Glenco Algebra 1 Chapter 1

Chapter 1Resource Masters 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) Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) 0-07-827753-1 0-07-827754-X 0-07-827747-7 0-07-827749-3 0-07-827748-5 0-07-827750-7 ANSWERS FOR WORKBOOKS The answers for Chapter 1 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Glencoe/McGraw-Hill 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, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: The McGraw-Hill Companies 8787 Orion Place Columbus, OH 43240-4027 ISBN: 0-07-827725-6 2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03 Algebra 1 Chapter 1 Resource Masters Contents Vocabulary Builder . . . . . . . . . . . . . . . . vii Lesson 1-7 Study Guide and Intervention . . . . . . . . . 37–38 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 39 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Reading to Learn Mathematics . . . . . . . . . . . 41 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Lesson 1-1 Study Guide and Intervention . . . . . . . . . . . 1–2 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 3 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Reading to Learn Mathematics . . . . . . . . . . . . 5 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Lesson 1-8 Study Guide and Intervention . . . . . . . . . 43–44 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 45 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Reading to Learn Mathematics . . . . . . . . . . . 47 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Lesson 1-2 Study Guide and Intervention . . . . . . . . . . . 7–8 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 9 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Reading to Learn Mathematics . . . . . . . . . . . 11 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Lesson 1-9 Study Guide and Intervention . . . . . . . . . 49–50 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 51 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Reading to Learn Mathematics . . . . . . . . . . . 53 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Lesson 1-3 Study Guide and Intervention . . . . . . . . . 13–14 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 15 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Reading to Learn Mathematics . . . . . . . . . . . 17 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter 1 Assessment Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Lesson 1-4 Study Guide and Intervention . . . . . . . . . 19–20 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 21 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Reading to Learn Mathematics . . . . . . . . . . . 23 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Lesson 1-5 Study Guide and Intervention . . . . . . . . . 25–26 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 27 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Reading to Learn Mathematics . . . . . . . . . . . 29 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1 Lesson 1-6 Study Guide and Intervention . . . . . . . . . 31–32 Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 33 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Reading to Learn Mathematics . . . . . . . . . . . 35 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 36 © Glencoe/McGraw-Hill 1 Test, Form 1 . . . . . . . . . . . . . . 55–56 1 Test, Form 2A . . . . . . . . . . . . . 57–58 1 Test, Form 2B . . . . . . . . . . . . . 59–60 1 Test, Form 2C . . . . . . . . . . . . . 61–62 1 Test, Form 2D . . . . . . . . . . . . . 63–64 1 Test, Form 3 . . . . . . . . . . . . . . 65–66 1 Open-Ended Assessment . . . . . . . 67 1 Vocabulary Test/Review . . . . . . . . 68 1 Quizzes 1 & 2 . . . . . . . . . . . . . . . . 69 1 Quizzes 3 & 4 . . . . . . . . . . . . . . . . 70 1 Mid-Chapter Test . . . . . . . . . . . . . 71 1 Cumulative Review . . . . . . . . . . . . 72 1 Standardized Test Practice . . . 73–74 ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A38 iii Glencoe Algebra 1 Remind them to add definitions and examples as they complete each lesson. Skills Practice There is one master for each lesson. © Glencoe/McGraw-Hill iv Glencoe Algebra 1 . The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Finally. extensions. These materials include worksheets. and assessment options. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Vocabulary Builder Practice Pages vii–viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. or as activities for days when class periods are shortened. It is also a helpful tool for ELL (English Language Learner) students.Teacher’s Guide to Using the Chapter 1 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. but are accessible for use with all levels of students. These exercises are of average difficulty. 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 Use these masters as WHEN TO USE This master can be used reteaching activities for students who need additional reinforcement. WHEN TO USE These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement. or widen students’ perspectives on the mathematics they are learning. WHEN TO USE These provide additional practice options or may be used as homework for second day teaching of the lesson. students are asked to summarize what they have learned using various representation techniques. These problems more closely follow the structure of the Practice and Apply section of the Student Edition exercises. offer an historical or multicultural look at the concepts. These provide computational practice at a basic level. There is one Study Guide and Intervention master for each objective. Enrichment There is one extension master for each lesson. There is one master for each lesson. WHEN TO USE These may be used as extra credit. Students are to record definitions and/or examples for each term. WHEN TO USE Give these pages to students before beginning Lesson 1-1. Reading to Learn Mathematics One master is included for each lesson. The answers for these pages appear at the back of this booklet. These activities may extend the concepts in the lesson. All of the materials found in this booklet are included for viewing and printing in the Algebra 1 TeacherWorks CD-ROM. Encourage them to add these pages to their Algebra Study Notebook. as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. short-term projects. These are not written exclusively for honors students. You may suggest that students highlight or star the terms with which they are not familiar. Study Guide and Intervention Each lesson in Algebra 1 addresses two objectives. • The Standardized Test Practice offers continuing review of algebra concepts in various formats. • Form 3 is an advanced level test with free-response questions. • Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 64–65. • A Mid-Chapter Test provides an option to assess the first half of the chapter. Chapter Assessment CHAPTER TESTS Continuing Assessment • Form 1 contains multiple-choice questions and is intended for use with basic level students. It can also be used as a test. This master includes free-response questions. • Forms 2C and 2D are composed of freeresponse questions aimed at the average level student. • Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. • Forms 2A and 2B contain multiple-choice questions aimed at the average level student. This practice includes multiplechoice. includes a list of the vocabulary words in the chapter and ten questions assessing students’ knowledge of those terms. suitable for all students. This can also be used in conjunction with one of the chapter tests or as a review worksheet. • A Vocabulary Test. Grids without axes are provided for questions assessing graphing skills. v Glencoe Algebra 1 . Answers All of the above tests include a freeresponse Bonus question. • The Open-Ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. It is composed of both multiple-choice and free-response questions. and quantitativecomparison questions. grid-in.Assessment Options Intermediate Assessment The assessment masters in the Chapter 1 Resources Masters offer a wide range of assessment tools for intermediate and final assessment. Bubble-in and grid-in answer sections are provided on the master. © Glencoe/McGraw-Hill • Full-size answer keys are provided for the assessment masters in this booklet. Sample answers are provided for assessment. • The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. These tests are similar in format to offer comparable testing situations. The following lists describe each assessment master and its intended use. This improves students’ familiarity with the answer formats they may encounter in test taking. Grids with axes are provided for questions assessing graphing skills. • The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Algebra 1. These tests are similar in format to offer comparable testing situations. which may appear on the standardized tests that they may encounter. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.NAME ______________________________________________ DATE 1 ____________ PERIOD _____ Reading to Learn Mathematics This is an alphabetical list of the key vocabulary terms you will learn in Chapter 1. complete each term’s definition or description. Vocabulary Term Found on Page Definition/Description/Example      coefficient KOH·uh·FIH·shuhnt conclusion conditional statement coordinate system counterexample      deductive reasoning dih·DUHK·tihv dependent variable domain equation function (continued on the next page) © Glencoe/McGraw-Hill vii Glencoe Algebra 1 Vocabulary Builder Vocabulary Builder . As you study the chapter. NAME ______________________________________________ DATE 1 ____________ PERIOD _____ Reading to Learn Mathematics Vocabulary Builder Vocabulary Term (continued) Found on Page Definition/Description/Example        hypothesis hy·PAH·thuh·suhs independent variable inequality like terms order of operations power range replacement set solving an open sentence variables © Glencoe/McGraw-Hill viii Glencoe Algebra 1 . 3  3  3  3  3 Use 3 as a factor 4 times. 122 17.NAME ______________________________________________ DATE 1-1 ____________ PERIOD _____ Study Guide and Intervention Variables and Expressions Write Mathematical Expressions In the algebraic expression. a number divided by 8 3. 13. b. a number squared 4. w. a variable is used to represent unspecified numbers or values. four more than a number n 4n The algebraic expression is 4  n.  and w are called factors. a. four more than a number n The words more than imply addition. 7 more than the product of 6 and a number 12. a number decreased by 8 2. a number multiplied by 37 7. 52 14.  81 Multiply. Example 2 Evaluate each expression. 53  5  5  5 Use 5 as a factor 3 times. 4 Cubed means raised to the third power. a number divided by 6 6.  125 Multiply. 104 16. the letters  and w are called variables. 3 less than 5 times a number 9. In algebra. The letters  and w are used above because they are the first letters of the words length and width. the difference of a number squared and 8 The expression difference of implies subtraction. 34 Exercises Write an algebraic expression for each verbal expression. four times a number 5. 28 © Glencoe/McGraw-Hill 1 Glencoe Algebra 1 Lesson 1-1 Example 1 . one-half the square of b 11. five cubed a. Any letter can be used as a variable. Write an algebraic expression for each verbal expression. 1. 33 15. the sum of 9 and a number 8. twice the sum of 15 and a number 10. the difference of a number squared and 8 n2  8 The algebraic expression is n2  8. 83 18. 30 increased by 3 times the square of a number Evaluate each expression. In the expression w. b. and the result is called the product. n3  12m the difference of n cubed and twelve times m Exercises Write a verbal expression for each algebraic expression. Example Write a verbal expression for each algebraic expression.NAME ______________________________________________ DATE 1-1 ____________ PERIOD _____ Study Guide and Intervention (continued) Variables and Expressions Write Verbal Expressions Translating algebraic expressions into verbal expressions is important in algebra.  b2 12. 12c 5. 2n2  4 8. 81  2x 4. 84 6. w  1 2. 1 3 1. 6n2 the product of 6 and n squared b. 7n5 13.  a3 3. 6n2  3 © Glencoe/McGraw-Hill 2 3 2 Glencoe Algebra 1 . 32  23 18. 2x3 3 1 4 6k3 5 10.  11. 62 7. 3x  4 14. 3b2  2a3 16. a3  b3 9. 4(n2  1) 17. a.  k5 15. p4  6q 26. . 33 13.NAME ______________________________________________ DATE 1-1 ____________ PERIOD _____ Skills Practice Variables and Expressions 1. 9 less than g to the fourth power Evaluate each expression. 73 18. 19. c  2d 22. 52 21. 24 15. the product of 2 and the second power of y 8. 2b2 24. 44 17. 82 10. 8 increased by three times a number 6. 6 more than twice m 5. 4  5h 23. the difference of 17 and 5 times a number 7. 15 less than k 3. the product of 18 and q 4. 3n2  x © Glencoe/McGraw-Hill 3 Glencoe Algebra 1 Lesson 1-1 Write an algebraic expression for each verbal expression. 9a 20. 7x3  1 25. 34 11. 102 14. 72 16. the sum of a number and 10 2. 113 Write a verbal expression for each algebraic expression. 53 12. 9. x3  y4 23. 27. 4d3  10 22. 105 16. 112 10. the product of 33 and j 4. the sum of 18 and a number 3. 15 decreased by twice a number 6.NAME ______________________________________________ DATE 1-1 ____________ PERIOD _____ Practice Variables and Expressions Write an algebraic expression for each verbal expression. 64 15. write an expression that represents the surface area of its side. 83 11. 123 17. 1. 5m2  2 21. GEOMETRY The surface area of the side of a right cylinder can be found by multiplying twice the number  by the radius times the height. 54 12.  26. 93 14. b2  3c3 k5 6 24. 74 increased by 3 times y 5. two fifths the cube of a number Evaluate each expression. 91 more than the square of a number 7. 18. 9.50 and in fair condition for $0. Write an expression for the cost of buying e excellent-condition paperbacks and f fair-condition paperbacks. the difference of 10 and u 2. BOOKS A used bookstore sells paperback fiction books in excellent condition for $2. If a circular cylinder has radius r and height h.  4n2 7 25.50. © Glencoe/McGraw-Hill 4 Glencoe Algebra 1 . 45 13. three fourths the square of b 8. 1004 Write a verbal expression for each algebraic expression. 73 20. 23f 19. three more than a number n II. x to the fourth power Helping You Remember 5. In the expression xn. five times the difference of x and 4 1 2 c. What are the factors in the algebraic expression 3xy? 3. what is the base? What is the exponent? 4. Multiplying 5 times 3 is not the same as raising 5 to the third power. Why is the symbol  avoided in algebra? 2. I.NAME ______________________________________________ DATE 1-1 ____________ PERIOD _____ Reading to Learn Mathematics Variables and Expressions Pre-Activity What expression can be used to find the perimeter of a baseball diamond? Read the introduction to Lesson 1-1 at the top of page 6 in your textbook. 4 represents the of each side. one half the number r III. How does the way you write “5 times 3” and “5 to the third power” in symbols help you remember that they give different results? © Glencoe/McGraw-Hill 5 Glencoe Algebra 1 . Write the Roman numeral of the algebraic expression that best matches each phrase. 5(x  4) a. the product of x and y divided by 2 IV.  r d.  e. n  3 xy 2 V. Then complete the description of the expression 4s. In the expression 4s. Lesson 1-1 represents the of sides and s Reading the Lesson 1. x4 b. 2b. As you solve the puzzle. You may move only one disk at a time and a larger disk may never be put on top of a smaller disk. The object is to move all of the disks to another peg. Record your solution. Suppose you start with an odd number of disks and you want to end with the stack on peg c. For example. the first two moves in the table can be recorded as 1c. 1 2 3 2 3 3 1 2 1 4. record each move in the table shown.NAME ______________________________________________ DATE 1-1 ____________ PERIOD _____ Enrichment The Tower of Hanoi The diagram at the right shows the Tower of Hanoi puzzle. Solve the puzzle for five disks. This shows that disk 1 is moved to peg c. Suppose you start with an even number of disks and you want to end with the stack on peg b. Complete the table to solve the Tower of Hanoi puzzle for three disks. What should be your first move? © Glencoe/McGraw-Hill 6 Glencoe Algebra 1 . What should be your first move? 6. The first two moves are recorded. and then disk 2 is moved to peg b. Record your solution using letters. Notice that there are three pegs. Record your solution. On a separate sheet of paper. 3. Another way to record each move is to use letters. Peg a Peg b Peg c 1 2 3 Peg a Peg b Peg c Solve. 1. with a stack of disks on peg a. 5. solve the puzzle for four disks. 2.  2  42  82 (5  2)  2 15. 11 16  3 Evaluate power in denominator. 3(2)  4(2  6) 3(2)  4(2  6)  3(2)  4(8)  6  32 Divide 12 by 3. Step Step Step Step Example 1 1 2 3 4 Evaluate expressions inside grouping symbols.  13. 3  23 38   42  3 42  3 Evaluate power in numerator. Add 6 and 32. 3  23 4 3 b. Evaluate all powers.  52  3 20(3)  2(3) 18. 10  8  1 5. (8  4) 2 2. 82  (2  8)  2 8(2)  4 84 4  32 12  1 12. 12(20  17)  3  6 8. Subtract 4 from 15. b.  © Glencoe/McGraw-Hill 15  60 30  5 17. Find 4 squared. Example 2 Evaluate each expression. (12  4)  6 3. 11 4 3 Add 3 and 8 in the numerator. 7  2  4  4 7244784  15  4  11 a. 32  3  22  7  20  5 11. use the rules for order of operations shown below. Multiply 3 and 18. a. 24  3  2  32 9.  4(52)  4  3 4(4  5  2) 16.NAME ______________________________________________ DATE 1-2 ____________ PERIOD _____ Study Guide and Intervention Order of Operations Evaluate Rational Expressions Numerical expressions often contain more than one operation. Do all multiplication and/or division from left to right.  2 Add 2 and 6. 15  12  4 6.  10.  2   Exercises Evaluate each expression. 1. To evaluate them.  38 Evaluate each expression. 3[2  (12  3)2] 3[2  (12  3)2]  3(2  42)  3(2  16)  3(18)  54 Multiply 2 and 4.  7.  7 4  32  3  2 35 82  22 (2  8)  4 Glencoe Algebra 1 Lesson 1-2 Order of Operations . Add 2 and 16. 11 48 Multiply. 10  2  3 4. 250  [5(3  7  4)] 14. Multiply left to right. Do all addition and/or subtraction from left to right. Add 7 and 8. x  7 2.  8 Glencoe Algebra 1 . a2  2b z2  y2 x 14. and b   .   xz  19. z  4. Subtract 3 from 12. x(2y  3z) y2 x 7.  13.  25ab  y xz 17. First. Algebraic expressions can be evaluated if the values of the variables are known.NAME ______________________________________________ DATE 1-2 ____________ PERIOD _____ Study Guide and Intervention (continued) Order of Operations Evaluate Algebraic Expressions Algebraic expressions may contain more than one operation. 23  (a  b) 8. 6xz  5xy 15. Exercises 4 5 3 5 Evaluate each expression if x  2. 2xyz  5 9. The solution is 53. x3  5(y  3)      23  5(12  3) 8  5(12  3) 8  5(9) 8  45 53 Replace x with 2 and y with 12. (z  x)2  ax xz y  2z 21. 6a  8b 6. 1. Evaluate 23. Add 8 and 45. y  3. 2 10. replace the variables by their values.  2 16.  © 3xy  4 7x 11. (10x)2  100a 12. Then use the order of operations to calculate the value of the resulting numerical expression. Example Evaluate x3  5(y  3) if x  2 and y  12. a   . x3  y  z2 5.  2  yz    2 Glencoe/McGraw-Hill (z  y)2 x 5a2b y 18. Multiply 5 and 9. x  y2 4. 3x  5 3.     z y x   y z x  20. yz  x 19. (3  5)  5  1 7. (5  4)  7 2. 9  4(3  1) 8. [8  2  (3  9)]  [8  2  3] Lesson 1-2 9. 10  2  6  4 11. (9  2)  3 3. x2  y2  10z 24. xy  z 18. 2[12  (5  2)2] 16. 30  5  4  2 Evaluate each expression if x  6. 1. 2(x  z)  y 21. 5  [30  (6  1)2] 15. 4  6  3 4. z3  ( y2  4x) y  xz 2 25.  9 Glencoe Algebra 1 . and z  3. y  8. 4[30  (10  2)  3] 14. 6  3  7  23 13. 28  5  4 5. 14  7  5  32 12. 2  3  5  4 10. 2x  3y  z 20. 12  2  2 6.NAME ______________________________________________ DATE 1-2 ____________ PERIOD _____ Skills Practice Order of Operations Evaluate each expression. 17. 5z  ( y  x) 22.  © Glencoe/McGraw-Hill 3y  x2 z 26. 5x  ( y  2z) 23. 22  11  9  32 9. (15  5)  2 2. 28. 4(3  5)  5  4 8.  24. Carlyle rents the car for 5 days and drives 180 miles. 62  3  7  9 10. Carlyle to rent the car. b  9. Suppose Ms. b2  2a  c2 18. The length of a rectangle is 3n  2 and its width is n  1. The car rental company charges $36 per day plus $0. 29. © Glencoe/McGraw-Hill 10 Glencoe Algebra 1 .  2c3  ab 4 b2  2c2 acb CAR RENTAL For Exercises 26 and 27.NAME ______________________________________________ DATE 1-2 ____________ PERIOD _____ Practice Order of Operations Evaluate each expression. c2  (2b  a) bc2  a c 23.  2 15. and c  4. 16. Carlyle must pay the car rental company. 5  7  4 4. use the following information. Ann Carlyle is planning a business trip for which she needs to rent a car. use the following information. 2[52  (36  6)] 52  4  5  42 5(4) 13. 4a  2b  c2 20. 8  (2  2)  7 7.50 per mile over 100 miles. (a2  4b)  c 21. a2  b  c2 17.  2 Evaluate each expression if a  12. 12  5  6  2 5. 3[10  (27  9)] 11. Write an expression that represents the perimeter of the rectangle. 162  [6(7  4)2] 7  32 4 2 14.  22. 9  (3  4) 3. 27. Write an expression for how much it will cost Ms. The perimeter of the rectangle is twice the sum of its length and its width. 7  9  4(6  7) 6.  (2  5)2  4 3 5 12.  2(a  b)2 5c 25. 1. 2c(a  b) 19. Find the perimeter of the rectangle when n  4 inches. GEOMETRY For Exercises 28 and 29. 26. Evaluate the expression to determine how much Ms. regular monthly cost of internet service. 3. and represents the number of hours over 100 used by Nicole in a given month. Reading the Lesson 2. write addition. division. represents the represents the cost of each additional hour after 100 hours. . 