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Holt McDougal Math

South Carolina PASS Preparation and Practice, Grade 6

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ISBN-13: 978-0-03-093391-2 ISBN-10: 0-03-093391-9

1 2 3 4 179 11 10 09 08

To the Student

This book is designed to help you prepare and practice for PASS. PASS is based on the South Carolina academic content standards and academic performance level descriptors. The book contains practice questions arranged by topic, and PASS practice tests. The practice questions are organized by content strands. There are five strands: · Number and Operations · Algebra · Geometry · Measurement · Data Analysis and Probability Within each strand, there are several two-page worksheets on each topic. The questions are multiple-choice and contructed response. At the back of the book, the PASS practice tests contain mixed practice on all strands. It is a good idea to time yourself as you work on the practice questions to get used to working in a timed situation.

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PASS Preparation and Practice, Grade 6

Table of Contents

South Carolina Mathematics Academic Standards . . . . . . . . . . . . . . . . . . . . . . . . .vi

PASS Preparation

Number and Operations Percentages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Comparing Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Add and Subtract Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Multiply and Divide Rational Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Ratios and Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Powers of Ten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Prime Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Algebra Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Algebraic Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Equivalent Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Inverse Operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Geometry Ordered Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Coordinate Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Line and Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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PASS Preparation and Practice, Grade 6

Identify Transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Comparing Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Similar Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Complementary and Supplementary Angles . . . . . . . . . . . . . . . . . . . . . . . . 45 Measurement Circle Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Circumference and Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Surface Area of Rectangular Prisms and Cylinders . . . . . . . . . . . . . . . . . . 51 Estimating Perimeter and Area of Irregular Shapes . . . . . . . . . . . . . . . . . . 53 Perimeter and Area of Irregular Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Data Analysis and Probability Using Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Frequency Tables, Histograms, and Stem-and-Leaf Plots . . . . . . . . . . . . . . 63 Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Theoretical Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Probability of Complementary Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

PASS Practice

PASS Practice Test A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 PASS Practice Test B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

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v

PASS Preparation and Practice, Grade 6

South Carolina Mathematics Academic Standards

The following chart is a correlation of the South Carolina Mathematics Academic Standards to the pages in this workbook.

South Carolina Performance Indicator 6-2.1 6-2.2 6-2.3 Understand whole-number percentages through 100. Understand integers. Compare rational numbers and whole-number percentages through 100 by using the symbols , , <, >, and =. Apply an algorithm to add and subtract fractions. Generate strategies to multiply and divide fractions and decimals. Understand the relationship between ratio/rate and multiplication/division. Page(s) in this Workbook 1, 2 3, 4 5, 6

6-2.4 6-2.5 6-2.6 6-2.7 6-2.8 6-2.9 6-3.1 6-3.2 6-3.3 6-3.4 6-3.5

7, 8 9, 10 11, 12

Apply strategies and procedures to determine values of 13, 14 powers of 10, up to 10 6. Represent the prime factorization of numbers by using exponents. Represent whole numbers in exponential form. Analyze numeric and algebraic patterns and pattern relationships. Apply order of operations to simplify whole-number expressions. Represent algebraic relationships with variables in expressions, simple equations, and simple inequalities. Use the commutative, associative, and distributive properties to show that two expressions are equivalent. 15, 16 17, 18 19, 20 21, 22 23, 24 25, 26

Use inverse operations to solve one-step equations that 27, 28 have whole-number solutions and variables with wholenumber coefficients. Represent with ordered pairs of integers the location of points in a coordinate grid. 29, 30

6-4.1

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PASS Preparation and Practice, Grade 6

South Carolina Performance Indicator 6-4.2

Page(s) in this Workbook

Apply strategies and procedures to find the coordinates 31, 32 of the missing vertex of a square, rectangle, or right triangle when given the coordinates of the polygon's other vertices. Generalize the relationship between line symmetry and rotational symmetry for two-dimensional shapes. 33, 34

6-4.3 6-4.4 6-4.5 6-4.6 6-4.7 6-4.8 6-4.9 6-5.1 6-5.2

Construct two-dimensional shapes with line or rotational 35, 36 symmetry. Identify the transformation(s) used to move a polygon from one location to another in the coordinate plane. Explain how transformations affect the location of the original polygon in the coordinate plane. Compare the angles, side lengths, and perimeters of similar shapes. Classify shapes as similar. Classify pairs of angles as either complementary or supplementary. Explain the relationships among the circumference, diameter, and radius of a circle. Apply strategies and formulas with an approximate of 22 pi (3.14 or ___ ) to find the circumference and area of a 7 circle. Generate strategies to determine the surface area of a rectangular prism and a cylinder. Apply strategies and procedures to estimate the perimeters and areas of irregular shapes. 37, 38 39, 40 41, 42 43, 44 45, 46 47, 48 49, 50

6-5.3 6-5.4 6-5.5

51, 52 53, 54

55, 56 Apply strategies and procedures of combining and subdividing to find the perimeters and areas of irregular shapes. Use proportions to determine unit rates. Use scale to determine distance. Predict the characteristics of one population based on the analysis of sample data. 57, 58 59, 60 61, 62

6-5.6 6-5.7 6-6.1 6-6.2

Organize data in frequency tables, histograms, or stem- 63, 64 and-leaf plots as appropriate.

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vii

PASS Preparation and Practice, Grade 6

South Carolina Performance Indicator 6-6.3 Analyze which measure of central tendency (mean, median, or mode) is the most appropriate for a given purpose. Use theoretical probability to determine the sample space and probability for one- and two-stage events such as tree diagrams, models, lists, charts, and pictures. Apply procedures to calculate the probability of complementary events.

Page(s) in this Workbook 65, 66

6-6.4

67, 68

6-6.5

69, 70

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viii

PASS Preparation and Practice, Grade 6

PASS Progress Monitoring Chart

The following chart is a correlation of the South Carolina Mathematics Academic Standards to questions in PASS Practice Tests A and B.

SC Performance Indicator 6-2.1 6-2.2 6-2.3 6-2.4 6-2.5 6-2.6 6-2.7 6-2.8 6-2.9 6-3.1 6-3.2 6-3.3 6-3.4 6-3.5 6-4.1 6-4.2 6-4.3 6-4.4 6-4.5 6-4.6 6-4.7 6-4.8 6-4.9 6-5.1 14, 15, 18 16, 17 19, 22 20, 21, 23 24, 25, 26 27, 28, 29, 62 30 33 34 35 36 37 38 39, 40 42, 46, 47 25, 26 15, 57, 58 PASS Practice Test A 1, 2 3 4, 5 7 6, 8, 61 9, 10 11, 12 13 10, 23 4 14, 32 8, 37 12, 33, 47 38, 48 43, 46, 52 40, 62 21 3, 50 45 41 42 13, 34, 49, 61 PASS Practice Test B 9 36, 56 20 2, 63 7, 28 18, 29

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ix

PASS Preparation and Practice, Grade 6

SC Performance Indicator 6-5.2 6-5.3 6-5.4 6-5.5 6-5.6 6-5.7 6-6.1 6-6.2 6-6.3 6-6.4 6-6.5

PASS Practice Test A 48 31, 41 49 50 51, 52 53, 54 55, 58 43, 44 32, 45 56, 59, 60 57

PASS Practice Test B 11, 27, 59 19, 31 30

22, 24 6, 51

53, 54, 55 5, 17, 44 1, 16, 35, 39, 60

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x

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Percentages

South Carolina Mathematics Academic Standards 6-2.1 Understand whole-number percentages through 100. Select the best answer for each question. 1. The students at South Middle School want to raise $2,500 for new playground equipment at the elementary school. So far they have raised $1,700. What percent of their goal have they reached? 32% 45% 68% 147% 2. Ramon spent 40% of his savings on a new stereo system. If he had $275.50 in his savings account, how much did he spend on the stereo system? $40.00 $110.20 $120.20 $165.30 3. In Mrs. Wilson's class, 18 out of 24 students saw a new action movie. What percent of her class did NOT see the movie? 25% 30% 70% 75% 4. The students at Scott Middle School either ride the bus, walk, or are driven to school by a parent. According to the chart, what is the percentage of sixth graders who ride the bus? How We Get to School Grade 6th 7th 8th 38% 50% 52% 65% 5. Ralph used 75% of his study time to work on his research paper. If he worked on his paper for 3 hours, how much time did Ralph have left to work on his science homework? 1 hour 2 hours 3 hours 4 hours 6. Miguel has a garden that has an area of 315 square feet. If the corn in his garden covers 190 square feet, what percent of the garden is corn? 50% 55% 60% 65% 1

PASS Preparation and Practice, Grade 6

Bus 98 88 70

Walk 35 23 30

Driven 55 42 33

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Name _________________________________ Date ______________ Class ______________

7. The students at Highland Middle School can choose to pack a lunch or buy a hot lunch at school. What is the approximate difference between the percent of sixth graders who pack a lunch and the percent who buy a lunch? Lunch Choices (number of students) Grade 6th 7th 8th 20% 26% 47% 55% 8. A bike costs $225. It is on sale for 20% off the regular price. What is the sale price of the bike? $180 $200 $205 $220 9. Of the 56 pieces of mail that Bob received this week, 75% was junk mail. How many pieces of Bob's mail were NOT junk mail? 14 15 19 25 Buy Lunch 50 32 65 Pack Lunch 76 54 18

10. Tarik left a 22% tip for the waitress who served his family. The meal cost $82.50. How much tip did Tarik leave? $18.15 $18.90 $100.65 $104.65 11. The baseball coach keeps track of his players' at bats and hits. Use the chart to determine who had the greatest percent chance of getting a hit. Player Batting Statistics Player Barry Ken Pete Jose Barry Ken Pete Jose 12. A quality-control company found that 2% of a certain shipment was defective. If the shipment contained 23,865 pieces, how many pieces were defective? 48 pieces 477 pieces 4,773 pieces 47,730 pieces Constructed Response 13. Valerie finds 20 defective puzzle pieces in a puzzle with 1,000 pieces. What percentage of the pieces are defective? Hits 16 22 19 33 At Bats 55 59 62 80

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2

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Integers

South Carolina Mathematics Academic Standards 6-2.2 Understand integers. Select the best answer for each question. 1. Classify the number: -4. Whole Integer Irrational Natural 2. Which of the following sets of numbers are all integers? 4, 5, 6.5 1 -4, 0, __ 2 22 ___, , 3.14 7 -5, -4, 0 3. Samantha multiplied two integers together. What best describes her answer? Positive Negative Positive or negative Irrational 4. Which of the following set is NOT all integers? 4, 5, 6 -4, -5, -6 -4.5, -5.5. -6.5 4, -5, 6 5. Which set of numbers includes the natural numbers and zero? Integers Whole Rational Real 6. Which set of numbers includes all whole numbers and their opposites? Integers Whole Rational Real

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3

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Jerry is playing a game with his friends. He starts with 0 points. Then he gains 6 points. Then he loses 4 points. Then he loses 3 points. Then he gains 5 points. What is his final score? 1 point 2 points 3 points 4 points 8. Golf is scored using integers. A course has a par of 75 strokes. If a golfer completes the course in 72 strokes, his score would be -3. What is the score of a golfer with 76 strokes? 1 0 -1 3 9. A diver swims 30 meters below sea level. Express that as an integer. -30 meters 30 meters 3 ___ meters 10 |30| meters

10. A hot air balloon starts at an altitude of 300 meters. Then it descends 40 meters. What is the altitude of the balloon? 300 meters 340 meters 260 meters 270 meters 11. Which set has its integers ordered from greatest to least? 1, 0, -1 1 1, __ , 0 2 3, 2, -3, -2 -1, 2, 4 12. Which set has its integers ordered from least to greatest? 1, 0, -1 -1, -2, -3 -3, -2, 0 1 - __ , 0, 3 2 Constructed Response 13. Draw a Venn diagram with natural numbers, whole numbers, and integers.

Copyright © 2010 by Holt McDougal. All rights reserved.

4

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Comparing Rational Numbers

South Carolina Mathematics Academic Standards 6-2.3 Compare rational numbers and whole-number percentages through 100 by using the symbols , , <, >, and =. Select the best answer for each question. 1. According to the 2000 U.S. Census, these counties in Nebraska had the following populations. Dixon 6339 Boone 6259 Howard 6567 Sioux 6455 3. Jacob collected some rocks for a rock garden. The rocks weighed 13.05, 13.55, 13.055, and 13.5 kilograms. Which shows the weights of the rocks in order from greatest to least? 13.55, 13.5, 13.055, 13.05 13.55, 13.055, 13.5, 13.05 13.05, 13.055, 13.5, 13.55 13.05, 13.5, 13.055, 13.55 4. Which of the following shows the mixed numbers in order from least to greatest? 3 5 4 7 2 __ , 2 __ , 2 __ , 2 ___ 4 8 7 10 3 4 5 7 2 __ , 2 __ , 2 ___ , 2 __ 7 8 10 4 3 4 5 7 2 __ , 2 __ , 2 __ , 2 ___ 7 8 10 4 3 5 4 7 2 __ , 2 ___ , 2 __ , 2 __ 7 10 4 8 5. Four friends played a video game. Troy scored 24,538 points, Lauren scored 24,358 points, Matt scored 25,338 points, and Becky scored 23,485 points. Who won the game? Becky Lauren Matt Troy

Which county has the greatest population? Dixon Boone Howard Sioux 2. The lengths in miles of some major rivers are shown in the chart. Heilong River 2,758 miles Irtish River 2,704 miles Parana River 2,795 miles Zaire River 2,716 miles

Which of the following shows those lengths in order from least to greatest? 2,704, 2,716, 2,795, 2,758 2,795, 2,758, 2,716, 2,704 2,704, 2,758, 2,716, 2,795 2,704, 2,716, 2,758, 2,795

Copyright © 2010 by Holt McDougal. All rights reserved.

