 8 inches and height of 15 inches.

15 inches

8 inches What is the volume, in cubic inches, of the pyramid? A 40 cubic inches B 80 cubic inches C 320 cubic inches D 960 cubic inches

10

Which of the following is the equation of a line that has slope ­3/4 and passes through point (8, 5)?

3 A y = ­__x + 5 4 3 B y = ­__x + 8 4

© Houghton Mifflin Harcourt All rights reserved.

3 C y = ­__x + 11 4 3 D y = ­__x + 13 4

Grade 8 · Test 5

45

Test Preparation and Practice for the ISTEP+

Test 5

Grade 8 Mathematics

11

Which of the following is the simplified form of the expression below?

7 × 10­8 ______ 8 × 10­4

A 8.75 × 10­13 B 8.75 × 10­12 C 8.75 × 10­5 D 8.75 × 10­4

12

What is the simplified form of the expression below? 3 25 · 144 Mark your answer in the answer grid.

___ ____

0 1 2 3 4 5 6 7 8 9 / / /

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

46

Grade 8 · Test 5

Test 5

Grade 8 Mathematics

13

Look at the cone below. 18 cm

12 cm

What is the slant height of the cone? A 12 centimeters B 15 centimeters C 22 centimeters D 30 centimeters

14

Use the x- and y-intercepts to graph the system below. x+y=4 x + 2y = 3

{

y 4 2 0

© Houghton Mifflin Harcourt All rights reserved. -4 -2 -2 -4

x 2 4

What is the solution of the system? Answer

Grade 8 · Test 5

47

Test Preparation and Practice for the ISTEP+

Test 5

Grade 8 Mathematics

15

Solve and graph: ­6(x ­ 4) > 3(x ­ 7) Show All Work

0

1

2

3

4

5

6

16

Keiko recorded the number of problems she missed on her last 6 tests. 4, 3, 4, 4, 6, 3 Which measure of central tendency would change if on Keiko's seventh test she missed 5 problems? A mean B median C mode D range

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

48

Grade 8 · Test 5

Test 5

Grade 8 Mathematics

17

Carrie wants to know the percentage of students at her middle school who prefer organic food. She decides to ask the students in her health class. What type of sampling method did Carrie use? A random sampling B convenience sampling C systematic sampling D stratified sampling

18

For New Year's Eve, Andrea is serving punch in cone-shaped glasses. One of the glasses is shown in the diagram below. 6 cm

14 cm

What is the volume, in cubic centimeters, of the glass? Show All Work

© Houghton Mifflin Harcourt All rights reserved.

Answer

cubic centimeters

Grade 8 · Test 5

49

Test Preparation and Practice for the ISTEP+

Test 5

Grade 8 Mathematics

19

A coin is tossed and a number cube labeled 1 through 6 is rolled. What is the sample space? Answer __________________________________________ What is the probability of tossing tails and an even number? Show All Work

Answer _______________

20

2 h inc 1

5 4 3

Use your ruler as a straightedge.

Find the x- and y-intercepts for 2x ­ 3y = 15. Show All Work

Answer _______________

On the coordinate grid below, graph the equation. y 8 4 0

-8 -4 -4 -8 © Houghton Mifflin Harcourt All rights reserved.

x 4 8

Does your graph have a positive or negative slope? Answer ________________________ slope

Test Preparation and Practice for the ISTEP+

50

Grade 8 · Test 5

Test 6

Grade 8 Mathematics

1

Which of the following is the simplified form of the expression below?

34 ___ __ 3 8 A ____ 2 3 2 B ___ 2

__ __ __

2

C 3 2

6 __ D __ 2

__

2

Juan bought 300 shares of stock at an average price of $55 per share. Later, he bought 150 more shares of stock at $50 per share. To the nearest cent, what was the average price per share of ALL 450 shares of stock? Mark your answer in the answer grid.

/

/

/

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 6

51

Test Preparation and Practice for the ISTEP+

Test 6

Grade 8 Mathematics

3

The Carpenter family is putting an addition on their house. A diagram of the house and planned addition is shown below. 8 ft

8 ft 15 ft 11 ft 18 ft What is the volume, in cubic feet, of the house and the addition? A 704 cubic feet B 2,970 cubic feet C 3,674 cubic feet D 4,554 cubic feet

4

Look at the circle below. A

B

15 cm

C

© Houghton Mifflin Harcourt All rights reserved.

