Chapter 3: Resourse Managment

Chapter Chapter X3 Resource Resource Masters Masters Course 12 Course Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Study Guide and Intervention Workbook (Spanish) Practice: Skills Workbook Practice: Skills Workbook (Spanish) Practice: Word Problems Workbook Practice: Word Problems Workbook (Spanish) Reading to Learn Mathematics Workbook 0-07-860128-2 0-07-860134-7 0-07-860129-0 0-07-860135-5 0-07-860130-4 0-07-860136-3 0-07-861058-3 Answers for Workbooks The answers for Chapter 3 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Spanish Assessment Masters Spanish versions of forms 2A and 2C of the Chapter 3 Test are available in the Glencoe Mathematics: Applications and Concepts Spanish Assessment Masters, Course 2 (0-07-860138-X). Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with Glencoe Mathematics: Applications and Concepts, Course 2. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240 ISBN: 0-07-860110-X 1 2 3 4 5 6 7 8 9 10 024 Mathematics: Applications and Concepts, Course 2 Chapter 3 Resource Masters 12 11 10 09 08 07 06 05 04 03 CONTENTS Vocabulary Builder .............................vii Family Letter ............................................ix Family Activity ........................................x Lesson 3-1 Study Guide and Intervention ........................129 Practice: Skills ................................................130 Practice: Word Problems................................131 Reading to Learn Mathematics......................132 Enrichment .....................................................133 Lesson 3-2 Study Guide and Intervention ........................134 Practice: Skills ................................................135 Practice: Word Problems................................136 Reading to Learn Mathematics......................137 Enrichment .....................................................138 Lesson 3-3 Study Guide and Intervention ........................139 Practice: Skills ................................................140 Practice: Word Problems................................141 Reading to Learn Mathematics......................142 Enrichment .....................................................143 Lesson 3-4 Study Guide and Intervention ........................144 Practice: Skills ................................................145 Practice: Word Problems................................146 Reading to Learn Mathematics......................147 Enrichment .....................................................148 Lesson 3-6 Study Guide and Intervention ........................154 Practice: Skills ................................................155 Practice: Word Problems................................156 Reading to Learn Mathematics......................157 Enrichment .....................................................158 Lesson 3-7 Study Guide and Intervention ........................159 Practice: Skills ................................................160 Practice: Word Problems................................161 Reading to Learn Mathematics......................162 Enrichment .....................................................163 Chapter 3 Assessment Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter 3 Test, Form 1 ...........................165-166 3 Test, Form 2A.........................167-168 3 Test, Form 2B.........................169-170 3 Test, Form 2C ........................171-172 3 Test, Form 2D ........................173-174 3 Test, Form 3 ...........................175-176 3 Extended Response Assessment .177 3 Vocabulary Test/Review.................178 3 Quizzes 1 & 2................................179 3 Quizzes 3 & 4................................180 3 Mid-Chapter Test ...........................181 3 Cumulative Review........................182 3 Standardized Test Practice ....183-184 Standardized Test Practice Student Recording Sheet ..............................A1 Standardized Test Practice Rubric...................A2 ANSWERS ..............................................A3-A30 Lesson 3-5 Study Guide and Intervention ........................149 Practice: Skills ................................................150 Practice: Word Problems................................151 Reading to Learn Mathematics......................152 Enrichment .....................................................153 iii Teacher’s Guide to Using the Chapter 3 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 3 Resource Masters includes the core materials needed for Chapter 3. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Glencoe Mathematics: Applications and Concepts, Course 2, TeacherWorks CD-ROM. Vocabulary Builder Practice: Skills Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. There is one master for each lesson. These provide practice that more closely follows the structure of the Practice and Applications section of the Student Edition exercises. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson. When to Use Give these pages to students before beginning Lesson 3-1. Encourage them to add these pages to their mathematics study notebook. Remind them to add definitions and examples as they complete each lesson. Practice: Word Problems There is one master for each lesson. These provide practice in solving word problems that apply the concepts of the lesson. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson. Family Letter and Family Activity Page ix is a letter to inform your students’ families of the requirements of the chapter. The family activity on page x helps them understand how the mathematics students are learning is applicable to real life. Reading to Learn Mathematics One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use Give these pages to students to take home before beginning the chapter. Study Guide and Intervention There is one Study Guide and Intervention master for each lesson in Chapter 3. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students. iv There is one extension master for each lesson. These activities may extend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for use with all levels of students. • A Vocabulary Test, suitable for all students, includes a list of the vocabulary words in the chapter and ten questions assessing students’ knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet. When to Use These may be used as extra credit, short-term projects, or as activities for days when class periods are shortened. • Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. Enrichment Intermediate Assessment • A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and freeresponse questions. Assessment Options The assessment masters in the Chapter 3 Resources Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Continuing Assessment • The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Glencoe Mathematics: Applications and Concepts, Course 2. It can also be used as a test. This master includes free-response questions. Chapter Assessment Chapter Tests • Form 1 contains multiple-choice questions and is intended for use with basic level students. • The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which may appear on the standardized tests that they may encounter. This practice includes multiplechoice, short response, grid-in, and extended response questions. Bubble-in and grid-in answer sections are provided on the master. • Forms 2A and 2B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. • Forms 2C and 2D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with axes are provided for questions assessing graphing skills. Answers • Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 146–147. This improves students’ familiarity with the answer formats they may encounter in test taking. • Form 3 is an advanced level test with free-response questions. Grids without axes are provided for questions assessing graphing skills. All of the above tests include a free-response Bonus question. • Detailed rubrics for assessing the extended response questions on page 147 are provided on page A2. • The Extended-Response Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. • The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. • Full-size answer keys are provided for the assessment masters in this booklet. v NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics This is an alphabetical list of new vocabulary terms you will learn in Chapter 3. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add this page to your math study notebook to review vocabulary at the end of the chapter. Vocabulary Term Found on Page Definition/Description/Example absolute value additive inverse coordinate grid coordinate plane graph integer [IHN-tih-juhr] negative integer opposite © Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 2 Vocabulary Builder Vocabulary Builder NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Vocabulary Builder Vocabulary Term Found on Page (continued) Definition/Description/Example ordered pair origin positive integer quadrant x-axis x-coordinate y-axis y-coordinate © Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Dear Parent or Guardian: stuff?” Students in math “When am I ever going to use this rs are everywhere. We use classes often ask this question. Intege when finding elevation, balthem for golf scores. We use them temperature. There are ancing a checkbook, or talking about many practical uses of integers. r child will learn how to In Chapter 3, Algebra: Integers, you and find the absolute value order, add, subtract, multiply, divide, about the coordinate sysof integers. Your child will also learn study of this chapter, tem and how to graph points. In the daily classroom assignyour child will complete a variety of duce a chapter project . ments and activities and possibly pro it with your child, you By signing this letter and returning ting involved. Enclosed is agree to encourage your child by get ld that also relates the an activity you can do with your chi 3 to the real world. You math we will be learning in Chapter line Study Tools for selfmay also wish to log on to the On dy Guide pages, and check quizzes, Parent and Student Stu et. If you have any quesother study help at www.msmath2.n t me at school. tions or comments, feel free to contac Sincerely, Signature of Parent or Guardian ______________________________________ Date ________ © Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 2 Family Letter Family Letter NAME ________________________________________ DATE ______________ PERIOD _____ Family Activity Ordering Integers Consult a newspaper, watch the news, surf the Internet, or watch the weather channel with a family member. Find the high and low temperatures on the same day for eight cities: Buenos Aires, Moscow, Zurich, Tokyo, New York, Denver, Los Angeles, and your community. Record the date and the temperatures in the table. High and Low Temperatures on _____________ City High Temperature (F) Low Temperature (F) Buenos Aires Moscow Zurich Tokyo New York Denver Los Angeles 1. Which city has the highest high temperature? 2. Which city has the lowest low temperature? 3. List the cities in order from lowest high temperature to highest high temperature. 4. List the cities in order from lowest low temperature to highest low temperature. 5. Were the cities in the same order in the answers for Questions 3 and 4? Why or why not? © Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention Integers and Absolute Value Integers less than zero are negative integers. Integers greater than zero are positive integers. negative integers positive integers 7654321 0 1 2 3 4 5 6 7 8 zero is neither positive nor negative The absolute value of an integer is the distance the number is from zero on a number line. Two vertical bars are used to represent absolute value. The symbol for absolute value of 3 is 3. Write an integer that represents 160 feet below sea level. Evaluate |2|. On the number line, the graph of 2 is 2 units away from 0. So, 2  2. 4 3 2 1 0 1 2 3 4 Write an integer for each situation. 1. 12°C above 0 2. a loss of $24 3. a gain of 20 pounds 4. falling 6 feet Evaluate each expression. 5. 12 6. 150 7. 8 8. 75 9. 19 10. 84 © Glencoe/McGraw-Hill 129 Mathematics: Applications and Concepts, Course 2 Lesson 3–1 Because it represents below sea level, the integer is 160. NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills Integers and Absolute Value Write an integer for each situation. 1. 15C below 0 2. a profit of $27 3. 2010 A.D. 4. average attendance is down 38 people 5. 376 feet above sea level 6. a withdrawal of $200 7. 3 points lost 8. a bonus of $150 9. a deposit of $41 10. 240 B.C. 11. a wage increase of $120 12. 60 feet below sea level Evaluate each expression. 13. |1| 14. |9| 15. |23| 16. |107| 17. |45| 18. |19| 19. |0| 20. |6||2| 21. 84 22. |12||12| Graph each set of integers on a number line. 23. {0, 2, 3} 4 3 2 1 0 © Glencoe/McGraw-Hill 24. {4, 1, 3} 1 2 3 4 3 2 1 0 4 130 1 2 3 4 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems 1. DEATH VALLEY The lowest point in the United States is Death Valley in California. Its altitude is 282 feet below sea level. Write an integer to represent the altitude of Death Valley. 2. RAIN A meteorologist reported that in the month of April there were 3 inches more rainfall than normal. Write an integer to represent the amount of rainfall above normal in April. 3. ARCHIMEDES A famous mathematician and physicist named Archimedes was born in 287 B.C. Write an integer to express the year of his birth. 4. TEMPERATURE In our world’s tropical rain forests, the average temperature of every month is 64 degrees above zero or higher. Write an integer to express this temperature. 5. STOCK MARKET A certain stock gained 5 points in one day and lost 4 points the next day. Write integers to represent the stock’s gains and losses for the two days. 6. ALTITUDE An airplane pilot changed his altitude by 100 meters. Describe what this could mean. © Glencoe/McGraw-Hill 131 Mathematics: Applications and Concepts, Course 2 Lesson 3–1 Integers and Absolute Value NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Integers and Absolute Value Pre-Activity Read the introduction at the top of page 106 in your textbook. Write your answers below. 