5

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. Which of the following number sentences is true? 5 > 50% 50% > 0.5 50% = 5 50% < 0.05 7. Which of the following number sentences is true? 25% < 0.22 33% < 25 75% = 0.25 2 60% = __ 5 8. Which of the following number sentences is a true inequality? 60 > 60% 54% = 5.4 0.6 < 70% 67% = 6.7 9. Daniel says he got 80% on a test. Sandra says she got 15 out of 20 correct. Which is the correct expression to compare their scores? 80% > 70% 15 80% = ___ 20 15 ___ 80% > 20 15 80% < ___ 20

10. June is 50% done with her science project. Ali is three-fifths done with his project. David is one-quarter done with his project. Order their level of completion from least to greatest. Ali, June, David Ali, David, June David, June, Ali David, Ali, June 11. Jorge loves golfing. He has completed 7 of the 18 holes. Mary is 80% finished with the course. Samuel has 4 completed __ of the course. Order their 9 level of completion from greatest to least. Jorge, Mary, Samuel Mary, Samuel, Jorge Samuel, Mary, Jorge Jorge, Samuel, Mary Constructed Response 12. Sandra finds a sweater for $30. It is 30% off. Mary finds the same sweater for $35 but it is 35% off. Who is getting the better bargain? Show your work.

Copyright © 2010 by Holt McDougal. All rights reserved.

6

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Add and Subtract Fractions

South Carolina Mathematics Academic Standards 6-2.4 Apply an algorithm to add and subtract fractions. Select the best answer for each question. 1. What is a reasonable estimate for the 8 7 sum __ + ___ ? 9 12 1 __ 2 1 1 1 __ 2 2 4 2. What is the difference of 10 - 5 __ ? 9 4 4 __ 9 5 4 __ 9 4 5 __ 9 5 5 __ 9 3. Jan wants to add 8 3 least common denominator? 24 16 8 3 3 1 __ and __. What is the 1 1 4. Hector is asked to add __ , __ , 4 6 1 and __ . What is the least common 8 denominator? 24 48 96 192 5. What is the least common 4 1 1 denominator of __ , __ , and __ ? 5 3 2 2 3 15 30 1 4 6. Add the fractions: __ + __ . What 5 6 answer is in simplest form? 13 ___ 15 5 __ 6 26 ___ 30 22 ___ 30 4 3 7. Subtract: __ ­ __ . 5 8 7 __ 8 1 __ 3 17 ___ 40 7 ___ 20

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7

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

3 5 8. To find the sum __ + __ , use the 8 6 LCD, _?_. 5 __ 6 16 24 48 9. Which fraction is equivalent to 1 11 __ - ___? 4 32 5 - ___ 14 11 - ___ 32 3 - ___ 32 11 - ____ 128 5 3 2 10. Simplify __ + - ___ + - ___ . 14 7 21

12. Three of the fractions below are 8 12 equivalent to ___ ­ ___ . 10 24 Which answer is NOT equivalent? 72 ____ 240 36 ____ 120 6 ___ 20 5 ___ 10 Constructed Response 3 4 5 13. Jennie wants to add __ , __ , and ___ . 8 9 11 What is the answer? Show your work.

(

) (

)

1 - ___ 42 2 - ___ 21 1 - __ 2 37 - ___ 42 5 2 7 11. Deborah wants to add __ , ___ , and __ . 5 10 6 What is the least common denominator? 30 50 60 300

Copyright © 2010 by Holt McDougal. All rights reserved.

8

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Multiply and Divide Rational Numbers

South Carolina Mathematics Academic Standards 6-2.5 Generate strategies to multiply and divide fractions and decimals. Select the best answer for each question. 1. Multiply. 4 2 22 __ × __ 5 3 15 1 15 __ 2 11 15 ___ 15 1 15 __ 5 2 2. One chair in an auditorium is 18 __ 5 inches wide. How many chairs can be placed in a row that is 34 feet wide? 2 chairs 12 chairs 22 chairs 32 chairs 3. What is 8 ___ 15 4 __ 7 63 ___ 64 8 __ 7 16 3 __ of ___? 4 21 4. Eloise wants to buy a DVD player that costs $136.95. She plans to save $27.39 each month. At this rate, how many months will it take Eloise to save enough money? 5 months 6 months 7 months 8 months 5. Bill made a garden that had a total 3 area of 5 __ square meters. He planted 4 1 tomatoes in __ of the garden. In how 3 many square meters were tomatoes planted? 11 1 ___ square meters 12 2 1 __ square meters 3 2 square meters 1 2 __ square meters 3 6. Bob wants to cut a 32-inch board into 4 pieces that are 6 __ inches long. How 5 many pieces can he make? 3 pieces 4 pieces 5 pieces 6 pieces

Copyright © 2010 by Holt McDougal. All rights reserved.

9

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Directions for Neat-N-Clean soap call 2 for __ pint of soap for 1 gallon of water. 5 How much soap would be needed for 7 gallons of water? 17 ___ pint 35 4 1 __ pints 5 4 2 __ pints 5 1 3 __ pints 5 8. What is the difference between the product of 0.03 × 427 and the product of 0.3 × 427? 11.529 100 115.29 1,000 1 9. What is 40% divided by __ ? 2 20% 40% 80% 120% 1 10. What is __ multiplied by 25%? 3 1 ___ 12 1 __ 9 1 __ 6 1 __ 3

11. Jane is supposed to read half of her novel. She is 40% done with the required reading. How much of the book has she read? 1 __ 8 1 __ 5 1 __ 4 1 __ 2 12. Which description of the process of dividing fractions is correct? multiply by the inverse divide by the inverse add the inverse multiply by one 13. Find the numerator of the product without simplifying. 5 2 __ × __ 8 3 10 16 15 24

14. Find the denominator of the quotient. 1 1 __ ÷ __ 3 2 6 2 Constructed Response 3 15. A recipe calls for 1 __ cups of flour. 4 1 If you were going to make __ of the 2 recipe, how many cups of flour would you use? 10

PASS Preparation and Practice, Grade 6

3 1

Copyright © 2010 by Holt McDougal. All rights reserved.

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Ratios and Rates

South Carolina Mathematics Academic Standards 6-2.6 Understand the relationship between ratio/rate and multiplication/division. Select the best answer for each question. 1. On the map of a state park, the distance between the cave entrance and the observation tower is 4 inches. If the map scale is 1 inch = 80 yards, what is the actual distance between the cave entrance and the tower? 20 yards 40 yards 84 yards 320 yards 2. The scale on a map is 2 inches = 15 miles. If two cities are 75 miles apart, how far apart will they appear on the map? 2.5 inches 5 inches 10 inches 37.5 inches 3. The scale factor for a model ship is 3 inches = 20 feet. If the length of the ship is 150 feet, what is the length of the model? 7.5 inches 50 inches 22.5 inches 1,000 inches 4. The scale factor for a model plane is 2 inches = 25 feet. If the length of the model is 8 inches, how long is the plane? 200 feet 8 feet 80 feet 100 feet 5. Mr. David's class has 12 boys and 15 girls. What is the ratio of boys to girls? 4:5 12:27 15:27 12:1 6. Which ratio is equal to 5:3? 10:3 3:5 10:6 5:8 7. Which two ratios are equal to 2:8? 4:1 and 8:2 1:4 and 3:12 4:16 and 8:34 3:12 and 8:2

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11

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

8. A recipe calls for 2 eggs to make 24 muffins. How many muffins would you make if you increased the recipe and used 3 eggs? 36 muffins 48 muffins 60 muffins 72 muffins 9. Every week Jason gets paid $45.00 for working four days. What is his daily rate? $45.00 $22.50 $11.25 $10.00 10. If Denise makes $48 for 6 hours of babysitting, what is her hourly rate? $48 $24 $12 $8 11. The rate on a cell phone is $0.22 a minute. If Parminder uses her phone for 2 hours, how much does she pay? $0.44 $13.20 $26.40 $44.00

12. Maria makes $120 in an 8 hour day. Which is a correct expression that describes Maria's hourly rate? $120 ÷ 8 $120 × 8 8 ÷ $120 8 × $120 13. In the expression "miles per hour," which operation is represented by the word "per"? addition subtraction multiplication division 14. Which of the following is true? All ratios are rates. All rates are ratios. All ratios have a denominator of 1. All rates have a denominator of 1. Constructed Response 15. James bought a dozen tacos for $15. Use a rate to determine the cost of 9 tacos.

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12

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Powers of Ten

South Carolina Mathematics Academic Standards 6-2.7 Apply strategies and procedures to determine values of powers of 10, up to 106. Select the best answer for each question. 1. Which correctly identifies 10 × 10 × 10 × 10? 104 103 102 101 2. Which correctly identifies 100 x 100? 102 103 104 105 3. Diana bought ten jelly beans. Frank wants to buy ten times more jelly beans than Diana did. How many jelly beans will he buy? 102 103 104 105 4. 106 can also be represented as: 1,000,000 100,000 10,000 1,000 5. 100 can also be represented as: 1,000 100 10 1 6. Which is equal to 102 + 103? 2,000 1,100 200 105 7. Alejandro has read 102 pages. Milo has read 103 pages. How many more pages has Milo read than Alejandro? 1,100 1,000 900 90

Copyright © 2010 by Holt McDougal. All rights reserved.

13

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

8. A museum collection contains one million stamps. A private collector has 10,000 stamps. What are those numbers in exponential form? 105 and 104 104 and 103 106 and 104 106 and 105 9. Each week Carmen makes 102 dollars. How much will she have after 14 weeks? $14,000 $1,400 $140 $14 10. Which is a correct representation of 1,000,000? 10 × 10 × 10 × 10 × 10 × 10 10 × 10 × 10 × 10 × 10 10 × 10 × 10 × 10 10 × 10 × 10 11. Which is a correct representation of 100,000? 100 × 100 × 100 100 × 100 × 10 100 × 10 × 10 10 × 10 × 10

12. Which of these sets is ordered from least to greatest? 102, 103, 104 106, 103, 104 102, 100, 101 106, 105, 104

3 13. What does 4p equal when p = 10?

100 400 1000 4000 14. Write 10,000 as a power of 10. 102 103 104 105 Constructed Response 15. What is 106 ÷ 10? Write your answer in exponent form. Show your work.

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14

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Prime Factorization

South Carolina Mathematics Academic Standards 6-2.8 Represent the prime factorization of numbers by using exponents. Select the best answer for each question. 1. What is the correct prime factorization for 36? 22 × 3 33 22 × 32 34 2. What is the correct prime factorization for 144? 26 24 × 32 23 × 32 × 5 22 × 33 × 5 3. What number is the prime factor of 8? 1 2 4 8 2 3 4 12 5. What is the greatest prime factor in the prime factorization of 70? 2 5 7 10 6. What is the correct prime factorization for 175? 32 × 5 32 × 7 3×5×7 52 × 7 4. What factor is missing from this factor tree? 48 12 × 6×2×2×2 3×2×2×2×2

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15

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. What number is missing from this prime factorization? 7× × 2 × 2 × 2 = 112 2 3 5 12 8. Which set of numbers contains all the prime factors of 210? 2, 3, 5 2, 3, 5, 7 2, 3, 5, 11 2, 5, 7, 11 9. What prime factor is missing from this factor tree? 200 54 × 4 25 × 2 × 2 × 2 5× 2 3 5 25 10. Which factor appears four times in the prime factorization of 400? 2 3 5 11 ×2×2×2

11. Atlanta is 450 miles from Washington, D.C. What is the correct prime factorization of 450? 22 × 3 × 5 23 × 3 × 5 23 × 32 × 5 2 × 32 × 52 12. What is the correct prime factorization of 568? 2 3 × 69 2 3 × 71 3 3 × 69 3 3 × 71 13. Which common prime factors do 220 and 390 share? 2 and 3 2 and 5 2 and 13 2, 5, and 13 14. Which number has exactly three different prime factors? 12 57 70 210 Constructed Response 15. Represent the prime factorization of 54 with exponents. Show your work.

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16

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ NUMBER AND OPERATIONS

Exponents

South Carolina Mathematics Academic Standards 6-2.9 Represent whole numbers in exponential form. Select the best answer for each question. 1. Which expression is equal to 2 × 2 × 2 × 2? 22 23 24 25 2. Which expression is equal to 45? 4×4 4×4×4 4×4×4×4 4×4×4×4×4 3. What is another way to write 44? 24 26 28 210 4. Lynn has a petri dish of bacteria. Every hour, the number of bacteria doubles. How much bacteria will she have after 4 hours if she starts with 2 bacteria? 24 26 28 210 5. Jamie has 28 raisins. If she eats half every hour, how many raisins will she have at the end of 2 hours? 22 23 24 26 6. Which answer correctly lists the numbers in order from least to greatest? 2 3, 3 3, 4 2 3 3, 2 2, 1 2 3 2 2 2 ,3 ,4 42, 33, 24

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17

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Represent 5 in exponential form. 50 51 52 53 8. Which is NOT equivalent to 16? 16 1 42 24 160 9. Which is equal to 25? 53 25 0 55 52 10. If Philomena writes 42 and Judith writes 24, who has written a larger number? Philomena Judith Their numbers are equal. It cannot be determined.

11. An odd number is written in exponential form. Which statement must be true? The base is odd. The base is even. The exponent is odd. The exponent is even. 12. Which pair of expressions are both equal to 32? 25, 2 × 44 2 6, 2 × 42 25, 2 × 42 26, 2 × 44 Constructed Response 13. Will an odd number ever have even numbers in its exponential form? Explain why or why not.