26  8  14 c. a. The letter P represents parentheses and other grouping symbols.  51  729 9 f. What does evaluate powers mean? Use an example to explain. In the expression 4. 69  57  3  16  4 19  3  4 62 e.99(117  100). subtraction. 17  3  6 d. multiplication. For each of the following expressions. 400  5[12  9] b. or evaluate powers to tell what operation to use first when evaluating the expression.  2 Helping You Remember 4. List four types of grouping symbols found in algebraic expressions. Read the order of operations on page 11 in your textbook. The first step in evaluating an expression is to evaluate inside grouping symbols.NAME ______________________________________________ DATE 1-2 ____________ PERIOD _____ Reading to Learn Mathematics Order of Operations Pre-Activity How is the monthly cost of internet service determined? Read the introduction to Lesson 1-2 at the top of page 11 in your textbook.95  0. Write what each of the other letters in PEMDAS means when using the order of operations. The sentence Please Excuse My Dear Aunt Sally (PEMDAS) is often used to remember the order of operations. © Glencoe/McGraw-Hill 11 Glencoe Algebra 1 Lesson 1-2 1. 2. 3. Also. and 4. subtraction. and parentheses in any way you wish. Express each number as a combination of the digits 1. such as 12 or 34. 2. you can use two digits to make one number. Each digit is used only once. and 4. you will use the digits 1.NAME ______________________________________________ DATE 1-2 ____________ PERIOD _____ Enrichment The Four Digits Problem One well-known mathematic problem is to write expressions for consecutive numbers beginning with 1. On this page. exponents. You may use addition. 3. multiplication (not division). © Glencoe/McGraw-Hill 12 Glencoe Algebra 1 . 1  (3  1)  (4  2) 18  35  2(4 +1)  3 2 19  3(2  4)  1 36  3 20  37  4 21  38  5 22  39  6 23  31  (4  2) 40  7 24  41  8 25  42  9 26  43  42  13 10  27  44  11  28  45  12  29  46  13  30  47  14  31  48  15  32  49  16  33  50  17  34  Does a calculator help in solving these types of puzzles? Give reasons for your opinion. 10}. y  2  6 4.   p 15. a  23  1 1 4 5 8 11. 2(x  3)  7 8. the solution is 9. The set of all replacements for the variable that result in true statements is called the solution set for the variable. subtract in the denominator. 1 2 5 2 1. 4. Replace a in 3a  12  39 with each value in the replacement set. s   16. 2. Example 1 Find the solution set of 3a  12  39 if the replacement set is {6. is called an equation. w  62  32 15  6 27  24 13.NAME ______________________________________________ DATE 1-3 ____________ PERIOD _____ Study Guide and Intervention Open Sentences Solve Equations A mathematical sentence with one or more variables is called an open sentence.  ( y  1)2   1 4 1 16 9 4 9. Open sentences are solved by finding replacements for the variables that result in true sentences. 9 false false 8 9 The solution is  .2  m 17. x2  1  8 5. 1. 3 4 2 and Y  {2. x     2.  . . n  62  42 18  3 23 12. 10. 8}. A sentence that contains an equal sign. 6.7 18.4  3. 3(6) 12  39 → 30 39 3(7) 12  39 → 33 39 3(8) 12  39 → 36 39 3(9) 12  39 → 39  39 3(10) 12  39 → 42 39 Example 2 2(3  1) 3(7  4) Solve   b. The set of numbers from which replacements for a variable may be chosen is called the replacement set.8  5. k  9. 7. 8. 9. The solution set is {9}. c  3   2  © Glencoe/McGraw-Hill 13 1 2 1 4 Glencoe Algebra 1 Lesson 1-3 Exercises . y2  2  34 6. x  8  11 3. 1 1  Find the solution of each equation if the replacement sets are X   . true false Since a  9 makes the equation 3a  12  39 true. 3(3) false 8   b Simplify. y2  y  20 Solve each equation. 2(3  1)   b Original equation 3(7  4) 2(4)   b Add in the numerator.     k 14. x2  5  5  7. 18. NAME ______________________________________________ DATE 1-3 ____________ PERIOD _____ Study Guide and Intervention (continued) Open Sentences Solve Inequalities An open sentence that contains the symbol . . . Example Find the solution set for 3a  8  10 if the replacement set is {4. or is called an inequality. 5. Replace a in 3a  8 . 6. 7.. Inequalities can be solved the same way that equations are solved. 8}. 10 with each value in the replacement set. 3(4) 3(5) 3(6) 3(7) 3(8)      8 8 8 8 8 ? . 10 ? . 10 ? . 10 ? . 10 ? . 10 → → → → → 4 . 10 7 . 10 10 . 10 13 . 10 16 . 10 false false false true true Since replacing a with 7 or 8 makes the inequality 3a  8 . 6. Exercises Find the solution set for each inequality if the replacement set is X  {0. x  2 . 1. 7}. 8}. 3. 2. the solution set is {7. 10 true. 1. 4. 5. 3x . 4 2. x  3 6 x 3 3.  . 18 3x 8 x 5 4.  2 6. 1 5. 3x  4 .   2 7. 5 8. 3(8  x)  1  6 9. 4(x  3) 20 Find the solution set for each inequality if the replacement sets are 14 1 2  X   ,  , 1, 2, 3, 5, 8 and Y  {2, 4, 6, 8, 10} 10. x  3 5 x 2 11. y  3 6 12. 8y  3 51 y 4 2y 5 13.  4 14.  2 15.   2 16. 4x  1 4 17. 3x  3 12 18. 2( y  1) 18 20. 3y  2  8 21.  (6  2x)  2  3 1 4 19. 3x   2 © Glencoe/McGraw-Hill 14 1 2 Glencoe Algebra 1 NAME ______________________________________________ DATE 1-3 ____________ PERIOD _____ Skills Practice Open Sentences Find the solution of each equation if the replacement sets are A  {4, 5, 6, 7, 8} and B  {9, 10, 11, 12, 13}. 1. 5a  9  26 2. 4a  8  16 3. 7a  21  56 4. 3b  15  48 5. 4b  12  28 6.   3  0 36 b Find the solution of each equation using the given replacement set. 1 2 5 4 12 3 4 5 4 7.   x   ;  ,  , 1,  1 4 5 6 23  3 5 4 4 4 3 9.  (x  2)   ;  ,  ,  ,  2 3 13 9 49 5 2 7 9 3 9 8. x     ;  ,  ,  ,    10. 0.8(x  5)  5.2; {1.2, 1.3, 1.4, 1.5} Solve each equation. 12. y  20.1  11.9 6  18 31  25 13.   a 46  15 3  28 14. c   2(4)  4 3(3  1) 16.   n 15.   b Lesson 1-3 11. 10.4  6.8  x 6(7  2) 3(8)  6 Find the solution set for each inequality using the given replacement set. 17. a  7 13; {3, 4, 5, 6, 7} 18. 9  y 17; {7, 8, 9, 10, 11} 19. x  2  2; {2, 3, 4, 5, 6, 7} 20. 2x 10} 21. 2. 4. 4b  1 . 6. 8. {0. 12. 8. 10. 9.  5. 2c  5  11. 11. 12. 12. 13} y 2 23. 6. 15} 22. 3. 12. 6. {8.  . 9. {4. {0. 10. 12} © Glencoe/McGraw-Hill x 3 24. {3. 7. 5. 6. 2. 4. 8} 15 Glencoe Algebra 1 . 6a  18  27 4.   x   . {2. 6. 0.   k 37  9 18  11 12. 3. 1.6.2}  10. 2. y   16. x  18.4.95 13.   3 4 27 8  21 1 2 1 2 8. {0.   9  16 28 b Find the solution of each equation using the given replacement set. 5.8 . 11.NAME ______________________________________________ DATE 1-3 ____________ PERIOD _____ Practice Open Sentences  1 3  Find the solution of each equation if the replacement sets are A  0.5. 3.  .  . 16.6} Solve each equation. w  20.5 5. 4.5.3  4.  (x  2)   . 2. 7} 18. {2. 5}. 1  . 3y 42. 7 8 17 12  12 13 7 5 2 24 12 8 3 7. 2. 4b  4 . 1. 2 2 2 and B  {3. 2.5.4.  .5.  . 1.8.0.8. 3. 4. 12. a    1 2.5} 20. 1.4(x  3)  5. 2  9. 17. 1 2 1. 1. {0. 4b  8  6 3. 12(x  4)  76. 3. 2. a  7 10.2.8 97  25 41  23 14.  . 1. 0.  .32.2  8. 1.   d 4(22  4) 3(6)  6 5(22)  4(3) 4(2  4) 15. 4x  2 5.  p 3 Find the solution set for each inequality using the given replacement set. 18} 19. 120  28a  78 6. 4. 7b  8  16. 14. {10.  .  . Gabriel talks an average of 20 minutes per long-distance call.2. 2.4. 4a 3. Write an inequality that represents the number of 20 minute state-to-state calls Gabriel can make this month. Write and then solve an equation that represents the number of lessons the teacher must teach per week if there is an average of 8. 1.  . 24. 10}  18 1 3 1 5 3 4 8 2 8 4 22.5 lessons per chapter.  . 2. 1.8.0} 3y 5 21.   2. he makes eight in-state long-distance calls averaging $2. What is the maximum number of 20-minute state-to-state calls that Gabriel can make this month? © Glencoe/McGraw-Hill 16 Glencoe Algebra 1 . TEACHING A teacher has 15 weeks in which to teach six chapters.50. 3. A 20-minute state-to-state call costs Gabriel $1.00 each. use the following information. 25. {0. 1.  .   23. {1. His long-distance budget for the month is $20. 4.6.  . 6. LONG DISTANCE For Exercises 24 and 25. 8. During one month. 50  5n? Reading the Lesson 1. How would you read each inequality symbol in words? Inequality Symbol Words . How is the open sentence different from the expression 15. How can you tell whether a mathematical sentence is or is not an open sentence? 2.NAME ______________________________________________ DATE 1-3 ____________ PERIOD _____ Reading to Learn Mathematics Open Sentences Pre-Activity How can you use open sentences to stay within a budget? Read the introduction to Lesson 1-3 at the top of page 16 in your textbook. b. 2. 1. Suppose the replacement set is {0. a. Describe how you would find the solutions of the equation. c. Describe how you would find the solutions of the inequality.  3. Helping You Remember 4. Look up the word solution in a dictionary. 4. 5}. 3. Explain how the solution set for the equation is different from the solution set for the inequality. What is one meaning that relates to the way we use the word in algebra? © Glencoe/McGraw-Hill 17 Glencoe Algebra 1 Lesson 1-3 . Consider the equation 3n  6  15 and the inequality 3n  6  15. It is the square of 2. Write an open sentence for each solution set. June} is called the solution set of the open sentence given above. {1. Indian. 8. It is the name of a state beginning with the letter A. she was the wife of a U. Pacific. Its capital is Harrisburg. E.S. I. 11. 4. O. May. 31  72  k 10. It is an even number between 1 and 13. August} 14. 2. {A. It is the name of a month that contains the letter r. Write the solution set for each open sentence. 9. 3. {June. It is a primary color. 5. {Atlantic. This set includes all replacements for the variable that make the sentence true. During the 1990s. 7. President. Arctic} © Glencoe/McGraw-Hill 18 Glencoe Algebra 1 . July.NAME ______________________________________________ DATE 1-3 ____________ PERIOD _____ Enrichment Solution Sets Consider the following open sentence. U} 12. 5. x  4  10 6. You know that a replacement for the variable It must be found in order to determine if the sentence is true or false. 7. The set {April. If It is replaced by either April. the sentence is true. It is a New England state. 3. or 4. May. 9} 13. 1. It is the name of a month between March and July. 3. or June. b 0. b. since 8  1  8 a 5454 Reflexive Property b. Then find the value of n. 7. then 4n  4  12. 6n  6 3 4 6. Multiplicative Identity For any number a. Reflexive Property For any number a. if a  b and b  c. Substitution Property If a  b. Substitution Property b. a. 9. Transitive Property For any numbers a. 12. 4  3  4  3 © Glencoe/McGraw-Hill 13. there is exactly one number  such that    1. a  0  0. Multiplicative Property of 0 For any number a. 0(15)  0 8. then b  a. b a Example 1 b a Example 2 Name the property used in each equation. since   3  1 Exercises Name the property used in each equation. n  0   3 8 Lesson 1-4 1. Name the property used to justify each statement.NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Study Guide and Intervention Identity and Equality Properties Identity and Equality Properties The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions. if a  b. (1)94  94 11. a  a. Symmetric Property For any numbers a and b. Multiplicative Inverse Property a b a b For every number  . Additive Identity For any number a. then a may be replaced by b in any expression.   n  1 Name the property used in each equation. If 4  5  9. If 3  3  6 and 6  3  2. a. 6  n  6  9 4. a  1  a. Then find the value of n. 0  21  21 10. If n  12. then 9  4  5. then a  c. n  3  1 Multiplicative Inverse Property 1 3 1 3 n   . then 3  3  3  2. (14  6)  3  8  3 19 Glencoe Algebra 1 . 2. and c. 8n  8 Multiplicative Identity Property n  1. 9  n  9 5. a  0  a. n  1  8 3. 24  1  24 Multiplicative Property of Zero. Example Evaluate 24  1  8  5(9  3  3). 5(0)  0 Substitution. 2(3  5  1  14)  4   4. 9  3  3 Substitution. 24  8  16 Additive Identity. 24  1  8  5(9  3  3)       24 24 24 24 16 16  1  8  5(3  3)  1  8  5(0)  8  5(0) 80 0 Substitution.NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Study Guide and Intervention (continued) Identity and Equality Properties Use Identity and Equality Properties The properties of identity and equality can be used to justify each step when evaluating an expression. 3  3  0 Multiplicative Identity. 3(5  5  12)  21  7 Glencoe/McGraw-Hill 20 Glencoe Algebra 1 . 10  5  22  2  13 6. 2    2 2. 15  1  9  2(15  3  5) 1 4 © 3. Name the property used in each step. 16  0  16 Exercises Evaluate each expression. Name the property used in each step.  41  21   1. 18  1  3  2  2(6  3  2) 5. 7(16  42) © Glencoe/McGraw-Hill 1 2 21 Glencoe Algebra 1 . 16. 1  n  8 3. 4  3[7  (2  3)] 18. 28  n  0 4. (7  3)  4  n  4 11. Then find the value of n.   n  1 6. 5  n  5 8. n  0  19 2. 2  n  2  3 9. Name the property used in each step. 2(6  3  1)   Lesson 1-4 15. 11  (18  2)  11  n Evaluate each expression. 3n  1 14. 1. 5  4  n  4 12. n  9  9 7. 0  n  22 1 4 5. 2(9  3)  2(n) 10. 2[5  (15  3)] 17. 6  9[10  2(2  3)] 20. n  14  0 13. 4[8  (4  2)]  1 19.NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Skills Practice Identity and Equality Properties Name the property used in each equation. use the following information. Katz only harvested one fourth of the tomatoes from each of these. Write an expression that represents the profit Althea made. Then find the value of n. Katz harvested 15 tomatoes from each of four plants.00. GARDENING For Exercises 11 and 12. Evaluate the expression. Name the property used in each step. 2  6(9  32)  2 1 4 8. Name the property used in each step. 5n  1 4. 1. n  9  9 2. 49n  0 6. (8  7)(4)  n(4) 3.NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Practice Identity and Equality Properties Name the property used in each equation.00 each for three bracelets and sold each of them for $9. © Glencoe/McGraw-Hill 22 Glencoe Algebra 1 . 10.5 5. Althea paid $5. Name the property used in each step. Evaluate the expression. 11. Mr. use the following information. She paid $8.5  0.1  0. but Mr. 7.00. 5(14  39  3)  4   SALES For Exercises 9 and 10. 12. 12  12  n Evaluate each expression.00 each for two bracelets and later sold each for $15. 9. Two other plants produced four tomatoes each. Write an expression for the total number of tomatoes harvested. n  0. 5 7 7 5 I. g.     1 a. © Glencoe/McGraw-Hill 23 Glencoe Algebra 1 . then 8  4  12. multiplicative identity c. additive identity II. If 2  4  5  1 and 5  1  6. If 12  8  4. 4  0  0 h. The prefix trans. 18  18 b. f. Substitution Property Helping You Remember 2.NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Reading to Learn Mathematics Identity and Equality Properties Pre-Activity How are identity and equality properties used to compare data? Read the introduction to Lesson 1-4 at the top of page 21 in your textbook. Symmetric Property VII. Write the Roman numeral of the sentence that best matches each term. then 2  4  6. Write an open sentence to represent the change in rank r of the University of Miami from December 11 to the final rank.” Explain how this can help you remember the meaning of the Transitive Property of Equality.means “across” or “through. Reading the Lesson 1. Explain why the solution is the same as the solution in the introduction. 6  0  6 e. V. 3  1  3 d. Multiplicative Inverse Property IV. Transitive Property Lesson 1-4 VIII. Reflexive Property VI. If n  2. Multiplicative Property of Zero III. then 5n  5  2. For example. nonprime numbers Tell whether the set of whole numbers is closed under each operation. 7. multiples of 5 11. the set of whole numbers is closed under addition because 4  5 is a whole number. the operation ©. give an example. division: a  b 15. If your answer is no. where sq(a) means to square the number a 4. The set of whole numbers is not closed under subtraction because 4  5 is not a whole number. the operation sq. where a © b means to cube the sum of a and b 3. the operation exp. Addition is a binary operation on the set of whole numbers. the set is said to be closed under the operation. If your answer is no. b) means to find the value of ab 5. It matches two numbers such as 4 and 5 to a single number. the operation ⇑. prime numbers 12. Tell whether each operation is binary. where exp(a. the operation ⇒. where a ↵ b means to choose the lesser number from a and b 2. 1. Write yes or no. where a ⇒ b means to round the product of a and b up to the nearest 10 Tell whether each set is closed under addition. give an example. exponentation: ab 16. odd numbers 9. multiplication: a  b 14. multiples of 3 10. If the result of a binary operation is always a member of the original set. their sum. where a ⇑ b means to match a and b to any number greater than either number 6. 13. even numbers 8. Write yes or no. squaring the sum: (a  b)2 © Glencoe/McGraw-Hill 24 Glencoe Algebra 1 . Write yes or no. the operation ↵.NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Enrichment Closure A binary operation matches two numbers in a set to just one number. 6(8  10)  6  8  6  10  48  60  108 Example 2 Distributive Property Multiply. Rewrite 6(8  10) using the Distributive Property. 3(2x  y) 14.  (12  4t) 12. (2  3x  x2)3 18. 3(8  2x) 9. b. 12 6   x  1 2 10. Add.  (16x  12y  4z) © Glencoe/McGraw-Hill  1 4 1 2  11. 2(3x  2y  z) 1 4 16. 6(12  5) 5. 2(10  5) . (x  2)y 15. a(b  c)  ab  ac and (b  c)a  ba  ca and a(b  c)  ab  ac and (b  c)a  ba  ca. Distributive Property Example 1 For any numbers a. Exercises Rewrite each expression using the Distributive Property. 2(3x2  5x  1)  2(3x2) (2)(5x)  (2)(1)  6x2  (10x)  (2)  6x2  10x  2 Distributive Property Multiply. Simplify. and c. 2(x  3) 7. Then simplify. 3(x  1) 4. 5(4x  9) 8. Then simplify. 2. Then evaluate. 6(12  t) 3. 2(2x2  3x  1) 25 Glencoe Algebra 1 Lesson 1-5 1.NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Study Guide and Intervention The Distributive Property Evaluate Expressions The Distributive Property can be used to help evaluate expressions. (x  4)3 6. 12 2   x  13. Rewrite 2(3x2  5x  1) using the Distributive Property. 2(3a  2b  c) 17. 2x  12 6. 3x  2x  2y  2y 14. 4x   (16x  20y) © Glencoe/McGraw-Hill 26 Glencoe Algebra 1 . 3x2  2x2 9. If not possible. An expression is in simplest form if it is replaced by an equivalent expression with no like terms or parentheses. Example Simplify 4(a2  3ab)  ab. 2  1  6x  x2 18.NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Study Guide and Intervention (continued) The Distributive Property Simplify Expressions A term is a number. 20a  12a  8 8. xy  2xy 15. 12a  a 2. with corresponding variables having the same powers. 2p   q 11. a variable. 4x2  3x2  2x 1 4 16. 12a  12b  12c 17. 4(a2  3ab)  ab     4(a2  3ab)  1ab 4a2  12ab  1ab 4a2  (12  1)ab 4a2  11ab Multiplicative Identity Distributive Property Distributive Property Substitution Exercises Simplify each expression. 12g  10g  1 5. write simplified. The Distributive Property and properties of equalities can be used to simplify expressions. 21c  18c  31b  3b 13. 1. 6x  3x2  10x2 1 2 10. 3x  1 4. 3x  6x 3. 10xy  4(xy  xy) 12. or a product or quotient of numbers and variables. Like terms are terms that contain the same variables. 4x2  3x  7 7. 2x2  6x2 22. 4(2b  b) 26. 11. 2(x  y  1) 10. 9  99 13. 2x  8x 18. (6  2)8 5. 12 1   31   18  16. 16m  10m 20. 3y2  2y 24. 15  104 14. 5  89 12.NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Skills Practice The Distributive Property Rewrite each expression using the Distributive Property. (x  y)6 9. 2(6  10) 3. write simplified. 15 2   14  15. 4(3  5) 2. 5(7  4) 4. 3(m  n) 8. 7(h  10) 7. Then simplify. 2(n  2n) 25. (a  7)2 6. 7a2  2a2 23. 12p  8p 21. Glencoe Algebra 1 . If not possible. 1. 8 3  17. 3(a  b  1) Use the Distributive Property to find each product. 17g  g 19. 3q2  q  q2 © Glencoe/McGraw-Hill 27 Lesson 1-5 Simplify each expression. 27. m(n  4) 9. 10.NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Practice The Distributive Property Rewrite each expression using the Distributive Property. x   x   2 3 x 3 DINING OUT For Exercises 25 and 26.75.5 14. Then simplify. Each day. (9  p)3 5. use the following information. 7  110 13. 3a2  6a  2b2 23. 25. 4(6p  2q  2p) 24. 16. and dessert that cost $2. Madison College conducted a three-day orientation for incoming freshmen. What was the attendance for all three days of orientation? © Glencoe/McGraw-Hill 28 Glencoe Algebra 1 . use the following information.25) 8. (5y  3)7 6. Each of the four family members ordered a pasta dish that cost $11. 14(2r  3) 19. 7(6  4) 3. c2  4d 2  d 2 22. 12b2  9b2 20. Write an expression that could be used to determine the total number of incoming freshmen who attended the orientation. The Ross family recently dined at an Italian restaurant. 3(5  6h) 18. 16 4  Simplify each expression. What was the cost of dining out for the Ross family? ORIENTATION For Exercises 27 and 28. 6(b  4) 4. 9(7  8) 2. w  14w  6w 17. 1. write simplified. 21  1004  31   41  15. 26. Write an expression that could be used to calculate the cost of the Ross’ dinner before adding tax and a tip. 16(3b  0. 9  499 11. 12  2. an average of 110 students attended the morning session and an average of 160 students attended the afternoon session.50. 28. If not possible. a drink that cost $1.50. (c  4)d  1 3  Use the Distributive Property to find each product. 27 2  12. 15 f   7. 25t3  17t3 21. Write three examples of each type of term.NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Reading to Learn Mathematics The Distributive Property Pre-Activity How can the Distributive Property be used to calculate quickly? Read the introduction to Lesson 1-5 at the top of page 26 in your textbook. How would you find the amount spent by each of the first eight customers at Instant Replay Video Games on Saturday? Reading the Lesson 1. How can the everyday meaning of the word identity help you to understand and remember what the additive identity is and what the multiplicative identity is? © Glencoe/McGraw-Hill 29 Glencoe Algebra 1 Lesson 1-5 Helping You Remember . Tell how you can use the Distributive Property to write 12m  8m in simplest form. 3. Explain how the Distributive Property could be used to rewrite 3(1  5). Term Example number variable product of a number and a variable quotient of a number and variable 4. Use the word coefficient in your explanation. Explain how the Distributive Property can be used to rewrite 5(6  4). 