1. What does a value of 2 represent? 2. On which down did they lose the most yards? 3. How can you represent a gain of 9 yards? Reading the Lesson 4. Express each of the following in words. Symbols Words 7 7 |7| 5. On the following number line, draw a circle around the negative integers and label them negative. Draw a rectangle around the positive integers and label them positive. 4 3 2 1 0 1 2 3 4 Helping You Remember 6. Show a classmate how a number line can be used to show negative and positive integers. Explain the difference between some integers and the absolute values of those integers. Draw a number line to show what you mean. © Glencoe/McGraw-Hill 132 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Jaime Escalante Jaime Escalante (1930– ) was born in La Paz, Bolivia, and came to the United States in 1963. For ten years, he worked at odd jobs to support himself and his family while pursuing his dream—becoming certified to teach high school mathematics in California. As a mathematics teacher, he has become well known for his ability to inspire students to succeed in mathematics at levels they never thought possible. In 1988, the story of Mr. Escalante and a group of his students was the subject of the popular motion picture Stand and Deliver. You know that 6  6 and 6  6. So, the equation y  6 has two solutions: 6 and 6. Solve each equation. (Hint: One equation has no solution.) 1. a  8 2. r  0 3. j  3 4. t  1  15 5. 10  m 3 6. c  4  16 7. 5z  60 8. 12  g  4 9. 48  8x 10. 2d  3  5 11. 4p  9  59 12. 7z  12  12 13. Suppose that the value of x can be selected from the set {2, 1, 0, 1, 2}. Find all of the solutions of the equation x  x. 14. One of these statements is false. Which one is it? Explain. a. The absolute value of every integer is positive. b. There is at least one integer whose absolute value is zero. c. The absolute value of an integer is never negative. © Glencoe/McGraw-Hill 133 Mathematics: Applications and Concepts, Course 2 Lesson 3–1 Mr. Escalante teaches concepts students must master if they are to succeed in high school and college mathematics. One of these is the concept of absolute value. For instance, a student should be able to solve an equation like y  6 quickly using mental math. Here’s how. NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention Comparing and Ordering Integers When two numbers are graphed on a number line, the number to the left is always less than (<) the number to the right. The number to the right is always greater than (>) the number to the left. Model Words Symbols 4 3 2 1 0 1 2 3 4 3 is less than 1. 1 is greater than 1. 3  1 1  3 The symbol points to the lesser number. Replace the  with  or  to make 1  6 a true sentence. Graph each integer on a number line. 7 6 5 4 3 2 1 0 1 2 3 4 Since 1 is to the right of 6, 1  6. Order the integers 2, 3, 0, 5 from least to greatest. To order the integers, graph them on a number line. 6 5 4 3 2 1 0 1 2 3 4 5 Order the integers by reading from left to right: 5, 3, 0, 2. 1. Replace the  with < or > to make 5  10 a true sentence. 2. Order 1, 5, 3, and 2 from least to greatest. 3. Order 0, 4, 2, and 7 from greatest to least. 4. Order 3, 2, 4, 0, and 5 from greatest to least. © Glencoe/McGraw-Hill 134 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills Comparing and Ordering Integers Replace each  with < or > to make a true sentence. 1. 15  16 2. 8  7 3. 0  2 4. 2  5 5. 25  3 6. 14  20 7. 4  3 8. 6  7 9. 7  2 10. 8  9 Determine whether each sentence is true or false. If false, change one number to make the sentence true. 11. 7  3 12. 2  0 13. 20  22 14. 12  15 Lesson 3–2 15. 3 5 16. 2 3 17. 810 18. 11 11 19. 4  4 20. 9  10 Order the integers from least to greatest. 21. 12, 6, 20, 47, 11 22. 9, 6, 0, 4, 17, 11 Order the integers from greatest to least. 23. 40, 65, 7, 24, 6, 15 © Glencoe/McGraw-Hill 24. 13, 0, 7, 8, 5, 2 135 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems Comparing and Ordering Integers HISTORY OF WRITING For Exercises 1 and 2, use the table below. It shows important events in the history of writing. Event Aprox. Year The Iliad and the Odyssey are composed by Homer. 700 BC T’sai Lun invents paper. 105 AD Date of oldest existing papyrus 2200 BC Ovid wrote Metamorphosis. 5 AD 450 BC 1241 AD Torah is compiled. Metal type developed in Korea EXTREME TEMPERATURES For Exercises 3–5, use the table below. It shows the extreme temperatures for four states. Temperatures are in degrees Fahrenheit. Extreme Temperatures (F) State Highest Lowest Alabama 104 3 Nebraska 118 47 Maine 101 30 Florida 109 2 1. Write each year as an integer. 2. Order the integers from Exercise 1 from least to greatest. Write a sentence describing the earliest and most recent events in the table. 3. Arrange the highest temperatures from greatest to least. 4. What is the median low temperature for these four states? 5. Nebraska’s lowest temperature was 47F, and Maine’s lowest temperature was 30F. Write a true statement using the two temperatures with the symbol  or . 6. MONEY Mr. Firewalks pays close attention to how much money is in his checking account. One week he deposited $230, spent $15 on a lunch, and loaned $25 to a friend. Write each transaction as an integer, and list them from least to greatest. © Glencoe/McGraw-Hill 136 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Comparing and Ordering Integers Pre-Activity Read the introduction at the top of page 109 in your textbook. Write your answers below. 1. What is the wind chill if there is a wind at 20 miles per hour and the temperature is 5? 2. Which is colder, a temperature of 15 with a 20 mile-per-hour wind or a temperature of 10 with a 10 mile-per-hour wind? 3. Graph both wind chills found in Exercise 2 on a number line. 5 4 3 2 1 0 1 2 3 Reading the Lesson For Exercises 4 and 5, express each of the following in words. Then graph the numbers on a number line. 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 Lesson 3–2 4. 1  0 5. 3  2 6. When two numbers are graphed on a number line, what can you tell about the number to the left? the number to the right? Helping You Remember 7. Write a set of six numbers, some positive and some negative. Explain how you can use a number line to order the numbers from least to greatest. © Glencoe/McGraw-Hill 137 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Quantitative Comparisons An unusual type of problem is found on some standardized multiple-choice tests. This problem type is called the quantitative comparison. In each quantitative comparison question, you are given two quantities, one in Column A and one in Column B. You are to compare the two quantities and shade one of four circles on an answer sheet. Shade circle A if the quantity in Column A is greater; Shade circle B if the quantity in Column B is greater; Shade circle C if the two quantities are equal; Shade circle D if the relationship cannot be determined from the information given. Shade the correct oval to the left of each problem number. Column A Column B A B C D 1. 0.006  2 0.002  6 A B C D 2. ten billion dollars 1,000 million dollars A B C D 3. 20 inches the perimeter of a square with an area of 25 square inches A B C D 4. half of one third one fifth A B C D 5. the greatest possible product of two odd positive numbers less than 20 the greatest possible product of two even positive numbers less than 20 A B C D 6. 0.000000001 x is x if greater than 0 A B C D 7. |x| |x  1| A B C D 8. |y| |y| A B C D 9. 2|x| if x A B C D 10. © Glencoe/McGraw-Hill 0 x if x is less than 0 |x| if x 0 |x| if x is less than 0 138 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention The Coordinate Plane The coordinate plane is used to locate points. The horizontal number line is the x-axis. The vertical number line is the y-axis. Their intersection is the origin. Points are located using ordered pairs. The first number in an ordered pair is the x-coordinate; the second number is the y-coordinate. The coordinate plane is separated into four sections called quadrants. Name the ordered pair for point P. Then identify the quadrant in which P lies. • Start at the origin. • Move 4 units left along the x-axis. • Move 3 units up on the y-axis. The ordered pair for point P is (4, 3). P is in the upper left quadrant or quadrant II. 4 3 2 1 P 432 2 3 4 Graph and label the point M(0, 4). O 1 2 3 4x M (0, 4) Start at the origin. Move 0 units along the x-axis. Move 4 units down on the y-axis. Draw a dot and label it M(0, 4). Name the ordered pair for each point graphed at the right. Then identify the quadrant in which each point lies. 1. P 2. Q 3. R 4. S S 432 Q 4 3 2 1 y O R 1 2 3 4x 2 3 4 P Lesson 3–3 • • • • y Graph and label each point on the coordinate plane. 5. A(1, 1) 6. B(0, 3) 7. C(3, 2) 8. D(3, 1) 4 3 2 1 432 9. E(1, 2) © Glencoe/McGraw-Hill O y 1 2 3 4x 2 3 4 10. F(1, 3) 139 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills The Coordinate Plane Name the ordered pair for each point graphed at the right. Then identify the quadrant in which each point lies. 1. A I 5 4 3 2 1 F 2. B A 3. C 5432 4. D H C 5. E 6. F 7. G 8. H 9. I y B E O 1 2 3 4 5x 2 3 4 5 D G J 10. J Graph and label each point on the coordinate plane. 11. N(1, 3) 12. V(2, 4) 13. C(4, 0) 14. P(6, 2) 15. M(5, 0) 16. K(1, 5) 17. I(3, 3) 6 5 4 3 2 1 65432 y O 1 2 3 4 5 6x 2 3 4 5 6 18. A(5, 3) 19. D(0, 5) Name the ordered pair for each point on the city map at the right. Grocery 20. City Hall 21. Theater 76 5432 Theater 22. Gas Station y 5 4 3 Gas Station 2 1 City Hall O 1 2 3 4 5 6 7x 2 3 4 5 23. Grocery © Glencoe/McGraw-Hill 140 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems The Coordinate Plane SCHOOL For Exercises 1–4, use the coordinate plane at the right. It shows a map of the rooms in a junior high school. Art Entrance Library Computer Lab Nurse 5432 5 4 3 2 1 y Special Services English Counselor History O 1 2 3 4 5x 2 Athletic Dept. Science 3 Math 4 Music 5 1. Thalia is in the room located at (2, 1). What room is she in? Describe in words how to get from the origin to this point. 2. Thalia’s next class is 8 units to the right and 5 units down on the map from where she is now. In what room is Thalia’s next class? Find the ordered pair that represents the location of that room. 3. Tyrone is in the Art room, but his next class is in the History room. Give Tyrone directions on how to get to the History room. 4. On the map, which classrooms are located in the third quadrant? Describe the coordinates of all points in the third quadrant. 5. NEIGHBORHOOD Delsin made a map of his neighborhood in such a way that each intersection is a point on a coordinate plane. Right now, Delsin stands at point (4, 3). Give the ordered pair of where he will be if moves 5 units to the right and 7 units up on the map. 6. NEIGHBORHOOD Refer to Exercise 5. In which quadrant is Delsin when he is done walking? Describe this quadrant. © Glencoe/McGraw-Hill 141 Mathematics: Applications and Concepts, Course 2 Lesson 3–3 Exit NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics The Coordinate Plane Pre-Activity Read the introduction at the top of page 112 in your textbook. Write your answers below. 1. Suppose Terrell starts at the corner of Russel and Main and walks 1 block north and 2 blocks east. Name the intersection of his location. 2. Using the words north, south, west, and east, write directions to go from the corner of School and Highland to the corner of Main and Oak. Reading the Lesson 3. The word coordinate comes from two Latin words that mean “to arrange together.” How are coordinates used together to locate a point in a coordinate plane? 4. Look at the coordinate plane at the right. Name the ordered pair for each point graphed. 5. In the coordinate plane in Exercise 4, tell which quadrant each of the points is in. A 432 4 3 2 1 O y B 1 2 3 4x 2 3 4 C Helping You Remember 6. Write a way to remember the names of the four quadrants of the coordinate plane. © Glencoe/McGraw-Hill 142 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Latitude and Longitude This world map shows some of the latitude and longitude lines. Latitude is measured in degrees north and south of the equator. Longitude is measured in degrees east and west of the prime meridian, a line passing through Greenwich, England. (Greenwich is a suburb of London.) The latitude is usually given first. For example, the location of 30S, 60W is lower South America. 60˚N 60˚N 30˚N Prime Meridian 30˚N Equator 0˚ 0˚ ˚E 0 18 0˚ E 30˚S 15 0˚ E 12 90 E ˚ 60˚ E 30 ˚W 60 ˚W W 90 ˚ W 0˚ 12 W 0˚ 15 0˚ 30˚E 30˚S, 60˚W 30˚S 60˚S 60˚S 1. 30N, 30W 2. 30S, 30E 3. 60N, 120W 4. 15N, 150W 5. 30S, 140E 6. 25N, 100W 7. 40N, 120W 8. 45N, 90W 9. 40N, 5W 10. 60N, 45W © Glencoe/McGraw-Hill 11. 35N, 140E 143 12. 0, 60E Mathematics: Applications and Concepts, Course 2 Lesson 3–3 Name a place near each location. Use an atlas or other reference source to check your answers. NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention Adding Integers For integers with the same sign: • the sum of two positive integers is positive. • the sum of two negative integers is negative. For integers with different signs, subtract their absolute values. The sum is: • positive if the positive integer has the greater absolute value. • negative if the negative integer has the greater absolute value. To add integers, it is helpful to use counters or a number line. Find 4  (6). Method 1 Use counters. Combine a set of 4 positive counters and a set of 6 negative counters on a mat.           4  (6) Method 2 Use a number line. • Start at 0. • Move 4 units right. • Then move 6 units left. 6   4   3 2 1 0 1 2 3 4  (6) 2   4 5   1   4  (6) 2 Add. 1. 5  (2) 2. 8  1 3. 7  10 4. 16  (11) 5. 22  (7) 6. 50  50 7. 10  (10) 8. 100  (25) 9. 35  20 Evaluate each expression if a  8, b  8, and c  4. 10. a  15 11. b  (9) 12. a  b 13. b  c 14. 10  c 15. 12  b © Glencoe/McGraw-Hill 144 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills Adding Integers Tell whether each sum is positive, negative, or zero without adding. Add. 1. 5  (8) 2. 3  3 3. 3  (8) 4. 7  (7) 5. 8  10 6. 7  13 7. 15  (10) 8. 11  (12) 9. 25  (12) 10. 14  (13) 11. 14  (27) 12. 28  16 13. 5  a 14. b  (9) 15. c  (5) 16. a  b 17. a  0 18. b  c 19. 12  b 20. a  (7) 21. 