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18

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ ALGEBRA

Patterns

South Carolina Mathematics Academic Standards 6-3.1 Analyze numeric and algebraic patterns and pattern relationships. Select the best answer for each question. 1. Which two shapes come next in this pattern? 3. Which number pattern matches the following rule? The numbers are increasing by 4. 16, 20 15, 20 16, 19 15, 21

4. Pauline is training for a race. On April 1, she runs for 15 minutes. Every day she runs for 2 minutes more than she did on the previous day. How many minutes will Pauline run on April 5? Day April 1 April 2 April 3 April 4 April 5 23 minutes 25 minutes 27 minutes 29 minutes 5. Identify the best rule for this pattern. 4 8 16 32 64 Time (min.) 15 17 19 21 ?

2. Which two numbers come next in this pattern? 27, 23, 19, 15, 11, ... 9, 5 7, 3 6, 3 8, 4

The numbers are increasing by 4. The numbers are increasing by 8. The numbers are doubling. The numbers are tripling.

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19

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. Jin is saving money for a new baseball glove. He puts $5 aside each week. How much money will Jin have put aside after 4 weeks? $15 $20 $25 $40

10. Which shape comes next in this pattern?

7. What is the missing number in the sequence? 5, 10, 16, ___, 31, 40 20 21 22 23

8. The table shows the amounts Dana spent for beads to make four necklaces. It also shows the amount she spent for all the supplies to make each necklace. Necklace Costs Beads, x ($) 6 10 15 22 All supplies, y ($) 12 20 30 44 Which expression best represents the cost of all supplies in terms of the cost of beads? x+6 y-6 2x y-2 9. A recipe calls for 2 eggs,1 cup of flour, and 2 teaspoons of oil. Which of the following amounts would you use if you wanted to double the recipe? 1 1 egg, __ c flour, 1 tsp oil 2 2 eggs, 2 c flour, 2 tsp oil 4 eggs, 2 c flour, 4 tsp oil 4 eggs, 1 c flour, 2 tsp oil

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11. Which number pattern matches the following rule? The numbers are increasing by 3. 0, 3, 5, 8 4, 7, 10, 13 6, 9, 15, 18 18, 15, 12, 9 Constructed Response 12. Write a rule for d in terms of r. r 2 4 6 d 5 9 13

20

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ ALGEBRA

Order of Operations

South Carolina Mathematics Academic Standards 6-3.2 Apply order of operations to simplify whole-number expressions. Select the best answer for each question. 1. Doreen bought 5 cakes for $12 each and 3 cartons of milk for $2 each. Which expression shows how much Doreen spent? 5 × 12 × 3 × 2 5 × 12 + 3 × 2 (5 + 3) × (12 + 2) (5 + 2) × (12 + 3) 2. Insert parentheses to make this number sentence true. 20 ÷ 5 × 2 + 3 = 5 (20 ÷ 5) × 2 + 3 = 5 20 ÷ (5 × 2) + 3 = 5 20 ÷ 5 × (2 + 3) = 5 20 ÷ (5 × 2 + 3) = 5 3. Use the order of operations to simplify. 22 - 6 ÷ 2 + 3 11 22 10 16 6. Insert parentheses to make this number sentence true. 12 + 10 ÷ 11 = 2 (12 + 10) ÷ 11 = 2 12 + (10 ÷ 11) = 2 (12 + 10 ÷ 11) = 2 ((12 + 10)) ÷ 11 = 2 4. Use the order of operations to simplify.

3 2 +8÷4

64 10 4 2.5 5. Which is the correct order of operations? Simplify inside grouping symbols, simplify exponents, add and subtract, multiply and divide Simplify inside grouping symbols, multiply and divide, add and subtract, simplify exponents Simplify exponents, simplify inside grouping symbols, multiply and divide, add and subtract Simplify inside grouping symbols, simplify exponents, multiply and divide, add and subtract

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21

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Insert parentheses to make this number sentence true. 2 × 6 2 - 8 = 56 2 × (6 2) - 8 = 56 (2 × 6 2) - 8 = 56 2 × (6 2 - 8) = 56 (2 × 6 2 - 8) = 56 8. Use the order of operations to simplify. 3 × (4 + 8) 60 36 216 72 9. Use the order of operations to simplify. 15 ÷ (5 ­ 2) + 8 9 13 1 8 10. The sentences below differ by the position of the parentheses. Which sentence has the greatest answer? (5 + 3) × 12 - 4 5 + 3 × (12 - 4) 5 + (3 × 12 - 4) (5 + 3 × 12) - 4

3

11. Which expression below is equal to this expression? (7 - 3) × 6 ÷ 2 (7 - 3 × 6) ÷ 2 7 - (3 × 6) ÷ 2 7 - (3 × 6 ÷ 2) (7 - 3) × (6 ÷ 2) 12. Which of the following sentences is true according to the order of operations? Multiply before dividing. Add before multiplying. Divide before multiplying. Multiply and divide from left to right. 13. Which of the following sentences is true according to order of operations? Simplify inside grouping symbols before simplifying exponents. Simplify exponents before simplifying inside grouping symbols. Add before subtracting. Add before simplifying exponents. 14. Use the order of operations to simplify. 18 - 3 × 2 - 2 16 22 4 10 Constructed Response 15. Describe what you would do to simplify this expression. 14 - 7 × 4 + 9 22

PASS Preparation and Practice, Grade 6

3

Copyright © 2010 by Holt McDougal. All rights reserved.

Name _________________________________ Date ______________ Class ______________ ALGEBRA

Algebraic Relationships

South Carolina Mathematics Academic Standards 6-3.3 Represent algebraic relationships with variables in expressions, simple equations, and simple inequalities. Select the best answer for each question. 1. In the input/output table below, what rule is performed on the input number in order to compute the output number? Input 4 6 8 y = 2x + 1 y = 3x - 5 Output 9 13 17 y = -2x + 18 y = x + 11 Andy and 2 friends each order the special plus 3 meatballs. Which expression gives the total cost? 3 · 4.50 + 9 · 0.75 9 · (4.50 + 0.75) 3 · 4.50 + 3 · 0.75 3 · 0.75 + 4.50 5. The Ortegas paid a 20% tip on their meal, m. Which expression correctly describes the amount of tip the Ortegas left? m ÷ 0.20 m ___ × 10 20 20m ÷ 100 m + 20 4. Andy sees this lunch special in a restaurant window.

2. Quick Clean house cleaning service costs $15 per room plus $12 per hour after the first hour. Which expression describes how to find the total cost? 15r + 12h 15r + 12(h - 1) 15r + 12(h + 1) 15r (12h) 3. Which expression describes the following sequence? 1 5 2 8 2n + 3 3n + 2 4n + 1 5n -1

Copyright © 2010 by Holt McDougal. All rights reserved.

3 11

4 14

n

23

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. A 200-foot sequoia was planted and grew 11 feet each year. Which algebraic expression best describes the height of the tree after t years? 11 + 200t 11t 200 + 11t 200t 7. Daniel is walking his dog, Spot. For every 10 steps that Daniel takes, Spot pulls him back 2. Which expression can represent the number of steps Spot pulled Daniel back for s number of steps?

10. In which algebraic expression is 2 added to the quotient of the product of 6 with n and 5? 6n · 5 + 2 (n ÷ 6 + 5) + 2 2 + (6n ÷ 5) 2 + 6n 11. Which equation is equal to the product of 2 and 3 plus x is equal to 10? (2 · 3)x = 10 (2 + 3)x = 10 2 · 3 · x = 10 2 · 3 + x = 10 12. Denise has $2.45 in coins in her pocket. She knows they are all quarters and nickels. What is an equation for Denise's change? 2.45 = 0.25q + 0.05n 2.45 = 0.25q - 0.05n 2.45 = (0.25 + 0.05)q 2.45 = 0.25q · 0.05n Constructed Response 13. Write an inequality for the number of dimes and nickels in a jar if the value is less than $3.50.

(s ÷ 10) · 2 s · (10 - 8)

2s 10 - 2 · s 8. Jean has q quarters in her pocket. She knows she has less than $2. What is the correct inequality for the number of quarters Jean has? 2 < q × 0.25 2 > q × 0.25 2 × 0.25 < q 2 × 0.25 > q 9. Which algebraic inequality represents the phrase "a number increased by 8 is less than 10?" 8x < 10 8 < 10 x + 8 < 10 x+8<1

Copyright © 2010 by Holt McDougal. All rights reserved.

24

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ ALGEBRA

Equivalent Expressions

South Carolina Mathematics Academic Standards 6-3.4 Use the commutative, associative, and distributive properties to show that two expressions are equivalent. Select the best answer for each question. 1. Which is an example of the Associative Property? 2+3=3+2 (1 + 2) + 3 = 1 + (2 + 3) 2(1 + 3) = 2 · 1 + 2 · 3 2·0=0 2. Which is an example of the Communtative Property? 2+3=3+2 (1 + 2) + 3 = 1 + (2 + 3) 2(1 + 3) = 2 · 1 + 2 · 3 2·0=0 3. Which is an example of the Distributive Property? 2+3=3+2 (1 + 2) + 3 = 1 + (2 + 3) 2(1 + 3) = 2 · 1 + 2 · 3 2·0=0 4. Peter wants to show that 2x + 3 is equivalent to 3 + 2x. What property would he use? Associative Distributive Communtative Algebraic 5. Janice solves the problem like this: 4(x + 5) = 20 + 4x 4x + 4 · 5 = 20 + 4x 4 · 5 + 4x = 20 + 4x 20 + 4x = 20 + 4x Which properties did she use? Associative and Distributive Associative and Communtative Distributive and Communtative Associative, Distributive, and Communtative 6. Dinish is given the expression 4 + (5 · 4). He wants to use the Communtative property. Which answer is NOT correct? (5 · 4) + 4 (4 · 5) + 4 4 + (4 · 5) (4 · 4) + (4 · 5) 7. Which expression is equivalent to 5 + (2 + 3) and shows Associative Property? (5 + 2) + (5 + 3) (5 + 2) + 3 5 + (3 + 2) (2 + 3) + 5

Copyright © 2010 by Holt McDougal. All rights reserved.

25

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

8. Which one of the properties is shown here? 3+0=3 Associative Communtative Distributive Identity 9. Which property is used to prove (4 + 3) + 5 + (3 + 1) = (3 + 1) + (4 + 3) + 5? Associative Communtative Distributive Identity 10. The Associative Property of Multiplication is demonstrated by which equation? b a a × __ = b × __ c c a × b × c = (a × b) × c (a × b) × c = a × (b × c) (a × b) × c = a × (b) × c

12. The Associative Property of Addition is demonstrated by which equation? d × (e + f) = d × d d + (e + f) = (d + e) + f d × (e + f) = (d × e) + (d × f) d + (e + f) = (d + e) × (d + f) 13. Which of the following expressions simplifies to -50r - 12? 4r - 6(9r - 2) -4r + 6(9r - 2) -4r + 6(9r + 2) 4r - 6(9r + 2) Constructed Response 14. Prove that x(3 + 4) = 7x. Include all the properties that you use.

()

()

11. The Distributive Property of Multiplication is demonstrated by which equation? a × (b + c) = a × a a × (b × c) = (a × b) × c a × (b + c) = (a × b) + (a × c) a + (b + c) = (a + b) × (a + c)

Copyright © 2010 by Holt McDougal. All rights reserved.

26

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ ALGEBRA

Inverse Operations

South Carolina Mathematics Academic Standards 6-3.5 Use inverse operations to solve one-step equations that have whole-number solutions and variables with whole-number coefficients. Select the best answer for each question. 1. Which of the following equations has the solution w = 3? 5+w=8 -5 = w + 8 w-5=8 5=w+8 2. What is the value of m in the equation m - 8 = -6? -14 -2 2 14 3. Which equation does NOT have a solution of 7? p - 16 = -9 p + 12 = -19 16 + p = 23 p - 23 = -16 4. What is the solution of the equation 6x = 144? 12 18 20 24 5. Brownsville received 42 inches of snow this year, which is 3 times the yearly average for the city. What is the yearly average of snowfall for Brownsville? 9 14 112 126 6. Which of the following is a solution to the equation x + 6 = 24? x=4 x = 30 x = 18 x = 36 7. Which of the following is the solution to the equation 15x = 225? x = 10 x = 15 x = 12 x = 188 8. What is the value of d in the following equation? d __ = 12 4 d=3 d = 16 d = 24 d = 48

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27

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

9. What is the solution to the following equation? x + 9 = 32 x = 23 x=9 x = -9 x = -112 10. Which of the following equations has a solution of 6? x + 13 = 26 x + 42 = 50 x + 24 = 32 x + 15 = 21 11. A rectangular envelope has a width of 4 inches and an area of 48 square inches. What is the length of the rectangle? 8 inches 12 inches 16 inches 192 inches 12. Which of the following equations does NOT have a solution of x = 4? 13x = 52 x + 16 = 20 x-6=2 x __ = 2 2

13. Jessie wants to solve the equation 4x = 112. What step should she take first? Add 4 to both sides. Subtract 4 from both sides. Multiply 4 to both sides. Divide by 4 on both sides. 14. Ursula is at the grocery store and sees the following:

Ursula wants to know the price, x, per orange if she buys a dozen. She uses the following equation. 12x = $3.60 What is the value of x? 30 cents 36 cents 42 cents 48 cents Constructed Response 15. Jacob has a box of cookies weighing 120 grams. Suppose there are c number of cookies in the box and each cookie weighs exactly 5 grams. Write an equation that can be used to find the number of cookies in the box.