The length of AC is 3. What is the measure, in degrees, of ABC? A 18º B 36º C 45º D 144º

Test Preparation and Practice for the ISTEP+

52

Grade 8 · Test 6

Test 6

Grade 8 Mathematics

5

Which of the following is a NONLINEAR function? A y=x+2 B 3x ­ 4y = 12 C y = ­x D y = x2 + 4

6

Which figure has a slant height?

A triangle B pyramid C square D cylinder

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 6

53

Test Preparation and Practice for the ISTEP+

Test 6

Grade 8 Mathematics

7

2 h inc 1

5 4 3

Use your ruler as a straightedge. ­2 On the coordinate grid below, graph the line with slope __ that passes 3 through point (­3, 4). y 4 2 0

-4 -2 -2 -4

x 2 4

Write an equation for the line. Equation

8

Which list is in order from LEAST to GREATEST?

__

A 0.66, 0.6, 0. 6

2 1 B __, 0. 5, __ 3 2

__ __

C 0.7, 1.7, 0. 7

__ __ __

D 0. 4, 0.0 4, 4. 4

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

54

Grade 8 · Test 6

Test 6

Grade 8 Mathematics

9

Below is a box-and-whisker plot of scores Ms. Jansen's students earned on their math test.

69 71 74 77 80 83 86 89 92 95 What is the median test score? A 73 B 86 C 90 D 95

10

What is the simplified form of the expression below?

3x y z _______ 6xyz xyz A______ 2 xy B ___ 3

4 2 4 2 3 3 3 2

2z y2 C ____ 2x4z3 2y2 D ___ x4z3

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 6

55

Test Preparation and Practice for the ISTEP+

Test 6

Grade 8 Mathematics

11

Kathleen went bowling with her friends. The Big Bowl charges $2.75 per game plus $1.50 to rent shoes. Kathleen spent $15.25 in all. How many games did Kathleen bowl? A 3 games B 4 games C 5 games D 6 games

12

4 -3 What is the simplified form of __ ? 3 Mark your answer in the answer grid.

0 1 2 3 4 5 6 7 8 9

()

/

/

/

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

56

Grade 8 · Test 6

Test 6

Grade 8 Mathematics

13

Amy and Steve were playing with a beach ball on the beach. The beach ball has a diameter of 16 inches. To the nearest hundredth of a cubic inch, what is the volume of the beach ball? A 682.67 cubic inches B 1205.76 cubic inches C 1607.68 cubic inches D 2143.57 cubic inches

14

An article on the Internet claims that if you study for a few hours every day prior to a test, you will retain material better than if you study for many hours the day before. On the lines below, describe how you can test this claim in your class.

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 6

57

Test Preparation and Practice for the ISTEP+

Test 6

Grade 8 Mathematics

15

The table below shows how much money Haley earns (y) for working x hours. Haley's Earnings Hours ( x) Earnings (y) 3 $15.75 5 $26.25 6 $31.50 8 $42.00 Write an equation for the function. Equation On the axes below, graph the function.

Money Earned

Hours Worked

© Houghton Mifflin Harcourt All rights reserved.

16

Monisha has a credit card balance of $800. The credit card company charges 3.5% interest on the unpaid balance each month. What is the interest charge on Monisha's current balance? A $2.80 B $28 C $280 D $2800

Test Preparation and Practice for the ISTEP+

58

Grade 8 · Test 6

Test 6

Grade 8 Mathematics

17

The Women's size 6 regulation basketball has a diameter of about 9 inches. What is the surface area of the basketball? A 56.52 square inches B 113.04 square inches C 254.34 square inches D 1017.36 square inches

18

Look at the right triangle below.

5 2

4 What is the perimeter of the triangle? Show All Work

© Houghton Mifflin Harcourt All rights reserved.

Answer

units

Grade 8 · Test 6

59

Test Preparation and Practice for the ISTEP+

Test 6

Grade 8 Mathematics

19

Solve and graph: 3(x ­ 2) 4(x + 6) Show All Work

-60

-50 -40

-30

-20

-10

0

20

A study was done to find how many hours people spend exercising and watching television. The scatter plot below shows this correlation. 14 Hours Spent Exercising 12 10 8 6 4 2 0 0 1 2 3 4 5 6 7 Hours Watching Television 8

© Houghton Mifflin Harcourt All rights reserved.