21  c 22. a  c © Glencoe/McGraw-Hill 145 Mathematics: Applications and Concepts, Course 2 Lesson 3–4 Evaluate each expression if a  8, b  12, and c  4. NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems Adding Integers Write an addition expression to describe each situation. Then find each sum. 1. FOOTBALL A team gains 20 yards. Then they lose 7 yards. 2. MONEY Roger owes his mom $5. He borrows another $6 from her. 3. GOLF Juanita’s score was 5 over par on the first 9 holes. Her score was 4 under par on the second 9 holes. 4. HOT AIR BALLOON A balloon rises 340 feet into the air. Then it descends 130 feet. 5. CYCLING A cyclist travels downhill for 125 feet. Then she travels up a hill 50 feet. 6. AIRPLANE A plane descends 1,200 feet. Then it descends another 500 feet. © Glencoe/McGraw-Hill 146 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Adding Integers Pre-Activity Read the introduction at the top of page 120 in your textbook. Write your answers below. 1. What is the charge at the top of a cloud where there are more protons than electrons? 2. What is the charge at the bottom of a cloud where there are more electrons than protons? Reading the Lesson For Exercises 3 and 4, tell how you would solve each of the following on a number line. Then solve. 3. 7  (9) 4. 7  9 5. When you use counters to add integers, what property are you applying when you remove zero pairs? 6. How many units away from 0 is the number 17? How many units away from 0 is the number 17? What are 17 and 17 called? Helping You Remember Lesson 3–4 7. Work with a partner. Tell your partner how to use absolute values to add integers with different signs when the positive integer has the greater absolute value. Then have your partner explain to you how to use absolute values to add integers with different signs when the negative integer has the greater absolute value. © Glencoe/McGraw-Hill 147 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Dartboard Puzzles Three darts are thrown. Each dart must land on a different space in order to count. Find the highest and the lowest possible scores. 1. 2. 1 7 2 6 1 3 8 7 2 6 5 2 0 6 3. 4 6 4 1 3 2 50 75 75 7 8 6 5 highest score: lowest score: 1 7 0 5 150 200 4 8 5 3 3 100 10 25 10 50 75 150 4 highest score: lowest score: 25 10 10 75 200 highest score: lowest score: In these problems, five darts are thrown. Each dart must land on a different space in order to count. Solve each puzzle. 4. Find three ways to make the score 5. 7 3 1 10 8 2 7 9 5 1 5 8 0 1 4 10 4 3 10 7 1 6 10 50 5 25 5 10 15 5 10 15 20 15 5 35 7 15 4 5 10 1 50 2 0 10 5 15 25 50 5 15 148 20 20 5 3 10 5 5 8 0 9 3 3 20 10 5 15 8 25 0 6 5 6 © Glencoe/McGraw-Hill 2 5 10 20 20 6 10 2 4 9 3 1 15 5 0 0 5 10 5 9 2 5. Find three ways to make the score 0. 20 5 10 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention Subtracting Integers Lesson 3–5 To subtract an integer, add its opposite. Find 6  9. 6  9  6  (9)  3 To subtract 9, add 9. Simplify. Find 10  (12). 10  (12)  10  12 2 To subtract 12, add 12. Simplify. Evaluate a  b if a  3 and b  7. a  b  3  7  3  (7)  10 Replace a with 3 and b with 7. To subtract 7, add 7. Simplify. Subtract. 1. 7  9 2. 20  (6) 3. 10  4 4. 0  12 5. 7  8 6. 13  18 7. 20  (5) 8. 8  (6) 9. 25  (14) 11. 15  65 10. 75  50 12. 19  (10) Evaluate each expression if m  2, n  10, and p  5. 13. m  6 14. 9  n 15. p  (8) 16. p  m 17. m  n 18. 25  p © Glencoe/McGraw-Hill 149 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills Subtracting Integers Subtract. 1. 5  2 2. 6  (7) 3. 3  2 4. 8  13 5. 7  (7) 6. 6  12 7. 15  (7) 8. 15  6 9. 3  8 10. 10  12 11. 13  (12) 12. 14  (22) 13. 10  (20) 14. 16  14 15. 25  25 16. 6  (31) 17. 18  (40) 18. 15  (61) Evaluate each expression if r  4, s  10, and t  7. 19. r  7 20. t  s 21. s  (8) 22. t  r 23. s  t 24. r  s © Glencoe/McGraw-Hill 150 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems Subtract. 1. FOOTBALL A team gained 5 yards on their first play of the game. Then they lost 6 yards. Find the total change in yardage. 2. CHECKING Your checking account is overdrawn by $50. You write a check for $20. What is the balance in your account? 3. TEMPERATURE The average temperature in Calgary, Canada, is 22C in July and 11C in January. Find the range of the highest and lowest temperatures in Calgary. 4. ROLLER COASTER A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent. 5. SAVINGS Sonia has $235 in her savings account. She withdraws $45. What is left in her savings account? 6. BEACH Wai and Kuri were digging in the sand at the beach. Wai dug a hole that was 15 inches below the surface, and Kuri dug a hole that was 9 inches below the surface. Find the difference in the depths of their holes. © Glencoe/McGraw-Hill 151 Mathematics: Applications and Concepts, Course 2 Lesson 3–5 Subtracting Integers NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Subtracting Integers Pre-Activity Complete the Mini Lab at the top of page 128 in your textbook. Write your answers below. 1. Write a related addition sentence for each subtraction sentence. Use a number line to find each difference. Write an equivalent addition sentence for each. 2. 1  5 3. 2  1 4. 3  4 5. 0  5 6. Compare and contrast subtraction sentences with their related addition sentences. Reading the Lesson Tell how you would solve each of the following on a number line. Then solve. 7. 8  (6) 8. 6  8 Helping You Remember 9. Write the rule that tells how to subtract integers. Then give an example. © Glencoe/McGraw-Hill 152 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Lesson 3–5 Distance on the Number Line To find the distance between two points on a number line, subtract their coordinates. Then, take the absolute value of the difference. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 4  3  7 7  7 You can also find the distance by finding the absolute value of the difference of the coordinates. 4  3  7 Graph each pair of points. Then write an expression using absolute value to find the distance between the points. 1. A at 5 and B at 2 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 4 3 2 1 0 1 2 3 4 5 6 7 8 4 3 2 1 0 1 2 3 4 5 6 7 8 4 3 2 1 0 1 2 3 4 5 6 7 8 4 3 2 1 0 1 2 3 4 5 6 7 8 2. C at 7 and D at 1 8 7 6 5 3. E at 5 and F at 5 8 7 6 5 4. W at 0 and X at 6 8 7 6 5 5. Y at 4 and Z at 0 8 7 6 © Glencoe/McGraw-Hill 5 153 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention Multiplying Integers The product of two integers with different signs is negative. The product of two integers with the same sign is positive. Multiply 5(2). 5(2)  10 The integers have different signs. The product is negative. Multiply 3(7). 3(7)  21 The integers have different signs. The product is negative. Multiply 6(9). 6(9)  54 The integers have the same sign. The product is positive. Multiply (7)2. (7)2  (7)(7)  49 There are 2 factors of 7. The product is positive. Simplify 2(6c). 2(6c)  (2 · 6)c  12c 6 Associative Property of Multiplication. Simplify. Simplify 2(5x). 2(5x)  (2 · 5)x  10x Associative Propery of Multiplication. Simplify. Multiply. 1. 5(8) 2. 3(7) 3. 10(8) 4. 8(3) 5. 12(12) 6. (8)2 ALGEBRA Simplify each expression. 7. 5(7a) 10. 7(6b) 8. 3(2x) 9. 4(6f) 11. 6(3y) 12. 7(8g) ALGEBRA Evaluate each expression if a  3, b  4, and c  5. 13. 2a 14. 9b 15. ab 16. 3ac 17. 2c2 18. abc © Glencoe/McGraw-Hill 154 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills Multiplying Integers 1. 4(6) 2. 2(8) 3. 12(4) 4. 6(5) 5. 10(9) 6. (5)2 7. (5)2 8. 30(5) 9. 20(6) 11. (13)2 10. 14(6) 12. 7(15) ALGEBRA Simplify each expression. 13. 3(4y) 14. 7(3x) 15. 7(5g) 16. 7(7w) 17. 3(3y) 18. 2(10h) ALGEBRA Evaluate each expression if g  5, h  3, and k  4. 19. 3g 20. 5h 21. 7gk 22. 2gh 23. 10h 24. 2h2 © Glencoe/McGraw-Hill 155 Mathematics: Applications and Concepts, Course 2 Lesson 3–6 Multiply. NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems Multiplying Integers Multiply. 1. TEMPERATURE Suppose the temperature outside is dropping 3 degrees each hour. How much will the temperature drop in 8 hours? 2. DIVING A deep-sea diver descends below the surface of the water at a rate of 60 feet each minute. What is the depth of the diver after 10 minutes? 3. STOCK A computer stock lost 2 points each hour for 6 hours. Find the total points the stock fell. 4. DROUGHT A drought can cause the level of the local water supply to drop by a few inches each week. Suppose the level of the water supply drops 2 inches each week. How far will it have dropped in 4 weeks? 5. MONEY Mrs. Rockwell lost money on an investment at a rate of $4 per day. How much did she lose after two weeks? 6. TENNIS BALLS Josh purchased 8 cans of tennis balls. The cans came with 3 balls in each can. How many balls did Josh purchase? © Glencoe/McGraw-Hill 156 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Multiplying Integers Pre-Activity Complete the Mini Lab at the top of page 134 in your textbook. Write your answers below. 1. Write a multiplication sentence that describes the model. 2. 3(2) 3. 4(3) 4. 1(7) 5. 5(2) 6. Write a rule for finding the sign of the product of a positive and negative integer. Reading the Lesson 7. Give an example that shows how multiplication is the same as repeated addition. In your example, tell what the addend is. 8. How does the sentence 4(2)  2(4) illustrate the Commutative Property of Multiplication? 9. Complete each of the following sentences with the word positive or negative. a. The product of two integers with different signs is _______________. b. The product of two integers with the same sign is _______________. Helping You Remember 10. You know the rule for determining the sign of the product of two integers when the signs are alike or different. Consider the product of three integers. With a partner summarize the signs of the products of 3 integers when three, two, one or none of the integers are positive. © Glencoe/McGraw-Hill 157 Mathematics: Applications and Concepts, Course 2 Lesson 3–6 Find each product using counters. NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Integer Maze Find your way through the maze by moving to the expression in an adjacent section with the next highest value. −[12 − (−8)] −3(5) −12 + 2 2[−5 • (−5)] −52 −35 + 5 3(5)(−5) 15 − 50 5(−9) −55 −8(5) 9(−1) 6(−10) 3(−3)(−5) 4 + (−12) 5(−4 + 9) −4(5)(−1) 9(−6) −50 20 − 20 Start (−4)2 −5(−6) −3 + (−4) −1(3) 0−6 6−8 −4(2) −2(−12 + 7) −32 + 28 −5 −13 + 12 3 + (−3) −2(−5)(−1) © Glencoe/McGraw-Hill 30 − (−10) −3(−5) −10 + 16 −2(−1) 158 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Study Guide and Intervention Dividing Integers The quotient of two integers with different signs is negative. The quotient of two integers with the same sign is positive. Divide 30  (5). 30  (5) The integers have different signs. 30  (5)  6 The quotient is negative. 100  (5) The integers have the same sign. 100  (5)  20 The quotient is positive. Divide. 1. 12  4 2. 14  (7) 3. 18 4. 6  (3) 5. 10  10 6. 80 7. 350  (25) 8. 420  (3) 2 9. 540 45 20 10. 256 16 ALGEBRA Evaluate each expression if d  24, e  4, and f  8. 11. 12  e 12. 40  f 13. d  6 14. d  e 15. f  e 16. e2  f 17. d 18. ef  2 e 19. f2 e2 © Glencoe/McGraw-Hill 20. de f 159 Mathematics: Applications and Concepts, Course 2 Lesson 3–7 Divide 100  (5). NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Skills Dividing Integers Divide. 1. 15  3 2. 24  (8) 3. 22  (2) 4. 49  (7) 5. 8  (8) 6. 36 7. 225  (15) 8. 0 9. 38  2 11. 500  (50) 4 9 10. 64 4 12. 189  (21) ALGEBRA Evaluate each expression if m  32, n  2, and p  8. 13. m  n 14. p  4 15. p2  m 16. m  p p n 18. p  n2 17. 19. p2 n2 21. m  (np) © Glencoe/McGraw-Hill 20. 18  n p 22. m  n p 160 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Practice: Word Problems Dividing Integers 1. STOCK MARKET During a 5-day workweek, the stock market decreased by 65 points. Find the average daily change in the market for the week. 2. MOTION Mr. Diaz decreased the speed of his car by 30 miles per hour over a period of 10 seconds. Find the average change in speed each second. 3. WEATHER Over the past seven days, Mrs. Cho found that the temperature outside had dropped a total of 35 degrees. Find the average drop in temperature each day. 4. BASKETBALL The basketball team lost their last 6 games. They lost by a total of 48 points. Find the average number of points by which each game was lost. 5. POPULATION The enrollment at Davis Middle School dropped by 60 students over a 5-year period. What is the average yearly drop in enrollment? 6. SUBMARINE A submarine descends at a rate of 60 feet each minute. How long will it take it to descend to a depth of 660 feet below the surface? © Glencoe/McGraw-Hill 161 Mathematics: Applications and Concepts, Course 2 Lesson 3–7 Divide. NAME ________________________________________ DATE ______________ PERIOD _____ Reading to Learn Mathematics Dividing Integers Pre-Activity Complete the Mini Lab at the top of page 138 in your textbook. Write your answers below. Find each quotient using counters. 1. 6  2 2. 12  3 Reading the Lesson Write two division sentences related to each of the following multiplication sentences. 3. 6(3)  18 4. 21(2)  42 5. 6(3)  18 6. 2(21)  42 7. Complete each of the following sentences with the word positive or negative. a. The quotient of two integers with different signs is _______________. b. The quotient of two integers with the same sign is _______________. 8. In the division sentence 72  8  9, identify the dividend, the divisor, and the quotient. Helping You Remember 9. Describe how the operations of multiplication and division are opposite of each other. Are these operations opposite in all cases? What is the one integer that cannot be a divisor? © Glencoe/McGraw-Hill 162 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Enrichment Division by Zero? Some interesting things happen when you try to divide by zero. For example, look at these two equations. 5 x 0 0 y 0 If you can write the equations above, you can also write the two equations below. 0 x5 0 y0 However, there is no number that will make the left equation true. This equation has no solution. For the right equation, every number will make it true. The solutions for this equation are “all numbers.” Describe the solution set for each equation. 1. 4x  0 2. x 0  0 3. x 0  x 4. 5. 0  x 6. 0  5 x 0 x 0 x What values for x must be excluded to prevent division by 0? 7. 12 8. x 9. 