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28

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Ordered Pairs

South Carolina Mathematics Academic Standards 6-4.1 Represent with ordered pairs of integers the location of points in a coordinate grid. Select the best answer for each question. Use this figure to answer questions 1­3.

y 10 9 8 7 6 5 4 3 2 1 O

3. Which ordered pair represents a point located inside both the triangle and the pentagon? (3, 3) (4, 8) (5, 5) (5, 7) 4. Which set of coordinates will form a square when connected? (1, 1), (1, 3), (3, 1), (3, 3) (1, 2), (4, 2), (1, 3), (4, 3) (1, 1), (4, 2), (3, 1), (3, 3) (1, 1), (2, 1), (1, 4), (2, 4) 5. Which set of coordinates will form an isosceles triangle when connected? (1, 1), (2, 5), (4, 5) (1, 1), (1, 5), (3, 1) (1, 1), (5, 1), (3, 5) (1, 1), (4, 1), (3, 4) 6. A parallelogram has vertices at (1, 1), (3, 1), and (4, 2). What are the coordinates of the fourth vertex? (2, 2) (2, 4) (1, 3) (4, 4)

Q R S

P x 1 2 3 4 5 6 7 8 9 10

1. Which point is located at the coordinates (6, 8)? Point P Point Q Point R Point S 2. Which of these ordered pairs is a vertex of the triangle? (1, 3) (5, 0) (7, 9) (9, 7)

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29

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use this figure to answer questions 7­9.

Constructed Response 10. Lily did part of her geometry homework and drew the graph below.

y

10 9 8 7 6 5 4 3 2 1 0

K

2

M J L

Q R S

1

O P

0 1

N

2

P

1 2 3 4 5 6 7 8 9 10

x

7. Which point has the greatest x-coordinate? J K L M 8. If points K, L, and J are three vertices of a parallelogram, what are the coordinates of the fourth vertex? 3 3 (__, 2__) 4 4 3 (1, 2__) 4 3 (1__, 2) 4 3 3 (2__, __) 4 4

What are the coordinates of the points she drew?

9. What are the coordinates of the vertices of isosceles triangle KOM? (0.75, 2.75), (1.5, 2.75), (1.25, 2.75) (1.5, 2.75), (1.5, 0.75), (2.25, 1.75) (1.75, 0), (0.5, 2.75), (2.5, 1.75) (2, 2.75), (2, 0.75), (2.25, 2.75)

Copyright © 2010 by Holt McDougal. All rights reserved.

30

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Coordinate Geometry

South Carolina Mathematics Academic Standards 6-4.2 Apply strategies and procedures to find the coordinates of the missing vertex of a square, rectangle, or right triangle when given the coordinates of the polygon's other vertices. Select the best answer for each question. Use the following diagram to answer questions 1­3.

y

3. A student connected point B and E together. Which third point would make this a right triangle? A C D F 4. Which set of coordinates will form a rectangle when connected? (-3, 0), (-2, -2), (-4, -2), (-3, -4) (0, 3), (3, 0), (5, 2), (5, 7) (-1, 1), (-1, 4), (-6, 4), (-6, 1) (5, 3), (5, 1), (0, 0), (0, 4) 5. Plot the points (1, 2), (2, 2), (3, 2), and (3, 3) and join them in order. What figure is formed? A triangle A square A parallelogram A trapezoid

A C E

I

B

x

H

G

F

D

1. Which set of points makes a square? A, D, G, I C, F, I, H C, G, H, I C, D, G, I 2. Which set of points makes a rectangle? A, D, G, H C, F, H, I C, G, H, I C, D, G, I

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31

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. ABCD is a square. If the three vertices are A (0, 1), B (2, 4), and C (5, 2), what are the coordinates for point D? (2, 0) (3, 0) (2, -1) (3, -1) 7. Plot these points and join them in order: (0, 2), (1.5, 4), (4, 4), and (5.5, 2). What figure is formed? A triangle A square A parallelogram A trapezoid 8. A triangle has vertices at (-1, 3) and (-3, 1). Debbie, Dante, and Sean wrote coordinates of a third vertex. Debbie: (-1, -1) Dante: (-1, 1) Sean: (-3, 3) Whose answer for the third vertex forms a right triangle? Debbie and Dante Debbie and Sean Sean and Dante Debbie, Dante, and Sean

9. Carey is given a right triangle with vertices at (2, 9), (2, 3), and (8, 3). If she translates the triangle so the first two vertices are (-2, 3) and (-2, -3), what is the correct third vertex? (-3, 4) (6, 3) (6, -3) (4, -3) Constructed Response 10. The coordinates of a right triangle are (8, y), (x, 2), and (5, 4). Give one possible set of values for x and y. Show your work.

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32

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Symmetry

South Carolina Mathematics Academic Standards 6-4.3 Generalize the relationship between line symmetry and rotational symmetry for two-dimensional shapes. Select the best answer for each question. 1. Which quadrilateral always looks the same after a 90° rotation? Rectangle Rhombus Square Parallelogram 2. Which figure does NOT show rotational symmetry? 4. Which design has rotational symmetry?

5. Which type(s) of symmetry does this hexagon have?

3. Which type of triangle always has rotational symmetry? Right Isosceles Equilateral Scalene

Line symmetry Rotational symmetry Line and rotational symmetry No symmetry 6. Which type of quadrilateral never has rotational symmetry? Rectangle Square Trapezoid Rhombus

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33

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Which quadrilateral always has four lines of symmetry? rectangle rhombus square parallelogram 8. Which figure does NOT show a line of symmetry?

10. Which design has line symmetry?

11. Which is a line of symmetry for this pentagon?

B A C D

9. How many lines of symmetry does a regular hexagon have? 0 1 3 6 Line A Line B Line C Line D Constructive Response 12. Draw four triangles, one with each type of symmetry listed below. line and rotational symmetry rotational symmetry only line symmetry only no symmetry

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34

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Line and Rotational Symmetry

South Carolina Mathematics Academic Standards 6-4.4 Construct two-dimensional shapes with line or rotational symmetry. Select the best answer for each question. 1. Which points can you connect to make a line of symmetry in this trapezoid?

B F C G D E A H

4. Which type of triangle always has three lines of symmetry? Right Isosceles Equilateral Scalene 5. Which of the squares labeled on the grid would you shade so the figure has line symmetry?

A D B C

Points B and D Points A and C Points H and F Points E and G 2. Which of these quadrilaterals has the greatest number of lines of symmetry? Rectangle Kite Square Rhombus 3. Which of the figures below have line symmetry?

A B C D

Squares B and D Square A Square D Square B 6. What is the greatest number of lines of symmetry a polygon with 14 sides can have? 14 7 2 0

All of the figures None of the figures Figure D only Figures A and D

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PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Which design does NOT look the same after a 180° rotation?

10. Which figure has exactly 4 lines of symmetry? Circle Rectangle Square Trapezoid 11. Which types of symmetry does this figure have?

8. Which of the squares would you shade so the figure has rotational symmetry?

Line symmetry Rotational symmetry Line and rotational symmetry No symmetry 12. Which figure has a 120° rotational symmetry? Equilateral Triangle Parallelogram Octagon Square Constructed Response

B D E A C

Squares B and D Square D Squares A and B Squares B, D, and E 9. How many lines of symmetry does an equilateral triangle have? 0 lines 1 line 2 lines 3 lines

13. Do all regular polygons have both rotational symmetry and line symmetry? Explain why or why not.

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36

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Identify Transformations

South Carolina Mathematics Academic Standards 6-4.5 Identify the transformation(s) used to move a polygon from one location to another in the coordinate plane. Select the best answer for each question. 1. What correctly describes this transformation?

y

3. A triangle is translated and rotated 90°. Which is a possible image?

y

1

x

2

x

4 3

Translation Translation and 90° rotation Translation and reflection over the y-axis Translation and reflection over the x-axis 2. Nisheeta wrote that the transformation was a dilation. What transformation did she miss?

Triangle 1 Triangle 2 Triangle 3 Triangle 4 4. A rectangle is translated and dilated 1 by a factor of __ . Which is a possible 2 image?

y

1

x

3

y

2 4

x

Reflection over the y-axis Reflection over the x-axis Translation Rotation of 90°

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Rectangle 1 Rectangle 2 Rectangle 3 Rectangle 4

37

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

5. Identify the transformation.

y

Use the following diagram to answer questions 7 and 8.

y

1

x

2

x

3 4

Rotation and reflection over the y-axis Translation and reflection Rotation Reflection over the y-axis 6. Yvonne has a square with length 2 and center at (1, 1). If there is a transformation and the new square has a center at (-1, -1), what is NOT a possible transformation? Rotation 180° about the origin Reflection over the x- axis and y-axis Translation Reflection over the x-axis and 180° rotation about the origin

7. Which could NOT be a possible transformation by translation? 1 2 3 4 8. Which describes the transformation for triangle 2? Rotation and translation Reflection over the y-axis and translation Reflection over the x-axis and translation Only a translation Constructed Response 9. Triangle ABC is reflected over the x-axis on a coordinate plane. The coordinates of vertex A are (-2, -4). What are the coordinates of vertex A on the reflected image?

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38

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Transformations

South Carolina Mathematics Academic Standards 6-4.6 Explain how transformations affect the location of the original polygon in the coordinate plane. Select the best answer for each question. Use the following diagram to answer questions 1­3.

y

3. For triangle 3, which transformation could not be used? Rotation Dilation Reflection Translation 4. How does a reflection affect the location of the original polygon? It changes its shape. It changes its size. It makes it a mirror image of the original. It changes its shape and size. 5. How does a dilation affect a polygon? It changes its shape. It changes its size. It makes it a mirror image of the original. It changes its shape and size. 6. Which transformation can change the area of a polygon? Rotation Dilation Reflection Translation

1 3 2

x

1. Which does NOT describe the transformation of triangle 1? Translation 4 right Reflection over the y-axis Translation 7 right and 1 left Reflection over the x-axis 2. Which correctly identifies the transformation of triangle 2? Reflection over the y-axis and translation 1 left and 1 down Reflection over the x-axis and translation 2 right and 1 down Rotation 180° about the origin Translation 3 right and 3 down

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39

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the following diagram to answer questions 7­9.

y

10. Andrea has a square. Which transformation will not affect its shape or location? Rotation 90° around the center of the square Dilation by a factor of 2 Reflection over the y-axis Translation 4 units up 11. If a trapezoid has a vertex at (8, 4) and is reflected over the y-axis, what is the new vertex of the trapezoid? (8, -4) (-8, 4) (-8, -4) (8, 4) 12. A triangle has vertices at (1, 2), (3, 4) and (-1, 2). If the triangle is translated 4 units left and 3 units down, what are the new coordinates of the vertices? (-3, 2), (0, 4), (-4, 2) (1, -1), (3, 1), (-1, -1) (-3, -1), (0, 1), (-4, -1) (5, 5), (7, 7), (3, 5) Constructed Response 13. A parallelogram's vertex (-3, 8) is translated to (6, -4). How was the parallelogram translated?

1

x

2 3

7. Which transformation of the shaded triangle has an image of triangle 1? Rotation Dilation Reflection Translation 8. Which transformation of the shaded triangle has an image of triangle 2? Rotation, dilation, and translation Reflection over y-axis, dilation, and translation Reflection over y-axis, reflection on x-axis, and dilation Dilation and rotation 9. Which transformation of the shaded triangle has an image of triangle 3? Rotation 180° Rotation 90° Reflection over x-axis Translation 4 units down

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40

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Comparing Polygons

South Carolina Mathematics Academic Standards 6-4.7 Compare the angles, side lengths, and perimeters of similar shapes. Select the best answer for each question. 1. Triangles ABC and DEF are similar. Which are corresponding sides?

B E F E A C D F D J

Use the similar quadrilaterals below to answer questions 4­6.

B C G H

-- -- AB and EF -- -- AB and BC -- -- AB and DF -- -- AB and ED 2. Triangles A and B are similar. What is x if the side that corresponds to 1.4 cm is x cm and the side that corresponds to 3 cm is 9 cm?

3 cm x A B 1.4 cm

4. Which statement shows the sides of the quadrilaterals are proportional? BC CD EB DE ___ = ___ = ___ = ___ HJ JF GH FG BC CD GH DE ___ = ___ = ___ = ___ BE HJ JF FG BC CD DE EB ___ = ___ = ___ = ___ JH JF FG GH BC GH FG EB ___ = ___ = ___ = ___ ED HJ JF CD 5. Suppose BC = 3.5 cm, GH = 2.1 cm, and FJ = 4.5 cm. What is ED? 2.7 cm 7.5 cm 4.5 cm 3.5 cm 6. What is the ratio of corresponding sides? 3.5 to 4.5 2.1 to 3.5 2.1 to 4.5 1 to 2

4.2 cm 19.3 cm

5.6 cm 2.8 cm

3. Triangles ABC and MNP are similar. AB = 7 cm, MN = 21 cm, and BC = 3 cm. What is the side length that corresponds to BE? 4 cm 9 cm 7 cm 3 cm

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41

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Two triangles are similar. The side lengths of the smaller triangle are half the side lengths of the larger triangle. The angles in the larger triangle measure 68°, 24°, and 88°. What are the angle measures of the smaller triangle? 136°, 48°, 176° 34°, 12°, 44° 68°, 24°, 88° 17°, 6°, 22° 8. Two triangles are similar. The side lengths of the larger triangle are double the corresponding side lengths of the smaller triangle. One side of the larger triangle measures 15 cm. What is the length of the corresponding side of the smaller triangle? 30 cm 15 cm 2 cm 7.5 cm 9. Which statement is NOT always true for similar triangles? Similar triangles have congruent corresponding angles. Similar triangles have the same shape. Similar triangles have the same size. Lengths of corresponding sides of similar triangles are equal.