Is there a positive, negative, or no correlation between the hours watching television and exercising? Answer Draw a line of best fit and find its equation. Equation

Test Preparation and Practice for the ISTEP+

60

Grade 8 · Test 6

Grade 8 Reference Sheet

Shape Triangle Rectangle Trapezoid Parallelogram Square

1

Formulas for Area (A) and Circumference (C) A = __bh = __ × base × height 2 2 A = lw = length × width A = __h(b1 + b2) = __ × sum of bases × height 2 2 A = bh = base × height A = s2 = side × side A = r2 = × square of radius C = 2r = 2 × × radius 22 3.14 or __ 7

1 1 1

Circle Figure Rectangular Prism General Prisms

Formulas for Volume (V) and Surface Area (SA) V = lwh = length × width × height SA = 2(length × width) + 2(height × width) + 2(length × height) = 2lw + 2hw + 2lh V = Bh = area of base × height SA = sum of the areas of the faces V = r2h = × square of radius × height SA = 2r2 + 2rh = 2 × × square of radius + 2 × × radius × height V = __r2 = __ × × cube of radius 3 3 SA = 4r2 = 4 × × square of radius

4 4

Cylinder

© Houghton Mifflin Harcourt All rights reserved.

Sphere

3.14 or 22 __ 7

Right Circular Cone

V = __r2h = __ × × square of radius × height 3 3

1

1

Regular Pyramid

V = __ Bh = __ × area of base × height 3 3

1

1

Grade 8

61

Test Preparation and Practice for the ISTEP+

Grade 8 Reference Sheet

Equation of a Line Slope-Intercept Form: y = mx + b where m = slope and b = y-intercept Point-Slope Form: y - y1 = m(x - x1) where m = slope and (x1, y1) is a point on a line Slope of a Line Let (x1, y1) and (x2, y2) be two points in the plane. slope = ________ = _____ x2 ­ x1 change in x where x2 x1 Pythagorean Theorem

a c

°C =

Distance Formula d = rt distance = rate × time Temperature Formulas

5 __(F - 32) 9 5 °Celsius = __ × (°Fahrenheit - 32) 9 9 °F = __(C + 32) 5 9 °Fahrenheit = __ × (°Celsius + 32) 5

Simple Interest Formula i = prt where i = interest, p = principal, r = rate, and t = time Quadratic Formula

b2 - 4ac x = -b ± ________ 2a

________

change in y

y2 ­ y1

a2 + b2 = c2

b

where ax2 + bx2 + c = 0, a 0, and b2 - 4ac 0

Conversions 1 yard = 3 feet = 36 inches 1 mile = 1760 yards = 5280 feet 1 acre = 43,560 square feet 1 hour = 60 minutes 1 minute = 60 seconds 1 liter = 1000 milliliters = 1000 cubic centimeters 1 meter = 100 centimeters = 1000 millimeters 1 kilometer = 1000 meters 1 gram = 1000 milligrams 1 kilogram = 1000 grams 1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts 1 pound = 16 ounces 1 ton = 2000 pounds

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

62

Grade 8

Scoring Guide Test 1 1. C 2. 25 3. C 4. D 5. C 6. D 7. Exemplary 2-Point Response: 138 square feet Sample Process: 10 × 12 = 120 6 × 3 = 18 120 + 18 = 138 OR Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other 8. C 9. D 10. B 11. A

© Houghton Mifflin Harcourt All rights reserved.

12. 3 13. C 14. Exemplary 2-Point Response: __ __ __ __ 1, 3 , 2, 5 , 7 , 9 , 4, 6 Sample Process: __ __ __ __ 3 < 2, 5 and 7 > 2 but less than 3, 9 = 3 OR Other valid process

Grade 8 · Test 1

63

Test Preparation and Practice for the ISTEP+

Scoring Guide Rubric: 2 points Exemplary response 1 point Four numbers in correct order 0 points Other 15. Exemplary 2-Point Response: 196x2 square inches Sample Process: A = s2 = (14x)2 = 196x2 OR Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other 16. C 17. D 18. Exemplary 2-Point Response: $12.37 Sample Process: 14.99 + 9.99 + 8.75 + 18.99 + 11.50 +10.00 74.22 _________________________________ = ____ = 12.37 OR Other valid process AND $10.75 Sample Process: 8.75, 9.99, 10.00, 11.50, 14.99, 18.99 10.00 + 11.50 ___________ = 10.75 2 OR Other valid process Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 19. Exemplary 2-Point Response: __ __ 8 is a little less than 9 which is equal to 3 AND

6 6

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

64

Grade 8 · Test 1

Scoring Guide

8

0

1

2

3

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 20. Exemplary 3-Point Response:

225 in.2 64 in.2 8 in.