11. 1 x1 1 x1 10. 0 1 2x  2 12. 2x 1 3x  6 Explain what is wrong with this “proof.” 13. Step 1 0 1  0 and 0 (1)  0 Step 2 Therefore, 0  1 and 0  1. Step 3 Therefore, 1  1. 0 © Glencoe/McGraw-Hill 0 163 Mathematics: Applications and Concepts, Course 2 Lesson 3–7 Because division by zero leads to impossible situations, it is not a “legal” step in solving a problem. People say that division by zero is undefined, or not possible, or simply not allowed. NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 1 SCORE _____ Write the letter for the correct answer in the blank at the right of each question. 1. Write an integer that represents 8C below 0. A. 8 B. 8 C. 8 D. 8 1. G. 3 H. 3 3. Evaluate 9. A. 0 B. 9 C. 18 I. 0 2. D. 9 3. 4. Write the integers represented by S and T on the number line. F. S, 4; T, 2 G. S, 4; T, 2 S H. S, 2; T, 4 I. S, 2; T, 4 T 6 5 4 3 2 1 0 1 2 3 4 5 5. Order 4, 5, 3, and 0 from least to greatest. A. 0, 3, 4, 5 B. 5, 0, 3, 4 C. 4, 3, 0, 5 6. Simplify 4(9a). F. 13a G. 5a D. 0, 5, 3, 4 H. 36a 7. What value of z makes 14  3  z a true sentence? A. 11 B. 17 C. 11 4. 5. I. 49a 6. D. 17 7. Replace each  to make a true sentence. 8. 4  0 F.  G.  H.  I.  8. 9. 3  6 A.  B.  C.  D.  9. Use the graph to name the ordered pair for each point. 10. J F. (0, 2) H. (2, 0) 4 3 2 1 G. (0, 2) I. (2, 0) J 432 O y R 10. 1 2 3 4x 11. M A. (3, 3) C. (3, 3) B. (3, 3) D. (3, 3) 12. R F. (2, 4) G. (4, 2) H. (2, 4) I. (2, 4) 12. 13. T A. (1, 4) B. (1, 4) C. (1, 4) D. (4, 1) 13. © Glencoe/McGraw-Hill T 165 2 3 4 M 11. Mathematics: Applications and Concepts, Course 2 Assessment 2. Evaluate 3. F. 6 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 1 (continued) Add, subtract, multiply, or divide. 14. 8  (7) F. 1 G. 1 H. 15 I. 15 14. 15. 7(6) A. 1 B. 42 C. 42 D. 13 15. 16. 18  (9) F. 9 G. 2 H. 9 I. 2 16. 17. 35  12 A. 23 B. 23 C. 47 D. 47 17. 18. (3)2 F. 9 G. 1 H. 6 19. 0  20 A. 20 B. 20 C. 2 I. 9 18. D. 0 19. Evaluate each expression if a  4, b  6, and c  1. 20. 10  a F. 6 G. 6 H. 14 21. bc A. 6 B. 6 C. 5 G. 6 H. 2 23. 9  b A. 54 B. 3 C. 3 24. b  2 F. 4 G. 4 25. c  5 A. 4 B. 4 I. 14 20. D. 5 21. I. 2 22. D. 15 23. H. 62 I. 3 24. C. 6 D. 6 25. 22. 12 b F. 18 Bonus Find |t  v| when t  9 and v  5. © Glencoe/McGraw-Hill B: 166 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2A SCORE _____ Write the letter for the correct answer in the blank at the right of each question. 1. Write an integer that represents a 5-yard loss. A. 5 B. 5 C. 5 G.  7 3. Evaluate 52. A. 7 B. 3 1. I. 7 H. 14 C. 3 D. 7 4. Write the integers represented by A and B on the number line. F. A, 3; B, 5 G. A, 3; B, 5 B A H. A, 3; B, 5 I. A, 5; B, 3 4 2 0 2 3. 4 5. Order 6, 2, 3, 0, and 1 from least to greatest. A. 2, 1, 0, 3, 6 B. 2, 0, 1, 3, 6 C. 1, 2, 0, 3, 6 D. 0, 1, 2, 3, 6 6. Simplify 8(3z). F. 24z G. 5z 2. 4. 5. H. 24z I. 11z 7. What value of q makes 15  (9)  q a true sentence? A. 24 B. 6 C. 24 6. D. 6 7. Replace each  to make a true sentence. 8. 5  2 F.  G.  H.  I.  8. 9. 1  7 A.  B.  C.  D.  9. Use the graph to name the ordered pair for each point. 10. Q F. (0, 3) H. (2, 3) G. (2, 3) I. (2, 3) Q 432 4 3 2 1 O y 10. E 1 2 3 4x 11. E A. (0, 3) C. (3, 0) B. (2, 3) D. (3, 0) 12. P F. (2, 3) G. (3, 2) H. (3, 2) I. (3, 2) 12. 13. B A. (1, 4) B. (1, 4) C. (4, 1) D. (1, 4) 13. © Glencoe/McGraw-Hill P 167 2 3 4 B 11. Mathematics: Applications and Concepts, Course 2 Assessment 2. Evaluate 7. F. 7 D. 5 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2A (continued) Add, subtract, multiply, or divide. 14. 12  (5) F. 7 G. 7 H. 17 15. 8(10) A. 80 B. 80 C. 18 D. 18 15. G. 2 H. 24 I. 0.5 16. B. 29 C. 45 D. 296 17. G. 4 H. 21 I. 21 18. B. 5 C. 0 I. 17 14. 16. 48 24 F. 2 17. 37  8 A. 45 18. 7(3) F. 2 1 3 19. 0  5 A. 10 D. 5 19. Evaluate each expression if x  3, y  8, and z  4. 20. y  (5) F. 3 G. 13 H. 13 I. 3 20. 21. xz A. 12 B. 12 C. 7 D. 1 21. 22. 8  y F. 0 G. 16 H. 1 I. 1 22. 23. x  11 A. 8 B. 14 C. 8 G. 8 H. 4 B. 1 C. 15 D. 14 23. 2 24. z 2 F. 4 25. x  y  z A. 1 Bonus Find q  r when q  3 and r  3. © Glencoe/McGraw-Hill 168 I. 8 D. 15 24. 25. B: Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2B SCORE _____ Write the letter for the correct answer in the blank at the right of each question. 1. Write an integer that represents a loss of $20. A. 20 B. 20 C. 20 D. 20 1. G.  4 3. Evaluate 73. A. 10 B. 4 H. 4 I. 8 C. 4 2. D. 10 4. Write the integers represented by Q and R on the number line. F. Q, 3; R, 1 G. Q, 3; R, 1 R Q H. Q, 1; R, 3 I. Q, 1; R, 3 4 2 0 2 3. 4 5. Order 3, 4, 0, 1, and 2 from least to greatest. A. 4, 2, 0, 1, 3 B. 3, 1, 0, 2, 4 C. 3, 1, 0, 4, 2 D. 2, 4, 0, 1, 3 6. Simplify 5(7r). F. 35r G. 35r 4. 5. I. 12r H. 2r 7. What value of s makes 18  (5)  s a true sentence? A. 13 B. 23 C. 23 D. 13 6. 7. Replace each  to make a true sentence. 8. 10  10 F.  G.  H.  I.  8. 9. 3  5 A.  B.  C.  D.  9. Use the graph to name the ordered pair for each point. 10. S F. (5, 5) H. (5, 5) G. (1, 3) I. (5, 5) 11. R A. (6, 5) C. (5, 5) B. (5, 6) D. (6, 5) R 5 4 3 2 1 5432 A 12. A F. (3, 4) G. (3, 4) H. (3, 4) 13. M A. (3, 1) B. (1, 3) C. (1, 3) © Glencoe/McGraw-Hill 169 O 2 3 4 5 y S 10. 1 2 3 4 5x M 11. I. (4, 3) D. (3, 1) 12. 13. Mathematics: Applications and Concepts, Course 2 Assessment 2. Evaluate 4. F. 4 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2B (continued) Add, subtract, multiply, or divide. 14. 11  (7) F. 4 G. 4 H. 18 15. 5(11) A. 16 B. 16 C. 55 16. 15  (3) F. 5 G. 5 17. 39  7 A. 46 I. 18 14. D. 55 15. H. 18 I. 18 16. B. 46 C. 273 D. 32 17. 18. 8(4) F. 2 G. 32 H. 4 I. 32 18. 19. 0  7 A. 0 B. 7 C. 14 D. 7 19. Evaluate each expression if a  4, b  7, and c  5. 20. b  (4) F. 3 G. 11 H. 3 21. ac A. 20 B. 20 C. 1 G. 0 H. 1 23. a  13 A. 17 B. 9 C. 17 24. c2  5 F. 5 G. 5 H. 2 25. a  b  c A. 16 B. 6 C. 16 I. 11 D. 9 20. 21. 22. 7 b F. 14 Bonus Find s  t when s  5 and t  5. © Glencoe/McGraw-Hill 170 I. 1 22. D. 9 23. I. 30 24. D. 6 25. B: Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2C SCORE _____ Write an integer for each situation. 1. a deposit of $45 1. 2. 5C below 0 2. For Questions 3 and 4, evaluate each expression. 3. |11| 3. 4. |4|  |6| 4. 5. Graph the set of numbers {3, 2, 5} on a number line. 5. 6 3 0 3 For Questions 6–8, replace each  with  or  to make a true sentence. 6. 16  22 6. 7. 5  1 7. 8. 12  1 8. 9. Order 2, 5, 0, 7, 1, and 3 from least to greatest. 9. Name the ordered pair for each point graphed at the right. Then identify in which quadrant each point lies. 11. S 4 3 2 1 S 432 12. T T O 2 3 4 10. Assessment 10. TEMPERATURE On the same day, a thermometer registered 4F in Athens and 9F in Seattle. Which Washington city was warmer? y 1 2 3 4x 11. 12. Graph and label each point. 13. Q(1, 2) 13–14. 4 3 2 1 14. W(0, 4) 432 O y 1 2 3 4x 2 3 4 © Glencoe/McGraw-Hill 171 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2C (continued) Add, subtract, multiply, or divide. 15. 25  (12) 15. 16. 8(11) 16. 17. 40  (8) 17. 18. 4  (2) 18. 19. (3)2 19. 20. 6  (9) 20. 21. 9  8 21. 22. 6 22. 3 Evaluate each expression if x  4, y  6, and z  3. 23. 15  (y) 23. 24. 20  x 24. 25. 7  z 25. 26. 2(3z) 26. 27. xy 27. 28. x  y 28. 29. xy 29. 30. x  z 30. 12 For Questions 31 and 32, simplify each expression. 31. 5(3a) 31. 32. 3(4c) 32. 33. What value of w makes 24  (13)  w a true sentence? 33. Bonus Find a  b when a  6 and b  6. © Glencoe/McGraw-Hill 172 B: Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2D 2C SCORE _____ Write an integer for each situation. 1. 300 feet above sea level 1. 2. a loss of $13 2. For Questions 3 and 4, evaluate each expression. 3. |13| 3. 4. |3||5| 4. 5. Graph the set of numbers on a number line: {6, 2, 3}. 5. 6 3 0 3 For Questions 6–8, replace each  with  or  to make a true sentence. 6. 7  5 6. 7. 0  35 7. 8. 1  1 8. 9. Order 3, 8, 4, 2, 5, and 1 from least to greatest. 9. Name the ordered pair for each point graphed at the right. Then identify in which quadrant each point lies. 11. R 4 3 2 1 432 O 2 3 4 12. Q 10. Assessment 10. TEMPERATURE On the same day, a thermometer registered 10F in Duluth and 7F in St. Paul. Which Minnesota city was warmer? y R 1 2 3 4x Q 11. 12. Graph and label each point. 13. A(3, 2) 13–14. 4 3 2 1 14. S(0, 2) 432 O y 1 2 3 4x 2 3 4 © Glencoe/McGraw-Hill 173 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 2D (continued) Add, subtract, multiply, or divide. 15. 2  4 15. 16. 7(10) 16. 17. 60 17. 18. 6  (3) 18. 19. (5)2 19. 20. 1  (11) 20. 21. 10  7 21. 22. 8  (4) 22. 3 Evaluate each expression if a  8, b  5, and c  2. 23. 8  (b) 23. 24. 16  c 24. 25. 9  c 25. 26. 5(3c) 26. 27. ab  10 27. 28. a  b 28. 29. ab 29. 30. a  c 30. For Questions 31 and 32, simplify each expression. 31. 6(5z) 31. 32. 4(2y) 32. 33. What value of d makes 25  (16)  d a true sentence? 33. Bonus Find |xy| when x  7 and y  7. © Glencoe/McGraw-Hill 174 B: Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 3 SCORE _____ Write an integer for each situation. 1. 380 meters above sea level 1. 2. a loss of 11 yards 2. For Questions 3 and 4, evaluate each expression. 3. |16| 3. 4. |3||1| 4. 5. Graph the set of numbers {5, 3, 2, 4} on a number line. 5. 4 2 0 2 4 For Questions 6–8, replace each  with  or  to make a true sentence. 6. 28  30 6. 7. 8  5 7. 8. 11  10 8. 9. Order 5, 7, 4, 0, 3, and 10 from least to greatest. 9. Name the ordered pair for each point graphed at the right. Then identify in which quadrant each point lies. 11. A A 432 4 3 2 1 O 2 3 4 12. B 10. Assessment 10. TEMPERATURE On the same day, a thermometer registered 8C in Chicago, Illinois and 5C in Detroit, Michigan. Which city was colder? y B 1 2 3 4x 11. 12. Graph and label each point. 13. L(2, 4) 13–14. 4 3 2 1 14. M(0, 3) 432 L © Glencoe/McGraw-Hill 175 O y 1 2 3 4x 2 M 3 4 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Test, Form 3 (continued) Add, subtract, multiply, or divide. 15. 40  12 15. 16. 6(4) 16. 17. 0 17. 18. 5  3  2 18. 19. (112) 19. 20. 13  18  (2) 20. 21. 18  (21) 21. 22. 56  (7) 22. 3 23. q  r 23. 24. 2qr 24. 25. 9  s 25. 26. qs  8 26. 27. rs2 27. 28. 10  q 28. s2 29. s  2 29. 30. q  r  s 30. For Questions 31 and 32, simplify each expression. 31. 5(7e) 31. 32. (2b)(3c) 32. 33. What value of a makes 18  (3)  a a true statement? 33. Bonus PATTERNS Find the next two numbers in the following pattern: 96, 48, 24, 12, … Then describe the pattern. © Glencoe/McGraw-Hill 176 B: Mathematics: Applications and Concepts, Course 2 Assessment Evaluate each expression if q  8, r  5, and s  3. NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Extended Response Assessment SCORE _____ Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solutions in more than one way or investigate beyond the requirements of the problem. If necessary, record your answer on another piece of paper. 1. Horatio, Glen, Carlos, and Meredith played in the company golf tournament. Their scores after the first round are listed below. Horatio: two over par (2) Glen: three under par (3) Carlos: four over par (4) Meredith: one under par (1) a. Explain how to compare integers. b. Order the golf scores from least to greatest. c. Explain what is meant by the absolute value of a number. d. Find the absolute value of Glen’s score. f. Meredith’s second round score is 3. Find her total score after two rounds. g. Horatio’s second round score is 3. Use counters to find the difference between Horatio’s first and second round scores. 2. On graph paper, draw a coordinate plane. a. Graph and label the point A(4, 6). Describe how you locate this point. Identify the quadrant in which the point lies. b. Multiply the x-coordinate of point A by 2 and multiply the y-coordinate of point A by 1. Name the new point B and give its coordinates. Graph point B and identify the quadrant in which it lies. c. Divide the x-coordinate of point B by 4 and divide the y-coordinate of point B by 3. Name the new point C and give its coordinates. Graph point C and identify the quadrant in which it lies. © Glencoe/McGraw-Hill 177 Mathematics: Applications and Concepts, Course 2 Assessment e. Glen’s second round score is 2. Use counters to find Glen’s total score after two rounds. NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Vocabulary Test/Review absolute value (p. 107) additive inverse (p. 121) coordinate grid (p. 112) coordinate plane (p. 112) graph (p. 106) integer (p. 106) negative integer (p. 106) opposite (p. 121) ordered pair (p. 112) origin (p. 112) positive integer (p. 106) quadrant (p. 113) SCORE _____ x-axis (p. 112) x-coordinate (p. 112) y-axis (p. 112) y-coordinate (p. 112) Choose from the terms above to complete each sentence. 1. Vertical bars before and after a number indicate _______________, the distance a number is from zero on a number line. 1. 2. A(n) _______________ is a number that can be graphed on a number line. 2. 3. When you _______________ a point, you locate its position on a coordinate plane by drawing a dot at the location of its ordered pair. 3. 4. The _______________ is the opposite of any number. When added to the number, the sum equals 0. 4. 5. The _______________ is the first number of an ordered pair. It corresponds to a number on the x-axis. 5. 6. The _______________ is the vertical number line of a coordinate plane. 6. 7. A(n) _______________ is an integer less than zero. 7. 8. The point at which the number lines of a coordinate plane intersect is called the _______________. 8. 9. Two integers that are the same distance from 0 on a number line, but on opposite sides of 0, are called _______________ . 9. 10. A(n) _______________ is one of four sections of a coordinate plane. 10. In your own words, define each term. 11. coordinate plane 12. ordered pair © Glencoe/McGraw-Hill 178 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ SCORE _____ Chapter 3 Quiz (Lessons 3-1 and 3-2) 1. MULTIPLE-CHOICE TEST ITEM Order the integers 2, 4, 7, 5, and 1 from least to greatest A. 2, 5, 1, 4, 7 B. 1, 2, 4, 5, 7 C. 5, 2, 1, 4, 7 D. 7, 4, 1, 2, 5 Write an integer for each situation. 2. 15F below 0 1. 2. 3. a deposit of $24 3. Evaluate each expression. 4. |3| 4. 5. |9| 5. 6. |13||2| 6. Replace each  with  or  to make a true sentence. 7. 34  134 7. 8. 27  8 8. 9. 12  12 9. 10. 111  888 NAME ________________________________________ DATE ______________ PERIOD _____ SCORE _____ Chapter 3 Quiz (Lessons 3-3 and 3-4) On the coordinate plane, graph and label each point. 