10. Which of these statements is true? All congruent triangles are similar. All similar triangles are congruent. Similar triangles always have equal corresponding sides. Similar triangles always have the same size. 11. The ratio of the corresponding side lengths of two triangles is 4 to 3. The perimeter of the larger triangle is 48 m. What is the perimeter of the smaller triangle? 36 m 64 m 192 m 144 m Constructed Response 12. In similar shapes, will the angle measures be equal or proportional? Explain your answer.

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42

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Similar Polygons

South Carolina Mathematics Academic Standards 6-4.8 Classify shapes as similar. Select the best answer for each question. 1. The side lengths of four triangles are given. A: 6, 8, 12 B: 3, 4, 6 C: 12, 14, 16 D: 12, 9, 18 Which are similar triangles? A and B B and C A, B and C A, C, and D 2. The radius of three circles is given. A: 3 B: 3.5 C: 6 Which are similar circles? A and B B and C A and C A, B, and C 3. Andrea draws quadrilaterals ABCD and MNPQ. AB = 8 cm, MN = 12 cm, and BC = 6 cm. She wants the quadrilaterals to be similar. What should be the length of NP if it corresonds to BC? 4 cm 9 cm 6 cm 3 cm 4. Jorge is given two side lengths of an equilateral triangle. Is this enough information to determine if it is similar to another equilateral triangle he has? Yes No, he needs to know at least one angle. No, he needs to know the third side. No, he needs to know at least two angles.

5. What shapes are always similar? rectangles pentagons squares octagons

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43

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. Triangle A has side lengths 4, 5, and 6. Triangle B has side lengths of 5, 6, and 7. Triangle C has side lengths 8, 10, and 12. Which of these triangles are similar? A, B, and C A and B A and C B and C 7. The largest angle on triangle X is 80°. The largest angle on triangle Y is 80°. The largest angle on triangle Z is 160°. Which could be similar triangles? X, Y, and Z X and Y Y and Z X and Z 8. If two polygons are similar, what is true about their perimeters? The perimeters must be equal. The perimeters must be proportional. Their sides must be proportional. The perimeter of one must be a whole number multiple of the perimeter of the other.

9. The width and height of four rectangles are given. A: 3, 9 B: 2, 8 C: 18, 6 D: 2, 10 Which are similar rectangles? A and B B and C A and C A, C, and D 10. Square A has a side length of 7. Square B has a side length of 9. Square C has a side length of 14. Which are proportional? A, B, and C A and B A and C B and C 11. A pentagon has side lengths 4, 4, 6, 7, and 7. Which would NOT describe the sides of a similar pentagon? 2, 2, 3, 3.5, and 3.5 5, 5, 7, 8, and 8 8, 8, 12, 14, and 14 12, 12, 18, 21, and 21 Constructed Response 12. What types of shapes are always similar? Are there any irregular shapes that are always similar? Explain why or why not.

Copyright © 2010 by Holt McDougal. All rights reserved.

44

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ GEOMETRY

Complementary and Supplementary Angles

South Carolina Mathematics Academic Standards 6-4.9 Classify pairs of angles as either complementary or supplementary. Select the best answer for each question. 1. Which term describes angles x and y? 4. Which angles are supplementary?

x y

Vertical angles Supplementary angles Complementary angles Linear pair 2. Which angle measure is supplementary to a 34° angle? 56° 146° 180° 124° 3. Which angle measure is complementary to a 74° angle? 74° 180° 106° 16°

Angles x and y Angle x and the 129° angle Angle y and the 51° angle All of the angles combined 5. A ray divides an angle into two complementary angles. Which statement is true about the original angle? The original angle is a right angle. The original angle is a straight angle. The original angle is an obtuse angle. The original angle is an acute angle. 6. Which statement is true? Two obtuse angles can be complementary. Two acute angles can be supplementary. Two complementary angles are acute. Two complementary angles are obtuse.

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45

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Which set of angles represent complementary angles? 45° and 135° 30° and 60° 60° and 60° 35° and 65° 8. Which set of angles represent supplementary angles? 45° and 135° 30° and 60° 60° and 60 35° and 65° 9. Which statement is false? Two sets of complementary angles makes a supplementary angle. Two right angles are always supplementary. Two right angles are always complementary. If two angles are complementary, they must both be acute.

10. Which angles are NOT supplementary?

3 1 2 4 5 6 7

1 and 2 3 and 4 5 and 6 6 and 7 Constructed Response 11. Draw the following angles: 67.5°, 60°, 45° Explain how you would construct the supplementary angle for each of the angles. Give another example of how you can create the supplementary angle.

Copyright © 2010 by Holt McDougal. All rights reserved.

46

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Circle Relationships

South Carolina Mathematics Academic Standards 6-5.1 Explain the relationships among the circumference, diameter, and raidus of a circle. Select the best answer for each question. 1. Which statement is true? The circumference of a circle is twice the radius. The radius of a circle is twice the diameter. The area of a circle is twice the circumference. The diameter of a circle is twice the radius. 2. Which statement is NOT true? A circle has many diameters, but all are the same length. To find the circumference of a circle, you need to calculate the area of the circle and divide by 2. The radius is any line from the center of the circle to any point on the circle. The circumference of a circle is the distance around the circle. 3. How many degrees are in a semicircle? 360° 270° 180° 90° C E J 4. Which statement below is true? -- The length of BC is equal to the -- length of HJ. -- The length of BC is half the -- length of DE. -- The length of HC is half the -- length of DE. -- The length of DE is half the -- length of BC. -- 5. What is the length of DC? 12 in. 10 in. 8 in. 6 in. Use the following figure to answer questions 4 and 5. H D

6 in. B

Copyright © 2010 by Holt McDougal. All rights reserved.

47

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use this figure to answer questions 6 and 7.

B C A G K H J

10. Which statement is true? is the ratio of the area of a circle to the radius. is the ratio of the area of a circle to the diameter. is the ratio of the circumference of a circle to twice the radius. is the ratio of the circumference of a circle to the arc length of a sector. 11. A line is drawn across a circle in such a way that the line segment contained by the circle is the longest possible for any line drawn across the circle. Which best describes the line segment contained by the circle? Chord Radius Diameter Circumference Constructed Response 12. What is the relationship between the circumference, diameter, and radius of a circle? Use formulas to explain your answer.

F D L

E

6. Which is NOT a radius of the circle? -- AB -- AK -- CD -- AL 7. Which is a diameter of the circle? -- AB -- HJ -- CE -- KL 8. The radius of one circle is 5 centimeters. What is the diameter of a circle with a radius 3 times larger? 15 centimeters 25 centimeters 20 centimeters 30 centimeters 9. Two circles are centered on the same point, but are different sizes. One circle has a radius of 7 inches; the other has a diameter of 12 inches. How many inches larger is the radius of the larger circle? 1 inch 2 inches 4 inches 5 inches

Copyright © 2010 by Holt McDougal. All rights reserved.

48

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Circumference and Area

22 6-5.2 Apply strategies and formulas with an approximation of pi (3.14, or ___ ) to find 7 the circumference and area of a circle. Select the best answer for each question. Use 3.14 for . 1. Which is the formula for the circumference of a circle? C = d C = r 2 C = 2r 2 C=l×w 2. A circle with a radius of 5 cm is inscribed in a square. When the circle is cut out, what is the area of the square that remains? Round your answer to the nearest hundredth. 3. A playground has a circular field that is 20 ft in diameter. What is the area of the field? 31.4 ft 2 62.8 ft 2 314 ft 2 1,256 ft 2 4. Jenny sewed 157 cm of fringe around the edges of a circular table cloth. What is the diameter of the cloth? 25 cm 50 cm 75 cm 100 cm 5. The seat on a stool is a semi-circle. The straight part of the seat is 30 cm long. What is the area of the seat? 125.5 cm 2 250 cm 2 353.25 cm 2 425 cm 2 12.67 cm 2 21.50 cm 2 45.33 cm 2 78.50 cm 2 6. A hula hoop is made by bending 2.5 m of plastic into a circle. What is the diameter of the hula hoop? 0.9 m 0.5 m 0.8 m 7.9 m South Carolina Mathematics Academic Standards

=

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49

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Which statement is NOT true? The radius of a circle is half the diameter. The distance around a circle is called the circumference. All diameters go through the center of a circle. is used to calculate the area of a circle, but not the circumference. 8. The circumference of one crop circle is about 628 feet. What is the radius of the crop circle? 100 feet 200 feet 300 feet 400 feet 9. How many square centimeters of glass are needed to replace a ship's circular porthole window that measures 22 centimeters across at its widest point? 34.54 69.08 379.94 1,519.76

10. Ray is planning to fence in a circular garden. The distance from the center of the garden to the edge of the garden is 15 feet. What is the area of the garden? 94.25 square feet 225.00 square feet 706.5 square feet 756.14 square feet 11. How many feet of fencing should Ray purchase for the garden in question 10? 47.12 feet 94.25 feet 141.37 feet 188.50 feet 12. Ray put a circular fountain at the center of the garden. The fountain has a radius of 2 feet. What is the remaining area of the garden? 566.75 square feet 625.23 square feet 693.94 square feet 705.56 square feet Constructed Response 13. Debra wants to make a circular pillow case. She knows that she needs to add a half inch all the way around. She knows the pillow has a diameter of 18 inches and she will need two circles for each side of the pillow. How much fabric will she need? Show your work.

Copyright © 2010 by Holt McDougal. All rights reserved.

50

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Surface Area of Rectangular Prisms and Cylinders

South Carolina Mathematics Academic Standards 6-5.3 Generate strategies to determine the surface area of a rectangular prism and a cylinder. Select the best answer for each question. 1. What is the surface area of the cube? 3. What is the surface area of this figure made by gluing three cubes together?

84 cm 2 147 cm 2 294 cm 2 343 cm 2

2 2. Kara has 1,000 in of wrapping paper. How many of the following gift boxes can she wrap?

216 cm 2 252 cm 2 504 cm 2 648 cm 2 4. What is the surface area of a 5-footlong, 3-foot-wide, and 2-foot-deep rectangular toy chest? 31 ft 2 47 ft 2 56 ft 2 62 ft 2 5. The surface area of a cube is 150 cm 2. What is the length of one edge of the cube? 5 cm 12.25 cm 25 cm 30 cm

2 boxes 3 boxes 4 boxes 5 boxes

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51

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. A rectangular prism is 4 in. × 6 in. × 8 in. Another rectangular prism has dimensions that are twice as long. How much greater is the surface area of the second prism than the first prism? 2 times 4 times 6 times 8 times 7. What is the surface area of this cabinet?

9. Danielle has 2,000 in 2 of fabric. How many of these pillows can she cover? Use 3.14 for .

3 pillows 4 pillows 5 pillows 10 pillows 10. A can has a radius of 2.4 in. and a height of 9.5 in. What is the area, to the nearest tenth, of a label that goes all around the can? Use 3.14 for . 71.6 in 2 143.2 in 2 171.8 in 2 179.4 in 2 Constructed Response 11. A cylinder has a surface area of 150 cm 2. If it has a radius of 2 cm, what is the height of the can? Show your work.

10,060 in 2 10,160 in 2 10,360 in 2 10,760 in 2 8. A can is 4 inches tall and has a radius of 3 inches. What is the correct surface area for the area of the label? 9.42 in 2 18.85 in 2 37.70 in 2 75.36 in 2

Copyright © 2010 by Holt McDougal. All rights reserved.

52

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Estimating Perimeter and Area of Irregular Shapes

South Carolina Mathematics Academic Standards 6-5.4 Apply strategies and procedures to estimate the perimeters and areas of irregular shapes. Select the best answer for each question. 1. A square has a semicircle attached to one side. Which expression can be used to find the perimeter? 1 4s + __ r2 2 __r2 3s + 1 2 1 s2 + __ s 2 (3 + )s 2. What is a good estimate of the area of a stop sign that is 18 inches tall? 324 square inches 300 square inches 250 square inches 200 square inches 3. What is a good estimate of the perimeter of a stop sign that is 18 inches tall? 144 inches 100 inches 72 inches 24 inches 4. What is a reasonable estimate for the area of the shape?

12 square units 10 square units 6 square units 4 square units 5. What is a reasonable estimate for the perimeter of this shape?

16 units 18 units 20 units 22 units

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53

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the following diagram for the questions 6 and 7.

12 feet

8. Estimate the area of the shape.

18 feet

6. Janice's living room makes an L-shape with a bay window on one end. What is a good estimate for the perimeter of the room? 60 feet 50 feet 40 feet 35 feet 7. What is a reasonable estimate for the area of the room? 216 square feet 162 square feet 108 square feet 54 square feet

14 12 10 8 Constructive Response 9. A polygon has vertices A(1, 2), B(4, 4), C(-1, 3), D(-2, -2), and E(4, -2). Estimate its area and perimeter. Show your work.

Copyright © 2010 by Holt McDougal. All rights reserved.

54

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Perimeter and Area of Irregular Figures

South Carolina Mathematics Academic Standards 6-5.5 Apply strategies and procedures of combining and subdividing to find the perimeters and areas of irregular shapes. Select the best answer for each question. 1. What is the area of the figure shown?

5

3. What is the perimeter of this shape?

2

3

8

8 ft 8 ft 6 ft 16 ft

4

70 ft 2 88 ft 2 104 ft 2 176 ft 2 2. What is the area of the figure shown?

10 cm 6 cm

22 24 26 30 4. A semi-circle has a radius of 4 in. If the flat side is attached to a square, what is the area of the figure? 41 in 2 66 in 2 89 in 2 114 in 2

4 cm 4 cm 20 cm

68 cm 2 132 cm 2 140 cm 2 280 cm 2

Copyright © 2010 by Holt McDougal. All rights reserved.