2. 5. 4. but one has a triangle at the bottom and the other does not. They are used in a very old Chinese puzzle called tangrams. Glue the seven tans on heavy paper and cut them out. Record your solutions below. Where does the second figure get this triangle? © Glencoe/McGraw-Hill 30 Glencoe Algebra 1 . 1. Use all seven pieces to make each shape shown. Each of the two figures shown at the right is made from all seven tans. 6. They seem to be exactly alike.NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Enrichment Tangram Puzzles The seven geometric figures shown below are called tans. 3. 5. 2. 5  2.8)  (2. The product is 180. 3   4  2   3 1 2 1 2 10. Multiply.5  2. 4  8  5  3 5.4  3.2  1.   18  25   14.   12  4  2 11.2  2. Add.5  2. 12  20  10  5 6. The Associative Properties state that the way you group three or more numbers when adding or multiplying does not change their sum or product. 1.2  1. 26  8  4  22 1 2 1 2 7. a  b  b  a and a  b  b  a.2  2.   10  16   Glencoe Algebra 1 Lesson 1-6 Commutative and Associative Properties .   7  16   3 4 1 2 18. The Commutative Properties state that the order in which you add or multiply numbers does not change their sum or product.6  4.6 1 2 13. Add. 10  7  2.5  2. The sum is 15.5  2. 62356325  (6  3)(2  5) 18  10 180 Evaluate 8. Commutative Prop. Example 1 Example 2 Evaluate 6  2  3  5.NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Study Guide and Intervention Commutative and Associative Properties The Commutative and Associative Properties can be used to simplify expressions.2 1 9 31 1 4 1 7 15. 2. Commutative Property 8. Associative Prop. b. 4   5    3 4 5 2 9 3 4 8.8  8. 12  10  8  5 2.5 4.5)  10 5  15 Associative Property Multiply. 3.5  3.8. 3.5  2 17. Associative Properties For any numbers a. (a  b)  c  a  (b  c ) and (ab)c  a(bc).8  2. Commutative Properties For any numbers a and b. 0. 16  8  22  12 3. and c.5  1.5  8  2.8  4 1 5 12.5  (8. 32      10 16. Exercises Evaluate each expression. 18  8     © Glencoe/McGraw-Hill 1 2 9.5  2.5  1.5  2.4  2. Example Simplify 8(y  2x)  7y. 5(0. 1.3x  0. 8rs  2rs2  7rs 4. Then simplify. 6(2x  4y)  2(x  9) Write an algebraic expression for each verbal expression. 6(a  b)  a  3b 8.2x 2 3 1 2 4 3 10. 3a  4b  a 3. a2. and 4 16. 5(2x  3y)  6( y  x) 9. 6n  2(4n  5) 7. 8(y  2x)  7y     8y  16x  7y 8y  7y  16x (8  7)y 16x 15y  16x Distributive Property Commutative () Distributive Property Substitution The simplified expression is 15y  16x. 3a2  4b  10a2 5. the product of five and the square of a. 6(x  y)  2(2x  y) 6.1y)  0. twice the sum of y and z is increased by y 14. 13. 4x  3y  x 2.    (x  10)   4 3 1 3 11. four times the product of x and y decreased by 2xy 15. three times the sum of x and y increased by twice the sum of x and y © Glencoe/McGraw-Hill 32 Glencoe Algebra 1 .NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Study Guide and Intervention (continued) Commutative and Associative Properties Simplify Expressions The Commutative and Associative Properties can be used along with other properties when evaluating and simplifying expressions. z2  9x2   z2   x2 12. Exercises Simplify each expression. increased by the sum of eight. 5  7  10  4 7. 16  8  14  12 2. 10. 1.NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Skills Practice Evaluate each expression. a  9b  6a 12. 32  14  18  11 4. Then simplify.3 8. 36  23  14  7 3. r  3s  5r  s 14. 5  3  4  3 5. twice the sum of p and q increased by twice the sum of 2p and 3q © Glencoe/McGraw-Hill 33 Glencoe Algebra 1 Lesson 1-6 Commutative and Associative Properties . 18.9  2. 2  4  5  3 6. 1. 6k2  6k  k2  9k 16. 2x  5y  9x 11. 1.8  1.4 9. 5m2  3m  m2 15. three times the sum of a and b increased by a 19.6  0. 2a  3(4  a) 17. indicating the properties used. 5(7  2g)  3g Write an algebraic expression for each verbal expression. 2p  3q  5p  2q 13.7  0. 4   6  5  1 2 1 2 Simplify each expression. 2  9.6  3. Using the commutative and associative properties to group the terms in a way that makes evaluation convenient. use the following information. What was the total cost of supplies before tax? GEOMETRY For Exercises 18 and 19. 18.75 each. two binders that cost $4.  q  2  q   r 1 2  14 1 2  15. SCHOOL SUPPLIES For Exercises 16 and 17.25 each. 16. Kristen purchased two binders that cost $1. 13  23  12  7 2.6  0.NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Practice Commutative and Associative Properties Evaluate each expression.3 4. 2(3x  y)  5(x  2y) 11. 7.15 each. 3(2c  d)  4(c  4d) 12. 0. Write an algebraic expression for four times the sum of 2a and b increased by twice the sum of 6a and 2b. 17. and four pencils that cost $. (p  2n)  7p 10.4  1. The lengths of the sides of a pentagon in inches are 1. Then simplify.4c)  b 14.6b  0. indicating the properties used.5. 3. and 0. 19. Write an expression to represent the total cost of supplies before tax. 7   2  1  3 4 1 3 6.9. 3   3   16 Simplify each expression. two packages of paper that cost $1. 2. What is the perimeter of the pentagon? © Glencoe/McGraw-Hill 34 Glencoe Algebra 1 .1. 1. write an expression to represent the perimeter of the pentagon. use the following information.25. 1. 6  5  10  3 3. 9s2  3t  s2  t 9. four blue pens that cost $1.25. 6s  2(t  3s)  5(s  4t) 13. 7. 5(0.35 each.50 per package. 6y  2(4y  6) 8.7  5 1 9 2 9 5. Commutative Property of Addition d. Commutative Property of Multiplication 2. How are the expressions 0. To use the Associative Property of Addition to rewrite the sum of a group of terms. 2  (3  4)  (2  3)  4 II. Find an everyday meaning that is close to the mathematical meaning and explain how it can help you remember the mathematical meaning. What property can you use to change the order of the terms in an expression? 3.4  1. what is the least number of terms you need? Helping You Remember 6. What property can you use to change the way three factors are grouped? 4. 2  (3  4)  2  (4  3) IV. 2  (3  4)  (2  3)  4 III. Write the Roman numeral of the term that best matches each equation. © Glencoe/McGraw-Hill 35 Glencoe Algebra 1 Lesson 1-6 Commutative and Associative Properties .5 and 1. Associative Property of Addition b.4 alike? different? Reading the Lesson 1.NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity How can properties help you determine distances? Read the introduction to Lesson 1-6 at the top of page 32 in your textbook. What property can you use to combine two like terms to get a single term? 5. Associative Property of Multiplication c. 3  6  6  3 I. a. Look up the word commute in a dictionary.5  0.  3  32  9 2 (1   2)   3  21   3  32  9 1. Let’s explore these operations a little further. What number is represented by 2   (1   3)? 6. Does the operation   appear to be commutative? 4. What number is represented by (2  3)  4? 11. What number is represented by 2  3? 8. What number is represented by (3   4)  (3   2)? 18. What number is represented by 1   (3  2)? 14. What number is represented by (2   1)   3? 5.NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Enrichment Properties of Operations Let’s make up a new operation and denote it by   . What number is represented by (1   3)  (1   2)? 15. What number is represented by 3  (4  2)? 17. What number is represented by 2  (3  4)? 12. Is the operation   actually distributive over the operation ? © Glencoe/McGraw-Hill 36 Glencoe Algebra 1 . What number is represented by 3   2? 3. 3  2  (3  1)(2  1)  4  3  12 (1  2)  3  (2  3)  3  6  3  7  4  28 7. What number is represented by 2   3? 2. Does the operation  appear to be commutative? 10. What number is represented by 3  2? 9. Does the operation  appear to be associative? 13. so that a   b means ba. Does the operation   appear to be associative? Let’s make up another operation and denote it by . so that a  b  (a  1)(b  1). Does the operation   appear to be distributive over the operation ? 16. 4. If the area of a square is 49. Example 2 Identify the hypothesis and conclusion of each statement. then x 7. 3. Identify the hypothesis and conclusion of each statement. If it is April. 5. Then write the statement in if-then form. A number that is divisible by 8 is also divisible by 4. The part of the statement immediately following the word then is called the conclusion. If 12  4x  4. a. a  3. If it is Monday. For a number a such that 3a  2  11. You and Marylynn can watch a movie on Thursday. then a  3. Hypothesis: it is Wednesday Conclusion: Jerri has aerobics class a. Statements in this form are called if-then statements. 6. If it is Wednesday.NAME ______________________________________________ DATE 1-7 ____________ PERIOD _____ Study Guide and Intervention Logical Reasoning Conditional Statements A conditional statement is a statement of the form If A. Hypothesis: it is Thursday Conclusion: you and Marylynn can watch a movie If it is Thursday. Exercises Identify the hypothesis and conclusion of each statement. Karlyn goes to the movies when she does not have homework. then B. then you and Marylynn can watch a movie. If 2x  4 10. b. Hypothesis: 3a  2  11 Conclusion: a  3 If 3a  2  11. then you can run fast. then it might rain. The part of the statement immediately following the word if is called the hypothesis. © Glencoe/McGraw-Hill 37 Glencoe Algebra 1 Lesson 1-7 Example 1 . then Jerri has aerobics class. then the square has side length 7. 2. Hypothesis: 2x  4 10 Conclusion: x 7 b. Then write the statement in if-then form. 1. Identify the hypothesis and conclusion of each statement. then x  2. 8. If you are a sprinter. A quadrilateral with equal sides is a rhombus. 7. then you are in school. 4. If 3x  2  10. 1. b. The sum of two numbers is 20. 12  8. There is no way to determine the two numbers. 6. use a counterexample. © Glencoe/McGraw-Hill 38 Glencoe Algebra 1 . one example for which the conditional statement is false. If a quadrilateral has 4 right angles. then the number is divisible by 5 for the given conditions. you will not get the correct answer. If a valid conclusion does not follow. Consider 13 and 7. 4 and 8 are even. 9. then she is in math class. 2. then the number must be greater than six. Therefore there is no valid conclusion. write no valid conclusion and explain why. Exercises Determine a valid conclusion that follows from the statement If the last digit of a number is 0 or 5. 13  7  20 However. or properties to reach a valid conclusion. To show that a conditional statement is false. a. definitions. Example 2 Provide a counterexample to this conditional statement. If Susan is in school. and 4  8  12. then you will get the answer correct. The number is 120. You need to find only one counterexample for the statement to be false. and 18  2 all equal 20. Counterexample: If the problem is 475  5 and you press 475  5. If you were born in New York. The number is a multiple of 4. Example 1 Determine a valid conclusion from the statement If two numbers are even. then their sum is even for the given conditions. Find a counterexample for each statement.NAME ______________________________________________ DATE 1-7 ____________ PERIOD _____ Study Guide and Intervention (continued) Logical Reasoning Deductive Reasoning and Counterexamples Deductive reasoning is the process of using facts. 8. write no valid conclusion and explain why. 5. Conclusion: The sum of 4 and 8 is even. If three times a number is greater than 15. 7. The two numbers are 4 and 8. then x 4. If a valid conclusion does not follow. 19  1. rules. then the quadrilateral is a square. then it is divisible by 2. The number is 101. 3. then you live in New York. If you use a calculator for a math problem. If a number is a square. 13.NAME ______________________________________________ DATE 1-7 ____________ PERIOD _____ Skills Practice Logical Reasoning Identify the hypothesis and conclusion of each statement. A polygon that has five sides is a pentagon. 1. 12. Hector scored an 86 on his science exam. Then write the statement in if-then form. then it is out of gas. then mail is not delivered. If a valid conclusion does not follow. 9. 4. 6. 8. If 2n  3 17. write no valid conclusion and explain why. then you are outdoors. 2. Identify the hypothesis and conclusion of each statement. 14. Hector did not earn an A in science. then he will earn an A in the class for the given condition. Martina works at the bakery every Saturday. If you are hiking in the mountains. If the car will not start. 7. 10. If 6n  4 . Hector scored 84 on the science exam. then n  7. then it holds for subtraction. © Glencoe/McGraw-Hill 39 Glencoe Algebra 1 Lesson 1-7 3. then they must be winning the game. If the Commutative Property holds for addition. Ivan only runs early in the morning. 5. 11. . Hector studied 10 hours for the science exam. Determine whether a valid conclusion follows from the statement If Hector scores an 85 or above on his science exam. Find a counterexample for each statement. If the basketball team has scored 100 points. If it is Sunday. 58, then n 9. NAME ______________________________________________ DATE 1-7 ____________ PERIOD _____ Practice Logical Reasoning Identify the hypothesis and conclusion of each statement. 1. If it is raining, then the meteorologist’s prediction was accurate. 2. If x  4, then 2x  3  11. Identify the hypothesis and conclusion of each statement. Then write the statement in if-then form. 3. When Joseph has a fever, he stays home from school. 4. Two congruent triangles are similar. Determine whether a valid conclusion follows from the statement If two numbers are even, then their product is even for the given condition. If a valid conclusion does not follow, write no valid conclusion and explain why. 5. The product of two numbers is 12. 6. Two numbers are 8 and 6. Find a counterexample for each statement. 7. If the refrigerator stopped running, then there was a power outage. 8. If 6h  7 5, then h  2. GEOMETRY For Exercises 9 and 10, use the following information. If the perimeter of a rectangle is 14 inches, then its area is 10 square inches. 9. State a condition in which the hypothesis and conclusion are valid. 10. Provide a counterexample to show the statement is false. 11. ADVERTISING A recent television commercial for a car dealership stated that “no reasonable offer will be refused.” Identify the hypothesis and conclusion of the statement. Then write the statement in if-then form. © Glencoe/McGraw-Hill 40 Glencoe Algebra 1 2.NAME ______________________________________________ DATE 1-7 ____________ PERIOD _____ Reading to Learn Mathematics Logical Reasoning Pre-Activity How is logical reasoning helpful in cooking? Read the introduction to Lesson 1-7 at the top of page 37 in your textbook. e. Write an example of a conditional statement you would use to teach someone how to identify an hypothesis and a conclusion. then it is raining. then x  2. d. b. If 3x  7  13. Write hypothesis or conclusion to tell which part of the if-then statement is underlined. Tell how you know it really is a counterexample. then that person has been on television. © Glencoe/McGraw-Hill 41 Glencoe Algebra 1 Lesson 1-7 What are the two possible reasons given for the popcorn burning? . I can tell you your birthday if you tell me your height. a. then x  2 is an odd number. Give a counterexample for the statement If a person is famous. then they will go to the playoffs. c. If it is Tuesday. If x is an even number. Helping You Remember 4. If our team wins this game. Reading the Lesson 1. What does the term valid conclusion mean? 3. NAME ______________________________________________ DATE 1-7 ____________ PERIOD _____ Enrichment Counterexamples Some statements in mathematics can be proven false by counterexamples. and 3. 2. a  b  b  a 4. You can prove that this statement is false in general if you can find one example for which the statement is false. a  (b  c)  (a  b)  c 3. a  b  b  a. a  (b  c)  (a  b)  c 2. Write the verbal equivalents for Exercises 1. for any numbers a and b. and c are any numbers. a2  a2  a4 7. 7337 4 4 In general. a  (bc)  (a  b)(a  c) 6. In each of the following exercises a. 8. © Glencoe/McGraw-Hill 42 Glencoe Algebra 1 . Exercises 4 and 5 prove that some operations do not distribute. You can make the equivalent verbal statement: subtraction is not a commutative operation. For the distributive property a(b  c)  ab  ac it is said that multiplication distributes over addition. the statement a  b  b  a is false. Consider the following statement. Prove that the statement is false by counterexample. a  (b  c)  (a  b)  (a  c) 5. Let a  7 and b  3. 1. Write a statement for each exercise that indicates this. Substitute these values in the equation above. b. For any numbers a and b. Example 1 Example 2 The graph below represents the price of stock over time. Then describe what is happening in the graph. then falls again.NAME ______________________________________________ DATE 1-8 ____________ PERIOD _____ Study Guide and Intervention Graphs and Functions Interpret Graphs A function is a relationship between input and output values. The independent variable is time. Identify the independent and dependent variable. The graph represents the speed of a car as it travels to the grocery store. Speed Time 2. In a function. Identify the independent and the dependent variable. then it falls. The price increases steadily. Account Balance (dollars) Time 3. Height Time © Glencoe/McGraw-Hill 43 Glencoe Algebra 1 Lesson 1-8 Time . then it loses altitude until it falls to the ground. and the dependent variable is height. The input values are associated with the independent variable. Then describe what is happening in the graph. The graph represents the balance of a savings account over time. Identify the independent and the dependent variable. Then describe what is happening in the graph. The graph represents the height of a baseball after it is hit. then increases. Then describe what is happening in the graph. It gains altitude until it reaches a maximum height. Then describe what is happening in the graph. The football starts on the ground when it is kicked. Price Height Time The independent variable is time and the dependent variable is price. there is exactly one output for each input. Exercises 1. The graph below represents the height of a football after it is kicked downfield. Functions can be graphed without using a scale to show the general shape of the graph that represents the function. Identify the independent and the dependent variable. and the output values are associated with the dependent variable. Identify the independent and dependent variable. Identify the independent and dependent variables.000). called the x-coordinate. (1. 32). dep: length 0 0 22 20 18 16 14 12 0 1 2 3 4 5 Age (months) 44 1 2 3 4 Age (years) 5 Glencoe Algebra 1 . or y-coordinate corresponds to the y-axis. ind: age. Age (years) Value ($) a. Graphs can be used to represent many real-world situations. Draw a graph that shows the relationship between the number of CDs and the total cost. 23). and the y-value. 48). Write a set of ordered pairs representing the data in the table. b. The table below represents the length of a baby versus its age in months. (1. 16. (5. CD Cost 80 Cost ($) a. Make a table showing the cost of buying 1 to 5 CDs. (3. Draw a graph showing the relationship between age and value.000 18. Example A music store advertises that if you buy 3 CDs at the regular price of $16. Draw a graph showing the relationship between age and length. b. Number of CDs 1 2 3 4 5 Total Cost ($) 16 32 48 48 64 c. Input and output values are represented on the graph using ordered pairs of the form (x.000 13. 13. corresponds to the x-axis. (1. Age (months) 0 1 2 3 4 Length (inches) 20 21 23 23 24 2.NAME ______________________________________________ DATE______________ PERIOD _____ 1-8 Study Guide and Intervention (continued) Graphs and Functions Draw Graphs You can represent the graph of a function using a coordinate system. 18. (2. Value (thousands of $) 25 Length (inches) 3 (0. Write a set of ordered pairs representing the data in the table. (4. 14. 24) © 1 a. 24 23 22 21 20 Glencoe/McGraw-Hill 2 b. 16). (2. (4. 48). 20). (3. 23). then you will receive one CD of the same or lesser value free. (2. (0.000 16. The table below represents the value of a car versus its age. 21). The x-value. 64) 60 40 20 0 1 2 3 4 5 Number of CDs 6 Exercises 1.000).000). y).000 c. 4 20.000). Identify the independent and dependent variables. (4. dep: value ind: age. Write the data as a set of ordered pairs. (3. 20.000 14.000) c. it rained lightly for a while. Distance from Trailhead Height 3. © Glencoe/McGraw-Hill 45 Glencoe Algebra 1 Lesson 1-8 Time Time . Use the data to predict the cost for washing and pressing 16 shirts. Which graph represents this situation? A B C Total Rainfall Total Rainfall Total Rainfall Time Time LAUNDRY For Exercises 4–7. The graph below represents a puppy exploring a trail. 6. WEATHER During a storm. The graph below represents the path of a football thrown in the air. Time Number of Shirts 2 4 6 8 10 12 Total Cost ($) 3 6 9 12 15 18 4. Then it rained moderately for a while before finally ending. Write the ordered pairs the table represents. 5. Describe what is happening in the graph. 2. use the table that shows the charges for washing and pressing shirts at a cleaners. Identify the independent and dependent variables. 