1. S(1, 0) 1–3. 4 3 2 1 2. R(3, 1) 3. T(3, 2) 432 O y 1 2 3 4x 2 3 4 4. Find 12  (7). 4. 5. Evaluate x  y if x  8 and y  4. 5. © Glencoe/McGraw-Hill 179 Mathematics: Applications and Concepts, Course 2 Assessment 10. NAME ________________________________________ DATE ______________ PERIOD _____ SCORE _____ Chapter 3 Quiz (Lessons 3-5 and 3-6) Subtract or multiply. 1. 8  5 1. 2. 10(3) 2. 3. (92) 3. 4. 15  (20) 4. Evaluate each expression if f  4, g  2, and h  7. 5. 9g 5. 6. h  3 6. 7. h  f 7. 8. fgh 8. Simplify each expression. 9. 2(9e) 9. 10. 5(4s) 10. NAME ________________________________________ DATE ______________ PERIOD _____ SCORE _____ Chapter 3 Quiz (Lesson 3-7) 1. Find the quotient of 56 and 14. 1. Divide. 2. 63  (9) 2. 3. 21  7 3. Evaluate each expression if r  18, s  4, and t  3. 4. r  t 4. 5. st  6 5. © Glencoe/McGraw-Hill 180 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Chapter 3 Mid-Chapter Test SCORE _____ (Lessons 3-1 through 3-4) 1. Evaluate |5|. A. 4 C. |5| B. 5 2. Evaluate |6||2|. F. 4 G. 8 H. 8 D. 5 1. I. 4 2. 3. Order the integers 6, 4, 18, 4, 3, and 7 from least to greatest. A. 3, 4, 6, 18, 4, 7 B. 18, 6, 4, 3, 4, 7 C. 4, 7, 3, 4, 6, 18 D. 7, 4, 3, 4, 6, 18 3. 4. Find 8  12. F. 20 I. 4 4. 5. Evaluate a  b if a  3 and b  14. A. 17 B. 11 C. 17 D. 11 5. 6. Identify the quadrant in which (1, 4) lies. F. I G. II H. III I. IV 6. G. 4 H. 20 Write an integer for each situation. 7. a deposit of $50 7. 8. 3 inches below normal 8. Replace each  with  or  to make a true sentence. 9. 9. 14  2 10. 111  11 10. Name the ordered pair for each letter and identify its quadrant. 11. Q Z 12. U 13. X 14. Z 5432 U 5 4 3 2 1 O 2 3 4 5 15. Find (12)  8  (7). © Glencoe/McGraw-Hill y Q 11. 12. 1 2 3 4 5x 13. X 14. 15. 181 Mathematics: Applications and Concepts, Course 2 Assessment Write the letter for the correct answer in the blank at the right of each question. NAME ________________________________________ DATE ______________ PERIOD _____ SCORE _____ Chapter 3 Cumulative Review (Chapters 1–3) 1. Evaluate the expression 2d  5f if d  4 and f  2. 1. (Lesson 1-4) TENNIS For Questions 2–4, use the stem-and-leaf plot below. It shows the number of matches won by each member of the East High School Tennis Team. 2. How many members are on the tennis team? (Lesson 2-5) 3. Find the mean, median, mode, and range for these data. (Lessons 2-3, 2-4) Stem 0 1 2 3 4 5 Leaf 34 578 02247 1355 0 4 2. 3. 3|1  31 4. Write a sentence or two to describe the distribution of the number of matches won. (Lesson 2-5) 4. 5. Evaluate |3|  |2|. (Lesson 3-1) 5. 6. Order 61, 72, 50, 31, 12, and 12 from least to greatest. 6. (Lesson 3-2) 7. Which is greater, 9 or 8? (Lesson 3-2) 7. Graph and label each point. (Lesson 3-3) 8. A(2, 2) 9. M(3, 1) 8–9. 4 3 2 1 432 O y 1 2 3 4x 2 3 4 Add, subtract, multiply, or divide. 10. 4  (4) (Lesson 3-4) 10. 11. 18  12 (Lesson 3-5) 11. 12. 5(6) (Lesson 3-6) 12. 13. 12  (3) (Lesson 3-7) 13. © Glencoe/McGraw-Hill 182 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Standardized Test Practice SCORE _____ (Chapters 1–4) Part 1: Multiple Choice Instructions: Fill in the appropriate oval for the best answer. 1. Evaluate 7b  a if a  5 and b  2. (Lesson 1-4) A. 9 B. 33 C. 12 D. 21 1. A B C D 2. If there are 28 basketball games during a season, how many games ended in a winning score of 70–79 points? (Lesson 2-1) F. 28 G. 8 H. 3 I. 5 Score Frequency 50–59 2 60–69 5 70–79 ? 80–89 12 2. F G H I 3. Find the median of the following data. 5, 9, 13, 4, 7, 5, 10 (Lesson 2-4) A. 5 B. 7 C. 8 90–99 6 3. A B C D 4. F G H I D. 15 5. A B C D I. 5 6. F G H I 7. In which quadrant is the point (5, 7) located? (Lesson 3-2) A. I B. II C. III D. IV 7. A B C D 8. Evaluate x  11 if x  10. (Lesson 3-5) F. 21 G. 21 H. 1 8. F G H I 9. A B C D U.S. Landfill Content (Lessons 2-3, 2-6) A. 5 B. 16 2 35 30% 30 24% Percent 25 21% 20 15 10 11% 8% 6% 5 4 6 8 O th er M et al Ru P bb la st er ic Fo & od Le at & h Ya rd er W as te Pa pe r 0 10 12 14 16 18 20 22 C. 7 6. Evaluate |9|  |4|. (Lesson 3-1) F. 13 G. 13 H. 5 I. 1 9. Evaluate ac  b if a  8, b  6, and c  3. (Lessons 3-6, 3-7) A. 144 B. 4 C. 16 D. 4 © Glencoe/McGraw-Hill 183 Mathematics: Applications and Concepts, Course 2 Assessment 4. ENVIRONMENT The bar graph represents the content (in percents) of U.S. landfills. Which is not a true statement? (Lesson 2-7) F. The mode is paper. G. Metal makes up 8% of landfills. H. Plastic and paper make up most of landfills. I. The median is 24%. 5. What is the range of data in the following box-and-whisker plot? D. 9 NAME ________________________________________ DATE ______________ PERIOD _____ Standardized Test Practice (continued) (Chapters 1–4) Part 2: Short Response\Grid In Instructions: Enter your grid in answers by writing each digit of the answer in a column box and then shading in the appropriate circle that corresponds to that entry. Write answers to short answer questions in the space provided. 10. Solve 20  n (Lesson 1-5) 10. 4 11. 11. Evaluate a if a  16 and b  2. (Lesson 3-7) b 0 1 2 3 4 5 6 7 8 9 12. The frequency table summarizes the number of DVDs owned by students in a classroom. Describe the interval and scale. (Lesson 2-1) 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 Number Tally Frequency of DVDs 13. Find 6  (12). (Lesson 3-4) 0–4 5 5 5–9 52 7 10–14 55 10 15–19 3 3 20–24 2 2 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 12. 13. Part 3: Extended Response Instructions: Write your answers below or to the right of the questions. 14. GEOMETRY Consider the points A(2, 4), B(3, 4), C(3, 0), and D(2, 0). (Lesson 3-3) a. Graph the points in the same coordinate plane. Describe how you locate point A. 4 3 2 1 432 b. Multiply the x-coordinate of point B by 1 and multiply the O y 1 2 3 4x 2 3 4 y-coordinate of point B by 1 . Name the new point B and give its 2 coordinates. Graph point B and identify the quadrant in which it lies. © Glencoe/McGraw-Hill 184 Mathematics: Applications and Concepts, Course 2 NAME ________________________________________ DATE ______________ PERIOD _____ Standardized Test Practice SCORE _____ Student Recording Sheet (Use with pages 146–147 of the Student Edition.) Multiple Choice Part 1: Select the best answer from the choices given and fill in the corresponding oval. 1. A B C D 4. F G H I 7. A B C D 2. F G H I 5. A B C D 8. F G H I 3. A B C D 6. F G H I 9. A B C D Part 2: 10. F G H I Short Response/Grid in Solve the problem and write your answer in the blank. For grid in questions, also enter your answer by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol. 11. 12. 12. 14. 19. (grid in) 13. 14. (grid in) 15. 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 Answers 16. 17. 18. 19. Part 3: (grid in) Extended Response Record your answer for Question 20 on the back of this paper. © Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 2 Standardized Test Practice Rubric (Use to score the Extended Response question on page 147 of the Student Edition.) General Scoring Guidelines • If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended response questions require the student to show work. • A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response. • Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit. Exercise 20 Rubric Score Specific Criteria 4 The 3 points are correctly graphed on a coordinate plane with all labels in place. The quadrant where no point on the graph is represented is recognized as quadrant IV. The figure formed by connecting the points is recognized as a triangle. An understanding that the way to double the size of the triangle is to multiply each ordered pair by 2 is demonstrated. The table in expanded and all values are correctly computed. 3 All of the parts of the question are correctly answered, but the graph is not correctly labeled. OR One of the points is not correctly graphed, but all other parts of the question are correct. OR The quadrant where no point on the graph is represented is not recognized as quadrant IV, but all other parts of the question are correct. OR The figure formed by connecting the points is not recognized as a triangle, but all other parts of the question are correct. OR There is no understanding that the way to double the size of the triangle is to multiply the ordered pair by 2, but all other parts of the question are correct. OR There are computational errors in the expanded table, but all other parts of the question are correct. 2 Two parts of the question (the graph, the recognition of the quadrant, the recognition of the triangle, the understanding of how to double the size of the figure, or the completion of the table) are incorrect. 1 Only one or two parts of the question (the graph, the recognition of the quadrant, the recognition of the triangle, the understanding of how to double the size of the figure, or the completion of the table) are correct. 0 Response is completely incorrect. © Glencoe/McGraw-Hill A2 Mathematics: Applications and Concepts, Course 2 © Glencoe/McGraw-Hill positive integers A3 12 20 © Glencoe/McGraw-Hill 9. 19 19 Mathematics: Applications and Concepts, Course 2 3 6 24 2 4 Mathematics: Applications and Concepts, Course 2 Answers 129 10. 84 84 8. 75 75 7. 8 8 1 6. 150 150 4. falling 6 feet 2. a loss of $24 4 3 2 1 0 5. 12 12 Evaluate each expression. 3. a gain of 20 pounds 1. 12°C above 0 Write an integer for each situation. 2 units away from 0. So, 2  2. On the number line, the graph of 2 is Evaluate |2|. Because it represents below sea level, the integer is 160. Write an integer that represents 160 feet below sea level. The absolute value of an integer is the distance the number is from zero on a number line. Two vertical bars are used to represent absolute value. The symbol for absolute value of 3 is 3. zero is neither positive nor negative 7654321 0 1 2 3 4 5 6 7 8 negative integers Integers less than zero are negative integers. Integers greater than zero are positive integers. Integers and Absolute Value Study Guide and Intervention NAME ________________________________________ DATE ______________ PERIOD _____ 15 0 45 23 120 376 © Glencoe/McGraw-Hill 4 3 2 1 0 23. {0, 2, 3} 1 2 3 4 27 150 9 19 22. |12||12| 4 107 20. |6||2| 18. |19| 16. |107| 14. |9| 130 1 2 3 4 60 200 Mathematics: Applications and Concepts, Course 2 4 3 2 1 0 24. {4, 1, 3} 0 12. 60 feet below sea level 10. 240 B.C. 240 8. a bonus of $150 6. a withdrawal of $200 4. average attendance is down 38 people 38 2. a profit of $27 Graph each set of integers on a number line. 21. 84 12 19. |0| 17. |45| 15. |23| 13. |1| 1 Evaluate each expression. 11. a wage increase of $120 41 3 9. a deposit of $41 7. 3 points lost 5. 376 feet above sea level 3. 2010 A.D. 2010 1. 15C below 0 Write an integer for each situation. Integers and Absolute Value Practice: Skills NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-1) Lesson 3–1 © Glencoe/McGraw-Hill A4 © Glencoe/McGraw-Hill 131 Mathematics: Applications and Concepts, Course 2 The airplane could be flying 100 meters higher or 100 meters lower, 100 or 100. 6. ALTITUDE An airplane pilot changed his altitude by 100 meters. Describe what this could mean. Sample answer: 4. TEMPERATURE In our world’s tropical rain forests, the average temperature of every month is 64 degrees above zero or higher. Write an integer to express this temperature. 64 3. ARCHIMEDES A famous mathematician and physicist named Archimedes was born in 287 B.C. Write an integer to express the year of his birth. 287 5. STOCK MARKET A certain stock gained 5 points in one day and lost 4 points the next day. Write integers to represent the stock’s gains and losses for the two days. 5; 4 2. RAIN A meteorologist reported that in the month of April there were 3 inches more rainfall than normal. Write an integer to represent the amount of rainfall above normal in April. 3 1. DEATH VALLEY The lowest point in the United States is Death Valley in California. Its altitude is 282 feet below sea level. Write an integer to represent the altitude of Death Valley. 282 Integers and Absolute Value Practice: Word Problems NAME ________________________________________ DATE ______________ PERIOD _____ 7 9 or 9 1 2 3 positive 4 © Glencoe/McGraw-Hill 132 Mathematics: Applications and Concepts, Course 2 6. Show a classmate how a number line can be used to show negative and positive integers. Explain the difference between some integers and the absolute values of those integers. Draw a number line to show what you mean. See students’ work. Helping You Remember 4 3 2 1 0 negative 5. On the following number line, draw a circle around the negative integers and label them negative. Draw a rectangle around the positive integers and label them positive. |7| 7 Words positive seven negative seven absolute value of seven Symbols 4. Express each of the following in words. Reading the Lesson 3. How can you represent a gain of 9 yards? 3rd down a 2-yard loss 2. On which down did they lose the most yards? 1. What does a value of 2 represent? Write your answers below. Pre-Activity Read the introduction at the top of page 106 in your textbook. Integers and Absolute Value Reading to Learn Mathematics NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-1) Mathematics: Applications and Concepts, Course 2 Lesson 3–1 © Glencoe/McGraw-Hill A5 17, 17 11. 4p  9  59 0 12. 7z  12  12 © Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2 Mathematics: Applications and Concepts, Course 2 Answers 133 false; the absolute value of 0 is 0, which is not positive. c. The absolute value of an integer is never negative. Statement a is b. There is at least one integer whose absolute value is zero. a. The absolute value of every integer is positive. 14. One of these statements is false. Which one is it? Explain. 13. Suppose that the value of x can be selected from the set {2, 1, 0, 1, 2}. Find all of the solutions of the equation x  x. 0, 1, 2 1, 1 10. 2d  3  5 6, 6 9. 48  8x 3, 3 20, 20 8. 12  g  4 12, 12 7, 7 7. 5z  60 14, 14 6. c  4  16 no solution 3. j  3 5. 