55

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the following diagram of Stanley's yard to answer questions 5 and 6.

96 ft

64 ft 116 ft 66 ft

8. Samuel is asked to measure the outerperimeter of the school track. The inside of the track is formed by a 100 yard by 60 yard rectangle with a semicircle on each end. The track is 4 yards wide. What is the best way for him to start? Find the circumference of each end using 60 yards as the diameter. Find the circumference of each end using 64 yards as the diameter. Find the circumference of each end using 68 yards as the diameter. Add two lengths of 100 yards to find the length. Constructed Response

5. Find the area of Stanley's yard. 4224 ft2 7704 ft2 10,368 ft2 11,136 ft2 6. Find the perimeter of Stanley's yard. 342 ft 360 ft 394 ft 424 ft 7. Julia wants to find the area of the shape. What subdivisions would make calculating the area the easiest?

9. Sanjay is given a regular octagon. Explain how he could find the area by subdividing.

Copyright © 2010 by Holt McDougal. All rights reserved.

56

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Proportions

South Carolina Mathematics Academic Standards 6-5.6 Use proportions to determine unit rates. Select the best answer for each question. 1. Stephanie bought 5 bananas for $1.25. What is the unit cost for 1 banana? $0.06 $0.25 $0.40 $6.25 2. Trevor reads 6 pages of a novel in 18 minutes. How long would it take him to read 150 pages? 30 minutes 50 minutes 300 minutes 450 minutes 3. Oranges are on sale at $2 for 5 oranges. How much will 8 oranges cost? $1.25 $3.20 $4 $5.20 4. Finest Foods sells 3 pounds of figs for $7.80. There are about 5 figs in each pound. What is the unit rate for 1 pound of figs? $1.56 $0.52 $2.60 $23.40 5. A catering company offers dinner selections that include fish and beef. From experience, the caterers know that fish dinners and beef dinners will 2 be ordered in a ratio close to __ . At 5 one dinner, 156 people ordered fish and 375 people ordered beef. Were the dinners ordered in the expected ratio? Yes. No, they would have expected 380 beef dinners. No, they would have expected 390 beef dinners. No, they would have expected 404 beef dinners.

Copyright © 2010 by Holt McDougal. All rights reserved.

57

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

6. A delivery truck can travel 240 miles on 30 gallons of gas. At that rate, how far could the truck travel on 136.5 gallons of gas? 1,092 miles 1,536 miles 4,095 miles 32,760 miles 7. The scale on a map states that 2 inches = 15 miles. What is the distance shown on the map for two towns that are 82.5 miles apart? 11 inches 17 inches 165 inches 618.75 inches 8. A dozen eggs costs $2.60. What is the value of a single egg? $0.13 $0.22 $0.24 $0.25 9. Sara used her cell phone for 1.4 hours. What is the minute rate if she paid $26? $18.57 $0.31 $84.00 $0.05

10. Yvette makes $75 in an 6 hour day. Which is a correct expression that describes Maria's hourly rate? $75 ÷ 6 $75 × 6 6 ÷ $75 6 × $75 11. The unit rate is calculated by: Multiplying the number of units by the total amount. Dividing the number of units by the total amount. Multiplying the total amount by the number of units. Dividing the total amount by the number of units. Constructed Response 12. Jamie pays a membership fee to her local gym. She spends 3.5 hours a week there and it costs $50 a month. How much does the membership cost per hour? Assume there are exactly four weeks in a month.

Copyright © 2010 by Holt McDougal. All rights reserved.

58

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ MEASUREMENT

Scale

South Carolina Mathematics Academic Standards 6-5.7 Use a scale to determine distance. Select the best answer for each question. 1. On the map of a state park, the distance between the cave entrance and the observation tower is 4 inches. If the map scale is 1 in. = 80 yd, what is the actual distance between the cave entrance and the tower? 20 yd 40 yd 84 yd 320 yd 2. The scale on a map is 2 in. = 15 mi. If two cities are 75 mi apart, how far apart will they appear on the map? 2.5 in. 5 in. 10 in. 37.5 in. 3. How far will Alex travel from home to school if he stops at the library on his way? 4. The scale factor for a model ship is 3 in. = 20 ft. If the length of the ship is 150 ft, what is the length of the model? 7.5 in. 50 in. 22.5 in. 1000 in. 5. The scale factor for a model plane is 2 in. = 25 ft. If the length of the model is 8 in., how long is the plane? 100 in. 8 ft 80 ft 100 ft 6. Jorge caught a fish 9 inches long and made this scale drawing of it. What scale did he use?

1 centimeter = 0.67 inch 1 centimeter = 1.5 inches 1 inch = 1.5 centimeters 1 inch = 3 centimeters 1.8 mi 9 mi 4.5 mi 3.5 mi

Copyright © 2010 by Holt McDougal. All rights reserved.

59

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. Alicia used the scale 1 inch = 1 foot to make a scale drawing of her 3 bedroom. She drew her dresser 1 __ 4 1 inches × 3 __ inches. What are the 2 actual dimensions of her dresser? 3 1 12 __ inches × 36 __ inches 4 2 3 1 13 __ inches × 15 __ inches 4 2 21 inches × 42 inches 30 inches × 56 inches 8. Kari wants to make a scale drawing of her family on a sheet of paper 11 inches long. Kari's father is 6.25 feet tall and is the tallest family member. Which scale could Kari use for her drawing? 1 inch = 0.5 foot 2 inches = 1 foot 3 inches = 2 feet 4 inches = 1.5 feet 9. The scale 1 inch = 6 feet was used to draw the plans for a house. If the drawing is 10.5 inches wide, how wide is the house? 10.5 feet 17.5 feet 60.5 feet 63.0 feet 10. On a map, the distance from your house to school is 3.6 inches. If the scale of the map is 1 inch = 5 miles, what is the actual distance in miles from your house to school? 1.0 mile 3.6 miles 5.0 miles 18.0 miles 60

11. The scale on a map of California is 3 inches = 40 miles. Which of the cities listed in the table is about 9 inches from Los Angeles on the map? Distance from Los Angeles (in miles) 327 127 387 91

City Monterey San Diego San Francisco Santa Barbara

Monterey San Diego San Francisco Santa Barbara 12. Jermaine found that a Tyrannosaurus Rex could be 20 feet tall and 49 feet long. If he wants to make a scale drawing of this dinosaur using the scale 2 inches = 5 feet, which of these size sheets of paper could he use for his drawing? 3 inches × 11 inches 5 inches × 8 inches 6 inches × 9 inches 7 inches × 12 inches Constructed Response 13. Mr. Quick made a 3 centimeter by 4 centimeter scale drawing of a rectangular dog pen. If he used the scale 1 centimeter = 6 feet, what is the actual perimeter of the pen? Show your work.

Copyright © 2010 by Holt McDougal. All rights reserved.

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ DATA ANALYSIS AND PROBABILITY

Using Sample Data

South Carolina Mathematics Academic Standards 6-6.1 Predict the characteristics of one population based on the analysis of sample data. Select the best answer for each question. 1. Dante bought 1 pound of jelly beans. He wanted to know what percentage of the jelly beans are red, so he took 4 ounces of the jelly beans and sorted them. The red jelly beans weighed 1 ounce. According to the sample, what percentage of the jelly beans are red? 50% 25% 17% 6% Use the following information to answer questions 2 and 3. A researcher polled 588 people to find out who they were voting for in the upcoming election. Candidate Carey Daniels Sanchez Wong Supporters 66 28 422 72 3. Suppose that Carey won the election. Which is NOT a likely reason the poll was inaccurate? The sample was taken on the street outside Sanchez's election headquarters. The sample was taken only one day before the election. The sample was taken from an online poll on a Spanish website. The sample was taken right after Sanchez made a speech to the media. 4. Which of the following statistics would be taken from a sample instead of the entire population? The average age in Mrs. Tan's grade six class is 12.6 years old. The average lifespan of a bee is 50 days. The average height of the men on the ping pong team is 5 feet 6 inches. The average time students in Mr. Douglas's class spend commuting to school is 15 minutes.

2. If 50,000 people vote in the election, what is the most likely number of people who will vote for Wong? 6,977 6,122 5,612 72

Copyright © 2010 by Holt McDougal. All rights reserved.

61

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the following information to answer questions 5 and 6. Mrs. Hudson sampled her grade 6 class for eye color. Eye Color Black Brown Blue Green Number of Students 7 15 6 2

7. A manufacturer makes 1,040,000 balloons. They test 200 and find that 32 have a hole in them. Approximately how many balloons of the total are likely to have holes? 32 163 166,368 166,400 8. Which poll is most likely an unbiased sample? A teacher asks all grade 6 students at her school their opinion on math. A researcher asks everyone in a foodcourt at noon their opinion of the taste of the food at the foodcourt. A political candidate calls every 100th person in the phone book to find out who they are voting for. A football coach finds the average age of his players. Constructed Response 9. If 40,000 people vote in the coming election, which is the likely number of votes each candidate will get, based on the sample results below? Poll Results Lawler 49

5. If the school has 800 students, how many would be expected to have black eyes, according to the sample? 160 184 243 400 6. Mrs. Hudson's class polled the entire school and found out that 200 students have blue eyes. How close is the sample to the actual results? There are 40 more students than expected. There are 40 less students than expected. There are 16 more students than expected. There are 16 less students than expected.

Ali 45

Zhang 55

Copyright © 2010 by Holt McDougal. All rights reserved.

62

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ DATA ANALYSIS AND PROBABILITY

Frequency Tables, Histograms, and Stem-and-Leaf Plots

South Carolina Mathematics Academic Standards 6-6.2 Organize data in frequency tables, histograms, or stem-and-leaf plots as appropriate. Select the best answer for each question. 1. The basketball coach recorded the ages of the players in a frequency table. How many players are older than 13? Age (years) Number of players 4 5 9 16 2. Which of the following sets of data would best be displayed on a stem-and-leaf plot? The population of the United States from 1900 to 2000. The population of the United States, by age. The results of a favorite United States survey. The ages at election of the first 30 United States presidents. 10 6 11 5 12 4 13 7 14 4 15 5 3. The quiz scores for Ms. Anderson's math classed are shown below. 65, 74, 88, 66, 90, 85, 78, 90, 99, 85, 100, 77, 82, 83, 99, 100, 99, 85, 100, 77 Ms. Anderson wants to display the quiz scores to her students so that they can see all the individual scores in an organized way. Which type of display is the best choice? Bar Graph Frequency Table Histogram Stem-and-Leaf Plot 4. The table below shows how many students read during the summer. Number of Books Read 0 1 2 3 4 5 6 Number of Students 2 3 5 2 4 3 2

Which interval would be most appropriate for making a histogram of this data? 0-4, 5-6 0-3, 3-6 0-2, 3-4, 5-6 0-1, 2-3, 4-7

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63

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the following graph to answer questions 5 and 6. Jed's Homework Time Stem Leaf 4 3577 5 2333489 6 014577 Key: 4 | 2 means 42 minutes 5. What are the leaves if the stem is 5? 3577 46 2333489 014577 6. The leaf 4 appears in which stems? 3577 5 6 56 Use the following information to answer questions 7 and 8. Tim, Ann, Beth, and Zak went bowling. The following chart shows their scores for the first five frames. Tim 9 5 6 3 9 Ann 8 8 8 8 8 Beth 7 8 9 8 7 Zak 6 6 8 9 9

7. If the data were represented in a frequency table, what would the frequency of a score of 9 be? 4 5 6 7 8. If the data were arranged into a histogram, which score would have the tallest bar? 6 7 8 9 Constructed Response 9. Levi runs every day. He keeps track of the time in minutes he spends running the same course. The following are his results: 15, 21, 22, 23, 18, 18, 16, 18, 21, 24 Construct a stem-and-leaf plot to show his times.

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64

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ DATA ANALYSIS AND PROBABILITY

Measures of Central Tendency

South Carolina Mathematics Academic Standards 6-6.3 Analyze which measure of central tendency (mean, median, or mode) is the most appropriate for a given purpose. Select the best answer for each question. Use the following information to answer questions 1­4. Haddox Fisheries Job Annual Salary President $425,000 Vice-President $210,000 Vice-President $210,000 Manager $50,000 Operator $41,000 Operator $39,000 Operator $37,000 Operator $35,000 Secretary $33,000 Mean: Median: Mode: $120,000 $41,000 $210,000 2. What is a disadvantage of using the mean to represent the employees' wages? No one makes $41,000. No one makes $210,000. More than half the employees make $50,000 or less. The president makes more than three times the mean. 3. What is a disadvantage of using the mode to represent the employees' wages? Only two employees make that amount. It does not incorporate the top and bottom data. It only counts frequency and not range. The mode has no disadvantage to represent this data. 4. What is a disadvantage of using the median to represent the employees' wages? Only one employee makes $41,000. The president's wage is over 10 times the median. It is too close to the smallest annual wage. The median has no disadvantage to represent this data.

1. Which measure of central tendency would be the most appropriate measurement? Mean Mode Median They are all equally appropriate measures of central tendency.

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65

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

5. The table below show Tom's scores for four tests. Test 1 2 3 4 Score 70 75 80 85

7. Which is the LEAST appropriate measure of central tendency for Class 2? Mode Mean Median They are all equally appropriate of central tendency. 8. Which measure of central tendency has the closest value between the two classes? Mode Mean Median They are all equally close in value. Constructed Response 9. The bowlers on the Aces team have averages of 200, 210, 220, and 230. The first three bowlers on the Dukes team have averages of 205, 215, and 225. Which is the best measure of central tendency for each team? Explain your answer.