21 Total Cost ($) 18 15 12 9 6 3 0 2 4 6 8 10 12 14 Number of Shirts 7. then poured heavily.NAME ______________________________________________ DATE 1-8 ____________ PERIOD _____ Skills Practice Graphs and Functions 1. and then stopped for a while. Draw a graph of the data. Describe what is happening in the graph. After firefighters answer the call. the fire grows slowly for a while.50 18. Number of Months Total Cost ($) 1 2 4.50 9.00 22. SAVINGS Jennifer deposited a sum of money in her account and then deposited equal amounts monthly for 5 months.50 4.00 4. The graph below represents a student taking an exam.50 18. Draw a graph of the data. Which graph represents this situation? A B C Area Burned Area Burned Area Burned Time Time Time INTERNET NEWS SERVICE For Exercises 4–6. nothing for 3 months. and then resumed equal monthly deposits.00 13. Sketch a reasonable graph of the account history. 7. 2. Total Cost ($) 27. but then the firefighters contain the fire before extinguishing it.50 9.00 22. use the table that shows the monthly charges for subscribing to an independent news server.50 0 1 2 3 4 5 6 Number of Months 6. Describe what is happening in the graph. Write the ordered pairs the table represents. The graph below represents the height of a tsunami (tidal wave) as it approaches shore.00 3 4 5 13. then rapidly as the wind increases. Account Balance ($) Time © Glencoe/McGraw-Hill 46 Glencoe Algebra 1 . Number of Questions Answered Height Time Time 3.NAME ______________________________________________ DATE 1-8 ____________ PERIOD _____ Practice Graphs and Functions 1. Describe what is happening in the graph. 5. FOREST FIRES A forest fire grows slowly at first. Use the data to predict the cost of subscribing for 9 months. In the alphabet. In your own words. x comes before y. dependent variable the distance it takes to stop a motor vehicle independent variable is a function of d the speed at which the vehicle is traveling s Helping You Remember 4. coordinate system b. Write another name for each term. 50% and 75% represent the and the numbers 0 through 10 represent the . a. tell what is meant by the terms dependent variable and independent variable. y y-axis x-axis origin O x 3. vertical axis 2. The numbers 25%. Use the example below. Reading the Lesson 1. © Glencoe/McGraw-Hill 47 Glencoe Algebra 1 . Identify each part of the coordinate system. horizontal axis Lesson 1-8 c.NAME ______________________________________________ DATE 1-8 ____________ PERIOD _____ Reading to Learn Mathematics Graphs and Functions Pre-Activity How can real-world situations be modeled using graphs and functions? Read the introduction to Lesson 1-8 at the top of page 43 in your textbook. Use this fact to describe a method for remembering how to write ordered pairs. Complete this frequency table for the first 200 digits of  that follow the decimal point. Which digit(s) appears most often? 5. 4. How many times would each digit appear in the first 200 places following the decimal point? 2. Explain how the cumulative frequency column can be used to check a project like this one. It is a nonrepeating and nonterminating decimal. Listed at the right are the first 200 digits that follow the decimal point of . Digit Frequency (Tally Marks) Frequency (Number) Cumulative Frequency 0 1 2 3 4 5 6 7 8 9 3. 3. The digits of  never form a pattern.14159 69399 86280 09384 84102 26433 59230 82148 53594 64462 26535 37510 34825 46095 70193 83279 78164 08651 08128 29489 89793 58209 34211 50582 85211 50288 06286 32823 34111 54930 23846 74944 70679 23172 05559 41971 20899 06647 74502 38196 Solve each problem.NAME ______________________________________________ DATE 1-8 ____________ PERIOD _____ Enrichment The Digits of  The number  (pi) is the ratio of the circumference of a circle to its diameter. Which digit(s) appears least often? © Glencoe/McGraw-Hill 48 Glencoe Algebra 1 . Suppose each of the digits in  appeared with equal frequency. 1. a.. International Visitors to the U.S.000 visitors? 59. What does the negative percent in the first quarter of 2001 indicate? Worker productivity decreased in this period.NAME ______________________________________________ DATE______________ PERIOD _____ 1-9 Study Guide and Intervention Statistics: Analyzing Data by Using Tables and Graphs Analyze Data Graphs or tables can be used to display data. 2000 a. companies over a 10-year period.1 2001 1. The graph shows the use of imported steel by U.000. how many were from Mexico? 50.2 Source: Chicago Tribune Glencoe Algebra 1 Lesson 1-9 40 a. A line graph is useful to show how a data set changes over time. S.000 Others 32% Canada 29% Mexico 20% United Kingdom Japan 9% 10% Source: TInet Exercises 1.891. A bar graph compares different categories of data.000. while a circle graph compares parts of a set of data as a percent of the whole set. If the percentage of visitors from each country remains the same each year. The table shows the percentage of change in worker productivity at the beginning of each year for a 5-year period. as compared to the productivity one year earlier.000  29%  17. Which year shows the greatest percentage increase in productivity? 1998 b. 30 20 10 0 b. What would be a reasonable prediction for the percentage of imported steel used in 2002? 1990 1994 1998 Year Source: Chicago Tribune about 30% 2. Imported Steel as Percent of Total Used Percent general trend is an increase in the use of imported steel over the 10-year period.178.200 b. Describe the general trend in the graph.891.) % of Change 1997 1 1998 4. © Glencoe/McGraw-Hill 49 Worker Productivity Index Year (1st Qtr.000 visitors.000  20%  10. how many visitors from Canada would you expect in the year 2003 if the total is 59. If there were a total of 50. Example The circle graph at the right shows the number of international visitors to the United States in 2000.110. with slight decreases in 1996 and 2000. by country.6 1999 2 2000 2. The . Or they may be constructed to make one set of data appear greater than another set. Explain how the graph misrepresents the data.NAME ______________________________________________ DATE______________ PERIOD _____ 1-9 Study Guide and Intervention (continued) Statistics: Analyzing Data by Using Tables and Graphs Misleading Graphs Graphs are very useful for displaying data. public schools for the school years from 1995 to 1999. Students per Computer. some graphs can be confusing. U. greenhouse gases emissions for 1999. It would be more appropriate to let each unit on the vertical scale represent 1 student rather than 5 students and have the scale go from 0 to 12. The graph below shows the amount of money spent on tourism for 1998-99.S. Another section needs to be added to account for the missing 1%. 1. These graphs may be mislabeled or contain incorrect data. This gives the impression that $400 billion is a minimum amount spent on tourism. easily misunderstood.S. However.S.6. Example The graph at the right shows the number of students per computer in the U. Public Schools Students 20 The values are difficult to read because the vertical scale is too condensed. 2. U. The graph below shows the U.S. Greenhouse Gas Emissions 1999 Billions of $ World Tourism Receipts Nitrous Oxide 6% Methane 9% Carbon Dioxide 82% 460 440 420 400 1995 1997 Year 1999 Source: The World Almanac HCFs. © Glencoe/McGraw-Hill The graph is misleading because the vertical axis starts at 400 billion. 50 Glencoe Algebra 1 . or 3. and Sulfur Hexafluoride 2% Source: Department of Energy The graph is misleading because the sum of the percentages is not 100%. and lead to false assumptions. PFCs. 15 10 5 0 1 2 3 4 5 Years since 1994 6 Source: The World Almanac Exercises Explain how each graph misrepresents the data. the table or the graph? Explain. If you want to know the exact number of people who preferred spaghetti over linguine in Survey 1. fettuccine. How can the graph be redrawn so that it is not misleading? To reflect accurate proportions. According to the graph. . How many more people preferred fettuccine to linguine in Survey 1? 6 people 8. How many hours per day does Keisha spend at school? 9 h Meals 8% 3. use the table and bar graph that show the results of two surveys asking people their favorite type of pasta.5% Sleep 37. How many more people preferred spaghetti in Survey 2 than preferred spaghetti in Survey 1? 10 people 7. 10. PLANT GROWTH For Exercises 9 and 10. what is the ranking for favorite pasta in both surveys? 5.NAME ______________________________________________ DATE______________ PERIOD _____ 1-9 Skills Practice Statistics: Analyzing Data by Using Tables and Graphs DAILY LIFE For Exercises 1–3. Spaghetti Fettuccine Pasta Favorites Linguine Survey 1 40 34 28 Survey 2 50 30 20 Spaghetti Survey 1 Survey 2 Fettucine Linguine 0 5 10 15 20 25 30 35 40 45 50 Number of People 4. 1. which is a better source. making it appear that the tree grew much faster compared to its initial height than it actually did. In Survey 1.5% PASTA FAVORITES For Exercises 4–8. What percent of her day does Keisha spend in the combined activities of school and doing homework? 50% School 37. © Glencoe/McGraw-Hill 51 15 Height (ft) 9. use the circle graph Keisha’s Day that shows the percent of time Keisha spends on activities in a 24-hour day. the number of votes for spaghetti is twice the number of votes for which pasta in Survey 2? linguine 6. because it gives exact numbers. use the line graph that shows the growth of a Ponderosa pine over 5 years. How many hours does Keisha spend on leisure and meals? 3 h Leisure 4.5% Homework 12. The table.5% 2. Growth of Pine Tree 16 14 13 12 11 10 1 2 3 4 Years 5 6 Glencoe Algebra 1 Lesson 1-9 The ranking is the same for both: spaghetti. The vertical axis begins at 10. linguine. the vertical axis should begin at 0. Explain how the graph misrepresents the data. how many would you expect to prefer drama? 305 9. What is the hardness of the unknown mineral? at least 7 4. then a steady increase to 2002.5% Science Fiction 10% Comedy 14% Foreign 0. use the circle graph that shows the percent of people who prefer certain types of movies. used as a guide to help identify minerals. Mineral Hardness Talc 1 Gypsum 2 Calcite 3 Fluorite 4 Apatite 5 Orthoclase 6 Quartz 7 Topaz 8 Corundum 9 Diamond 10 1.5. then dipped in 1999. gypsum. Beginning the 2000 Year 80 60 40 20 ld all all all tb otb Fie eyb e sk Fo k & oll c V Ba Tra Glencoe Algebra 1 . If an unknown mineral scratches all the minerals in the scale up to 7. MOVIE PREFERENCES For Exercises 7–9. A fingernail has a hardness of 2. © Glencoe/McGraw-Hill 52 100 Tickets Sold (hundreds) vertical axis at 20 instead of 0 makes the relative sales for volleyball and track and field seem low. use the following information.5% Ticket Sales that compares annual sports ticket sales at Mars High. then A’s hardness number is greater than B’s. calcite 2. Of 1000 people at a movie theater on a weekend. If 400 people were surveyed. and corundum scratches the unknown. use the line graph that shows CD sales at Berry’s Music for the years 1998–2002. Sales started off at about 6000 in 1998. how many chose action movies as their favorite? 180 8. showed a sharp increase in 2000. Suppose quartz will not scratch an unknown mineral. What percent of people chose a category other than action or drama? 24. use the bar graph 10. what is the hardness of the unknown? between 7 and 9 SALES For Exercises 5 and 6. Which mineral(s) will it scratch? talc.NAME ______________________________________________ DATE______________ PERIOD _____ 1-9 Practice (Average) Statistics: Analyzing Data by Using Tables and Graphs MINERAL IDENTIFICATION For Exercises 1–4. What could be done to make the graph more accurate? Start the vertical axis at 0. 2002 Movie Preferences TICKET SALES For Exercises 10 and 11. from 1999 to 2000 6. Which mineral(s) will fluorite scratch? talc. The table shows Moh’s hardness scale. 7.5% Total Sales (thousands) 5. Which one-year period shows the greatest growth in sales? CD Sales 10 8 6 4 2 0 1998 Action 45% Drama 30. gypsum 3. If mineral A scratches mineral B. Describe the sales trend. Describe why the graph is misleading. If B cannot scratch A. 11. then B’s hardness number is less than or equal to A’s. or data. Line graphs are useful when showing how a set of data changes over time. 2. compares different categories of numerical information. Reading the Lesson 1. b. Bar graphs can be used to display multiple sets of data in different categories at the same time. bar graph a. See students’ work. Choose from the following types of graphs as you complete each statement. Sample answer: Stock Price 300 Price ($) The first interval is from 0-200 and all other intervals are in units of 25. A bar graph circle graph should always have a sum of 100%. Line graphs are helpful when making predictions. bar graphs—number of slices left in a loaf of bread © Glencoe/McGraw-Hill 53 Glencoe Algebra 1 Lesson 1-9 e.NAME ______________________________________________ DATE______________ PERIOD _____ 1-9 Reading to Learn Mathematics Statistics: Analyzing Data by Using Tables and Graphs Pre-Activity Why are graphs and tables used to display data? Read the introduction to Lesson 1-9 at the top of page 50 in your textbook. 275 250 225 200 1 2 3 4 Day 5 6 7 Helping You Remember 3. f. d. Write a brief description of which presentation works best for you. while a stack of Al Gore’s votes would be 970 feet tall with your reaction to the graph shown in the introduction. so the price rise appears steeper than it is.1 feet tall. Sample answer: circle graphs—parts of a pizza. The percents in a . Bush’s votes from Florida would be 970. A stack containing George W. Describe something in your daily routine that you can connect with bar graphs and circle graphs to help you remember their special purpose. A circle graph circle graph line graph compares parts of a set of data as a percent of the whole set. Explain how the graph is misleading. c. Compare your reaction to the statement. a score of 62 12. So.NAME ______________________________________________ DATE 1-9 ____________ PERIOD _____ Enrichment Percentiles The table at the right shows test scores and their frequencies. a score of 81 © Glencoe/McGraw-Hill 54 Glencoe Algebra 1 . a score of 85 10. 1. Example 1 What score is at the 16th percentile? A score at the 16th percentile means the score just above the lowest 16% of the scores. Seven scores are at 75. 58th percentile 6. a score of 50 8. The fourth of these seven is the midpoint of this group. Adding 4 scores to the 29 gives 33 scores. starting at the lowest score and adding up. 33rd percentile 4. a score of 58 11. the score at the 16th percentile is 56. 42nd percentile 2. The 8th score is 55. Use the table above to find the percentile of each score. Use the table above to find the score at each percentile. The frequency is the number of people who had a particular score. a score of 75 is at the 66th percentile. Thus. 90th percentile 5. 33 out of 50 is 66%. The cumulative frequency is the total frequency up to that point. a score of 77 9. 7. 70th percentile 3. Score Frequency Cumulative Frequency 95 90 85 80 75 70 65 60 55 50 45 1 2 5 6 7 8 7 6 4 3 1 50 49 47 42 36 29 21 14 8 4 1 The score just above this is 56. 80th percentile Example 2 At what percentile is a score of 75? There are 29 scores below 75. Notice that no one had a score of 56 points. 16% of the 50 scores is 8 scores. 2. 5}. 7. 1 B. m  27 27 D. Write a verbal expression for x  y. 6. the difference of 19 and a number D. 5b  3c 11. 2. 14. 5. A. 3. {7} 8. Find the solution of x  4  7 if the replacement set is {1. Write a verbal expression for 19a. 5. Find the solution set for x  2  3 if the replacement set is {1.NAME 1 DATE PERIOD Chapter 1 Test. 7g  3 C. 2. the product of 19 and a number 3. 10g  15 D. A. {1. 6. 7g  8 12. {1. the quotient of 19 and a number B. 27  m . A. 20 D. Simplify 7b  2b  3c. 27  m C. 4. 2184 B. Multiplicative Inverse Property C. the sum of 19 and a number C. 12. B. 8x B. 5} C. the difference of x and y D. Glencoe Algebra 1 Assessment A. 8 D. A. Simplify 5(2g  3). 45 B. 0 C. x  8 C. 12(100)  12(13) B. 12(18)  12(5) C. 30 10. 185 13. 32 B. 4. Name the property used in n  0  7. 8. 6} B. 2. 11 D. Form 1 SCORE Write the letter for the correct answer in the blank at the right of each question. A. 4. A. 3. Additive Identity Property 9. A. 7}. 30 C. 4. 3. 29 C. 13. 9b  3c C. A. 100 B. Write an algebraic expression for the sum of a number and 8. 3 C. 11. 2 7. A. B. Substitution Property D. 4 D. Evaluate 4  1  6  16  0. 27 D. the quotient of x and y B. A.   2. 18 6. Evaluate 13  6  7  4. 12bc B. 66 5. 7b  5c D. x  8 1. 5. Evaluate 6(8  3). the sum of x and y C. 7} D. 12(100)  12(80)  12(5) © Glencoe/McGraw-Hill 55 14. 10g  3 B. A. m 3. 9. 216 C. 12(1)  12(8)  12(5) D. the product of x and y 4. A. 4. x  8 D. 3. {6. Which of the following uses the Distributive Property to determine the product 12(185)? A. 1. Write an algebraic expression for 27 decreased by a number. Multiplicative Identity Property 10. 2. Evaluate 2k  m if k  11 and m  5. Accident rate B. D.000 B. Choose the numbers that are counterexamples for the following statement. Age For Questions 19 and 20. a  2. a  18. a  1.700. B. It is not appropriate to display this set of data in a circle graph because it A. Accident rate A. Which statement best describes the graph of the price of one share of a company’s stock shown at the right? A. b  2 17. 17.2 4 $431. C. There is no hypothesis. $30. Time of Day A.NAME 1 DATE Chapter 1 Test. The price decreased more in the afternoon than in the morning. 15. is too large. The price increased more in the afternoon than in the morning.200. B. A.000 D.0 2 $290. b  5 C. D. Form 1 PERIOD (continued) 15. B. © Glencoe/McGraw-Hill 19. which shows the amount grossed (in millions of dollars) by a series of four science fiction movies. a  9. 16. b B. Accident rate D.M. a  4. Identify the hypothesis in the statement If it is Monday. use the table.0 19. B: 56 Glencoe Algebra 1 . does not represent a whole set. Accident rate C. C. Age Age Episode Gross (millions) 1 $461.M. is not given in percents. $140. The price decreased more in the morning than in the afternoon. D. then the basketball team is playing. It is Monday. For all numbers a and b. The accident rate for middle-aged automobile drivers is lower than the rate for younger and older drivers.000 C. Age 18. The basketball team is playing. How much more did Episode 4 gross than Episode 3? A. Identify the graph that represents the following statement.000. Price A. C. The price increased more in the morning than in the afternoon. b  10 16.3 3 $309. 20.000 20. $121.800. must be adjusted. $309. Bonus Simplify (4x  2)3. D. It is not Monday. b  4 Noon P. 18. 9(1  0)  9(1) B. 4} B. 28. Evaluate 6  2  3  1. 31}. 1. Simplify r2  2r3  3r2. Simplify 2(a  3b)  3(4a  b). 4r2  2r3 B. 5 A. a  10. 3  x2 4 4 2. Evaluate 32  7  41. 28 9. 16 D. A. 13. 23 B. 5} C. 3. 91 B. 2 A. {2. A. Write an algebraic expression for three-fourths of the square of a number. A. 15 x2 C. B. 30 C. 7 more than twice a number 3. 30 D. C. Which numbers are not counterexamples for the following statement? For any numbers a and b. 843 D. Evaluate 2(11  5)  9  3. 8} 7. 4. 28 C. Find the solution of n  11  3 if the replacement set is {26. x2  3 1. {6. 3  1  1 8. 30. 31 6. Evaluate 29  1  2(20  4  5). C. 11 3. 0  16  0 D. 10. Find the solution set for 15  3x 30 if the replacement set is {2. 8}. 4r2 10. 4. 7. A. 42 D. n. A. 3r2  2r3 D. y  5. 8} D. 14. 69 4 D. 73  7 10 5 B. 12. A. a  4. the product of 2. 3 9. A. 85 D. 6a  6b B.  xyz if x  3. and 7 C. 1(48)  48 . 14a  4b D. Which equation illustrates the Multiplicative Inverse Property? A. a  8. 7 more than n and 2 2. 26 B. Evaluate A. b  3 D. 29. 126 C. 4. 2r C. 11. 4 B. 21 5. b  4 B. 7. 10 5. A. 3. A. 3. A. a  b  a  b. b  5 C. 5x  11y 11. a  6. 7. 3  x2 B. 7 less than a number times 2 D. and z  4. 29 D. 6. 30 D. 0 B. 56 12. 18 B. 7. Use the Distributive Property to find 6(14  7). 14a  9b C. 6x  9y C. 8. 11 4. Glencoe Algebra 1 Assessment C. 63 C. 5. Form 2A SCORE Write the letter for the correct answer in the blank at the right of each question. 6. b  2 © Glencoe/McGraw-Hill 57 15. 143 14. 3x2 6. 6x  3y D. 5x  6y B. 143 10 5 5 15.NAME 1 DATE PERIOD Chapter 1 Test. Simplify 3(2x  4y  y). {2. 6a  7b 13. Write a verbal expression for 2n  7. {5. A. C. 000 metric tons D. Time of Day A. Wheat (thousands of metric tons) 19.231 13.M.860. The numbers do not sum to 100. If today is Monday. Identify the graph that represents the following statement. The price of a share of the company’s stock increased. © Glencoe/McGraw-Hill 58 Glencoe Algebra 1 . 7. the equation f  4(200  m)  a 5 B: is used to find a bowler’s final score f. Temperature Noon P.000 metric tons 27. C. As the temperature increases. D. which shows the world’s leading exporters of wheat in thousands of metric tons in 1998. 4. D. then it is Monday.000 metric tons B. If today is Monday. A. C. where m  bowler’s average score and a  actual score. The price of a share of the company’s stock decreased.000 0 . C. then I am at school. No break is shown on the vertical axis.733 15. The price of a share of the company’s stock increased in the morning and decreased in the afternoon. Country 20. A. Bonus In some bowling leagues.NAME 1 DATE Chapter 1 Test.000 metric tons C. The price of a share of the company’s stock did not change. then school is in session. Source: World Almanac A. Temperature Cups of Hot Chocolate Sold Cups of Hot Chocolate Sold Cups of Hot Chocolate Sold 18. B. Write School is in session on Monday in if-then form. 2. Price 16. 