15 in.

289 in.2

© Houghton Mifflin Harcourt All rights reserved.

17 in.

Sample Process: 82 + 152 = c2 64 + 225 = c2 289 = c2 17 = c Rubric: 3 points Exemplary response 2 points Two correct components 1 point One correct component 0 points Other

Grade 8 · Test 1

65

Test Preparation and Practice for the ISTEP+

Scoring Guide Test 2 1. C 2. 6561 3. C 4. D 5. D 6. B 7. Exemplary 2-Point Response: The central angle is formed by two radii of the circle. AND

central angle radius radius

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 8. B 9. B 10. D 11. D 12. 275 13. C 14. Exemplary 2-Point Response:

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

66

Grade 8 · Test 2

Scoring Guide

First Toss

Second Toss H

Third Toss H T H T H T H T

Outcome HHH HHT HTH HTT THH THT TTH TTT

H T H T T

AND 1 __

8

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 15. Exemplary 2-Point Response: 483,000,000 AND 4.83 × 108 Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 16. C

© Houghton Mifflin Harcourt All rights reserved.

17. C 18. Exemplary 2-Point Response: __ 1 1 __ 0.0 7 , __ , __ , 0.7, 0. 7

7 3

Sample Process: 1 1 __ 0.333, __ 0.143, 0.__ 0.777, 0.7 = 0.700, 0.0__ 0.077 7 7

3 7

OR Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other

Grade 8 · Test 2

67

Test Preparation and Practice for the ISTEP+

Scoring Guide 19. Exemplary 2-Point Response: 150 square feet Sample Process: Area of rectangle: 15 · 6 = 90 square feet Find x using the Pythagorean Theorem. 152 + x2 = 172 225 + x2 = 289 x2 = 64 x=8 1 Area of triangle: __(8)(15) = 60 square feet 2 Area of figure: 90 + 60 = 150 square feet OR Other valid process Rubric: 2 points Exemplary response 1 point One area correct 0 points Other 20. Exemplary 3-Point Response: $38.95 Sample Process: 35.47 + 39.26 + 42.01 + 47.54 + 37.41 + 29.86 + 30.31 + 44.45 + 36.07 + 49.64 + 42.01 + 33.36 ___________________________________________________________________ 38.95 OR Other valid process AND $38.34 Sample Process: 37.41 + 39.26 ___________ = 38.335 38.34 OR Other valid process AND $42.01 Rubric: 3 points Exemplary response 2 points Two correct components 1 point One correct component 0 points Other

2 12

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Test Preparation and Practice for the ISTEP+

68

Grade 8 · Test 2

Scoring Guide Test 3 1. D

1 2. __ 32

3. B 4. C 5. B 6. D 7. Exemplary 2-Point Response: y = x and y = 2x ­ 1 AND (1, 1) Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 8. B 9. B 10. B 11. A 12. 7

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13. A 14. Exemplary 2-Point Response:

4 2 0

-4 -2 -2 -4

y

x 2 4

AND

Grade 8 · Test 3

69

Test Preparation and Practice for the ISTEP+

Scoring Guide positive slope Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 15. Exemplary 2-Point Response: Julia's friends probably are all in the same grade and have the same teachers, homework assignments, and similar study habits. Her sample is not representative of other grade levels and other teachers' homework assignments. Rubric: 2 points Exemplary response 1 point Two correct biases 0 points Other 16. B 17. C 18. Exemplary 2-Point Response: 48 minutes Sample Process: 8 4 __ = __

x 24 8 1 __ = __ x 6

x = 48 OR Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other 19. Exemplary 2-Point Response: 144 cubic centimeters Sample Process: Front of one tower = 12 × 5 = 60 Both towers have the same dimensions, so multiply the front of one tower by 2. 60 × 2 = 120 Front of walkway = 3 × 8 = 24; 120 + 24 = 144

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

70

Grade 8 · Test 3

Scoring Guide OR Other valid process Rubric: 2 points Exemplary response 1 point One correct volume 0 points Other 20. Exemplary 3-Point Response: c = $12x + $400 AND $952 Sample Process: c = 12x + 400 = 12(46) + 400 = 552 + 400 c = 952 OR Other valid process AND about $20.70 Sample Process: Divide $400 by 46 to find the cost of the party room per person. $400 ÷ 46 $8.70 Add the cost of the party room per person to the cost of a meal per person. $12 + $8.70 = $20.70 OR Other valid process Rubric: 3 points Exemplary response 2 points Two correct components 1 point One correct component 0 points Other

© Houghton Mifflin Harcourt All rights reserved.