10  m 3 0 2. r  0 4. t  1  15 8, 8 1. a  8 Solve each equation. (Hint: One equation has no solution.) So, the equation y  6 has two solutions: 6 and 6. You know that 6  6 and 6  6. Mr. Escalante teaches concepts students must master if they are to succeed in high school and college mathematics. One of these is the concept of absolute value. For instance, a student should be able to solve an equation like y  6 quickly using mental math. Here’s how. Jaime Escalante (1930– ) was born in La Paz, Bolivia, and came to the United States in 1963. For ten years, he worked at odd jobs to support himself and his family while pursuing his dream—becoming certified to teach high school mathematics in California. As a mathematics teacher, he has become well known for his ability to inspire students to succeed in mathematics at levels they never thought possible. In 1988, the story of Mr. Escalante and a group of his students was the subject of the popular motion picture Stand and Deliver. Jaime Escalante Enrichment NAME ________________________________________ DATE ______________ PERIOD _____ 4 Replace the 䊉 with  or  to make 1 䊉 6 a true sentence. The symbol points to the lesser number. 1  3 3 1 is greater than 1. 2 3  1 1 3 is less than 1. 4 3 2 1 0 1 2 3 4 1 2 3 4 5 © Glencoe/McGraw-Hill 4, |2|, 0, 3, 5 7, 0, 2, 4 3, 1, 2, 5 134  Mathematics: Applications and Concepts, Course 2 4. Order 3, 2, 4, 0, and 5 from greatest to least. 3. Order 0, 4, 2, and 7 from greatest to least. 2. Order 1, 5, 3, and 2 from least to greatest. 1. Replace the 䊉 with < or > to make 5 䊉 10 a true sentence. Order the integers by reading from left to right: 5, 3, 0, 2. 6 5 4 3 2 1 0 To order the integers, graph them on a number line. Order the integers 2, 3, 0, 5 from least to greatest. Since 1 is to the right of 6, 1  6. 7 6 5 4 3 2 1 0 Graph each integer on a number line. Words Symbols Model When two numbers are graphed on a number line, the number to the left is always less than (<) the number to the right. The number to the right is always greater than (>) the number to the left. Comparing and Ordering Integers Study Guide and Intervention NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lessons 3-1 and 3-2) Lesson 3–1 © Glencoe/McGraw-Hill A6 true false; Sample answer: 20  22 true © Glencoe/McGraw-Hill 65, 24, 15, 6, 7, 40 23. 40, 65, 7, 24, 6, 15 11, 6, 4, 0, 9, 17 135 Mathematics: Applications and Concepts, Course 2 24. 13, 0, 7, 8, 5, 2 13, 7, 2, 0, 5, 8 22. 9, 6, 0, 4, 17, 11 Order the integers from greatest to least. 47, 11, 6, 12, 20 21. 12, 6, 20, 47, 11 Order the integers from least to greatest. 20. 9  10 true 19. 4  4 true 18. 11 11 17. 810 true 16. 2 3 false; Sample answer: 2 3 15. 3 5 false; Sample answer: 3 1 14. 12  15 13. 20  22 12. 2  0 true 11. 7  3 true Determine whether each sentence is true or false. If false, change one number to make the sentence true. 10. 8 䊉 9  8. 6 䊉 7  7. 4 䊉 3  9. 7 䊉 2  6. 14 䊉 20  5. 25 䊉 3  2. 8 䊉 7  4. 2 䊉 5   3. 0 䊉 2  1. 15 䊉 16 700 105 The Iliad and the Odyssey are composed by Homer. T’sai Lun invents paper. 700, AD © Glencoe/McGraw-Hill Sample answer: 47  30 5. Nebraska’s lowest temperature was 47F, and Maine’s lowest temperature was 30F. Write a true statement using the two temperatures with the symbol  or . 104, 101 3. Arrange the highest temperatures from greatest to least. 118, 109, 105, 2200, 5, 450, 1241 1241 1. Write each year as an integer. Metal type developed in Korea BC AD 450 5 Ovid wrote Metamorphosis. Torah is compiled. BC Date of oldest existing papyrus 2200 AD BC Aprox. Year Event use the table below. It shows important events in the history of writing. 2 30 136 Mathematics: Applications and Concepts, Course 2 230 6. MONEY Mr. Firewalks pays close attention to how much money is in his checking account. One week he deposited $230, spent $15 on a lunch, and loaned $25 to a friend. Write each transaction as an integer, and list them from least to greatest. 25, 15, 4. What is the median low temperature for these four states? 16 450, 5, 105, 1241; See students’ work. 109 Florida 47 3 Lowest 2. Order the integers from Exercise 1 from least to greatest. Write a sentence describing the earliest and most recent events in the table. 2200, 700, 101 118 104 Highest Maine Nebraska Alabama State Extreme Temperatures (F) EXTREME TEMPERATURES For Exercises 3–5, use the table below. It shows the extreme temperatures for four states. Temperatures are in degrees Fahrenheit. Comparing and Ordering Integers Comparing and Ordering Integers HISTORY OF WRITING For Exercises 1 and 2, Practice: Word Problems Practice: Skills Replace each 䊉 with < or > to make a true sentence. NAME ________________________________________ DATE ______________ PERIOD _____ Lesson 3–2 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-2) Mathematics: Applications and Concepts, Course 2 © Glencoe/McGraw-Hill 0 1 2 3 A7 1 2 4 3 2 1 0 1 2 3 is greater than negative 2 0 3 3 4 4 © Glencoe/McGraw-Hill See students’ work. Mathematics: Applications and Concepts, Course 2 Mathematics: Applications and Concepts, Course 2 Answers 137 7. Write a set of six numbers, some positive and some negative. Explain how you can use a number line to order the numbers from least to greatest. Helping You Remember Sample answer: The number to the left is always less than the number to the right. The number to the right is always greater than the number to the left. 6. When two numbers are graphed on a number line, what can you tell about the number to the left? the number to the right? 5. 3  2 4 3 2 1 4. 1  0 negative 1 is less than 0 For Exercises 4 and 5, express each of the following in words. Then graph the numbers on a number line. Reading the Lesson 5 4 3 2 1 3. Graph both wind chills found in Exercise 2 on a number line. 2. Which is colder, a temperature of 15 with a 20 mile-per-hour wind or a temperature of 10 with a 10 mile-per-hour wind? 10 with 10 mph wind 1. What is the wind chill if there is a wind at 20 miles per hour and the temperature is 5? 15 Write your answers below. Pre-Activity Read the introduction at the top of page 109 in your textbook. if the two quantities are equal; if the relationship cannot be determined from the information given. Shade circle B Shade circle C Shade circle D A C B B B B B B B B B B C C C C C C C C C C D D D D D D D D D D 10. 9. 8. 0 x if x is less than 0 2|x| if x |y| 0 138 Mathematics: Applications and Concepts, Course 2 |x| if x is less than 0 |x| if x |y| |x  1| x is x if greater than 0 0.000000001 6. |x| the greatest possible product of two even positive numbers less than 20 the greatest possible product of two odd positive numbers less than 20 5. 7. one fifth half of one third the perimeter of a square with an area of 25 square inches 4. 20 inches 1,000 million dollars ten billion dollars 2. 3. 0.002  6 0.006  2 Column B 1. © Glencoe/McGraw-Hill A A A A C D A A A A A B A A A C A B Column A Shade the correct oval to the left of each problem number. if the quantity in Column A is greater; if the quantity in Column B is greater; Shade circle A In each quantitative comparison question, you are given two quantities, one in Column A and one in Column B. You are to compare the two quantities and shade one of four circles on an answer sheet. An unusual type of problem is found on some standardized multiple-choice tests. This problem type is called the quantitative comparison. Quantitative Comparisons Enrichment Reading to Learn Mathematics Comparing and Ordering Integers NAME ________________________________________ DATE ______________ PERIOD _____ Lesson 3–2 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-2) © Glencoe/McGraw-Hill A8 Start at the origin. Move 0 units along the x-axis. Move 4 units down on the y-axis. Draw a dot and label it M(0, 4). (1, 3), I 4. S (2, 2), II 2. Q (3, 2), III © Glencoe/McGraw-Hill 10. F(1, 3) 139 8. D(3, 1) 7. C(3, 2) 9. E(1, 2) 6. B(0, 3) 5. A(1, 1) D O O 2 3 4 R 2 3 4 4 3 2 1 M (0, 4) O 1 2 3 4x y C B E 1 2 3 4x F P 1 2 3 4x y y 4 3 2 1 2 3 4 A 432 Q 432 S 4 3 2 1 432 P Mathematics: Applications and Concepts, Course 2 Graph and label each point on the coordinate plane. 3. R 1. P (2, 3), IV Name the ordered pair for each point graphed at the right. Then identify the quadrant in which each point lies. • • • • Graph and label the point M(0, 4). • Start at the origin. • Move 4 units left along the x-axis. • Move 3 units up on the y-axis. The ordered pair for point P is (4, 3). P is in the upper left quadrant or quadrant II. Name the ordered pair for point P. Then identify the quadrant in which P lies. The coordinate plane is separated into four sections called quadrants. Points are located using ordered pairs. The first number in an ordered pair is the x-coordinate; the second number is the y-coordinate. (3, 6), II (5, 4), II 16. K(1, 5) 15. M(5, 0) (5, 5) © Glencoe/McGraw-Hill 23. Grocery (7, 2) (7, 5) (0, 0) 22. Gas Station 21. Theater 20. City Hall Name the ordered pair for each point on the city map at the right. 19. D(0, 5) 140 M N K H O 2 3 4 5 O O 1 2 3 4 5 6 7x E B C J D 1 2 3 4 5x G y V A 1 2 3 4 5 6x D y 2 3 4 5 2 3 4 5 6 y 5 4 3 Gas Station 2 1 City Hall I 65432 C 6 5 4 3 2 1 A 5432 F 5 4 3 2 1 Mathematics: Applications and Concepts, Course 2 Theater 76 5432 Grocery 18. A(5, 3) 14. P(6, 2) 13. C(4, 0) 17. I(3, 3) 12. V(2, 4) 11. N(1, 3) P 10. J (3, 5), IV 8. H (2, 2), III 6. F 4. D (4, 3), IV 2. B (5, 5), I Graph and label each point on the coordinate plane. 9. I 7. G (0, 5), y-axis 5. E (3, 0), x-axis 3. C (5, 5), III 1. A (1, 1), II I The Coordinate Plane The Coordinate Plane The coordinate plane is used to locate points. The horizontal number line is the x-axis. The vertical number line is the y-axis. Their intersection is the origin. Practice: Skills Study Guide and Intervention Name the ordered pair for each point graphed at the right. Then identify the quadrant in which each point lies. NAME ________________________________________ DATE ______________ PERIOD _____ Lesson 3–3 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-3) Mathematics: Applications and Concepts, Course 2 © Glencoe/McGraw-Hill A9 O English Special Services 1 2 3 4 5x Counselor History y Exit © Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2 Mathematics: Applications and Concepts, Course 2 Answers 141 Quadrant I; Sample answer: Quadrant I is the upper-right quadrant. 6. NEIGHBORHOOD Refer to Exercise 5. In which quadrant is Delsin when he is done walking? Describe this quadrant. rooms; the x- and y-coordinates are all negative. Walk 9 units to the right, and then 5 units down. 5. NEIGHBORHOOD Delsin made a map of his neighborhood in such a way that each intersection is a point on a coordinate plane. Right now, Delsin stands at point (4, 3). Give the ordered pair of where he will be if moves 5 units to the right and 7 units up on the map. (1, 4) 4. On the map, which classrooms are located in the third quadrant? Describe the coordinates of all points in the third quadrant. Science and Math 2. Thalia’s next class is 8 units to the right and 5 units down on the map from where she is now. In what room is Thalia’s next class? Find the ordered pair that represents the location of that room. Music room; (6, 4) Science 2 Athletic Dept. 3 Math 4 Music 5 5432 Computer Lab Nurse Library 3. Tyrone is in the Art room, but his next class is in the History room. Give Tyrone directions on how to get to the History room. Sample answer: Computer Lab; move 2 units to the left and one unit up. 1. Thalia is in the room located at (2, 1). What room is she in? Describe in words how to get from the origin to this point. coordinate plane at the right. It shows a map of the rooms in a junior high school. 5 4 3 2 1 432 A 1 2 3 4x C B O y 2 3 4 4 3 2 1 © Glencoe/McGraw-Hill 142 Mathematics: Applications and Concepts, Course 2 both coordinates are positive (the upper-right quadrant). This is quadrant I. Name the rest of the quadrants by going counterclockwise around the quadrants: II (upper-left quadrant), III (lower-left quadrant), IV (lower-right quadrant). 6. Write a way to remember the names of the four quadrants of the coordinate plane. Sample answer: Begin in the quadrant where Helping You Remember quadrant II, point B is in quadrant I, and point C is in quadrant IV. 5. In the coordinate plane in Exercise 4, tell which quadrant each of the points is in. Point A is in A(3, 3); B(3, 2); C(3, 2) 4. Look at the coordinate plane at the right. Name the ordered pair for each point graphed. coordinate plane depends on position along an x-axis and position along a y-axis. Both positions, called the x-coordinate and the y-coordinate, are needed in order to locate a point in a coordinate plane. The pair of coordinates is called an ordered pair. The pair of coordinates is ordered such that the x-coordinate is always the first number of the pair and the y-coordinate is always the second number of the pair. 3. The word coordinate comes from two Latin words that mean “to arrange together.” How are coordinates used together to locate a point in a coordinate plane? Sample answer: The location of a point in a Reading the Lesson Sample answer: Walk 6 blocks west, 1 block south, and 1 block west. 2. Using the words north, south, west, and east, write directions to go from the corner of School and Highland to the corner of Main and Oak. Highland and Mobile 1. Suppose Terrell starts at the corner of Russel and Main and walks 1 block north and 2 blocks east. Name the intersection of his location. Write your answers below. Pre-Activity Read the introduction at the top of page 112 in your textbook. The Coordinate Plane Entrance The Coordinate Plane Art Reading to Learn Mathematics Practice: Word Problems SCHOOL For Exercises 1–4, use the NAME ________________________________________ DATE ______________ PERIOD _____ Lesson 3–3 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-3) Equator W 0˚ 15 60˚S 30˚S, 60˚W 30 ˚W 60 ˚W W 90 ˚ W 0˚ 12 A10 0˚ 60˚ E 30˚E Prime Meridian 60˚N 60˚S 30˚S © Glencoe/McGraw-Hill Japan 143 11. 35N, 140E 10. 60N, 45W Greenland Wisconsin 8. 45N, 90W Australia 5. 30S, 140E South Africa 2. 30S, 30E California 7. 40N, 120W Hawaii 4. 15N, 150W Atlantic Ocean 1. 30N, 30W Mathematics: Applications and Concepts, Course 2 Indian Ocean 12. 0, 60E Spain 9. 40N, 5W Mexico 6. 25N, 100W Canada 3. 60N, 120W Name a place near each location. Use an atlas or other reference source to check your answers. 0˚ 30˚N (Sample answers are given. Students may provide more specific places.) 30˚S 0˚ 30˚N 60˚N 90 E ˚ The latitude is usually given first. For example, the location of 30S, 60W is lower South America. 