20. If school is in session.000 17. If I am at school. U. The tick-marks on the vertical axis do not have the same-sized intervals. Describe why the graph is misleading.004 30. D. B. Cups of Hot Chocolate Sold 17. Which statement best describes the graph? A. 16. 18.471. 17.S nce Fra ada Can alia str Au ina ent Arg 19. C. Form 2A PERIOD (continued) 16.000 20.633. use the bar graph. B. the number of cups of hot chocolate sold decreases. Temperature Temperature For Questions 19 and 20.702 15. How much more wheat did Canada export than Argentina? A. D. B. then school is in session.331. Half of the wheat credited to France is grown in Italy.000 10.371 10.M. Find the final score if Peter averages 110 but bowled a 132 this game. 152 5 5 59 10 Glencoe Algebra 1 Assessment C. 5 A. 3 times n less than 8 D. 20 B. 3. 7. A. 2. and p  7. Evaluate 4  5  7  1. A. 8}. 85 12. 9n  7m C. 17 D. 22x2y3 B. Which equation illustrates the Additive Identity Property? A. 33 B. 5} D. 25 C. 2. Evaluate 3(16  9)  12  3. 17. 6. n minus 8 times 3 2. 12. and 8 C. 4(0)  0 . Evaluate 16  1  4(18  2  9). 6} 7. 17x4y3  5 10. A. 28 4. {1. 4. 18}. 15. 14. Simplify 2(7n  5m  3m). 80 9. A. C. 9a  9b 13. n. 4. 4 9. Write a verbal expression for 3n  8. 3x2  4x D. 3. 14n  2m B. {1. Find the solution of 3n  13  38 if the replacement set is {12. 38 3. 5. 4. 100 6. 41 D. 87 C. 173 14. 174 D. 13. 139 B. 8  1  8 D. 9a  5b B. A. 3. 8} B. 4  3x C. 21 C. A. 18 6. n  4. 2. A. Evaluate 41  9  23. Form 2B SCORE Write the letter for the correct answer in the blank at the right of each question. 9n  m D. 16 D. 8} C. 0 C. 2. 15 C. Simplify 7x2  10x2  5y3. 5. A.NAME 1 DATE PERIOD Chapter 1 Test. 1. 19a  11b D. Find the solution set for 4x  10  14 if the replacement set is {1. Use the Distributive Property to find 7(11  8). 3(x2  4x) 1. 14. {6. Write an algebraic expression for 3 times x squared minus 4 times x. {7. 3(2x)  4x B. 133 B. 154 5 © Glencoe/McGraw-Hill 5 B. 4. D. Evaluate m2  mnp if m  3. 8. 7. A. A. 5. 19a  3b C. 1  4  1 8. 69 D. Simplify 3(5a  b)  4(a  2b). 3. 22x4  y3 D. A. the product of 3. 93 B. 34 D. 15 C. 7. 10. 23 5. 12 B. 17x2  5y3 C. 8 less than the product of 3 and n B. 8(9  0)  8(9) B. A. 11. 14n  4m 11. Write Trees lose their leaves in the Fall in if-then form.75 4. B. $0.65 D. Noon P. A.55 4. Source: World Almanac A. A circle graph would represent the data better. Then the price decreased sharply. Then the price increased sharply. D. Time of Day A.90 C. the number sold increases as the price decreases.65 '94 '95 '96 '97 '98 '99 Year 20. which shows the price in dollars for a bushel of wheat in the United States from 1994 to 1999. then the trees lose their leaves. C. B. a  1 15. If trees lose their leaves then it is Fall. B.55 5 4 3 2 3. $1.M. Bonus Simplify 8(a2  3b2)  24b2. Wheat is not sold by the bushel. Number Sold Number Sold 18. Price per Bushel of Wheat (dollars) 19. If it is Fall. How much more did a bushel of wheat cost in 1996 than in 1998? A. At first. C. The price of a share of the company’s stock declined sharply and then leveled off. 20. Number Sold Number Sold For Questions 19 and 20. B. Identify the graph that represents the following statement. Price 17. A. 16. D. C. then it will be colder outside. $1. The price of a share of the company’s stock rose sharply and then leveled off.38 2. a  0 C. the price of a share of the company’s stock was unchanged. A. $1. use the line graph. If it is cold outside.30 3. At first. D. 17.45 0 2.M.92 B. a  5 D. C. 2a  5 17. 16. Describe why the graph is misleading. If it is Fall. Price Price Price Price 18. then the trees lose their leaves. The numbers do not sum to 100. Which number is a counterexample for the following statement? For all numbers a. the price of a share of the company’s stock was unchanged. B: 60 Glencoe Algebra 1 . Form 2B PERIOD (continued) 15. a  6 B.NAME 1 DATE Chapter 1 Test. Which statement best describes the graph? A. No break is shown on the vertical axis. For many items. D. © Glencoe/McGraw-Hill 19. Then simplify. Rewrite 3(14  5) using the Distributive Property. 15. 5. 1. Solve    y. 4. Then find the value of n. Identify the hypothesis and conclusion of the following statement. Simplify each expression. 71 8. name the property used in each equation. 17. 7  (4  6)  7  n 9. 12. Glencoe Algebra 1 . I will attend football practice on Monday. 7. the product of 5 and twice a number 2. write an algebraic expression for each verbal expression. 11. Write a verbal expression for 4n3  6. 7. 11. v  5 and t  2. 18. Find the solution of 5b  13  22 if the replacement set is {5. 32  5  8  15 16. 15. 7(2y  1)  3y For Questions 15 and 16. Evaluate 3w  (8  v)t if w  4. Evaluate 4(5  1  20). 17. 3. 9}. Name the property used in each step. 10. 2. © Glencoe/McGraw-Hill 61 Assessment 9. then the two numbers are odd numbers. For Questions 9 and 10. 6. 1  4  9  1 3 2 14. 4. 6. 2. Evaluate 23[(15  7)  2]. 1. 15w  6w  14w2 14. 13. 5. 6. evaluate each expression. the sum of the square of a number and 34 1. Find the solution set for 2(6  x) 10 if the replacement set is {0.NAME 1 DATE PERIOD Chapter 1 Test. 18. If the sum of two numbers is odd. 13. 3. 6  32(4) 7. 4}. Find a counterexample for the following statement. 12. 5  0  n 8. 3. 8. Form 2C SCORE For Questions 1 and 2. 16. 10. 60 8.S.0 8. Time 9 A.M. 7 A.M.M. 10 A.7 1999–00 11. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost. public schools.1 1969–70 12. a.0 6. 25. 6 b. use the table that shows 2001 airmail letter rates to Greenland. Glencoe Algebra 1 . 9. Explain how the graph can be fixed so it is not misleading. 9 © Glencoe/McGraw-Hill 62 5. c. Name the ordered pair at point C and explain what it represents. b. Between what two consecutive school years did the percent change the most? 1959–60 16.0 5. 24.0 7. 81 0 6 A. The line graph shows the number of students per computer in U.0 6.80 6. Students per Computer in U.1 1979–80 12. subtraction.M. Weight (oz) Rate ($) 5. 23.3 21. 8.M. School Year Percent Enrolled 20. Write the data as a set of ordered pairs.0 4. 8 A. 7 6 5 4 3 2 1 0 Bonus Use grouping symbols.40 Source: World Almanac 24. 25.0 1989–90 11. A 23.80 7. For Questions 24 and 25. Describe the trend in enrollment in private schools since 1959. Source: World Almanac 90 89 88 Temperature (°F) Use the graph that shows temperature as a function of time. 7 c. (continued) 19. and 7 (in that order) to form expressions that will yield each value. 21. D C E 87 86 85 84 83 82 B 22. 22.NAME 1 DATE Chapter 1 Test. Public Schools Number of Students PERIOD 15 13 11 9 7 5 9 – '9 '98 8 – '9 '97 7 – '9 '96 6 – '9 '95 5 – '9 '94 4 – '9 '93 0 Year Source: World Almanac Use the table that shows the percent of students enrolled in private schools.0 B: a.0 4. and division with the digits 1.S. Identify the independent and dependent variables. Form 2C 19. and symbols for addition. multiplication. 20. exponents. Find the solution set for 3(x  4)  15 if the replacement set is {0. 3. 18. 1. evaluate each expression. 8. 7  n  7  3 10. 8. 7. 4w2  7w2  7z2 14. Simplify each expression. 6. 4. 12. 15. 17. 3. 15. 8.NAME 1 DATE PERIOD Chapter 1 Test. 13. 3. Then find the value of n. If the sum of 2 numbers is even. Then simplify. 6. the sum of one-third of a number and 27 1. 13. Find the solution of 3x  8  16 if the replacement set is {5. Write a verbal expression for 5n3  9. We will go to the beach on a hot day. 5. Form 2D SCORE For Questions 1 and 2. 5. 9}. and t  4. 4. Find a counterexample for the following statement. Name the property used in each step. Evaluate 32[(12  4)  2]. 11. Rewrite (10  3)5 using the Distributive Property. the product of a number squared and 4 2. 1. 17. © Glencoe/McGraw-Hill Assessment 10  1 63 Glencoe Algebra 1 . 17  6  3  14 14. 6  42  3 7. 3x  4(5x  2) For Questions 15 and 16. write an algebraic expression for each verbal expression. 2. 2. 6. 7. 9. Identify the hypothesis and conclusion of the following statement. Evaluate 6(6  1  36). 5  13  4  1 16. 11. 11  n  1 10. Evaluate 4w  (v  5)t if w  2. For Questions 9 and 10. name the property used in each equation. 12. 18. 4}. 9. v  8. then the 2 numbers are even numbers. Solve    y. 16. 0 3.7 1980 6.0 B: Glencoe Algebra 1 .0 1. 2 5 1 4 1 © Glencoe/McGraw-Hill 64 1. 23.4 20. Describe what may have happened between the first and fourth games. PERIOD 200 180 160 (3. 6 5 4 3 2 1 0 Bonus Insert brackets. Source: World Almanac Use the graph that shows Robert’s bowling scores for his last four games.S. 25.0 2000 10.4 Score 22. 24.0 2. 87) 40 (1. 1990 8. 103) 120 100 80 60 (4. 21.0 3. parentheses. since 1960. use the table that shows 2001 airmail letter rates to New Zealand. 23. 122) 140 (2.50 5. Between what two consecutive decades did the percent change the most? 1970 4.0 5. Year Population (percent) 1960 5.60 4. For Questions 24 and 25. and the symbols for addition. Score 19. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost. 24.0 2. Describe the trend in the percent of foreign-born people in the U. Identify the independent and dependent variables. The line graph shows a player’s golf scores in the first 8 rounds of the season. 72) 20 0 1 2 3 4 Game Weight (oz) Rate ($) 2. Write the data as a set of ordered pairs.NAME 1 DATE Chapter 1 Test. subtraction. population that is foreignborn. and division in the following sequence of numbers to create an expression whose value is 4.2 21.0 4.70 3. 24.S. 20. 120 115 110 105 100 1 2 3 4 5 6 Round 7 8 Use the table that shows the percent of the U.40 Source: World Almanac 22.0 4. Explain how the graph can be fixed so it is not misleading. Form 2D (continued) 19. n  8. 12. Write a verbal expression for  . 12. w2  n(v2  t) 6. 42 decreased by twice some number 2. © Glencoe/McGraw-Hill 65 Glencoe Algebra 1 . name the property used in each equation. 4 4 2 4 For Questions 9 and 10. Solve    x. 32  6  4  7  4  16 16. Assessment in each step. 7y  y  7y  ny 10. 4. 6  8  29  7  3  7 15. v  5.NAME 1 DATE PERIOD Chapter 1 Test. Then simplify. 5. the sum of the cube of a number and 12 1. write an algebraic expression for each verbal expression. 3. Simplify each expression. write simplified. Evaluate  2   11. 2. (6  n)x  15x 11. 1. 5 3 7 For Questions 5 and 6. 11. 3. 3. Evaluate 2(3  2)  (32  9). 5. 9. 7 . If not possible. 4[33  5(8  6)] 4. For Questions 15 and 16.  set is 1. 14. and t  2. Name the property used 3 9. 8. 3  6(5a  4an)  9na 13. 3nw  w2  t3 5  23  4  32 7. evaluate each expression. 7. 13 8. 13. Form 3 SCORE For Questions 1 and 2. 7a  7a2  14b2 14. Find the solution set for 2b  1 3 if the replacement 2 2 5. Then find the value of n. 15. 6. 16. Rewrite 2(x  3y  2z) using the Distributive Property. evaluate each expression if w  4. 6g2 3. 10. 1. B: Glencoe Algebra 1 .S. 62  (3  4)2  (21  3  4  2) Bonus Simplify  .7 18–24 21. drives back to work. Write a description of what the graph displays. 21. Each day David drives to work in the morning. U. A polygon with 5 sides is called a pentagon. If the mathematical operation * is defined for all numbers x and y as 2x  3y. 4 3 14  3  1  2  (5  1)  2 © Glencoe/McGraw-Hill 20. 25. Identify the independent and dependent variables.9 Source: World Almanac 22. How many more people visited France than the United States? 80 Visitors (in millions) Use the bar graph at the right that shows the world’s top 10 tourist destinations in 1999. Newspapers Sold (thousands) 23. and then goes to a gym to exercise before he returns home for the evening. For Questions 23 and 24. Determine if the following statement is always true. 66 24. television viewing time in hours per week for different age groups. Then write the statement in if-then form. If it is not.NAME 1 DATE Chapter 1 Test. 1990 1991 1992 1992 1992 Year 25. Draw a reasonable graph to show the distance David is from his home for a two-day period. Time 2–11 19. provide a counterexample.3 25–54 29. 23. use the graph that shows the average daily circulation of the Evening Telegraph. Form 3 PERIOD (continued) 17. 0 20.1 55+ 38. 24.S ain Sp e nc Fra 19. 18.7 12–17 19. Identify the hypothesis and conclusion of the following statement. Display the data in a bar graph that shows little difference in time. 60 40 20 19. 17. How many tourists visited Canada and the United States? an ssi n Ru eratio Fed o xic Me a nad Ca . 22. Country Source: World Almanac Use the table at the right. 18. then the operation * is commutative. U. Age y 80 70 60 50 40 30 20 10 0 21. returns home for lunch. Is the graph drawn for Question 21 misleading? Explain. that shows the average U.K ina Ch ly Ita . 5. Describe a set of data that is best displayed in a circle graph. Then label the axes of the graph and write several sentences describing the situation. Name the property used in the equation. O Assessment y x 6. a. Write a conditional statement in if-then form that is not always true. b. then display your data in a circle graph. Write an equation that demonstrates one of the identity properties. Describe how to use the Commutative and Associative Properties to simplify the evaluation of 18  33  82  67. a. Provide a counterexample for your statement. Be sure to include all relevant drawings and justify your answers. b. a. Write Write b. an algebraic expression for your verbal expression. a. 2. c. b. a verbal expression for your algebraic expression. Explain how a replacement set and a solution set are used with an open sentence. You may show your solution in more than one way or investigate beyond the requirements of the problem. 1. 4.NAME 1 DATE Chapter 1 Open-Ended Assessment PERIOD SCORE Demonstrate your knowledge by giving a clear. a verbal expression that includes a difference and a quotient. Write Write an algebraic expression that includes a sum and a product. Think of a situation that could be modeled by this graph. Provide a logical conclusion for the hypothesis I do well in school. Explain how to use the Distributive Property to find 7  23. concise solution to each problem. 3. © Glencoe/McGraw-Hill 67 Glencoe Algebra 1 . and write your statement in if-then form. Describe ways in which a bar graph could be drawn so that it is misleading. or  is ? called an . Conditional statements Like terms Replacement sets ? 6. is called a(n) equation hypothesis ? . 1. coordinate system function conditional statement 9. there is exactly one output for each input. In a . The set of second numbers of the ordered pairs in a relation is ? the of the relation. . The power of a term is the numerical factor. replacement set © Glencoe/McGraw-Hill 68 Glencoe Algebra 1 . domain range replacement set ? 8. The process of finding a value for a variable that results in a true ? sentence is called . ? are terms that contain the same variables. 11. with corresponding variables having the same power. A sentence that contains an equals sign.” conditional statement counterexample power 3. An expression like c3 is an example of a and is read “c cubed. conditional statement 12. . The set of the first number of the ordered pairs of a function is the . In the algebraic expression 8q. >. inequality 4. deductive reasoning solving an open sentence 5. equation inequality identity 10. An open sentence that contains one of the symbols <. variable ? 2.NAME 1 DATE PERIOD Chapter 1 Vocabulary Test/Review coefficient conclusion conditional statement coordinate system counterexample deductive reasoning dependent variable domain equation function hypothesis identity SCORE range replacement set solving an open sentence variables independent variable inequality like terms order of operations power Underline or circle the term that would best complete each sentence. the letter q is called a power coefficient ? . domain coefficient ? 7. domain range replacement set In your own words— Define each term. 2. 43  8 6. 3. 7. 8 to the fourth power increased by 6 1. Find the solution set for 3  2x 7 if the replacement set is {1. 12x2  3x2 4. Simplify each expression. 9. 9. 9. 3. b  5.NAME 1 DATE PERIOD Chapter 1 Quiz SCORE (Lessons 1–1 through 1–3) For Questions 1 and 2. 4. 5. Use the Distributive Property to find 7  98. 62  32  8  11 5. 12}. Then find the value of n. 4. 4. 2. Write a verbal expression for 3n2  1. 7(16  5) 8. 3. 6}. © Glencoe/McGraw-Hill 69 Glencoe Algebra 1 . 5. 1. Solve r   . 3. 2. 3. Evaluate 54. 10. write simplified. three times the cube of a number 2. 10. 5. Find the solution of 1(x  3)  4 if the replacement set is 2 {8. Evaluate 2[3  (10  8)]. Evaluate a(4b  c2) if a  2. 10. 16a2  2b2  1 5. write an algebraic expression for each verbal expression. 7. evaluate each expression. 11. Name the property used in 2. and c  1. 4. Name the property used in 5  n  2  0. 3  4(2) NAME 1 DATE PERIOD Chapter 1 Quiz SCORE 1. 8. 3 Assessment (Lessons 1–4 and 1–5) each step. For Questions 5 and 6. 1. 6. If not possible. 1.NAME 1 DATE PERIOD Chapter 1 Quiz SCORE (Lessons 1–6 and 1–7) 1. 5. 6 D.50 1.9 1980 6. A. Identify the hypothesis and conclusion of the following statement. 7 NAME 1 5.50 0 2. and $5 for each additional ticket. Use a table showing the cost of buying 1 to 5 tickets to draw a graph that shows the relationship between the number of tickets bought and the total cost. How much has the viewing time changed between 1960 and 1990? 4.00 0.9 Source: Nielsen Television Research 5. 1. © Glencoe/McGraw-Hill 70 10 15 35 30 25 20 15 10 5 0 3. The dog will have a bath when it is dirty. then the sum is also an odd number. 5. $7 for a second ticket. 8 B. 3 3 DATE PERIOD Chapter 1 Quiz SCORE (Lessons 1–8 and 1–9) 1. Simplify 8(2x  1)  6x.6 1990 6. 3. 1. Would it be appropriate to display this data in a circle graph? Explain. Glencoe Algebra 1 . 4. Standardized Test Practice Which numbers are counterexamples for the statement below? If two odd numbers are added. 5 1 2 3 4 5 3. 4. 3. 2.1 1970 5. If a number is divisible by 4.10. Draw a graph showing the cost of long-distance telephone calls if the rate per minute is $0. Evaluate 7  2  7  5. The cost of tickets at a museum is $10 for the first ticket. then the number is divisible by 2. 2. Hours 1960 5. 3. 1 C. Between what two consecutive decades did the viewing time increase the most? Year 2. 1. Use the table that shows the average daily television viewing in hours per household in the United States. Identify the independent and dependent variables. Determine a valid conclusion that follows from the following statement given that the number is 12. 2. Then write the statement in if-then form. 4. 4. 16 C. x1 9. 71 Glencoe Algebra 1 . 180 Evaluate each expression if a  4. 22 D. 240 4. Additive Identity B. 7. A. 42  32(2)  a A. 2. Rewrite 6(10  2) using the Distributive Property. 13. 2 For Questions 10 and 11. b  6. 4. 10. write a verbal expression for each algebraic expression. 12. Multiplicative Identity C. Reflexive Property D. and c  2. Then simplify. 26 2. 3. 4. Name two properties used to evaluate 7  1  4  1. 34 Part II Find the solution set for each inequality if the replacement set is {0. 84 C. ab  c A. 11. C.NAME 1 DATE PERIOD Chapter 1 Mid-Chapter Test SCORE (Lessons 1–1 through 1–5) Part I Write the letter for the correct answer in the blank at the right of each question. For Questions 5 and 6. 50 C. 96 D. A. 12  7n D. solve each equation. 8 3. 36 B. 18p 11. 6. Evaluate 20  3(8  5). 29 B. 2. 1. Name the property used in (5  2)  n  7  n. 3. Substitution Property 7. 12 7n C. 14. 13. Write an algebraic expression for 12 less than a number times 7. 20 D. w    2 A. 1. 14 5. 4 © Glencoe/McGraw-Hill Assessment 8. x2  5 10. B.   2 9. Simplify 6b  7b  2b2. 7n  12 1. 3a  b2c A. 5}. 14. 39 D. 32 C. 4 B. 16  4 5. 28 6. 12. 12 B. 6 D. A. 12 7n B. 3x  4 2 8. 0 Housing Affordability. 3 (Lesson 1-1) 7.5 10. 3.5 8.0 7. His mailbox is on the edge of the lawn. 7n  4n 13. (Lesson 1-9) © Glencoe/McGraw-Hill 10. and c  6. 13. Evaluate  .6 16 4. 6.5 7. simplify each expression. Write an algebraic expression for six less than twice a number. 7. '90 '91'92'93 '94'95 '96 '97 '98 '99 '00 Year 72 Glencoe Algebra 1 . 16. Estimate the change in the average mortgage rate between 1990 and 2000. Write a verbal expression for 4m2  2. 5}. Draw a reasonable graph that shows the distance Alvin is from the mailbox as he mows. if a  2. 0. 11. (Lesson 1-3) 10. refer to the line graph below. (Lesson 1-2) 8. Evaluate 13  1(11  5).0 9. 5y  3(2y  1) (Lesson 1-5) 12. Let the horizontal axis show the time and the vertical axis show the distance from the mailbox. (Lesson 1-6) 14. a 9. 5. 2. 9. Solve 2(7)  4  x. 1. 11. predict the average mortgage rate in 2005. (Lesson 1-2) 2b  c2 8. 4. 2 (Lesson 1-4) For Questions 12 and 13. (Lesson 1-8) 14. 8    9 3 3. Find the solution set for 3x  4 2 if the replacement set is {0. 17  8 2.5 9. 84  7 3. 1990–2000 Average Mortgage Rate (percent) 15.NAME 1 DATE PERIOD Chapter 1 Cumulative Review (Chapter 1) For Questions 1–4. 12. For Questions 15 and 16.0 8. (Lesson 1-9) 0 15. Alvin is mowing his front lawn. 6. (Lesson 1-1) 5. 1. 1.9  5. (Prerequisite Skill) 2. find each product or quotient. Evaluate 3(5  2  9)  2  1. 16. 4. If the rate of growth between 1998 and 2000 continues. b  4. (Lesson 1-3) 10. x  12 44 B. {8. 6} 3. 30  c C. Find the solution of 3(y  7)  39 if the replacement set is {2. E. 10. distance 9. 12}. 4. x  12 C. Symmetric H. Which type of graph is used to show the change in data over time. 6. 3 2 (Lesson 1-6) 7. 4 G. bar graph C. 8. 7x2  9x B. Simplify 7(2x  y)  6(x  5y). . and c  4. 0 to 18 miles F. {2. 10. Write an algebraic expression to represent the number of pens that can be bought with 30¢ if each pen costs c cents. 8. 0 to 15 gallons H. 11 (Lesson 1-2) G. Substitution F. The distance Omari drives before refueling is a function of the number of gallons of gasoline in the tank. 12x3  4x D. 30  c D. A B C D 10. 7x2  x 5. (Lesson 1-9) A. 4. 44 11. time B. Identify a reasonable domain for this situation. (Lesson 1-5) A. Identify the dependent variable. (Lesson 1-8) A. 4} B. 10. 