Grade 8 · Test 3

71

Test Preparation and Practice for the ISTEP+

Scoring Guide Test 4 1. C 2. 18 3. B 4. D 5. C 6. B 7. Exemplary 2-Point Response: 3x + 8 > 14 AND x>2

-2 -1

0

1

2

3

4

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 8. C 9. A 10. B 11. B

© Houghton Mifflin Harcourt All rights reserved.

12. 64 13. C 14. Exemplary 2-Point Response: y = 2x ­ 1 and y = ­2x + 3 AND (1, 1) Rubric: 2 points Exemplary response 1 point One correct component 0 points Other

Test Preparation and Practice for the ISTEP+

72

Grade 8 · Test 4

Scoring Guide 15. Exemplary 2-Point Response: diameter AND central angle AND radii Rubric: 2 points Exemplary response 1 point Two correct components 0 points Other 16. B 17. D 18. Exemplary 2-Point Response: 489 square feet Sample Process:

45 ft 21 ft 10 ft 12 ft 22 ft 12 ft 12 ft 10 ft

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Area of rectangle 1: 22 × 12 = 264 Area of rectangle 2: 10 × 12 = 120 1 Area of triangle: __ (21)(10) = 105 2 Total area: 264 + 120 + 105 = 489 OR Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other 19. Exemplary 2-Point Response: Possible outcomes: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. The probability 7 1 of tossing tails at least once is __, and of not tossing tails is __. Scott is more likely to

8 8

toss tails.

Grade 8 · Test 4

73

Test Preparation and Practice for the ISTEP+

Scoring Guide OR Other valid explanation Rubric: 2 points Exemplary response 1 point Correct complete process; error in probabilities 0 points Other 20. Exemplary 3-Point Response:

100 90 80 70 60 50 40 30 20 10 1 2 3 4 Number of Hours 5

AND y = 10x + 40 Rubric: 3 points Exemplary response 2 points Correct graph, incorrect equation 1 point Incorrect graph, correct equation 0 points Other

© Houghton Mifflin Harcourt All rights reserved.

Test Preparation and Practice for the ISTEP+

Score

74

Grade 8 · Test 4

Scoring Guide Test 5 1. B 2. 384 3. D 4. B 5. C 6. D 7. Exemplary 2-Point Response: $1,800 Sample Process: $1,000 × 0.04 = $40 per year; $40 × 20 = $800 for 20 years Total in account after 20 years: $1,000 + $800 = $1,800 OR Other valid process AND $2,191.12 Sample Process: f = P(1 + r)n = $1,000(1 + 0.04)20 = $1,000(1.04)20 = $2,191.12 OR Other valid process Rubric: 2 points Exemplary response 1 point One correct component 0 points Other

© Houghton Mifflin Harcourt All rights reserved.

8. D 9. C 10. C 11. C 12. 180 13. B

Grade 8 · Test 5

75

Test Preparation and Practice for the ISTEP+

Scoring Guide 14. Exemplary 2-Point Response:

y 4 2 0

-4 -2 -2 -4

x 2 4

AND (5, ­1) Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 15. Exemplary 2-Point Response: 14 x < __

3

Sample Process: ­6(x ­ 4) > 3(x ­ 7); ­6x + 24 > 3x ­ 21; ­9x + 24 > ­21; ­9x > ­45; x < 45 ÷ 9; x < 5 AND

0 1 2 3 4 5 6

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 16. A 17. B 18. Exemplary 2-Point Response: 131.88 cubic centimeters Sample Process: 1 1 V = __ r2h = __ (3.14)(32)(14) 3 3 = (3.14)(3)(14) = 131.88

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Test Preparation and Practice for the ISTEP+

76

Grade 8 · Test 5

Scoring Guide OR Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other 19. Exemplary 2-Point Response: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} AND 1 __