0˚ E 12 E 0˚ 15 ˚E 18 © Glencoe/McGraw-Hill 0 This world map shows some of the latitude and longitude lines. Latitude is measured in degrees north and south of the equator. Longitude is measured in degrees east and west of the prime meridian, a line passing through Greenwich, England. (Greenwich is a suburb of London.) Latitude and Longitude Enrichment NAME ________________________________________ DATE ______________ PERIOD _____ 20 8. 100  (25) 5. 22  (7) 2. 8  1 9 4  (6) 2 1           75 29 23 © Glencoe/McGraw-Hill 13. b  c 4 10. a  15 17 144 14. 10  c 6 11. b  (9) 4 5 15 Mathematics: Applications and Concepts, Course 2 15. 12  b 4 12. a  b 0 0 3 9. 35  20 6. 50  50 3. 7  10 3 2 1 0 1 2 3 4  (6) 2 4 6 Method 2 Use a number line. • Start at 0. • Move 4 units right. • Then move 6 units left. Evaluate each expression if a  8, b  8, and c  4. 5 7 7. 10  (10) 4. 16  (11) 1. 5  (2) Add. 4  (6)           Method 1 Use counters. Combine a set of 4 positive counters and a set of 6 negative counters on a mat. Find 4  (6). To add integers, it is helpful to use counters or a number line. For integers with different signs, subtract their absolute values. The sum is: • positive if the positive integer has the greater absolute value. • negative if the negative integer has the greater absolute value. For integers with the same sign: • the sum of two positive integers is positive. • the sum of two negative integers is negative. Adding Integers Study Guide and Intervention NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lessons 3-3 and 3-4) Mathematics: Applications and Concepts, Course 2 Lesson 3–3 Adding Integers Adding Integers © Glencoe/McGraw-Hill 2 11 3 A11 13 6 12. 28  16 12 10. 14  (13) 27 20. a  (7) 19. 12  b 145 © Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2 Answers Mathematics: Applications and Concepts, Course 2 22. a  c 12 15 3 21. 21  c 17 0 18. b  c 8 17. a  0 8 14. b  (9) 16. a  b 4 3 15. c  (5) 9 13. 5  a 23 14 8. 11  (12) 6. 7  13 4. 7  (7) 2. 3  3 0 Evaluate each expression if a  8, b  12, and c  4. 11. 14  (27) 9. 25  (12) 13 7. 15  (10) 5 5. 8  10 3. 3  (8) 1. 5  (8) Add. Tell whether each sum is positive, negative, or zero without adding. Practice: Word Problems Practice: Skills © Glencoe/McGraw-Hill 5. CYCLING A cyclist travels downhill for 125 feet. Then she travels up a hill 50 feet. 125  50; 75 5  (4); 1 3. GOLF Juanita’s score was 5 over par on the first 9 holes. Her score was 4 under par on the second 9 holes. 1. FOOTBALL A team gains 20 yards. Then they lose 7 yards. 20  (7); 13 146 Mathematics: Applications and Concepts, Course 2 1,200  (500); 1,700 6. AIRPLANE A plane descends 1,200 feet. Then it descends another 500 feet. 4. HOT AIR BALLOON A balloon rises 340 feet into the air. Then it descends 130 feet. 340  (130); 210 (5)  (6); 11 2. MONEY Roger owes his mom $5. He borrows another $6 from her. Write an addition expression to describe each situation. Then find each sum. NAME ________________________________________ DATE ______________ PERIOD _____ Lesson 3–4 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-4) © Glencoe/McGraw-Hill A12 © Glencoe/McGraw-Hill 147 Mathematics: Applications and Concepts, Course 2 7. Work with a partner. Tell your partner how to use absolute values to add integers with different signs when the positive integer has the greater absolute value. Then have your partner explain to you how to use absolute values to add integers with different signs when the negative integer has the greater absolute value. See students’ work. Helping You Remember opposites or additive inverses 6. How many units away from 0 is the number 17? How many units away from 0 is the number 17? What are 17 and 17 called? 17; 17; 5. When you use counters to add integers, what property are you applying when you remove zero pairs? Additive Inverse Property 9 units; 2. 4. 7  9 Starting at 0, move left 7 units, then move right Starting at 0, move left 7 units, then move left another 9 units; 16. 3. 7  (9) For Exercises 3 and 4, tell how you would solve each of the following on a number line. Then solve. Reading the Lesson 2. What is the charge at the bottom of a cloud where there are more electrons than protons? negative 1. What is the charge at the top of a cloud where there are more protons than electrons? positive Write your answers below. Pre-Activity Read the introduction at the top of page 120 in your textbook. 3 0 6 7 8 7 1 3 5 2 5 4 highest score: 18 lowest score: 21 6 2 1 4 6 2. 2 7 4 8 6 0 4 8 5 5 3 3 highest score: 2 lowest score: 23 6 2 1 7 1 3. 1 2 10 9 9 4 3 5 0 1 © Glencoe/McGraw-Hill 8 5 2 3 1 2 5 6 0 6 3 8 7 10 2 10 1 5 1 6 4 9 7 9 7 0 7 8 2 1 10 8 6 4 3 200 15 10 15 50 10 148 20 5 50 0 0 10 35 10 20 15 20 5 10 10 15 5 50 5 5 20 25 15 10 15 5 20 25 5 15 Mathematics: Applications and Concepts, Course 2 15 5 10 5 25 5 5 10 10 20 5 5 5 20 5 25 75 5. Find three ways to make the score 0. Answers will vary. 3 4 0 3 4. Find three ways to make the score 5. 10 10 50 100 75 150 10 10 highest score: 500 lowest score: 375 25 75 150 50 75 200 In these problems, five darts are thrown. Each dart must land on a different space in order to count. Solve each puzzle. 1. Three darts are thrown. Each dart must land on a different space in order to count. Find the highest and the lowest possible scores. Dartboard Puzzles Enrichment Reading to Learn Mathematics Adding Integers NAME ________________________________________ DATE ______________ PERIOD _____ Lesson 3–4 NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-4) Mathematics: Applications and Concepts, Course 2 © Glencoe/McGraw-Hill a  b  3  7  3  (7)  10 A13 15 50 12. 19  (10) 10. 75  50 149 © Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2 Answers Mathematics: Applications and Concepts, Course 2 18. 25  p 30 16. p  m 7 14. 9  n 1 29 125 2 5 17. m  n 12 13 8 15. p  (8) 13. m  6 26 12 8. 8  (6) 6. 13  18 4. 0  12 2. 20  (6) Replace a with 3 and b with 7. To subtract 7, add 7. Simplify. Evaluate each expression if m  2, n  10, and p  5. 11. 15  65 9. 25  (14) 39 7. 20  (5) 5. 7  8 15 3. 10  4 14 1. 7  9 2 To subtract 12, add 12. Simplify. Evaluate a  b if a  3 and b  7. 10  (12)  10  12 2 Subtract. To subtract 9, add 9. Simplify. Find 10  (12). 6  9  6  (9)  3 Find 6  9. To subtract an integer, add its opposite. Subtracting Integers Study Guide and Intervention NAME ________________________________________ DATE ______________ PERIOD _____ Subtracting Integers 22 0 30 25 6 5 13 18. 15  (61) 16. 6  (31) 14. 16  14 12. 14  (22) 10. 10  12 18 © Glencoe/McGraw-Hill 23. s  t 17 21. s  (8) 19. r  7 11 3 150 Mathematics: Applications and Concepts, Course 2 24. r  s 14 22. t  r 20. t  s 17 76 37 30 36 22 8. 15  6 21 6. 6  12 4. 8  13 2. 6  (7) Evaluate each expression if r  4, s  10, and t  7. 22 50 17. 18  (40) 15. 25  25 13. 10  (20) 11. 13  (12) 9. 3  8 11 7. 15  (7) 5. 7  (7) 3. 3  2 5 1. 5  2 3 Subtract. Practice: Skills NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-5) Lesson 3–5 © Glencoe/McGraw-Hill A14 © Glencoe/McGraw-Hill 5. SAVINGS Sonia has $235 in her savings account. She withdraws $45. What is left in her savings account? $190 4. ROLLER COASTER A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent. 3. TEMPERATURE The average temperature in Calgary, Canada, is 22C in July and 11C in January. Find the range of the highest and lowest temperatures in Calgary. 33°C 151 Mathematics: Applications and Concepts, Course 2 6. BEACH Wai and Kuri were digging in the sand at the beach. Wai dug a hole that was 15 inches below the surface, and Kuri dug a hole that was 9 inches below the surface. Find the difference in the depths of their holes. 6 in. 15 ft 2. CHECKING Your checking account is overdrawn by $50. You write a check for $20. What is the balance in your account? $70 Subtracting Integers 1. FOOTBALL A team gained 5 yards on their first play of the game. Then they lost 6 yards. Find the total change in yardage. 1 yd Subtract. Practice: Word Problems NAME ________________________________________ DATE ______________ PERIOD _____ © Glencoe/McGraw-Hill 152 Mathematics: Applications and Concepts, Course 2 To subtract an integer, add its opposite. Sample answer: 12  (3)  12  3  15 9. Write the rule that tells how to subtract integers. Then give an example. Helping You Remember Sample answer: Change the subtraction sentence to an addition sentence. To subtract negative 6, add positive 6. Then, on a number line start at 0, move left 8 units, then move right 6 units; 2. 8. 6  8 Sample answer: Change the subtraction sentence to an addition sentence. To subtract 8, add negative 8. Then, on a number line start at 0, move right 6 units, then move left 8 units; 2. 7. 8  (6) Tell how you would solve each of the following on a number line. Then solve. Reading the Lesson give the same answer as their related addition problems. Subtracting a positive integer is the same as adding a negative integer. 6. Compare and contrast subtraction sentences with their related addition sentences. Sample answer: The subtraction problems 5. 0  5 0  5  5; 0  (5)  5 4. 3  4 3  4  7; 3  (4)  7 3. 2  1 2  1  3; 2  (1)  3 2. 1  5 1  5  4; 1  (5)  4 Use a number line to find each difference. Write an equivalent addition sentence for each. Sample answers: 3  (5)  2; 1  (4)  5 1. Write a related addition sentence for each subtraction sentence. Write your answers below. Pre-Activity Complete the Mini Lab at the top of page 128 in your textbook. Subtracting Integers Reading to Learn Mathematics NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-5) Mathematics: Applications and Concepts, Course 2 Lesson 3–5 © Glencoe/McGraw-Hill 7 6 5 4 3 2 1 1 2 7  7 4  3  7 0 3 4 5 6 7 A15 7 6 5 4 3 2 1 0 C 7 6 5 7 6 5 7 6 5 7 6 © Glencoe/McGraw-Hill 8 5 5. Y at 4 and Z at 0 8 4. W at 0 and X at 6 8 E 3. E at 5 and F at 5 8 3 2 D 1 3 2 3 2 1 1 4 Y 3 Mathematics: Applications and Concepts, Course 2 1 153 0 Z 0 W 0 0 2 2 2 2 2 B 3 3 3 3 3 4 4 4 4 4 5 5 5 F 5 5 6 6 X 6 6 6 7 7 7 7 7 8 8 8 8 8 8 Mathematics: Applications and Concepts, Course 2 1 1 1 1 1 Answers 2 4  0  4 4 0  6  6 4 5  5  10 4 2. C at 7 and D at 1 7  (1)  6 8 A 1. A at 5 and B at 2 5  2  7 Graph each pair of points. Then write an expression using absolute value to find the distance between the points. 4  3  7 You can also find the distance by finding the absolute value of the difference of the coordinates. 8 To find the distance between two points on a number line, subtract their coordinates. Then, take the absolute value of the difference. Distance on the Number Line Enrichment NAME ________________________________________ DATE ______________ PERIOD _____ 5. 12(12) 144 8. 3(2x) 6x 11. 6(3y) 18y 45 16. 3ac © Glencoe/McGraw-Hill 6 13. 2a 9. 4(6f) 24f 18. abc 60 Mathematics: Applications and Concepts, Course 2 15. ab 17. 2c2 50 12 12. 7(8g) 56g 14. 9b 36 154 80 6. (8)2 64 3. 10(8) ALGEBRA Evaluate each expression if a  3, b  4, and c  5. 10. 7(6b) 42b 7. 5(7a) 35a ALGEBRA Simplify each expression. 2. 3(7) 1. 5(8) 40 21 Associative Propery of Multiplication. Simplify. Simplify 2(5x). Associative Property of Multiplication. Simplify. Simplify 2(6c). There are 2 factors of 7. The product is positive. Multiply (7)2. The integers have the same sign. The product is positive. 4. 8(3) 24 Multiply. 2(5x)  (2 · 5)x  10x The integers have different signs. The product is negative. Multiply 6(9). 2(6c)  (2 · 6)c  12c 6 The integers have different signs. The product is negative. Multiply 3(7). (7)2  (7)(7)  49 6(9)  54 3(7)  21 5(2)  10 Multiply 5(2). The product of two integers with the same sign is positive. The product of two integers with different signs is negative. Multiplying Integers Study Guide and Intervention NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lessons 3-5 and 3-6) Lesson 3–5 Multiplying Integers © Glencoe/McGraw-Hill 90 5. 10(9) 120 A16 16 105 12. 7(15) 18. 2(10h) 20h 17. 3(3y) 9y Mathematics: Applications and Concepts, Course 2 155 30 © Glencoe/McGraw-Hill 22. 2gh 24. 2h2 18 140 20. 5h 15 23. 10h 30 21. 7gk 19. 3g 15 ALGEBRA Evaluate each expression if g  5, h  3, and k  4. 16. 7(7w) 49w 14. 7(3x) 21x 84 150 10. 14(6) 8. 30(5) 6. (5)2 25 4. 6(5) 30 2. 2(8) 15. 7(5g) 35g 13. 3(4y) 12y ALGEBRA Simplify each expression. 11. (13)2 169 9. 20(6) 7. (5)2 25 48 3. 12(4) 1. 4(6) 24 Multiply. Practice: Skills NAME ________________________________________ DATE ______________ PERIOD _____ Multiplying Integers © Glencoe/McGraw-Hill 5. MONEY Mrs. Rockwell lost money on an investment at a rate of $4 per day. How much did she lose after two weeks? $56 12 points 3. STOCK A computer stock lost 2 points each hour for 6 hours. Find the total points the stock fell. 1. TEMPERATURE Suppose the temperature outside is dropping 3 degrees each hour. How much will the temperature drop in 8 hours? 24 Multiply. 156 Mathematics: Applications and Concepts, Course 2 6. TENNIS BALLS Josh purchased 8 cans of tennis balls. The cans came with 3 balls in each can. How many balls did Josh purchase? 24 tennis balls 4. DROUGHT A drought can cause the level of the local water supply to drop by a few inches each week. Suppose the level of the water supply drops 2 inches each week. How far will it have dropped in 4 weeks? 8 in. 600 ft 2. DIVING A deep-sea diver descends below the surface of the water at a rate of 60 feet each minute. What is the depth of the diver after 10 minutes? Practice: Word Problems NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-6) Mathematics: Applications and Concepts, Course 2 Lesson 3–6 © Glencoe/McGraw-Hill 5. 5(2) 7 4. 1(7) 10 12 4(2)  8 The addend is 9. A17 positive b. The product of two integers with the same sign is _______________. © Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2 Mathematics: Applications and Concepts, Course 2 Answers 157 product of 3 integers is positive when all 3 integers are positive or when only one integer is positive and the product is negative in other cases. 10. You know the rule for determining the sign of the product of two integers when the signs are alike or different. Consider the product of three integers. With a partner summarize the signs of the products of 3 integers when three, two, one or none of the integers are positive. The Helping You Remember negative a. The product of two integers with different signs is _______________. 