16x4 C. {2. Reflexive G. Identify the hypothesis of the statement. Simplify 7x2  5x  4x. 2 2. E. 0 to 270 miles G. E F G H 7. 32 H. E F G H 3. 15x  6y 6. E F G H A B C D c 7a  b 2. The car’s gasoline tank holds 15 gallons. 13x  42y H. 12} D. 31 bc 3 F. (Lesson 1-1) 30 B. A B C D 8. A B C D H. Transitive 4. 20x  6y G.   A. (Lesson 1-8) E. b  6. 10 8. if a  2. 0 to 60 mph 10. Evaluate  . 12} C. then x  12  44. 1.NAME 1 DATE PERIOD Standardized Test Practice (Chapter 1) Part 1: Multiple Choice Instructions: Fill in the appropriate oval for the best answer. (Lesson 1-7) A. table 11. line graph © Glencoe/McGraw-Hill B. Which number is a counterexample for the statement? (Lesson 1-7) E. A B C D 6. A B C D 4. {6. 2 F. The distance an airplane travels increases as the duration of the flight increases. x is even D. 30c 1. 20x  37y F. direction C. (Lesson 1-3) A. airplane D. If x is even. Omari drives a car that gets 18 miles per gallon of gasoline. E F G H 9. Glencoe Algebra 1 Assessment For Questions 7 and 8. circle graph 73 D. use the following statement. The equation 4  9  4  9 is an example of which property of equality? (Lesson 1-4) E. E F G H 5. and z  4. (Lesson 1-4) 19. Evaluate 2  x(2y  z) if x  5. / . / . . . 16. A B C D a1 a0 17. . / . / . 12. For Questions 16–19.85  c. . . (Lesson 1-2) 14. C if the quantities are equal. b  0. and c  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 (Lesson 1-5) Part 3: Quantitative Comparison Instructions: Compare the quantities in columns A and B. Evaluate 4(16  2  6). 13.NAME 1 DATE PERIOD Standardized Test Practice (continued) Part 2: Grid In Instructions: Enter your answer by writing each digit of the answer in a column box and then shading in the appropriate oval that corresponds to that entry. / . Shade in A if the quantity in column A is greater. . (Lesson 1-2) 13. A B C D b c    c b 2 18. / . B if the quantity in column B is greater. / . Use the Distributive Property to find 12  99. 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 14. (Lesson 1-6) 18. Column A Column B (a  b)  c b  (a  c) 16. A B C D (Lesson 1-6) 17. (Lesson 1-3) 15. a  0. Solve 15. 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 . A B C D 3(2a  4) 4(2  3) 19. or D if the relationship cannot be determined from the information given. y  3. 12. (Lesson 1-5) © Glencoe/McGraw-Hill 74 Glencoe Algebra 1 . 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 15.6  7. / . 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 .NAME 1 DATE PERIOD Standardized Test Practice Student Record Sheet (Use with pages 64–65 of the Student Edition. © Glencoe/McGraw-Hill A1 Glencoe Algebra 1 . Part 4 Open-Ended Record your answers for Question 17 on the back of this paper. / .) Part 1 Multiple Choice Select the best answer from the choices given and fill in the corresponding oval. / . 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 Part 3 Quantitative Comparison 12 A B C D 13 A B C D 14 A B C D 15 A B C D 16 A B C D Answers Select the best answer from the choices given and fill in the corresponding oval. Also enter your answer by writing each number or symbol in a box. / . Then fill in the corresponding oval for that number or symbol. . 9 (grid in) 10 (grid in) 11 9 (grid in) 10 . / . / . / . . 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 11 . . 1 A B C D 4 A B C D 7 A B C D 2 A B C D 5 A B C D 8 A B C D 3 A B C D 6 A B C D Part 2 Short Response/Grid In Solve the problem and write your answer in the blank. a3  b3 the square of 6 6. a. a number multiplied by 37 37n n2 b ⫺8 5. n3  12m the difference of n cubed and twelve times m a. 1–18.  81 Multiply. 6n2 the product of 6 and n squared Example is important in algebra. a number divided by 6 ᎏ 3. a number divided by 8 ᎏ 6. 7n5 6 times the cube of k divided by 5 6k3 5 10. 6n2
3 of the square of n and 1 16. a number decreased by 8 Write an algebraic expression for each verbal expression. 28 256 Glencoe Algebra 1 15. Exercises Evaluate each expression. Example 2 b. 122 144 © 14. Translating algebraic expressions into verbal expressions Variables and Expressions (continued) ____________ PERIOD _____ Study Guide and Intervention Write Verbal Expressions 1-1 NAME ______________________________________________ DATE Answers (Lesson 1-1) Glencoe Algebra 1 Lesson 1-1 . four more than a number n 4
n The algebraic expression is 4
n. 53  5  5  5 Use 5 as a factor 3 times. Write Mathematical Expressions 1-1 NAME ______________________________________________ DATE Write a verbal expression for each algebraic expression. 62 12 times c 4. the sum of 9 and a number 9 ⫹ n 6 h 8 2. 3 less than 5 times a number 5n ⫺ 3 n 4. In the expression ᐉw. 33 27 13. a number squared 1. w  1 are given. 4(n2
1) 4 times the sum two-thirds the fifth power of k 14. one-half the square of b 11. 3x
4 the sum of three one-fourth the square of b 1 11. 2 Glencoe Algebra 1 the sum of 6 times n squared and 3 18. Write an algebraic expression for each verbal expression. 2n2
4 the sum of 4 eight to the fourth power 5. five cubed a.© ____________ PERIOD _____ Variables and Expressions Study Guide and Intervention Glencoe/McGraw-Hill A2 1 ᎏb 2 2 Glencoe/McGraw-Hill 17. ᐉw.000 10. 83 512 16.  a3 Write a verbal expression for each algebraic expression. 34 Cubed means raised to the third power. 84 eighty-one increased by twice x 3. 34  3  3  3  3 Use 3 as a factor 4 times. the letters ᐉ and w are called variables. Sample answers Exercises b. twice the sum of 15 and a number 8. 52 25 Evaluate each expression. a variable is used to represent unspecified numbers or values. four times a number 4n 7.  125 Multiply. 12c one third the cube of a 1 3 2.  k5 2 3 seven times the fifth power of n 12. The letters ᐉ and w are used above because they are the first letters of the words length and width. 1 12. the difference of a number squared and 8 n2  8 The algebraic expression is n2  8. 81
2x one less than w 1. Any letter can be used as a variable. and the result is called the product. Example 1 In the algebraic expression. 2x3 and twice the square of n 7. 32
23 b squared plus 2 times a cubed 15.  a cubed times b cubed 8. 30 increased by 3 times the square of a number 30 ⫹ 3n2 18. 7 more than the product of 6 and a number 6n ⫹ 7 2(15 ⫹ n) 9. four more than a number n The words more than imply addition. the difference of a number squared and 8 The expression difference of implies subtraction. 104 10.  b2 4 9. In algebra. 3 the difference of twice a number cubed and 3 © Glencoe/McGraw-Hill 3 squared plus 2 cubed 17. 3b2
2a3 3 times times a number and 4 13. b. ᐉ and w are called factors. the sum of a number and 10 Write an algebraic expression for each verbal expression. 24 16 16. BOOKS A used bookstore sells paperback fiction books in excellent condition for $2. Sample answers are given. If a circular cylinder has radius r and height h. 83 512 9. 3 ᎏ b2 4 7. the product of 2 and the second power of y 8 ⫹ 3x 5.000 10. 73 343 © Glencoe/McGraw-Hill Glencoe Algebra 1 3 Glencoe Algebra 1 3 times n squared minus x 26. 2y 2 7. 45 1024 15. 102 100 15. 93 729 12. 113 1331 11. 1-1 NAME ______________________________________________ DATE (Average) Variables and Expressions Practice 2 ᎏ x3 5 17. 2b2 the sum of c and twice d 21. 4d3  10 seven cubed © Glencoe/McGraw-Hill 4 Glencoe Algebra 1 27.  6 x cubed times y to the fourth power 2 more than 5 times m squared 22. two fifths the cube of a number x2 ⫹ 91 6. 52 Answers p to the fourth power plus 6 times q 25. Write an expression for the cost of buying e excellent-condition paperbacks and f fair-condition paperbacks. 15 decreased by twice a number 33j 3. 23f 19. b2  3c3 4 times d cubed minus 10 21.000. 33 27 14.50e ⫹ 0. the product of 18 and q x ⫹ 10 1.50.50f one sixth of the fifth power of k k5 24.50 and in fair condition for $0. 82 64 Evaluate each expression. Write a verbal expression for each algebraic expression. 74 increased by 3 times y 18 ⫹ x 2. 34 81 g4 ⫺ 9 8. write an expression that represents the surface area of its side. 72 49 17. 123 1728 13. the difference of 17 and 5 times a number 2m ⫹ 6 4. 15 less than k 9. x3  y4 20. 73 16. 7x3  1 the difference of 4 and 5 times h 22. 64 1296 11. 53 125 13. the sum of 18 and a number ____________ PERIOD _____
2 one seventh of 4 times n squared 4n2 7 25. 91 more than the square of a number 74 ⫹ 3y 4. 9a are given. 54 625 8. the difference of 10 and u Write an algebraic expression for each verbal expression. 105 100. 4  5h 5 squared 20. 112 121 Evaluate each expression. p4
6q 2 times b squared 23. 18–25.000 14. 2. Sample answers 10. 9 less than g to the fourth power 17 ⫺ 5x 6. 1-1 NAME ______________________________________________ DATE Answers (Lesson 1-1) Lesson 1-1 . 2␲rh 26. GEOMETRY The surface area of the side of a right cylinder can be found by multiplying twice the number ␲ by the radius times the height.© Variables and Expressions Skills Practice Glencoe/McGraw-Hill ____________ PERIOD _____ A3 12. 6 more than twice m k ⫺ 15 2. three fourths the square of b 15 ⫺ 2x 5. 8 increased by three times a number 18q 3. 44 256 18. the product of 33 and j 10 ⫺ u 1. c
2d the product of 9 and a 19. 3n2  x 1 less than 7 times x cubed 24. 19–26. 5m2 the product of 23 and f Write a verbal expression for each algebraic expression. 18.  b squared minus 3 times c cubed 23. 1004 100. 4 represents the Read the introduction to Lesson 1-1 at the top of page 6 in your textbook. 1b. 1a. 5. 1a. 1b. 1b. Suppose you start with an even number of disks and you want to end with the stack on peg b. solve the puzzle for four disks. 2b. 2c. 1c. 2a. five times the difference of x and 4 a. “5 to the third power” is written as 53. 1b 3. 2c. 3c. 2a. n
3 1 III. 2a. x. It is easily confused with the variable x. 5c.  r 2 II. Multiplying 5 times 3 is not the same as raising 5 to the third power. 1a. 1a. 1c. 1a. Another way to record each move is to use letters. 3c. Write the Roman numeral of the algebraic expression that best matches each phrase. 2b. As you solve the puzzle. 1b. 3c. Solve the puzzle for five disks. Record your solution. the first two moves in the table can be recorded as 1c. 1c 2. record each move in the table shown. x. In the expression what is the base? What is the exponent? 2. Then complete the description of the expression 4s. 1b. 3a. x4 I. Solve. and then disk 2 is moved to peg b. 2b. 2b. The diagram at the right shows the Tower of Hanoi puzzle. What expression can be used to find the perimeter of a baseball diamond? Variables and Expressions Reading the Lesson 3. 1b. Record your solution using letters. What should be your first move? 1c 5. Complete the table to solve the Tower of Hanoi puzzle for three disks. On a separate sheet of paper. 1a. What are the factors in the algebraic expression 3xy? xn. What should be your first move? 1c. with a stack of disks on peg a. 1a. The Tower of Hanoi 1-1 1 2 3 Peg a NAME ______________________________________________ DATE 1 1 3 3 2 3 1 2 3 Peg a 1 2 3 2 3 3 3 1 1 Peg c Peg c Glencoe Algebra 1 2 1 2 1 2 2 Peg b Peg b ____________ PERIOD _____ Answers (Lesson 1-1) Glencoe Algebra 1 Lesson 1-1 . 1a. 2c. 4b. 1b. 1c. Why is the symbol  avoided in algebra? length In the expression 4s. three more than a number n Helping You Remember © of sides and s 4. 2c. the product of x and y divided by 2 c. number of each side. 2b. 1. one half the number r b. Record your solution. x to the fourth power V I V. 3b. 3b. y ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-1 NAME ______________________________________________ DATE Enrichment © Glencoe/McGraw-Hill 1c 6 6. 4c. The object is to move all of the disks to another peg. 1c 4. 2b. 1. The first two moves are recorded. 1c. 2c. n 3. How does the way you write “5 times 3” and “5 to the third power” in symbols help you remember that they give different results? II d. For example. 1c. This shows that disk 1 is moved to peg c. 1c. 1b.© Glencoe/McGraw-Hill represents the A4 IV III e. 2b. 5(x  4) Glencoe/McGraw-Hill 5 Glencoe Algebra 1 Sample answer: “5 times 3” is written with the numbers 5 and 3 on the same level. as in 5 ⭈ 3 or 5(3). 1c. 3c. Notice that there are three pegs. with the exponent 3 on a higher level than the number 5. 1c. You may move only one disk at a time and a larger disk may never be put on top of a smaller disk. xy  2 IV. Suppose you start with an odd number of disks and you want to end with the stack on peg c. 4b. 24  3  2  32 7 7. First. a. 3
8 3
23   42  3 42  3 2. 2xyz
5 53 5. Evaluate x3 ⫹ 5(y ⫺ 3) if x ⫽ 2 and y ⫽ 12. (z  x)2
ax 5 ᎏ (z  y)2 1 x 2 15. 3(2) ⫹ 4(2 ⫹ 6) 3(2)
4(2
6)  3(2)
4(8)  6
32 Subtract 4 from 15. 10
8  1 18 Evaluate power in denominator. Evaluate all powers. a2
2b 1 ᎏ 9. Step Step Step Step a. x3 Evaluate Algebraic Expressions Algebraic expressions may contain more than one operation. 7 ⫹ 2 ⭈ 4 ⫺ 4 7
2447
84  15  4  11 Example 1 Order of Operations Numerical expressions often contain more than one operation.  3. Do all multiplication and/or division from left to right. Evaluate 23. 6xz
5xy 78 3xy  4 7x 11. Algebraic expressions can be evaluated if the values of the variables are known.  ᎏ 14. z ⫽ 4. replace the variables by their values.  1 4
32 12
1 5. x(2y
3z) 36 6.  1 8.  ᎏ 52  3 1 20(3)
2(3) 3 4  32  3  2 35 16. 12(20  17)  3  6 18 82  22 (2  8)
4 Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 7 Glencoe Algebra 1 18. Find 4 squared.  ᎏ 2 10.  25ab
y xz 16. 
 1 ᎏ 18.  3 17. Multiply left to Add 2 and 6. To evaluate them. Add 2 and 16. x
y2 11 Evaluate each expression if x ⫽ 2. right.  1 ᎏ z2  y2 7 x 4 13. x3
y
z2 27 1. Then use the order of operations to calculate the value of the resulting numerical expression.  ᎏ 5a2b 16 y 25 17. ᎏ 42  3 1. y ⫽ 3. 11  48 4. 15  12  4 12 Multiply. Add 7 and 8. 23  (a
b) 21 ᎏ 3. 32  3
22  7  20  5 27 11. Divide 12 by 3. 2 ᎏ 4. Subtract 3 from 12. 250  [5(3  7
4)] 2 4(52)  4  3 4(4  5
2) 3 9. x
7 9 3 5 x
z 6 y
2z 11 8 20. Replace x with 2 and y with 12. 10
2  3 16 Add 3 and 8 in the numerator.  ᎏ 21 25 12. 23
5(12  3) 8
5(12  3) 8
5(9) 8
45 53 The solution is 53. Multiply 2 and 4. 1-2 NAME ______________________________________________ DATE Answers (Lesson 1-2) Lesson 1-2 . (10x)2
100a 480 y2 9 x 4 7. Exercises Add 8 and 45. a ⫽ ᎏ . 6a
8b 9 ᎏ 2. Do all addition and/or subtraction from left to right. 3x  5 1 3 5 3 5 1 24 Glencoe Algebra 1 冢 z y x 冣 冢 y z x 冣 21. use the rules for order of operations shown below. Exercises  38 b. 3 ⫹ 23 b. 82  (2  8)
2 6 15
60 6.  6 15. 11 16  3 Evaluate power in numerator.  2 10. Evaluate each expression. (12
4)  6 96 Add 6 and 32. Evaluate each expression.© ____________ PERIOD _____ Order of Operations Study Guide and Intervention Glencoe/McGraw-Hill 1 2 3 4 A5 8.  30  5 14. and b ⫽ ᎏ . 3[2 ⫹ (12 ⫼ 3)2] 3[2
(12  3)2]  3(2
42)  3(2
16)  3(18)  54 Example 2 Evaluate expressions inside grouping symbols.  1 © 8(2)  4 84 12. 11  42  3 Multiply 3 and 18.  2 2  42  82 (5
2)  2 13. Evaluate Rational Expressions 1-2 NAME ______________________________________________ DATE Order of Operations Study Guide and Intervention (continued) ____________ PERIOD _____
5(y  3)      Example 4 5 3 5 © 7 8 2 冢 yz 冣
 13 ᎏ 16 Glencoe/McGraw-Hill 2 冢 xz 冣 19. Multiply 5 and 9. (8  4) 2 8 Evaluate each expression. 2[52
(36  6)] 62 © Glencoe/McGraw-Hill 10 29. 9 3y
x2 z
( y2  4x) 67 26. 2c(a
b) 168 16.5(180 ⫺ 100) 26. 2x
3y  z 33 x2 18. 5
[30  (6  1)2] 10 4. Evaluate the expression to determine how much Ms. use the following information.© Order of Operations Skills Practice Glencoe/McGraw-Hill 6. 4(3
5)  5  4 12 9 5. Ann Carlyle is planning a business trip for which she needs to rent a car. Write an expression that represents the perimeter of the rectangle. 22  11  9  7.  26 2 (2  5)2
4 3 5 11. [8  2  (3
9)]
[8  2  3] 6 Evaluate each expression if x ⫽ 6. GEOMETRY For Exercises 28 and 29. The car rental company charges $36 per day plus $0. 14  7  5  32 1 A6 42 y
xz 2
 10z 70 © Glencoe/McGraw-Hill 25. Suppose Ms. 4[30  (10  2)  3] 24 2.  39 20. 25. 7  9  4(6
7) 11 4. 28  5  4 8 3. 5x  ( y
2z) 16 21.  13 23. 10
2  6
4 26 12. 9
4(3
1) 25 9. b2
2a  c2 89 22. 2[12
(5  2)2] 14. 34 in. (15  5)  2 20 Evaluate each expression. a2
b  c2 137 Evaluate each expression if a ⫽ 12. 5z
( y  x) 17 y2 20. 5
7  4 33 17. The perimeter of the rectangle is twice the sum of its length and its width. $220. 1-2 NAME ______________________________________________ DATE Answers (Lesson 1-2) Glencoe Algebra 1 Lesson 1-2 . xy
z 51 Glencoe Algebra 1 16.00 5(36) ⫹ 0.50 per mile over 100 miles. Write an expression for how much it will cost Ms. CAR RENTAL For Exercises 26 and 27. z3 22. 8  (2
2)  7 14 19. 4
6  3 22 13. 2
3  5
4 21 10.  5 24. 4a
2b  c2 50 2c3  ab 4 bc2 ____________ PERIOD _____ 3. 15. 2[(3n ⫹ 2) ⫹ (n ⫺ 1)] 28.  1 52  4  5  42 5(4) 10. Carlyle rents the car for 5 days and drives 180 miles. 6  3  7
23 22 5. use the following information. 30  5  4
2 12 11.  ᎏ 2 12. and z ⫽ 3. (a2  4b)
c 8 18. 13. 12
2  2 16 7. (5
4)  7 63 Evaluate each expression.  ᎏ
a c 21. b ⫽ 9. 27. yz  x 18 17.  7 b2  2c2 a
cb 2(a  b)2 9 5c 10 23. Carlyle to rent the car. 162  [6(7  4)2] 3 9. 62
3  7  9 48 6. Find the perimeter of the rectangle when n  4 inches. and c ⫽ 4. c2  (2b  a) 96 7
32 1 4 2 2 15. Glencoe Algebra 1 The length of a rectangle is 3n
2 and its width is n  1. Carlyle must pay the car rental company.  20 24. y ⫽ 8. 12
5  6  2 5 32 2. (9  2)  3 21 ____________ PERIOD _____ 1. 3[10  (27  9)] 21 8. 2(x
z)  y 10 19. 9  (3
4) 63 1. 1-2 NAME ______________________________________________ DATE (Average) Order of Operations Practice 14. (3
5)  5
1 41 8. For each of the following expressions. 2.  62 d. such as 12 or 34. You may use addition.99(117  100). Does a calculator help in solving these types of puzzles? Give reasons for your opinion. and fraction bars 1. A—add. The letter P represents parentheses and other grouping symbols. braces. To evaluate 43. brackets.  evaluate powers 2 51  729 9 19
3  4 e. The Four Digits Problem 1-2 NAME ______________________________________________ DATE Answers (Lesson 1-2) Lesson 1-2 . subtraction. 2. Using a calculator is a good way to check your solutions. and 4. you can use two digits to make one number. Also. 3. multiplication. 69
57  3
16  4 division c. 17
3  6 multiplication b. and (117 ⫺ 100) In the expression 4. 2. How is the monthly cost of internet service determined? Order of Operations multiplication Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 11 Glencoe Algebra 1 E—exponents (powers). exponents. Helping You Remember f. multiplication (not division). 26  8
14 subtraction a. represents the cost of each additional hour after 100 hours. M—multiply. write addition. 400  5[12
9] addition 3. 3. and 4. Answers will vary. subtraction. Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-2 NAME ______________________________________________ DATE Enrichment ____________ PERIOD _____ (4 ⫻ 3) ⫺ (2 ⫺ 1) 4⫹3⫹2⫹1 4 ⫹ 2 ⫹ (3 ⫻ 1) 4⫹3⫹2⫺1 3(4 ⫺ 1) ⫺ 2 4⫹3⫹1⫺2 (4 ⫺ 2) ⫹ (3 ⫻ 1) (4 ⫺ 2) ⫹ (3 ⫺ 1) (4 ⫺ 3) ⫹ (2 ⫻ 1) (4 ⫺ 3) ⫹ (2 ⫺ 1) 3(2 ⫹ 4) ⫺ 1 (4 ⫻ 2) ⫻ (3 ⫺ 1) 2(3 ⫹ 4) ⫹ 1 (4 ⫻ 3) ⫹ (2 ⫻ 1) (4 ⫻ 3) ⫹ (2 ⫺ 1) (2 ⫻ 3) ⫻ (4 ⫺ 1) 21 ⫺ (4 ⫺ 3) (2 ⫹ 4) ⫻ (3 ⫹ 1) 34  33  32  31  30  29  28  27  26  2 ⫻ (14 ⫹ 3) 21 ⫹ (3 ⫻ 4) 42 ⫻ (3 ⫺ 1) 34 ⫺ (2 ⫹ 1) (2 ⫻ 3) ⫻ (4 ⫹ 1) 2(4 +1) ⫺ 3 21 ⫹ 3 ⫹ 4 3 ⫻ (4 ⫺ 1) 2 24 ⫹ (3 ⫺ 1) 25  (2 ⫹ 3) ⫻ (4 ⫹ 1) 24  23  31  (4  2) 22  21 ⫹ (4 ⫺ 3) 21  (4 ⫹ 3) ⫻ (2 ⫹ 1) 20  19  3(2
4)
1 18  43 ⫺ (2 ⫺ 1) 43 ⫺ (2 ⫻ 1) 41 ⫺ (3 ⫺ 2) 42 ⫺ (3 ⫻ 1) 42 ⫺ (3 ⫹ 1) 31 ⫹ 2 ⫹ 4 34 ⫹ (2 ⫻ 1) 50  49  48  47  46  45  44  41 ⫹ 32 41 ⫹ 23 42 ⫻ (3 ⫻ 1) 31 ⫹ 42 43 ⫹ (2 ⫹ 1) 43 ⫹ (2 ⫻ 1) 43 ⫹ (2 ⫺ 1) 43  42
13 42  41  40  39  38  37  36  35  2(4 +1)
3 © Glencoe/McGraw-Hill 12 Glencoe Algebra 1 Answers will vary. The first step in evaluating an expression is to evaluate inside grouping symbols. D—divide. 4. Each digit is used only once. division. Read the order of operations on page 11 in your textbook. S—subtract 4. parentheses. Read the introduction to Lesson 1-2 at the top of page 11 in your textbook. or evaluate powers to tell what operation to use first when evaluating the expression.99 regular monthly cost of internet service. Sample answers are given. Write what each of the other letters in PEMDAS means when using the order of operations. What does evaluate powers mean? Use an example to explain.95
0. find the value of 4 ⫻ 4 ⫻ 4. One well-known mathematic problem is to write expressions for consecutive numbers beginning with 1. and parentheses in any way you wish. 17  16  15  14  13  12  (4 ⫻ 3) ⫻ (2 ⫺ 1) 11  10  9 8 7 6 5 4 3 2 1  (3  1)  (4  2) Express each number as a combination of the digits 1.© Glencoe/McGraw-Hill A7 represents the number of hours over 100 used by Nicole in a given month. List four types of grouping symbols found in algebraic expressions.95 represents the 0. On this page. you will use the digits 1. Sample answer: To evaluate a power means to find the value of the power. The sentence Please Excuse My Dear Aunt Sally (PEMDAS) is often used to remember the order of operations. w  62  32 324 9. 9 冦1 1 冧 2(4)   b Add in the numerator. y  2  6 {8} Find the solution of each equation if the replacement sets are X  ᎏ . y2  2  34 {6} 4. .7 15. Solve Equations 1-3 NAME ______________________________________________ DATE Find the solution set for 3a ⫺ 8 ⬎ 10 if the replacement set is {4. The set of all replacements for the variable that result in true statements is called the solution set for the variable. 8 9 The solution is  . x2  1  8 {3} 1 9 8. ᎏ . 8}.4  3. n  62  42 20 {2} 13. 6. Find the solution set of 3a ⫹ 12 ⫽ 39 if the replacement set is {6. Example 1 A mathematical sentence with one or more variables is called an open sentence. k  9.© ____________ PERIOD _____ Open Sentences Study Guide and Intervention Glencoe/McGraw-Hill false true false false false A8 2(3 ⫹ 1) 3(7 ⫺ 4) Solve ᎏᎏ  b. is called an equation. 8   b Simplify. 4. 7. 