4

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 20. Exemplary 3-Point Response: 15 (0, ­5) and (__, 0) 2 Sample Process: 2 2x ­ 3y = 15; ­3y = ­2x + 15; y = __ x ­ 5; 3 2 __(0) ­ 5; y = ­ 5; y-intercept: y = AND

3 3 3 2 15 2 2 x-intercept: 0 = __ x ­ 5; 5 = __ x; (__)5 = (__) __ x; __ = x 3 3 2 2 3 2

y 4 2 0

-4 © Houghton Mifflin Harcourt All rights reserved. -2 -2 -4

x 2 4

AND positive slope Rubric: 3 points Exemplary response 2 points Two correct components 1 point One correct component 0 points Other

Grade 8 · Test 5

77

Test Preparation and Practice for the ISTEP+

Scoring Guide Test 6 1. C 2. 53.33 3. C 4. B 5. D 6. B 7. Exemplary 2-Point Response:

y 4 2 0

-4 -2 -2 -4

x 2 4

AND 2 y = ___ x + 2

3

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 8. B 9. B 10. C 11. C

27 12. __ 64

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13. D 14. Exemplary 2-Point Response:

Test Preparation and Practice for the ISTEP+

78

Grade 8 · Test 6

Scoring Guide For a test, have one group study for 30 minutes over 5 days, and have a different group study for 150 minutes the night before. Compare the results. OR Other valid explanation Rubric: 2 points Exemplary response 1 point One of the processes is mentioned 0 points Other 15. Exemplary 2-Point Response: y = 5.25x AND

40 Money Earned 30 20 10 0

0

1

2

3

4 5 6 Hours Worked

7

8

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other

© Houghton Mifflin Harcourt All rights reserved.

16. B 17. C 18. Exemplary 2-Point Response: __ 10 + 2 5 units Sample Process: Use the Pythagorean Theorem to find the length of the third side. __ (2 5 )2 + 42 = c2; 20 + 16 = c2; 36 = c2; 6 = c To find the __ perimeter, add the lengths of the sides. __ 5 = 10 + 2 5 4+6+2 OR

Grade 8 · Test 6

79

Test Preparation and Practice for the ISTEP+

Scoring Guide Other valid process Rubric: 2 points Exemplary response 1 point Correct complete process; error in computation 0 points Other 19. Exemplary 2-Point Response: x ­30 Sample Process: 3(x ­ 2) 4(x + 6) 3x ­ 6 4x + 24 3x 4x + 30 ­x 30 x ­30 AND

-60 -50 -40 -30 -20 -10

0

Rubric: 2 points Exemplary response 1 point One correct component 0 points Other 20. Exemplary 3-Point Response: negative correlation AND

14 Hours Spent Exercising 12 10 8 6 4 2 0 0 1 2 3 4 5 6 7 Hours Watching Television 8

© Houghton Mifflin Harcourt All rights reserved.

AND y = ­3x + 14 Rubric: 3 points Exemplary response 2 points Two correct components 1 point One correct component 0 points Other

Test Preparation and Practice for the ISTEP+

80

Grade 8 · Test 6

© Houghton Mifflin Harcourt All rights reserved.

Grade 8

Class Recording Form: Tests 1­3

Practice Test Results for the ISTEP+ Grade 8 Mathematics

Practice Test 1 Multiple Gridded Choice Response Open Ended Total Points* Multiple Gridded Choice Response Open Ended Total Points* Practice Test 2 Practice Test 3 Multiple Gridded Choice Response Open Ended Total Points*

Teacher/Class

Student's Name

1.

2.

3.

4.

5.

6.

7.

81

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

Test Preparation and Practice for the ISTEP+

*Multiple-Choice Points + Gridded-Response Points + Open-Ended Points = Total Points (27 possible Total Points per test)

© Houghton Mifflin Harcourt All rights reserved.

Class Recording Form: Tests 4­6

Practice Test Results for the ISTEP+ Grade 8 Mathematics

Teacher/Class Practice Test 4 Multiple Gridded Choice Response Open Ended Total Points* Practice Test 5 Multiple Gridded Choice Response Open Ended Total Points*

Practice Test 6

Student's Name 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Multiple Gridded Choice Response

Open Ended

Total Points*

*Multiple-Choice Points + Gridded-Response Points + Open-Ended Points = Total Points (27 possible Total Points per test)

Test Preparation and Practice for the ISTEP+

82

Grade 8

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