What is the most appropriate measure of central tendency for this data? Mode Median Mean Median and mean Use the following test scores for questions 6­8. Class 1 Scores Class 2 Leaf 33579 0 2344

Leaf Stem 653 7 9775 8 620 9 Key: 7 | 3 means 73

6. Which is the LEAST appropriate measure of central tendency for Class 1? Mode Mean Median They are all equally appropriate of central tendency.

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66

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ DATA ANALYSIS AND PROBABILITY

Theoretical Probability

South Carolina Mathematics Academic Standards 6-6.4 Use theoretical probability to determine the sample space and probability for one- and two-stage events such as tree diagrams, models, lists, charts, and pictures. Select the best answer for each question. 1. What is the probability of getting a six when rolling a fair number cube one time? 12.5% 16.7% 20% 25% 2. What is the probability of getting two heads when two fair coins are tossed? 12.5% 25% 37.5% 50% 3. If two fair coins are tossed, which has the greatest probability? Getting one head and one tail Getting two heads Getting two tails All have the same probability. 4. A coin is flipped 12 times. Which experimental outcome is most consistent with theoretical probabilities? Two heads and ten tails Four heads and eight tails Six heads and six tails Eight heads and four tails 5. What is the theoretical probability of having four girls in a row in one family? (Assume boys and girls are equally likely.) 1 ___ 32 1 ___ 16 1 __ 8 1 __ 2 6. If a fair coin lands on heads four times in a row, what is the theoretical probability that the next toss will also land on heads? 1 ___ 32 1 ___ 16 1 __ 8 1 __ 2

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67

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

7. What is the sample space for the experiment consisting of tossing a single coin? {heads} {heads, tails} {tails} {heads, heads, tails, tails} 8. What is the sample space for the experiment consisting of rolling a standard number cube? {2, 4, 6} {1, 2, 3} {1, 2, 3, 4, 5, 6} {all real numbers} 9. Which answer could NOT be a sample space for an experiment consisting of drawing one card from a standard deck? {black card, red card} {ace, two, three ... queen, king} {heart, diamond, club, spade} {suit, number, picture card} 10. Which answer could NOT be a sample space for an experiment consisting of tossing two coins? {0 heads, 1 head, 2 heads} {HH, HT, TH, TT} {heads, tails} {2 tails, 1 tail, 0 tails}

11. How many possible outcomes are in the sample space for rolling a pair of number cubes? 6 12 36 72 12. What is the sample space for drawing two marbles from a bag of red (R) and green (G) marbles? {R, G, R, G} {R, G} {R, R, G, G} {RR, RG, GR, GG} 13. Which of these events has a probability of 0? Drawing a green marble from a bag containing three red marbles A fair coin landing on tails A number cube landing on three Two number cubes landing with a sum of 12 on the faces Constructed Response 14. A bag contains one red marble and one green marble. You pick a red marble and you put it back. Draw a tree diagram for the experiment of drawing a marble three times.

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68

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________ DATA ANALYSIS AND PROBABILITY

Probability of Complementary Events

South Carolina Mathematics Academic Standards 6-6.5 Apply procedures to calculate the probability of complementary events. Select the best answer for each question. 1. Which events are complementary? Rolling a number greater than four or less than four. Flipping heads twice in a row. Flipping either heads or tails. Rolling a die and getting either two or four 2. David wants to roll either a three or a four on a fair number cube. What is the likelihood that the complement will occur? 17% 33% 50% 67% 3. The probability of an event is 0.72. What is the likelihood of the complementary event? 1 0.72 0.28 0.14 4. The Eagles are a football team. If they reach the playoffs, their rival team, the Falcons, will not. If these are complementary events and the Eagles have a 54% chance of going to the playoffs, what is the sum of the probabilities of both events? 1 0.54 0.46 0.08 5. Anand tossed a fair coin a number of times. He got heads on seven of the tosses. Which is most likely the total number of times he tossed the coin? 7 14 18 21 6. What is the probability of rolling a fair number cube and getting a six and then rolling it again and getting a three? 1 ___ 36 1 ___ 18 1 ___ 12 1 __ 9

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69

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the following information to answer questions 7 and 8. A jar contains six quarters, five dimes, seven nickels, and ten pennies. 7. Which correctly describes the complement to drawing a penny? drawing a penny drawing a nickel or a quarter. drawing a nickel, a dime, or a quarter. drawing a penny, a nickel, a dime, or a quarter. 8. Janice wants to draw either a nickel or a quarter. What is the probability of the complementary event occuring? 18% 36% 46% 54% 9. What is the theoretical probability of having three girls and one boy in any order in one family? 1 ___ 32 1 ___ 16 1 __ 8 1 __ 2

10. If a family has four girls in a row, what is the theoretical probability that the next child will also be a girl? 1 ___ 32 1 ___ 16 1 __ 8 1 __ 2 11. Cheryl tossed a coin several times. She got tails on 11 of the tosses. What is the best estimate of the total number of times she tossed the coin? 7 12 18 21 Constructed Response 12. Define complementary events. Use the example of a coin toss.

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70

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

PASS PRACTICE TEST A

Select the best answer for each question. 1. Which is the correct representation of 60% in fraction form? 1 ___ 60 1 ___ 16 3 __ 5 60 ___ 1 2. What is 44% of 95,628? 4,207.632 42,076.32 420,763.2 4,207,632 3. Which set of numbers are all integers? 3, 4, 5.5 3, 4, -4 1 1 1 __, __, __ 2 3 4 3, , 4 4. Which statement is correct? 0.45 = 450% 1 __ 30% 3 4 ___ 1/3 10 5. June starts a mathematical statement: 8 ___ > ___. Which answer makes this 10 statement correct? 80% 0.75 85% 0.80 5 2 6. What is __ × __ ? 3 8 5 ___ 12 4 __ 3 15 ___ 16 6 __ 5 7. Add. 1 1 17 __ + 6 __ = 3 4

1 19 __ 2 1 20 __ 3 7 23 ___ 12 24

40% < 0.4

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71

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

5 2 8. What is __ of __ ? 3 8 5 ___ 12 4 __ 3 15 ___ 16 6 __ 5 9. The ratio 16 with which ratio? 25 ____ 100 20 ___ 64 34 ___ 70 16 ___ 25 5 ___ would form a proportion

12. What is the value of 5 4? 5 25 175 625 13. What factor is missing from this factor tree? 64 8 4×2 × × 4×2

2×2×2×2×2×2 2 4 8 12 14. Identify the best rule for this pattern. 4, 8, 16, 32, 64 The numbers are increasing by 4. The numbers are increasing by 8. The numbers are doubling. The numbers are being squared. 15. Which number pattern matches the following rule? The numbers are decreasing by 4. 20, 16, 12, 8 23, 19, 16, 12 30, 24, 18, 12 32, 28, 16, 8

10. The ratio of the corresponding side lengths of two triangles is 5 to 3. The perimeter of the larger triangle is 48 m. What is the perimeter of the smaller triangle? 28.8 m 64 m 192 m 144 m 11. David divides one million by one hundred. What is his answer in exponential form? 10 3 10 4 10 5 106

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72

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

16. Use the order of operations to find the value of the expression. 16 + 5 · 6 - 4 6 15 42 122 17. Melanie evaluated the expression 2 · 3 + 5 · 2 and got 22. Explain where she made her error. She added 3 and 5 first, then multiplied. She added 5 to the product of 2 and 3 before multiplying. She multiplied all four numbers together. She did nothing wrong; the answer is correct. 18. Which expression is a rule for the pattern below? 2, 7, 12, 17, ... 2x + 5 3x - 1 4x + 3 5x - 3

19. Alberta needs 18 hours of training to be a basketball coach. She has already completed 6 hours. Which expression shows the total number of training hours Alberta needs to complete to become a coach? 18 + h 18 - h h - 18 h ÷ 18 20. Which is an example of the Distributive Property? a+b=b+a a + (b + c) = (a + b) + c a(b + c) = a · b + a · c a·1=a 21. Which is an example of the Associative Property? a+b=b+a a + (b + c) = (a + b) + c a(b + c) = a · b + a · c a·1=a

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73

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

22. Which situation can be modeled by the equation 1.5s = 80? A fax machine sends 80 pages in 1 hour. How many pages can it send in 1.5 hours? After dishing out 1.5 pounds of beans from a bin, 80 pounds of beans remain. How many pounds did the bin originally contain? A hummingbird travels 1.5 miles in 80 seconds. At what speed is the bird flying? Ted has 80 kilograms of granola bars with which to make 1.5kilogram boxes. How many boxes of granola bars can Ted put together? 23. Which is an example of the Commutative Property? a+b=b+a a + (b + c) = (a + b) + c a(b + c) = a · b + a · c a·1=a 24. Jessie wants to solve the equation 4x = 112. What step should she take first? Add 4 to both sides. Subtract 4 from both sides. Multiply 4 to both sides. Divide both sides by 4.

25. Ursula is at the grocery store and sees the following:

Ursula wants to know the price, x, per orange if she buys a dozen. She uses the following equation. 12x = $3.60 What is the value of x? 30 cents 36 cents 42 cents 48 cents 26. What is the solution to n - 14 = 325? 304 310 339 353

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74

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the figure below to answer questions 27­29.

y 4 3 2 1 K R X H 1 T 3 4 M x

30. Three vertices of a square are given as (4, 0), (4, 2), and (6, 0). What is the fourth vertex? (6, 2) (4, 6) (6, 4) (2, 4) 31. Find the surface area of the prism.

E

24 23 22 21 O P 22 23 S 24

27. What point is located at (3, 4)? R K P M 28. Which of these points is a vertex of the quadrilateral? R E H S 29. Which of these points is inside the triangle? (-1, -2) (3, 2) (2, 4) (2, 3) 13 cm 2 40 cm 2 76 cm 2 200 cm 2 32. The table below shows Vijay's scores for four tests. Test 1 2 3 4 Score 75 77.5 80 95

What is his mean test score? 80 81.875 85 90.5

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75

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

33. A regular pentagon has which of the following? Line symmetry Rotational symmetry Line and rotational symmetry Neither line nor rotational symmetry 34. Which shape always has line and rotational symmetry? circle rectangle pentagon hexagon 35. How could one triangle in the figure have been transformed to result in the other triangle?

36. How does a dilation affect the original polygon? It makes it bigger. It makes it smaller. It makes it either bigger or smaller. It changes its orientation. 37. Rectangle A is 3.4 feet by 8.5 feet. Rectangle B is similar to rectangle A. Which could be the dimensions of rectangle B? 2 feet by 4 feet 2 feet by 4.5 feet 2.5 feet by 4 feet 2 feet by 5 feet 38. Triangle A has side lengths 4, 5, and 7. Triangle B has side lengths 8, 10, and 13. Triangle C has side lengths 10, 8, and 14. Which statement is true? Triangles A and B are similar. Triangles A and C are similar. Triangles A and B are similar. None of the triangles are similar. 39. Angle A has a measure of 44°. Angle B has a measure of 6°. Which statement is true? Angles A and B are complementary angles. Angles A and B are supplementary angles. Angles A and B are neither complementary nor supplementary. Angles A and B make a straight angle.

y

x

Rotated and translated Reflected over the y-axis and translated Reflected over the x-axis and translated Rotated and reflected over the yaxis

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76

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

40. What is the definion of supplementary angles? Two angles with measures that add to 90° Two angles with measures that add to 180° Angles with measures that add to 90° Angles with measures that add to 180° 41. What is the surface area of the cube to the nearest hundredth?

Use the stem-and-leaf plot below to answer questions 43 and 44. Jed's Homework Time Stem Leaf 4 3577 5 2333489 6 012577 Key: 4 | 2 means 42 minutes 43. How many times did Jed spend more than an hour doing homework? 4 5 6 7

8.25 m 2 12.67 m 2 20.00 m 2 108.38 m 2 42. Which expresion correctly relates the circumference to the diameter? d=·c d=÷c d=c÷ d = c ÷ 2

44. What is Jed's most common amount of time spent on homework (in minutes)? 47 minutes 53 minutes 59 minutes 67 minutes 45. What is the mean of the set of data? 4, 6, 6, 7, 9, 11, 15, 20, 21 9 10 11 14

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77

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

46. Which line segment identifies the radius of the circle below? C A D E -- CD -- CB -- EF -- AB 47. Lisa uses a compass to draw a circle with a radius of 3 centimeters. She uses a piece of string to measure the circumference to the nearest tenth of a centimeter. She finds that the circumference is 18.85 centimeters. What is the ratio of the circumference to the diameter rounded to the nearest hundredth? 2.09 centimeters 3.14 centimeters 6.28 centimeters 56.55 centimeters B F

48. The formula for the area of a circle is: A = 2r 4 A = __ r 3 3 A = 2r A = r 2 49. Estimate the area of the irregular shape.

14 square units 16 square units 18 square units 20 square units 50. What is the perimeter of this shape?