  k ᎏ 1 4 10. 3(3) 2(3
1)   b Original equation 3(7  4) Example 2 © Glencoe/McGraw-Hill 13 17.   p 3 5 8 11. 10}. a  23  1 7 Solve each equation. A sentence that contains an equal sign. 5.2 7 8 14. s   3 12. 8. the solution is 9. 2.2  m 15. Exercises Since a  9 makes the equation 3a
12  39 true. 1. 6. 1 7. x
8  11 {3} 5 2 1. 3(6)
12
39 → 30 39 3(7)
12
39 → 33 39 3(8)
12
39 → 36 39 3(9)
12
39 → 39  39 3(10)
12
39 → 42 39 Replace a in 3a
12  39 with each value in the replacement set.8
5. subtract in the denominator. 3 4 2 and Y  {2.  ( y
1)2   4 4 2. x
   {2} 1 2
y  20 {4} 冦ᎏ41 冧 3 5ᎏ 4 Glencoe Algebra 1 1 1 18. 2(x
3)  7 ᎏ 2 冦 冧 5. Open sentences are solved by finding replacements for the variables that result in true sentences. 18. c  3 
2  2 4 15  6 27  24 15. 8}. 9. The solution set is {9}.      8 8 8 8 8 ? . x2
5  5  1 16 3. 7.5 18  3 2
3 16. y2 6. The set of numbers from which replacements for a variable may be chosen is called the replacement set. 10 ? . 10 ? . 10 ? . 10 ? . 10 → → → → → 4 . 10 7 . 10 10 . 10 13 . 10 16 . 8} 16. 3x   2 4 {1. 5冧 x 13. 5. 4x
1 4 冦ᎏ14 . 8} 10. 3. 5. 10 true true false false false 1 2 冧 © Glencoe/McGraw-Hill 冦ᎏ14 . 2. x
3 .  4 2 {3. ᎏ12 冧 1 19. ᎏ12 . 3. 2. 1. 7} 9. 3(8  x)
1  6 no numbers x 5. 4. 6.  2 5 {0. 3. 6. 3y
2  8 {3. 2.  2 4 {2. 1. 5. 3. 3. 8} 17. 7} 2. 10} 11. 10} 冦 14 {7} 8. 4. 8 and Y ⫽ {2. 6. 1. 5 {2} 14 20. 5. 5. 2. ᎏ . x  3 6 {2. 10} y 14. 8. 3x
3 12 {8. 5} 3x 8 6. 4. 5. 2. 4.   2 {7} 3. 4. 4(x
3) 20 {0. 6. 1. 3. y  3 6 X ⫽ ᎏ . 3x . 8. 4} 2y 5 15.   2 {6. 3. 3x  4 . 8y
3 51 Find the solution set for each inequality if the replacement sets are {4. 7} 7.  (6  2x)
2  3 {8. 5. 8} 1 2 21. 10} 12. 5. 6. 10} 18. 2( y
1) 18 {2. 8. 18 Glencoe Algebra 1 {2. 7} x 4. 5 {4. 5. 6.  . x
2 . 1 3 {3. 6. 5. 7} 1. 4. 5. 3. 4. 1. 7}. 4 Find the solution set for each inequality if the replacement set is X ⫽ {0. 6. Exercises Since replacing a with 7 or 8 makes the inequality 3a  8 . 2. the solution set is {7. 8}. 3(4) 3(5) 3(6) 3(7) 3(8) Replace a in 3a  8 . 10 true. . 10 with each value in the replacement set. Example An open sentence that contains the symbol . . Inequalities can be solved the same way that equations are solved. Open Sentences (continued) ____________ PERIOD _____ Study Guide and Intervention Solve Inequalities 1-3 NAME ______________________________________________ DATE Answers (Lesson 1-3) Glencoe Algebra 1 Lesson 1-3 .. or is called an inequality. {8.1  11.2 10. 2c  5  11.8(x
5)  5.  5.  ᎏ y 2 © Glencoe/McGraw-Hill Glencoe Algebra 1 15 Answers 23. 12} x 3 22. 12} {10. 0.  .   n 1 6(7  2) 3(8)
6 14. 10. 11. 4b
1 .5 2 3 8. {4. {1.  .5} 1. 9.2. 8.© Open Sentences Skills Practice ____________ PERIOD _____ Glencoe/McGraw-Hill 5 4 冦 12 3 4 5 4 冧 3 4 A9 冧 4 ᎏ 3 13 9 冦 49 5 2 7 9 3 9 冧 7 9 16. 13} {8} 21.3. x
   . 6.2.4.  . 1. y  20. c   4 6
18 31  25 12. 10.9 8. 1. 12. 1. 6. 15} Glencoe Algebra 1 24. 9. 12. 3. 12.  . {0. 6. {3. 8} {7. 7. 2. 8} 20. 5. 2x . 4. 2. 4a  8  16 6 1. 7a
21  56 5 5.  冦 18 {1. 8} and B ⫽ {9.4  6. 10. 4b  12  28 10 2. 3b
15  48 11 3. 4a 3.25 5(22)
4(3) 4(2  4) 16. 3.  . 9. 6. 11. x  2  2. 12. 6. 11} {7} 17.  .  . a
7 13. 6.  4 6 3 4 4 3 冦 7.  p 2 3 37  9 18  11 13. y   3 12. 10. 1-3 NAME ______________________________________________ DATE (Average) Open Sentences Practice 冦 1 3 冧 ____________ PERIOD _____ 28 b 17 12 冦 12 13 7 5 2 24 12 8 3 冧 13 24 27 8 冦 21 1 2 冧 4(22  4) 3(6)
6 15.6 Solve each equation. w  20. 6. 2. 7. 3. 4b  4 . 5} Find the solution set for each inequality using the given replacement set. 8.   3  0 12 36 b 4.  .0} 冧 冦ᎏ43 冧 20. 4} {3. 4. 6.   b 2 2(4)
4 3(3  1) 13.95 11. 5. 9
y 17. 7} {2. {7.  ᎏ 1 2 Find the solution of each equation using the given replacement set.  .   a 1 46  15 3
28 11. 1. 9. {2. 4.4 15 22.8  x 3.  .  .  . 3. 8. 10} {8.  . 10} 19. 
x   . 12.8. 13}. 15. 10. 7} {3. 1 5 2 3 5 4 9.  .2  8. 4. {0. 5. 12. 4.   d 4 1 3 1 5 3 4 8 2 8 4 n⫽ᎏ . 6. 5a  9  26 7 Find the solution of each equation if the replacement sets are A ⫽ {4.  (x
2)   . 15} 18. 5. {3.   k 4 11. 0. a
7 10.6. 2 2 2 and B ⫽ {3.5.8 .5) there is an average of 8. {2. 10} 5 {0. 3. 4. LONG DISTANCE For Exercises 24 and 25.5 1 2 1. 5. 3. 1. 2. 0.5 Solve each equation. 12.8 13. use the following information. 2.0. 4.4(x
3)  5. 2} 3y 21. 120  28a  78 ᎏ 4. 3y 42.5} {2} 17. 97  25 41  23 14.8. 14.  . {0. Write and then solve an equation that represents the number of lessons the teacher must teach per week if 6(8. 12(x
4)  76.4 3 4 8.8.00 each. {10.5. 1. What is the maximum number of 20-minute state-to-state calls that Gabriel can make this month? 2 24. he makes eight in-state long-distance calls averaging $2. Write an inequality that represents the number of 20 minute state-to-state calls Gabriel can make this month.3  4. 1. 3. His long-distance budget for the month is $20. 8. 1-3 NAME ______________________________________________ DATE Answers (Lesson 1-3) Lesson 1-3 . 2. 1. During one month. 1. 
9  16 4 3 2 3. 2.2. ᎏ . 7b  8  16. 16. 5.8. 0.  .5 lessons per chapter. ᎏ .50. 4x  2 5.  .32.  ᎏ 1 2 6. 5}. 1.6.6} 2. 
x   . 2. 1.4. {0. 6a
18  27 ᎏ Find the solution of each equation using the given replacement set.4.4. 6. 4. {0. 1.5.5. 1.5. 8(2) ⫹ 1.   2. {0. 18} © Glencoe/McGraw-Hill 16 Glencoe Algebra 1 25.8 9. 2.  (x
2)   .5} 19.5 3 2 2.  . 7} 1 2 10. 1.  . 6. x  18.2. 3. 4. 3.0} {14. {2. A 20-minute state-to-state call costs Gabriel $1. TEACHING A teacher has 15 weeks in which to teach six chapters. a
  1 ᎏ 1 2 Find the solution of each equation if the replacement sets are A ⫽ 0. 1.5s ⱕ 20 Gabriel talks an average of 20 minutes per long-distance call. 23. {1.5 3. 2. 2  2 ᎏ Find the solution set for each inequality using the given replacement set. 18} 18. 16.2} 7 8 7. 1. 4b  8  6 3. 1  . {1. Explain how the solution set for the equation is different from the solution set for the inequality. What is one meaning that relates to the way we use the word in algebra? Helping You Remember The solution set for the equation contains only one number. {Maine. Hillary Clinton} 7. The members of the replacement set that make the inequality true are the solutions. yellow. a. August} It is a summer month. {Pennsylvania} {red. {Alabama. It is a New England state. 9. Describe how you would find the solutions of the inequality. The set {April. If It is replaced by either April. Look up the word solution in a dictionary. Arkansas} 1. How is the open sentence different from the expression 15. 3. 1. President. 4. New Hampshire. How can you tell whether a mathematical sentence is or is not an open sentence? ____________ PERIOD _____ © Glencoe/McGraw-Hill 18 14. Arizona. Connecticut} 4. O. It is an even number between 1 and 13. Replace n with each member of the replacement set. Apr. Consider the equation 3n  6  15 and the inequality 3n  6  15. 3. Glencoe Algebra 1 You know that a replacement for the variable It must be found in order to determine if the sentence is true or false. It is the square of 2. 3. is greater than or equal to is greater than   is less than Words  Inequality Symbol 2. The members of the replacement set that make the equation true are the solutions. 13.50  5n? The is less than or equal to  Glencoe/McGraw-Hill 17 Sample answer: answer to a problem Glencoe Algebra 1 4.© Glencoe/McGraw-Hill A10 open sentence has two expressions joined by the  symbol. {2. Sept. 5. How would you read each inequality symbol in words? An open sentence must contain one or more variables. c. Feb.S. 9} It is an odd number between 0 and 10. {Atlantic. 7. 11. 2. Arctic} It is an ocean. July. Oct. E.12} {Barbara Bush. Massachusetts. May. b. Consider the following open sentence. Rhode Island. Dec} 6.{4. U} It is a vowel. she was the wife of a U. or 4. Write the solution set for each open sentence. x  4  10 {6} Vermont. 1. Write an open sentence for each solution set. blue} 2. Its capital is Harrisburg. Pacific. June} is called the solution set of the open sentence given above. or June. Mar. {June. 12. Lesson 1-3 How can you use open sentences to stay within a budget? Open Sentences Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-3 NAME ______________________________________________ DATE Answers (Lesson 1-3) Glencoe Algebra 1 . Enrichment Solution Sets 1-3 NAME ______________________________________________ DATE Read the introduction to Lesson 1-3 at the top of page 16 in your textbook. 3. {Jan. 6. The solution set for the inequality contains the four numbers 0. 31  72  k {41} 8. Describe how you would find the solutions of the equation. May. 10. This set includes all replacements for the variable that make the sentence true. During the 1990s. 10. 1. It is the name of a month that contains the letter r. It is the name of a month between March and July. It is a primary color. Suppose the replacement set is {0. {A. Nov. It is the name of a state beginning with the letter A. 16} 9. I. 2. 8. Alaska. Indian. and 3. 3. the sentence is true. 5. 4. 3. 5}. Replace n with each member of the replacement set. 9  n
9 Mult. Substitution Property a 5⫹4⫽5⫹4 Reflexive Property a. Multiplicative Inverse Property b For any number a. Exercises 24 24 24 24 16 16 Evaluate 24 ⭈ 1 ⫺ 8 ⫹ 5(9 ⫼ 3 ⫺ 3). Identity. Identity and Equality Properties 1-4 NAME ______________________________________________ DATE  1  8
5(3  3)  1  8
5(0)  8
5(0) 8
0
0 Substitution. then a  c. 15  1  9
2(15  3  5) 20 ⫹ 13 Subst. Inverse Substitution Substitution 3. 0
21  21 3. If n ⫽ 12. Multiplicative Property of 0 a For any number a. since   3  1 b. Then find the value of n. Name the property used in each step. Identity ⫽ 18 ⫺ 6 ⫹ 2(0) ⫽ 18 ⫺ 6 ⫹ 0 ⫽ 12 ⫹ 0 ⫽ 12 Mult. 4. 3(5 ⫺ 5) ⫹ 21 ⫼ 7 Mult. n  1  8 Name the property used in each equation. 4
3  4
3 10. Inverse Substitution 1 2(15⭈1 ⫺ 14) ⫺ 4 ⭈ ᎏ Subst. Identity 6⫺0 Substitution 6 Substitution Substitution ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ Glencoe Algebra 1 3(5 ⫺ 5 ⭈ 1) ⫹ 21 ⫼ 7 Subst. b 0. 6n  6 Name the property used in each equation. 24  1  8
5(9  3  3)       Example The properties of identity and equality can be used to justify each step when evaluating an expression. 4 1 2(15 ⫺ 14) ⫺ 4 ⭈ ᎏ Mult. Identity 4 1 2(1) ⫺ 4 ⭈ ᎏ Substitution 4 1 2⫺4⭈ᎏ Mult. b. n ⭈ 3 ⫽ 1 Multiplicative Inverse Property Name the property used to justify each statement. if a  b and b  c. Identity ⫽ 18 ⫺ 3 ⭈ 2 ⫹ 2(0) ⫽ 18 ⭈ 1 ⫺ 3 ⭈ 2 ⫹ 2(0) Substitution ⫽ 18 ⭈ 1 ⫺ 3 ⭈ 2 ⫹ 2(2 ⫺ 2) Subst. 10  5  22  2
13 ⫽2⫺1 ⫽1 ⫽ ⫽ ⫽ ⫽ 15 ⭈ 1 ⫺ 9 ⫹2(5 ⫺ 5) Substitution 15 ⭈ 1 ⫺ 9 ⫹2(0) Substitution 15 ⭈ 1 ⫺ 9 ⫹ 0 Mult. (14  6)
3  8
3 19 3 Glencoe Algebra 1 4 Mult. Transitive Property Substitution Property A11 1 3 1 3 © Glencoe/McGraw-Hill Reflexive Property 12. If 3
3  6 and 6  3  2. a  0  0. 2 
 冤 41 冢 12 冣 冥 1 1 ⫽ 2冢 ᎏ ⫹ᎏ 4 4冣 1 ⫽ 2冢 ᎏ 2冣 Evaluate each expression. then 9  4
5. then 4n ⫽ 4 ⭈ 12. a  1  a. 0(15)  0 Mult. ᎏ 5. then 3
3  3  2. a
0  a. Inverse. Zero Substitution Add. Prop. 3  3  0 Multiplicative Identity. Prop. 6  n  6  9 Substitution Property. Identity Glencoe Algebra 1 Answers Substitution Property 13. Identity 4 1 4 Mult. Name the property used in each equation. If a  b. Exercises n   . If 4
5  9. then a may be replaced by b in any expression. of Zero Symmetric Property 7. Identity. Identity. Substitution Substitution Substitution Additive Identity Mult. 2(3  5  1  14)  4   ⫽1 1. n
0   3 8 Mult. Multiplicative Identity b For any number a. a  a. 18  1  3  2
2(6  3  2) ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ 2. Add. 3(5  5  12)
21  7 Mult. 8 3 Add. Transitive Property 9.© ____________ PERIOD _____ Identity and Equality Properties Study Guide and Intervention Glencoe/McGraw-Hill For any numbers a. 24  8  16 Additive Identity. there is exactly one number  such that    1. 8 2. Example 2 For any numbers a and b. 9  3  3 Substitution. Name the property used in each step. 16
0  16 Substitution. a. Prop. ᎏ 3 4 6.   n  1 Add. since 8  1  8 b. Identity. Additive Identity The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions. Reflexive Property a a b a b For every number  . (1)94  94 Mult. 9 11. 5(0)  0 © 2 10 ⫼ 5 ⫺ 4 ⫼ 2 2 ⫺ 4 ⫼ 2 ⫹ 13 2 ⫺ 2 ⫹ 13 0 ⫹ 13 13 Glencoe/McGraw-Hill ⫽ ⫽ ⫽ ⫽ ⫽ 5. Zero 0⫹3 Substitution 3 Additive Identity 6. Then find the value of n. 0 4. 1 1. Identity 3(0) ⫹ 21 ⫼ 7 Substitution 0 ⫹ 21 ⫼ 7 Mult. then b  a. 24  1  24 Multiplicative Property of Zero. if a  b. Prop. Identity 8. Symmetric Property Example 1 For any number a. Identity and Equality Properties (continued) ____________ PERIOD _____ Study Guide and Intervention Use Identity and Equality Properties 1-4 NAME ______________________________________________ DATE Answers (Lesson 1-4) Lesson 1-4 . and c. Zero 15 ⫺ 9 ⫹ 0 Mult. 8n ⫽ 8 Multiplicative Identity Property n  1. 2
6(9  32)  2 4 Multiplicative Identity. 4[8  (4  2)]
1 9[10 ⫺ 2(5)] Substitution 9(10 ⫺ 10) Substitution 9(0) Substitution 0 Mult.00 each for two bracelets and later sold each for $15. 3n  1 Reflexive Prop. of Zero. 7(16  42) Evaluate each expression. 6
9[10  2(2
3)] ⫽ ⫽ ⫽ ⫽ 17. Name the property used in each step. 0
n  22 Multiplicative Identity. 0 7. Write an expression for the total number of tomatoes harvested. n  9  9 Additive Identity. of Zero 16. 2(15 ⫺ 5) ⫹ 3(9 ⫺ 8) ⫽ 2(10) ⫹ 3(1) ⫽ 20 ⫹ 3(1) ⫽ 20 ⫹ 3 ⫽ 23 10. 4  3[7  (2  3)] ⫽ 2(5 ⫺ 5) Substitution ⫽ 2(0) Substitution ⫽0 Mult.. 0.00. Evaluate the expression.1  0. She paid $8. ᎏ 13. 1 6. Mr. of Zero.1 4. 2(15 ⫺ 5) ⫹ 3(9 ⫺ 8) SALES For Exercises 9 and 10.. n  14  0 Substitution Prop. Katz harvested 15 tomatoes from each of four plants. 2(6  3  1)   ⫽ ⫽ ⫽ ⫽ 18. use the following information.© Identity and Equality Properties Skills Practice ____________ PERIOD _____ Glencoe/McGraw-Hill 3 A12 Substitution Prop. Prop. 1 4 冣 Glencoe Algebra 1 冢 11.5  0. 1  n  8 4 ⫺ 3(7 ⫺ 6) Substitution 4 ⫺ 3(1) Substitution 4 ⫺ 3 Multiplicative Identity 1 Substitution © ⫹ ⫹ ⫹ ⫹ 1 2 4(8 ⫺ 8) ⫹ 1 Substitution 4(0) ⫹ 1 Substitution 0⫹1 Mult. 3 8.. use the following information. of Zero 2 Additive Identity Substitution 1 4 Multiplicative Identity Multiplicative Inverse Substitution 4 ⫽5⫹1 ⫽6 Substitution 1 ⫽5⫹4⭈ᎏ 4 1 ⫽ 5(1) ⫹ 4 ⭈ ᎏ 1 ⫽ 5(14 ⫺ 13) ⫹ 4 ⭈ ᎏ Substitution 8. of Zero 1 Additive Identity 21 ⫽1 Glencoe Algebra 1 Multiplicative Inverse 1 ⫽ 2(2 ⫺ 1) ⭈ ᎏ Substitution 2 1 ⫽ 2(1) ⭈ ᎏ Substitution 2 1 ⫽2⭈ᎏ Multiplicative Identity 2 20. Katz only harvested one fourth of the tomatoes from each of these. 1-4 NAME ______________________________________________ DATE Answers (Lesson 1-4) Glencoe Algebra 1 Lesson 1-4 . Then find the value of n. of Zero Additive Identity Glencoe/McGraw-Hill ⫽6 ⫽6 ⫽6 ⫽6 ⫽6 19. n  0.00 each for three bracelets and sold each of them for $9. Name the property used in each step. 2  n  2  3 Multiplicative Identity. 1 Multiplicative Inverse. 19 1.. (7  3)
4  n
4 Reflexive Prop. Write an expression that represents the profit Althea made. 5 11. ᎏ 3.5 Substitution Prop. 4(15) ⫹ 2 4 ⭈ ᎏ GARDENING For Exercises 11 and 12. 8 2. Althea paid $5. 12  12  n Reflexive Prop.   n  1 1 4 Multiplicative Prop. 9. 21 10. Evaluate the expression.. 5n  1 Additive Identity. 0 3. 15 2. 2(9  3)  2(n) Additive Identity. (8
7)(4)  n(4) Evaluate each expression. of Zero. 5(14  39  3)
4   Substitution Substitution Multiplicative Identity Substitution © Glencoe/McGraw-Hill 4 ⫽ 60 ⫹ 2(1) ⫽ 60 ⫹ 2 ⫽ 62 4 1 4(15) ⫹ 2冢4 ⭈ ᎏ 冣 ⫽ 60 ⫹ 2冢4 ⭈ ᎏ1 冣 22 Multiplicative Inverse Multiplicative identity Substitution Substitution 12. 0 5.00. ⫽ ⫽ ⫽ ⫽ ⫽ 7. Prop. 5
4  n
4 Substitution Prop. 6 9. n
0  19 Name the property used in each equation. 5  n
5 Multiplicative Inverse. n
9  9 Name the property used in each equation. 0 1. 0 12. 49n  0 1 Multiplicative Inverse. 9 14. but Mr.. 22 4. 2[5  (15  3)] ⫽ 7(16 ⫼ 16) Substitution ⫽ 7(1) Substitution ⫽7 Multiplicative Identity 15. 1-4 NAME ______________________________________________ DATE (Average) Identity and Equality Properties Practice ____________ PERIOD _____ 5 2 2 2 2 0 ⫹ ⫹ ⫹ ⫺ 6(9 ⫺ 9) ⫺ 2 Substitution 6(0) ⫺ 2 Substitution 0⫺2 Mult.. 28  n  0 Additive Identity. Name the property used in each step. 4 5. Multiplicative Prop. Name the property used in each step. 1 6. Two other plants produced four tomatoes each. Then find the value of n. Prop. 11  (18  2)  11  n Multiplicative Prop. Prop. their sum. the operation ⇒. Write the Roman numeral of the sentence that best matches each term.     1 f. b) means to find the value of ab yes 3. Reflexive Property VIII III c. Write yes or no. Transitive Property h. Multiplicative Inverse Property e. even numbers yes Tell whether each set is closed under addition. Helping You Remember VII VII. multiplication: a  b yes Tell whether the set of whole numbers is closed under each operation. nonprime numbers no. additive identity 1. prime numbers no. 6
0  6 IV. the operation sq.© Glencoe/McGraw-Hill A13 2 ⫹ r ⫽ 2. Lesson 1-4 How are identity and equality properties used to compare data? Identity and Equality Properties Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-4 NAME ______________________________________________ DATE Answers (Lesson 1-4) . Write yes or no. 6. If the result of a binary operation is always a member of the original set. Addition is a binary operation on the set of whole numbers. the set of whole numbers is closed under addition because 4
5 is a whole number. where exp(a. where a ⇒ b means to round the product of a and b up to the nearest 10 yes 5. give an example. Enrichment ____________ PERIOD _____ Closure 1-4 NAME ______________________________________________ DATE Read the introduction to Lesson 1-4 at the top of page 21 in your textbook. 3 ⫹ 7 ⫽ 10 © Glencoe/McGraw-Hill 24 Glencoe Algebra 1 16. For example. It matches two numbers such as 4 and 5 to a single number. Explain why the solution is the same as the solution in the introduction. III. 4 ⫼ 3 is not a 13. the operation exp. 22 ⫹ 9 ⫽ 31 10. division: a  b no. If your answer is no. If 12  8
4. Write an open sentence to represent the change in rank r of the University of Miami from December 11 to the final rank. then 2
4  6. the operation ⇑. where sq(a) means to square the number a no II. The set of whole numbers is not closed under subtraction because 4  5 is not a whole number. squaring the sum: (a
b)2 yes 15. the set is said to be closed under the operation. where a © b means to cube the sum of a and b yes 5 7 1. If your answer is no. Symmetric Property II I d. 18  18 7 5 ↵.means “across” or “through. IV V. 4  0  0 Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 23 Glencoe Algebra 1 Sample answer: The Transitive Property of Equality tells you that when a ⫽ b and b ⫽ c. If 2
4  5
1 and 5
1  6. give an example. Tell whether each operation is binary. A binary operation matches two numbers in a set to just one number. then 5n  5  2. 2. odd numbers no. 11. 3  1  3 12. multiples of 5 yes 8. multiples of 3 yes 7. exponentation: ab yes whole number 14. Substitution Property VI. The prefix trans. Sample answer: The rank did not change for either team from the date given to the final rank. VI g. where a ⇑ b means to match a and b to any number greater than either number no 4. you can go from a through b to get to c. Write yes or no. If n  2. V VIII. Multiplicative Property of Zero b. multiplicative identity a. then 8
4  12. 3 ⫹ 5 ⫽ 8 9. the operation I.” Explain how this can help you remember the meaning of the Transitive Property of Equality. where a ↵ b means to choose the lesser number from a and b yes 2. the operation ©. or a product or quotient of numbers and variables. An expression is in simplest form if it is replaced by an equivalent expression with no like terms or parentheses. 21c
18c
31b  3b ⫺6x ⫹ 13x2 9. 3(2x  y) 6x ⫺ 3y 9. 12g  10g
1 11a 1. 3x
6x Simplify each expression. If not possible. 12 6   x 72 ⫺ 6x 冣 8. 2(3x
2y  z) 1 10. 12 2
 x 2 Glencoe Algebra 1 ⫺4x2 ⫺ 6x ⫺ 2 18. Multiply. 6x
3x2
10x2 simplified 6. 3x  2x  2y
2y simplified 1 2 10. 5(4x  9) 20x ⫺ 45 1 2 6. 2(x
3) ⫺2x ⫺ 6 5.