9. Complete each of the following sentences with the word positive or negative. change the order of the numbers, the result is still the same. From the example in the Mini Lab, we know that 4(2)  8. Therefore, by the Commutative Property of Multiplication, 2(4)  8. 8. How does the sentence 4(2)  2(4) illustrate the Commutative Property of Multiplication? Sample answer: The sentence shows that if you 3(9)  (9)  (9)  (9)  27 7. Give an example that shows how multiplication is the same as repeated addition. In your example, tell what the addend is. Sample answer: Reading the Lesson negative integer. 6. Write a rule for finding the sign of the product of a positive and negative integer. A positive integer times a negative integer equals a 3. 4(3) 6 2. 3(2) Find each product using counters. 1. Write a multiplication sentence that describes the model. Write your answers below. Pre-Activity Complete the Mini Lab at the top of page 134 in your textbook. Multiplying Integers Reading to Learn Mathematics NAME ________________________________________ DATE ______________ PERIOD _____ −5 −2(−5)(−1) −2(−12 + 7) −10 + 16 −5(−6) 5(−4 + 9) 30 − (−10) 3(−3)(−5) Mathematics: Applications and Concepts, Course 2 −2(−1) 3 + (−3) −4(2) 158 6−8 (−4)2 −3(−5) 2[−5 • (−5)] 3(5)(−5) −4(5)(−1) 6(−10) −52 −[12 − (−8)] −55 Start −13 + 12 −1(3) 20 − 20 −32 + 28 −3 + (−4) −50 5(−9) −35 + 5 −8(5) 9(−6) 15 − 50 4 + (−12) © Glencoe/McGraw-Hill 0−6 9(−1) −12 + 2 −3(5) Find your way through the maze by moving to the expression in an adjacent section with the next highest value. Integer Maze Enrichment NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-6) Lesson 3–6 © Glencoe/McGraw-Hill The quotient is negative. 30  (5)  6 The quotient is positive. A18 1 12 10. 256 16 16 8. 420  (3) 4 2 140 2 18. ef  2 16 17. d e e2 f2 4 © Glencoe/McGraw-Hill 19. 6 159 Mathematics: Applications and Concepts, Course 2 12 16. e2  f 2 15. f  e 2 f 14. d  e 6 13. d  6 4 20. de 12. 40  f 5 11. 12  e 3 ALGEBRA Evaluate each expression if d  24, e  4, and f  8. 9. 540 45 7. 350  (25) 14 5. 10  10 6. 80 20 4. 6  (3) 9 3. 18 2 2. 14  (7) 1. 12  4 3 Divide. The integers have the same sign. 100  (5) 100  (5)  20 Divide 100  (5). The integers have different signs. 30  (5) Divide 30  (5). The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative. Dividing Integers Study Guide and Intervention NAME ________________________________________ DATE ______________ PERIOD _____ Dividing Integers 10 16 0 9 7 3 12. 189  (21) 4 10. 64 9 8. 0 4 6. 36 4. 49  (7) 2. 24  (8) 9 n2 p2 p n 16 4 © Glencoe/McGraw-Hill 21. m  (np) 2 19. 17. 16. m  p 15. p2  m 2 160 p 2 Mathematics: Applications and Concepts, Course 2 22. m  n 6 p 20. 18  n 18. p  n2 2 4 14. p  4 2 13. m  n 16 ALGEBRA Evaluate each expression if m  32, n  2, and p  8. 11. 500  (50) 9. 38  2 19 15 1 5. 8  (8) 7. 225  (15) 11 3. 22  (2) 1. 15  3 5 Divide. Practice: Skills NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-7) Mathematics: Applications and Concepts, Course 2 Lesson 3–7 Dividing Integers © Glencoe/McGraw-Hill A19 © Glencoe/McGraw-Hill 12 students annually Mathematics: Applications and Concepts, Course 2 161 Mathematics: Applications and Concepts, Course 2 11 min 6. SUBMARINE A submarine descends at a rate of 60 feet each minute. How long will it take it to descend to a depth of 660 feet below the surface? 8 points per game 4. BASKETBALL The basketball team lost their last 6 games. They lost by a total of 48 points. Find the average number of points by which each game was lost. mph per s 2. MOTION Mr. Diaz decreased the speed of his car by 30 miles per hour over a period of 10 seconds. Find the average change in speed each second. 3 Answers 5. POPULATION The enrollment at Davis Middle School dropped by 60 students over a 5-year period. What is the average yearly drop in enrollment? per day 3. WEATHER Over the past seven days, Mrs. Cho found that the temperature outside had dropped a total of 35 degrees. Find the average drop in temperature each day. 5 degrees 13 points 1. STOCK MARKET During a 5-day workweek, the stock market decreased by 65 points. Find the average daily change in the market for the week. Divide. Practice: Word Problems NAME ________________________________________ DATE ______________ PERIOD _____ 42  (21)  2; 42  2  21 6. 2(21)  42 42  (21)  2; 42  (2)  21 4. 21(2)  42 positive b. The quotient of two integers with the same sign is _______________. © Glencoe/McGraw-Hill 162 Mathematics: Applications and Concepts, Course 2 division in that the product of a quotient and divisor gives the dividend. Even though you can take the product of zero and a number, zero cannot be a divisor. 9. Describe how the operations of multiplication and division are opposite of each other. Are these operations opposite in all cases? What is the one integer that cannot be a divisor? Multiplication is the opposite of Helping You Remember 8. In the division sentence 72  8  9, identify the dividend, the divisor, and the quotient. dividend: 72; divisor: 8; quotient: 9 negative a. The quotient of two integers with different signs is _______________. 7. Complete each of the following sentences with the word positive or negative. 18  3  6; 18  (6)  3 5. 6(3)  18 18  (3)  6; 18  (6)  3 3. 6(3)  18 Write two division sentences related to each of the following multiplication sentences. Reading the Lesson 2. 12  3 4 1. 6  2 3 Find each quotient using counters. Write your answers below. Pre-Activity Complete the Mini Lab at the top of page 138 in your textbook. Dividing Integers Reading to Learn Mathematics NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-7) Lesson 3–7 © Glencoe/McGraw-Hill 0 y 0 0 y0 A20 0 x 0 no solution x all numbers but 0 6. 0  5 4. all numbers 2. x 0  0 1 1 2x  2 11. © Glencoe/McGraw-Hill Therefore, 1  1. 0 Step 3 0 Therefore, 0  1 and 0  1. 0 1  0 and 0 (1)  0 Step 2 13. Step 1 8. 12. 0 2 1 163 Mathematics: Applications and Concepts, Course 2 Step 2 involves division by zero. 1 3x  6 2x 1 x1 10. 0 Explain what is wrong with this “proof.” 1 1 x1 0 9. x 7. 12 What values for x must be excluded to prevent division by 0? no solution x 5. 0  x 0 3. x 0  x 0 1. 4x  0 Describe the solution set for each equation. Because division by zero leads to impossible situations, it is not a “legal” step in solving a problem. People say that division by zero is undefined, or not possible, or simply not allowed. However, there is no number that will make the left equation true. This equation has no solution. For the right equation, every number will make it true. The solutions for this equation are “all numbers.” 0 x5 If you can write the equations above, you can also write the two equations below. 5 x 0 Some interesting things happen when you try to divide by zero. For example, look at these two equations. Division by Zero? Enrichment NAME ________________________________________ DATE ______________ PERIOD _____ Answers (Lesson 3-7) Mathematics: Applications and Concepts, Course 2 Lesson 3–7 Chapter 3 Assessment Answer Key Form 1 Page 165 1. A 2. H 3. B 14. F 1. C 15. C 2. F I 3. D 16. 4. G 5. A 6. H 7. B 8. G 9. A 10. I 11. C 12. G 13. D 4. I 17. B 5. B 18. I 7. 8. 9. 10. 11. 12. H 19. A 20. H 21. B 22. H 23. D G A H 24. F 25. B D F B: 13. A Answers 6. Form 2A Page 167 Page 166 4 B © Glencoe/McGraw-Hill A21 (continued on the next page) Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Form 2A (continued) Page 168 Form 2B Page 169 14. F 1. B B 2. H 15. 3. A 16. F 17. C 18. I 19. B 20. 21. Page 170 14. F 15. C 16. G 4. I 17. A 5. A 18. I 6. G 19. B 7. D 20. I 21. B H 8. F 9. B B H 22. I 22. A 23. C 23. 24. F 25. D 24. 10. I 11. 25. B: H B A 12. G 13. D B: 10 6 © Glencoe/McGraw-Hill A22 Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Form 2C Page 171 Page 172 1. 45 15. 37 2. 5 16. 88 17. 5 3. 11 18. 6 4. 10 19. 9 20. 3 21. 17 22. 2 23. 21 24. 5 25. 4 26. 18 27. 2 28. 2 29. 24 30. 1 31. 15a 32. 12c 33. 11 B: 12 5. 6 3 0 3   7.  8. 9. 2, 1, 0, 3, 5, 7 10. Athens 11. (3, 2); II 12. (1, 3); III 13–14. 4 3 2 1 432 O 2 3 4 Answers 6. y W 1 2 3 4x Q (continued on the next page) © Glencoe/McGraw-Hill A23 Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Form 2D Page 173 Page 174 1. 300 2. 13 15. 2 16. 70 17. 20 3. 13 18. 9 4. 8 19. 25 20. 12 21. 17 22. 2 23. 13 24. 8 25. 7 26. 30 27. 4 28. 3 29. 40 30. 6 31. 30z 32. 8y 33. 9 B: 14 5. 6 3 0 6.  7.  8.  3 9. 8, 5, 1, 2, 3, 4 10. St. Paul 11. (3, 1); I 12. (1,2); IV 13–14. 4 3 2 1 432 A O 2 3 4 © Glencoe/McGraw-Hill y S 1 2 3 4x A24 Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Form 3 Page 175 1. 380 15. 28 2. 11 16. 24 17. 0 18. 6 19. 121 20. 3 21. 3 22. 8 23. 13 24. 80 25. 12 26. 3 27. 45 28. 2 29. 1 30. 6 31. 35e 32. 6bc 33. 6 B: 6, 3; Divide the previous term by 2. 3. 16 4. 2 5. 4 2 0 2 6.  7.  8.  4 9. 7, 5, 3, 0, 4, 10 10. Chicago 11. (3, 3); II 12. (2, 0); x-axis 13–14. 4 3 2 1 432 L O y 1 2 3 4x 2 M 3 4 © Glencoe/McGraw-Hill A25 Mathematics: Applications and Concepts, Course 2 Answers Page 176 Chapter 3 Assessment Answer Key Page 177, Extended Response Assessment Scoring Rubric Level Specific Criteria 4 The student demonstrates a thorough understanding of the mathematics concepts and/or procedures embodied in the task. The student has responded correctly to the task, used mathematically sound procedures, and provided clear and complete explanations and interpretations. The response may contain minor flaws that do not detract from the demonstration of a thorough understanding. 3 The student demonstrates an understanding of the mathematics concepts and/or procedures embodied in the task. The student’s response to the task is essentially correct with the mathematical procedures used and the explanations and interpretations provided demonstrating an essential but less than thorough understanding. The response may contain minor errors that reflect inattentive execution of the mathematical procedures or indications of some misunderstanding of the underlying mathematics concepts and/or procedures. 2 The student has demonstrated only a partial understanding of the mathematics concepts and/or procedures embodied in the task. Although the student may have used the correct approach to obtaining a solution or may have provided a correct solution, the student’s work lacks an essential understanding of the underlying mathematical concepts. The response contains errors related to misunderstanding important aspects of the task, misuse of mathematical procedures, or faulty interpretations of results. 1 The student has demonstrated a very limited understanding of the mathematics concepts and/or procedures embodied in the task. The student’s response to the task is incomplete and exhibits many flaws. Although the student has addressed some of the conditions of the task, the student reached an inadequate conclusion and/or provided reasoning that was faulty or incomplete. The response exhibits many errors or may be incomplete. 0 The student has provided a completely incorrect solution or uninterpretable response, or no response at all. © Glencoe/McGraw-Hill A26 Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Page 177, Extended Response Assessment Scoring Rubric In addition to the scoring rubric found on page A26, the following sample answers may be used as guidance in evaluating extended response assessment items. 1. a. You can use a number line to compare integers. The values increase as you go right and decrease as you go left. c. The absolute value of a number is the number of units its graph is from the graph of 0 on the number line. d. |3|3 e. 3  (2)  O y A (4, 6) 2 4 6 8x 4 6 B (8, 6) 8 a. Graph A(4, 6) by starting at the origin, moving 4 units to the right and 6 units up. Point A lies in quadrant I. b. 4 · (2)  8 and 6 · (1)  6, so point B has coordinates (8, 6). Point B lies in quadrant III.     8 6 C (2, 2) 4 2 864 b. 3, 1, 2, 4  2.  c. 8  4  2 and 6  (3)  2, so point C has coordinates (2, 2). Point C lies in quadrant II. Glen’s score after two rounds is 1. f. 1  (3)  4 g. 2  (3)                Answers The difference between Horatio’s first and second round scores is 5. © Glencoe/McGraw-Hill A27 Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Vocabulary Test/Review Page 178 1. absolute value 2. integer 3. graph 4. additive inverse 5. x-coordinate 6. y-axis 7. negative integer Quiz (Lessons 3-1 and 3-2) Page 179 2. 15 3. 24 4. 3 origin 5. 9. opposites 6. 10. quadrant 11. Sample answer: a plane in which a horizontal number line and a vertical number line intersect at their zero points C 1. 8. Quiz (Lessons 3-5 and 3-6) Page 180 9 15 7.  8.  9.  10.  1. 13 2. 30 3. 81 4. 35 5. 18 6. 10 7. 11 8. 56 9. 18e 10. 20s 12. Sample answer: the pair of numbers (xcoordinate, y-coordinate) used to locate a point in the coordinate plane Quiz (Lessons 3-3 and 3-4) Page 179 1–3. 4 3 2 1 432 R © Glencoe/McGraw-Hill O 2 3 4 4. 5 5. 4 A28 Quiz (Lesson 3-7) Page 180 1. 4 2. 7 3. 3 4. 6 5. 2 y S 1 2 3 4x T Mathematics: Applications and Concepts, Course 2 Chapter 3 Assessment Answer Key Mid-Chapter Test Page 181 1. B 2. F Cumulative Review Page 182 1. 18 2. 16 3. 25; 23; 22 and 35; 51 D 4. I 5. A 6. G Sample answer: The mean and median number of wins are close, indicating the data are fairly wellcentered in the middle of the range of possible wins. About half of the data values cluster from 17 to 35. 4. 1 5. 7. 8. 50 3 10.   11. (5, 4); I 9. 12. (6, 1); III 13. (3, 2); IV 14. 15. 6. 72, 31, 12, 12, 50, 61 7. 8 8–9. 4 3 2 1 432 M y O 2 3 4 10. 0 (1, 4); II 11. 30 11 12. 30 13. 4 © Glencoe/McGraw-Hill A29 1 2 3 4x A Mathematics: Applications and Concepts, Course 2 Answers 3. Chapter 3 Assessment Answer Key Standardized Test Practice Page 183 1. A B C Page 184 D 10. 2. F G H I 3. A B C D 4. 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 G H interval 5; scale 0 to 24 13. 6 I B D 432 5. A B C 8 0 1 2 3 4 5 6 7 8 9 12. A F 11. 80 4 3 2 1 O y 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 B C 1 2 3 4x 2 3 4 D 14. a. Graph A(2, 4) by starting at 6. F G H the origin, moving 2 units to the left and 4 units up. I 1 2 b. 1  3  3 and   4  2, so 7. A B C D 8. F G H I 9. A B C D © Glencoe/McGraw-Hill point B has coordinates (3, 2). Point B lies in quadrant II. A30 Mathematics: Applications and Concepts, Course 2