12 + units 14 + units 16 + units 18 + units

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78

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

51. Denise bought 12 gallons of gasoline for her car. It cost $41.40. What is the unit price? $0.29 $3.45 $29.40 $496.80 52. Raoul wants to buy some candy. Chocolate covered peanuts cost $6 for 450 g and candied nuts cost $4 for 230 g. Which is the better price? Chocolate covered peanuts Candied nuts Both are the same price. It cannot be determined because he is buying different amounts. 53. Bryce knows Panther Mountain is 412 m away from him. On the map, it is represented as 3 cm. What is the scale of the map? 133 cm : 1 m 1 cm : 133 m 1,200 cm : 1 m 1 cm : 1,200 m 54. Joanne is looking at a map of California. What is the most reasonable estimate of the distance on the map between San Fransciso and Los Angeles? 15 mm 15 cm 15 m 15 km

55. At each basketball practice, the assistant coach records how many times each player tries a free throw and how many times the free throw is made. Which player has the highest percent of free throws made? Player Tiffany Shelly Sarah Adrienne Free Throws Free Throws Made Tried 35 50 25 35 48 60 10 15

Tiffany Shelly Sarah Adrienne 56. Andrea has a bag full of colored balls. In the bag are 4 blue, 3 red and 2 green balls. What is the sample space if she draws one ball? {R, G, B} {B,B,B,B,R,R,R,G,G} {GRB,GBR,RGB,RBG,BGR,BRG} {BBBB, RRR, GG} 57. Ron wants to get heads in a coin toss. What is the probability of the complementary event happening? 50% 25% 100% 75%

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79

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

58. Which question cannot be answered by collecting data? What is the most popular style of hair? What is the average size of ants? Will it snow on January 4, 2082? Which baseball player has the highest batting average? 59. Heather has five sisters. What is the theoretical probability her next sibling will be a boy? 1 __ 2 1 __ 6 1 __ 3 1 ___ 49 60. If Thomas wants to toss a coin and get 8 heads, theoretically, how many times will he need to toss it? 8 16 32 48

Constructed Response 1 61. Frank's backyard is a total of 57 __ 4 square meters. 1 Frank has cut __ of the grass in his 3 backyard. How many square meters has he cut? Express the size of Frank's backyard as a decimal. 62. Plot the points A(-1, 3), B(-1, 7), and C(4, 3) and join them in order.What kind of triangle did you make?

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80

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

PASS PRACTICE TEST B

Select the best answer for each question. 1. How many outcomes are in the sample space for drawing a card from a standard deck? 56 26 52 104 2. Subtract. 7 3 7 __ 8 1 8 __ 4 1 10 __ 6 3. Which figure does NOT have line symmetry? 6. This is the route Ian takes to get home from baseball practice. How much farther would Ian have to travel if he wanted to visit his friend Bill before going home? 4. What is the value of 4 3 ÷ 12? 4 5.33 12 24.5 5. What is the mode of this set of data? 1, 3, 5, 6, 7, 9, 10, 12, 13 7 7.33 9 This set of data has no mode.

1 1 31 __ - 24 __ = 2 8

1.5 miles 2.5 miles 5.5 miles 8 miles

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81

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

3 1 7. How many __ s are in 17 __ ? 8 4 50 75 3 100 __ 4 142 8. Which expression below is equal to this expression? 4-7×3÷6 (4 - 7 × 3) ÷ 6 4 - (7 × 3) ÷ 6 4 - 7 × (3 ÷ 6) (4 - 7) × 3 ÷ 6 9. Anderson got 45 out of 50 questions on the math test correct. What is his score expressed as a percent? 80% 85% 90% 95% 10. Which number has exactly four different prime factors? 12 90 756 1050 11. A circular flower bed in the park has a diameter of 20 ft. What is the area of the field? Use 3.14 for . 31.4 ft 2 62.8 ft 2 314 ft 2 1256 ft 2

12. The cost C in dollars for mixed nuts varies directly with the weight w in ounces. w (oz) C ($) 0 0 3 5.00 6 9

10.00 15.00

Which equation relates C and w? C = 1.67w w = 3.00C C = 6.00w w = 1.50C 13. A quadrilateral has sides of 1.2 cm, 4.5 cm, 3.8 cm, and 7.9 cm. Which are the dimensions of a similar quadrilateral? 1.2 cm, 9 cm, 3.8 cm, 15.8 cm 2.4 cm, 9 cm, 11.4 cm, 23.7 cm 2.4 cm, 9 cm, 7.6 cm, 15.8 cm 12 cm, 38 cm, 90 cm, 79 cm 14. Which number is missing from the sequence? 1, ___, 39, 117, 1521, 4563, ... 2 3 4 5

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82

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

15. A can has a diameter of 4 in. and a height of 11 in. What is the area, to the nearest tenth, of a label that goes around the can? Use 3.14 for . 64.9 in.2 138.2 in.2 231.8 in.2 300.5 in.2 16. Kelly rolled a number cube and got 3 five times in a row. Based on her results, what is the probability of rolling a 3? 100% 16.7% 50% 30% 17. What is the median of this set of data? 12, 12, 15, 16, 17, 20, 20, 27, 30 2 17 20 30 18. Which of the following ratios are NOT in proportion? 15 2 __ and ___ 5 18 6 24 ___ and ___ 15 60 60 12 ___ and ____ 25 125 9 27 ___ and ___ 25 75

19. Calculate the surface area of the prism.

30 cm 2 45 cm 2 135 cm 2 177 cm 2 20. Which of the following is false? - 2 __ = 0.66 3 6 7 __ < __ 7 6 4 4 __ > __ 5 6 7 7 __ < __ 2 3 21. A rectangle has vertices at (1, 1), (4, 1) and (4, 3). What are the coordinates of the fourth vertex? (2, 2) (2, 4) (1, 3) (4, 4) 22. Students raised money for a charity by holding a walk-a-thon. The amount of money raised varied directly with the distance walked, in miles. Shane raised $35.00 by walking 7 miles. How much would he have raised by walking 15 miles? $22.50 $41.75 $50.00 $75.00

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83

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

23. What number is missing from the prime factorization? 24 × 14 7 4 12 24. Jamie bought 4 oranges for $1.60. What is the unit cost for one orange? $0.06 $0.25 $0.40 $6.40 = 112

27. Amanda wants to decorate the edges of a circular table cloth. The diameter of the cloth is 60 cm. How many centimeters of fringe does she need? Use 3.14 for . 94.2 cm 188.4 cm 2826 cm 11304 cm 28. Multiply.

1 1 11 __ × 9 __ 3 2

25. Which angles are NOT examples of supplementary angles?

2 99 __ 3 2 107 __ 3 125 1 140 __ 3 29. A catering company offers dinner selections that include chicken and pasta. From experience, the caterers know that chicken dinners and pasta dinners will be ordered in a ratio close to 3:1. At one dinner, 250 people ordered pasta and 750 people ordered chicken. Were the dinners ordered in the expected ratio? Yes. No, they would have expected 700 chicken dinners. No, they would have expected 825 chicken dinners. No, they would have expected 900 chicken dinners.

2 and 3 1 and 2 1 and 3 1 and 4 26. Which is the measure of an angle that is supplementary to angle y?

123° 90° 57° 39°

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84

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

30. Which is the best estimate for the area of this shape?

32. Edgar is training for a race. On June 14, he ran for 20 minutes. Every day he runs for 3 more minutes than he did on the previous day. How many minutes will Edgar run on June 22? Day June 14 June 15 June 16 June 17 June 18 ... June 22 35 minutes 38 minutes 41 minutes 44 minutes 33. Which expression gives a rule for s in terms of r in the table below? Time (min.) 20 23 26 29 32 ... ?

11 square units 13 square units 15 square units 17 square units 31. What is the surface area of the prism?

84 cm 2 150 cm 2 228 cm 2 400 cm 2

r 6 9 15 6r - 17 6s + 15 7r + 3 7r ÷ 4

s 19 37 73

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85

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

-- 34. How long is side EF ?

37. Insert parentheses to make this number sentence true. 20 ÷ 5 × 2 + 3 = 5 (20 ÷ 5) × 2 + 3 = 5 20 ÷ (5 × 2) + 3 = 5 20 ÷ 5 × (2 + 3) = 5 20 ÷ (5 × 2 + 3) = 5

2 cm 2.4 cm 3 cm 6 cm 35. A brand of sticky notepaper comes in yellow, pink, or blue. It is offered in 3 sizes ­ mini, standard, or wide. It is also offered in three different package sizes. How many different packages are available? 6 9 11 18 36. Which is a factor of 115? 2 15 23 25

38. Jeremy wants to prove that 3(4 + 5) = 12 + 15. Which property proves this? Associative Commutative Identity Distributive 39. For a weekend trip, you pack a blue shirt, a white shirt, and a green shirt. You also pack two pairs of pants ­ one blue and one tan. If you randomly select an outfit, what is the probability that you will wear the same color pants and shirt? 1 __ 6 1 __ 4 1 __ 3 1 __ 2

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86

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

40. Which set of coordinates will form an isosceles right triangle when connected? (1, 1), (3, 5), (5, 5) (1, 1), (1, 5), (7, 1) (1, 1), (5, 1), (1, 5) (1, 1), (4, 1), (3, 4) Use this figure to answer questions 41 and 42.

y 10 9 8 7 6 5 4 3 2 1 O E

43. Samantha sees the following at the grocery store: Dinner rolls $3 a dozen 30 cents each Samantha wants to know the price d per dinner roll if she buys a dozen. She uses the following equation. 12d = $3.00 What is the value of d? $0.25 $0. 32 $0.48 $0.50 44. This table shows Paulina's scores for four tests. Test 1 2 3 4 Score 90 83 78 92

H

F

G

x 1 2 3 4 5 6 7 8 9 10

41. Which translation would not have point H lie on (3, 4)? 90º rotation about the center of the square. Translation 3 right and 3 down. Translation -3 left and -3 up. 90º rotation about point G. 42. If G was reflected across the diagonal, which transformation would move G to (3, 7)? Reflect G across y = x and translate G 2 units up. Translate G 3 units up. Translate G 1 unit left. Then reflect G across the line y = 5. Move G 4 units up and 4 units to right. Then reflect G across y = x.

What score will Paulina need on her fifth test to score more than the mean of her first four test scores? 80 87 85 82

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87

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

45. How many lines of symmetry does a square have? 0 1 2 4 46. Jessie wants to solve the equation 4x = 112. What step should she take first? Add 4 to both sides. Subtract 4 from both sides. Multiply both sides by 4. Divide both sides by 4. 47. Jerry is saving for a new MP3 player. He deposits 40% of his allowance into his savings account each week. If the MP3 player costs $245 and Jerry's allowance is $25 per week, how many weeks will it take him to save enough money to buy the MP3 player? 8 weeks 15 weeks 20 weeks 25 weeks 48. Which equation describes the Commutative Property? a+b=b+a a + (b + c) = (a + b) + c a(b + c) = a · b + a · c a·1=a

49. A triangle has sides that are 4 inches, 3 1 10 __ inches, and 18 __ inches long. 4 2 Which are the dimensions of a similar triangle? 3 1 2 inches, 5 __ inches, 9 __ inches 8 4 3 1 2 inches, 10 __ inches, 18 __ inches 4 2 3 1 4 inches, 5 __ inches, 9 __ inches 8 4 3 8 inches, 10 __ inches, 37 inches 4 50. Which regular polygon always looks the same after a 120° rotation? Pentagon Rectangle Equilateral triangle Octagon 51. On the map of a zoo, the distance between the lion's den and the zoo entrance is 5 inches. If the map scale 1 is 1 __ inches = 250 feet, what is the 2 actual distance between the lion's den and the zoo entrance? 100 feet 250 feet 700 feet 833 feet 52. What is the solution to the following equation?

2 y ÷ 16 = 4

y=4 y=8 y = 32 y = 64

Copyright © 2010 by Holt McDougal. All rights reserved.

88

PASS Preparation and Practice, Grade 6

Name _________________________________ Date ______________ Class ______________

Use the plot to answer questions 53­55. The following stem-and-leaf plot shows how much money students in a drama club from two classes raised for the spring show.

Class 1 Leaf 3 6 5 3 5 6 6 9 0 2 2 Stem 10 20 30 Class 2 Leaf 0 3 3 6 1 4 6 8 9 0 1 4

56. Which list contains only integers? 0, 1, 2, 2.5 -1, 2, 5 1 1 __, __, 4 2 3 1 - __ , 2, 5 2 Use the following figure to answer questions 57­59. A D C E

Key: 20 4 means $24 2 30 means $32

B 53. According to the plot, how many students in each class raised exactly $26? 1 in Class 1 and 1 in Class 2 1 in Class 1 and 2 in Class 2 2 in Class 1 and 1 in Class 2 2 in Class 1 and 2 in Class 2 54. How much did students in Class 1 raise in all? $67 $220 $167 $267 57. Which statement below is true? -- The length of CD is half the length -- of CE. -- The length of AB is equal to the -- length of CD. -- The length of BC is half the length -- of CD. -- The length of BC is half the -- length of AB. 58. If the circle C has a radius of 5 cm, -- what is the length of AB? 5 cm 10 cm 7.5 cm 31.4 cm 59. Which expression can be used to find the area of the circle? r 2 d 2 2r 2d 89

PASS Preparation and Practice, Grade 6

55. Which of the following statements is true? One student in each class raised exactly $30. The student who raised the most money is in Class 1. Class 2 had more students raise over $30 than Class 1 did. There are the same number of students in the drama club in both classes.

Copyright © 2010 by Holt McDougal. All rights reserved.

Name _________________________________ Date ______________ Class ______________

60. A fair coin is tossed 25 times. Which outcome is most likely? 8 heads and 17 tails 10 heads and 15 tails 12 heads and 13 tails 20 heads and 5 tails 61. ABC ~ MNP. AB = 8 cm, MN = 32 cm, and BC = 4 cm. What is NP? 4 cm 9 cm 10 cm 16 cm Constructed Response 62. Plot the coordinates A(1, 2), B(3, 3), C(7, 3), and D(5, 2) and join them in order. What figure did you create? 63. The seventh graders at Churchill Elementary School collected cans for a food drive. Room 203 4 52 ___ 15 pounds Room 204 5 48 ___ 12 pounds Room 205 1 58 __ 5 pounds Room 206 7 52 ___ 20 pounds

How many pounds did they collect in total? How many fewer pounds did room 204 collect than room 205?

Copyright © 2010 by Holt McDougal. All rights reserved.

90

PASS Preparation and Practice, Grade 6

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