3ab)  ab     Exercises 4(a2 Example A term is a number. 6(12
5) 102 冢 3.© Glencoe/McGraw-Hill A14 Simplify. a variable. Then simplify. 4x2
3x2
2x simplified ⫺xy 17. 2(10  5) 10 Rewrite each expression using the Distributive Property. 2x  12 9x 2. 3(x  1) 3x ⫺ 3 2. 6(8
10)  6  8
6  10  48
60  108 Example 1 Distributive Property The Distributive Property can be used to help evaluate The Distributive Property expressions. a(b
c)  ab
ac and (b
c)a  ba
ca and a(b  c)  ab  ac and (b  c)a  ba  ca. Exercises 2(3x2)
Rewrite ⫺2(3x2 ⫹ 5x ⫹ 1) using the Distributive Property. The Distributive Property and properties of equalities can be used to simplify expressions. 2(3x2 ____________ PERIOD _____ Study Guide and Intervention Evaluate Expressions 1-5 NAME ______________________________________________ DATE Substitution Distributive Property Distributive Property Multiplicative Identity 1 4 © Glencoe/McGraw-Hill 8x ⫺ 5y 16. 4(a2
3ab)  1ab 4a2
12ab  1ab 4a2
(12  1)ab 4a2
11ab Simplify 4(a2 ⫹ 3ab) ⫺ ab. Multiply. (2  3x
x2)3 1 4 16. Then evaluate. For any numbers a. 3(8  2x) 24 ⫺ 6x 7.  (16x  12y
4z) 3⫺t xy ⫺ 2y 14. 4x
 (16x  20y) x 13.  (12  4t) 4 6x ⫹ 4y ⫺ 2z 13. 3x  1 14. b. xy  2xy 2xy 11. 2  1  6x
x2 15. Distributive Property Rewrite 6(8 ⫹ 10) using the Distributive Property. The Distributive Property (continued) ____________ PERIOD _____ Study Guide and Intervention Simplify Expressions 1-5 NAME ______________________________________________ DATE Answers (Lesson 1-5) Glencoe Algebra 1 Lesson 1-5 . 6(12  t) 72 ⫺ 6t 1. Then simplify. with corresponding variables having the same powers. 3x2
2x2 simplified 5. 12a  12b
12c 39c ⫹ 28b 12. 10xy  4(xy
xy) 5x 2 8. 12a  a 1 ⫺ 6x 26 ⫹x2 7x2 ⫹ 2x Glencoe Algebra 1 18. (x  4)3 3x ⫺ 12 4. (x  2)y 1 11. Like terms are terms that contain the same variables. 2(3a  2b
c) 12. 4x2
3x
7 simplified 3. write simplified. 2p
 q 32a ⫺ 8 7. 2(2x2
3x
1) 6a ⫺ 4b ⫹ 2c 15. Distributive Property 冢 冣 24 ⫹ 6x © Glencoe/McGraw-Hill 4x ⫺ 3y ⫹ z 25 6 ⫺ 9x ⫹ 3x2 17. 20a
12a  8 2g ⫹ 1 4.
5x
1)  (2)(5x)
(2)(1)  6x2
(10x)
(2)  6x2  10x  2 Example 2 Add. and c. 2(x ) ⫺ 2(y ) ⫹ 2(1). 4(6p
2q  2p) 16p ⫹ 8q 19. Each day.75) The Ross family recently dined at an Italian restaurant. 3a2
6a
2b2 simplified 2x 2 x 24. 48b ⫺ 4 7. 9(7
8) Rewrite each expression using the Distributive Property. write simplified. 1-5 NAME ______________________________________________ DATE (Average) The Distributive Property Practice ____________ PERIOD _____ m ⭈ n ⫹ m ⭈ 4. 35y ⫺ 21 5. Then simplify. 13. What was the cost of dining out for the Ross family? $63. (x  y)6 6. ORIENTATION For Exercises 27 and 28. 3a ⫹ 3b ⫺ 3 Simplify each expression. 27 ⫺ 3p 4. 15  104 1560 11. (c  4)d 1 15 ⭈ f ⫹ 15 ⭈ ᎏ . 2(n
2n) 6n 20. (6  2)8 6 ⭈ 8 ⫺ 2 ⭈ 8. (a
7)2 2. 3 15f ⫹ 5 冣 DINING OUT For Exercises 25 and 26. 12p  8p 4p 19.© The Distributive Property Skills Practice ____________ PERIOD _____ Glencoe/McGraw-Hill m ⫹ 3 ⭈ n. 17. c 2 ⫹ 3d 2 18. 15 2  35 冢 31 冣 12. Each of the four family members ordered a pasta dish that cost $11. If not possible. 2x2
6x2 8x2 24. 2(6
10) 2 ⭈ 6 ⫹ 2 ⭈ 10. 3m ⫹ 3n A15 冢 18 冣 16. 21  1004 21. 32 3. 3(a
b  1) 8. an average of 110 students attended the morning session and an average of 160 students attended the afternoon session. 3(5
6h) 15 ⫹ 18h 16. 6b ⫹ 24 3. 4(3
5) 4 ⭈ 3 ⫹ 4 ⭈ 5. Write an expression that could be used to determine the total number of incoming freshmen who attended the orientation. 6x ⫺ 6y 10. 3(110 ⫹ 160) Madison College conducted a three-day orientation for incoming freshmen. 5 ⫹ 1. 15 f
 冢 6 ⭈ b ⫹ 6 ⭈ 4. 6(b
4) Simplify each expression. 3q2
q  q2 2q2 ⫹ 25.25) 9 ⭈ 3 ⫺ p ⭈ 3. 5  89 445 h ⫺ 7 ⭈ 10. Write an expression that could be used to calculate the cost of the Ross’ dinner before adding tax and a tip. write simplified. 2a ⫹ 14 4. 25t3  17t3 8t 3 23. 2x
8x 10x q Glencoe Algebra 1 3(a) ⫹ 3(b) ⫺ 3(1). 135 1.5 30 10. What was the attendance for all three days of orientation? 810 Glencoe Algebra 1 27.084 c ⭈ d ⫺ 4 ⭈ d. use the following information. 4(11. 14 2. use the following information. m(n
4) 5y ⭈ 7 ⫺ 3 ⭈ 7. 7h ⫺ 70 x ⭈ 6 ⫺ y ⭈ 6.25. Then simplify. a drink that cost $1. c2
4d 2  d 2 © Glencoe/McGraw-Hill 28 28.5 ⫹ 2. 9  499 4491 Use the Distributive Property to find each product. 2x ⫺ 2y ⫹ 2 9. 4(2b  b) 4b 22. 32 Rewrite each expression using the Distributive Property. 7(h  10) 7 ⭈ Use the Distributive Property to find each product. 1-5 NAME ______________________________________________ DATE Answers (Lesson 1-5) Lesson 1-5 . x
 x
 3 3 21. 3y2  2y simplified 18. 32 1.75. 7(6  4) 1 14. (9  p)3 9 ⭈ 7 ⫹ 9 ⭈ 8.00 25. 12b2
9b2 21b 2 22. 5(7  4) 5 ⭈ 7 ⫺ 5 ⭈ 4. w
14w  6w 9w 1 3 6. 15. 17g
g 18g 17. cd ⫺ 4d 9. 14(2r  3) 28r ⫺ 42 冢 41 冣 15. 2(x  y
1) 7. 8 3  25 14. 16(3b  0. 7  110 770 20. 3(m
n) 3 ⭈ a ⭈ 2 ⫹ 7 ⭈ 2. 12 1  15 冢 14 冣 13. 27 2  3 冢 冣 63 11. 12  2. and dessert that cost $2. (5y  3)7 7 ⭈ 6 ⫺ 7 ⭈ 4.50. 7a2  2a2 5a2 21. 16 4  68 12. 16m  10m 6m 23. 16 ⭈ 3b ⫺ 16 ⭈ 0. mn ⫹ 4m 8. 26. 15 5. 9  99 891 © Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 27 26.50. If not possible. Write the difference of 5 times 6 and 5 times 4. x variable quotient of a number and variable 3. Glencoe/McGraw-Hill 30 In the left figure. ᎏ.95. Each of the two figures shown at the right is made from all seven tans. 17. ᎏ 3 7 5t w. Glencoe Algebra 1 Glue the seven tans on heavy paper and cut them out. the body is made from 4 pieces rather than 3. The extra piece becomes the triangle at the bottom in the right figure. They seem to be exactly alike. Write three examples of each type of term. 0. but one has a triangle at the bottom and the other does not. t 2. Use the word coefficient in your explanation. Sample answers are given. The seven geometric figures shown below are called tans.95 and $34. The same is true if you multiply the number by 1 (the multiplicative identity). How would you find the amount spent by each of the first eight customers at Instant Replay Video Games on Saturday? 8 1 4y. that is 5 ⭈ 6 ⫺ 5 ⭈ 4. Lesson 1-5 How can the Distributive Property be used to calculate quickly? The Distributive Property Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-5 NAME ______________________________________________ DATE Answers (Lesson 1-5) Glencoe Algebra 1 . 2.25 Example number Term 3. the result is the very same number you started with. Where does the second figure get this triangle? 5. 3. 2. 4. Explain how the Distributive Property can be used to rewrite 5(6  4). They are used in a very old Chinese puzzle called tangrams. 0. Enrichment Tangram Puzzles 1-5 NAME ______________________________________________ DATE Read the introduction to Lesson 1-5 at the top of page 26 in your textbook. ᎏ r product of a number and a variable Glencoe/McGraw-Hill 29 Glencoe Algebra 1 Sample answer: When you add 0 (the additive identity) to a number. 1. Record your solutions below. 6. Explain how the Distributive Property could be used to rewrite 3(1
5).© Glencoe/McGraw-Hill A16 Add $14. 1. 5. Tell how you can use the Distributive Property to write 12m
8m in simplest form. How can the everyday meaning of the word identity help you to understand and remember what the additive identity is and what the multiplicative identity is? Helping You Remember Sample answer: Add the coefficients of the two terms and multiply by m. x 2s 6 ᎏ. Use all seven pieces to make each shape shown. ____________ PERIOD _____ © 4. Find the sum of 3 times 1 and 3 times 5.78z. 8y
16x
7y 8y
7y
16x (8
7)y
16x 15y
16x Simplify 8(y ⫹ 2x) ⫹ 7y.5
2.2
1. Then simplify. 12
10
8
5 35 Evaluate each expression. 3 
4
2 
3 13 1 2 5. 8(y
2x)
7y     Example The Commutative and Associative Properties can be used along with other properties when evaluating and simplifying expressions.5
1.2 ⫹ 2. (a
b)
c  a
(b
c ) and (ab)c  a(bc). 1-6 NAME ______________________________________________ DATE Answers (Lesson 1-6) . 1 7⫹ᎏ x 2 2 3 10. 8rs
2rs2
7rs © Glencoe/McGraw-Hill 5x ⫹ 5y 32 16.4
2.5
2. a2.   18  25   5 9 80 11.6 1 2 3 4 8.5
2. a
b  b
a and a  b  b  a. 6(2x
4y)
2(x
9) 1. 3a
4b
a 5x ⫹ 3y 4 3 Simplify each expression. 4 
5

3 13 1 2 7. Commutative Prop. 18  8     8 32 1 1 14. 10  7  2. and 4 2xy 14. 12
20
10
5 47 4.8  4 5.4
3. Lesson 1-6 Add. The Associative Properties state that the way you group three or more numbers when adding or multiplying does not change their sum or product. the product of five and the square of a. Exercises 1. and c.3x
0.5
2.2
1.8
2. 4  8  5  3 480 1 2 2. three times the sum of x and y increased by twice the sum of x and y 6a 2 ⫹ 12 Glencoe Algebra 1 15. 3. 
 (x
10)
 7a ⫹ 9b 7. For any numbers a.7x ⫹ 0.7 6.1y)
0. 3. Exercises The product is 180. The Commutative Properties state that the order in which you add or multiply numbers does not change their sum or product.   7  16   4 7 12. 5(0.2 13. four times the product of x and y decreased by 2xy 3y ⫹ 2z 13. twice the sum of y and z is increased by y Write an algebraic expression for each verbal expression. Commutative and Associative Properties (continued) ____________ PERIOD _____ Study Guide and Intervention Simplify Expressions 1-6 NAME ______________________________________________ DATE Add.2
2. Substitution Distributive Property Commutative (
) Distributive Property The simplified expression is 15y
16x. Associative Property Commutative Property © Glencoe/McGraw-Hill 16.5
2.5
3.   12  4  2 72 10.8. 62356325  (6  3)(2  5) 18  10 180 Evaluate 6 ⭈ 2 ⭈ 3 ⭈ 5.5)  10
5  15 Example 2 1. 26
8
4
22 60 1 2 7 28 ᎏz 2 ⫹ ᎏx 2 3 3 4 3 1 3 11. Multiply.5 ⫹ 2.2x 14n ⫹ 10 6. 16
8
22
12 58 3 4 Glencoe Algebra 1 1 2 4 18. 8.5
8
2. 5(2x
3y)
6( y
x) 10x ⫹ 8y 14x ⫹ 24y ⫹ 18 12. Evaluate 8. z2
9x2
 z2
 x2 16x ⫹ 21y 8.© Commutative and Associative Properties Study Guide and Intervention ____________ PERIOD _____ Glencoe/McGraw-Hill A17 Multiply.5  (8.6
4.6 11 9.5
2 16 1 2 1 9 Glencoe Algebra 1 Answers 31 17. b.8  8.5y 9.5  2. increased by the sum of eight. Associative Properties Example 1 For any numbers a and b. Associative Prop. 4x
3y
x 3.5 175 The sum is 15. 3a2
4b
10a2 2.5 ⫹ 1. 6n
2(4n
5) 15rs ⫹ 2rs 2 3. 0. 32      10 5 2 4 2 13.   10  16   60 1 1 15. 6(a
b)
a
3b 13a 2 ⫹ 4b 5.8)
(2. Commutative Properties Commutative and Associative Properties The Commutative and Associative Properties can be used to simplify expressions. 6(x
y)
2(2x
y) 4a ⫹ 4b 4. 2. (p
2n)
7p 8p ⫹ 2n 1 3 Distributive Property Multiply. Commutative (⫹) Associative (⫹) Distributive Property Substitution 19. 3(2c
d)
4(c
4d) 10c ⫹ 19d 9. 11. write an expression to represent the perimeter of the pentagon. use the following information.50 per package. Commutative (⫹) Associative (⫹) Distributive Property Substitution © Glencoe/McGraw-Hill 34 19.3 21. 2p
3q
5p
2q 7p ⫹ 5q 14. Write an algebraic expression for four times the sum of 2a and b increased by twice the sum of 6a and 2b.4
1. twice the sum of p and q increased by twice the sum of 2p and 3q 3(a ⫹ b) ⫹ a ⫽ 3(a) ⫹ 3(b) ⫹ a ⫽ 3a ⫹ 3b ⫹ a ⫽ 3a ⫹ a ⫹ 3b ⫽ (3a ⫹ a) ⫹ 3b ⫽ (3 ⫹ 1)a ⫹ 3b ⫽ 4a ⫹ 3b 18. indicating the properties used.25. 9s2
3t
s2
t 10s 2 ⫹ 4t Simplify each expression. 1. 6s
2(t
3s)
5(s
4t) 17s ⫹ 22t 10.25) ⫹ (0. and 0. 7 
2
1  9 9 2.9 4.7
0.35 each.75 ⫹ 1. use the following information. 6k2
6k
k2
9k 7k2 ⫹ 15k 17. 1. r
3s
5r
s 6r ⫹ 4s 15.75 each.25 ⫹ 0.4c)
b 4b ⫹ 2c 11. 1.5 1 2 5.5 The lengths of the sides of a pentagon in inches are 1. 5m2
3m
m2 6m2 ⫹ 3m 16. 2.1.15 ⫹ 0. Kristen purchased two binders that cost $1.2
9.6b
0. Using the commutative and associative properties to group the terms in a way that makes evaluation convenient. 13. 2a
3(4
a) 5a ⫹ 12 A18 Distributive Property Multiply. 16
8
14
12 50 3. 0. and four pencils that cost $. 5  3  4  3 180 7. 6  5  10  3 900 1. 4(2a ⫹ b) ⫹ 2(6a ⫹ 2b) ⫽ 4(2a) ⫹ 4(b) ⫹ 2(6a) ⫹ 2(2b) ⫽ 8a ⫹ 4b ⫹ 12a ⫹ 4b ⫽ 8a ⫹ 12a ⫹ 4b ⫹ 4b ⫽ (8a ⫹ 12a) ⫹ (4b ⫹ 4b) ⫽ (8 ⫹ 12)a ⫹ (4 ⫹ 4)b ⫽ 20a ⫹ 8b 15. What is the perimeter of the pentagon? 6 in. 4 
6
5  16 1 2 6. 7.25. GEOMETRY For Exercises 18 and 19.7  5 12. 32
14
18
11 75 Commutative and Associative Properties Skills Practice Evaluate each expression. Then simplify.  q
2  q
 r 1 2 12.5. a
9b
6a 7a ⫹ 9b 9. 36
23
14
7 80 1. 2(3x
y)
5(x
2y) 11x ⫹ 12y 8. three times the sum of a and b increased by a Glencoe Algebra 1 Write an algebraic expression for each verbal expression.9
2.25 ⫹ 4. What was the total cost of supplies before tax? $21. 2  4  5  3 120 8.6
3. Commutative (⫹) Associative (⫹) Distributive Property Substitution © Glencoe/McGraw-Hill 2(p ⫹ q) ⫹ 2(2p ⫹ 3q ) ⫽ 2(p) ⫹ 2(q ) ⫹ 2(2p ) ⫹ 2(3q ) ⫽ 2p ⫹ 2q ⫹ 4p ⫹ 6q ⫽ 2p ⫹ 4p ⫹ 2q ⫹ 6q ⫽ (2p ⫹ 4p ) ⫹ (2q ⫹ 6q ) ⫽ (2 ⫹ 4)p ⫹ (2 ⫹ 6)q ⫽ 6p ⫹ 8q 33 Distributive Property Multiply. 3.6  0. 6y
2(4y
6) 14y ⫹ 12 7.4 4. Write an expression to represent the total cost of supplies before tax.1) ⫹ 2. Glencoe Algebra 1 18. indicating the properties used.6 1 10 ᎏ 3 3.© ____________ PERIOD _____ Glencoe/McGraw-Hill 5.8
1. 3   3   16 200 4.6
0. 2.50) ⫹ 4(1.00 2(1. four blue pens that cost $1. 5(7
2g)
3g 35 ⫹ 13g 12.25 each. 3 4 6. Then simplify.9 ⫹ 1. Sample answer: (1.9. 17.15 each. 1-6 NAME ______________________________________________ DATE (Average) ____________ PERIOD _____ Commutative and Associative Properties Practice 冢 14 1 2 冣 q⫹r 14.8 1 2 13. 1-6 NAME ______________________________________________ DATE Answers (Lesson 1-6) Glencoe Algebra 1 Lesson 1-6 . 5  7  10  4 1400 10.35) 16. 5(0. two binders that cost $4.3 3. two packages of paper that cost $1. 2x
5y
9x 11x ⫹ 5y Simplify each expression. 13
23
12
7 55 Evaluate each expression. SCHOOL SUPPLIES For Exercises 16 and 17. 2  (3  4)  2  (4  3) I IV. the order of the numbers is different. What number is represented by (1   3)  (1   2)? 12 13. so that a 䊝 b ⫽ (a ⫹ 1)(b ⫹ 1). What number is represented by 1   (3  2)? 12 12. 2  (3  4)  (2  3)  4 b. Does the operation   appear to be distributive over the operation ? yes 14.© Glencoe/McGraw-Hill A19 The numbers and the operation are the same. Helping You Remember 5.5 and 1. What property can you use to combine two like terms to get a single term? Associative Property of Multiplication 3.4 alike? different? Read the introduction to Lesson 1-6 at the top of page 32 in your textbook. what is the least number of terms you need? three Distributive Property 4. What number is represented by 2  3? 12 3  2  (3
1)(2
1)  4  3  12 (1  2)  3  (2  3)  3  6  3  7  4  28 Let’s make up another operation and denote it by 䊝. Does the operation   appear to be associative? no 5. What number is represented by 3   2? 23 ⫽ 8 1. What property can you use to change the order of the terms in an expression? II c. What number is represented by 2   3? 32 ⫽ 9  3  32  9 2 (1   2)   3  21   3  32  9 ____________ PERIOD _____ Let’s make up a new operation and denote it by 䊊 ⴱ . 3
6  6
3 1.4
1. Write the Roman numeral of the term that best matches each equation. How can properties help you determine distances? Commutative and Associative Properties III IV d. Look up the word commute in a dictionary.5
0. What property can you use to change the way three factors are grouped? Commutative Property of Addition 2. Does the operation  appear to be associative? no 11. so that a 䊊 ⴱ b means ba. What number is represented by (3   4)  (3   2)? 585 Glencoe Algebra 1 16. Associative Property of Multiplication I. To use the Associative Property of Addition to rewrite the sum of a group of terms. What number is represented by 2  (3  4)? 63 10. 6. in the Commutative Property of Addition. What number is represented by 3  2? 12 7. What number is represented by (2  3)  4? 65 9. as between a suburb and a city. Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-6 NAME ______________________________________________ DATE Enrichment © Glencoe/McGraw-Hill 36 18. 6. 2
(3
4)  (2
3)
4 a. What number is represented by 3  (4  2)? 3375 15. Let’s explore these operations a little further. What number is represented by 2   (1   3)? 9 4. How are the expressions 0. Does the operation  appear to be commutative? yes 8. a ⫹ b ⫽ b ⫹ a. Does the operation   appear to be commutative? no 2. the quantities a and b are switched back and forth. Associative Property of Addition Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 35 Glencoe Algebra 1 Sample answer: To travel back and forth. Find an everyday meaning that is close to the mathematical meaning and explain how it can help you remember the mathematical meaning. Commutative Property of Multiplication III. What number is represented by (2   1)   3? 3 3. Is the operation   actually distributive over the operation ? no 17. Commutative Property of Addition II. Properties of Operations 1-6 NAME ______________________________________________ DATE Answers (Lesson 1-6) Lesson 1-6 . C: the square has side length 7 5. H: Karlyn does not C: the number is divisible by 4. Determine a valid conclusion that follows from the statement If the last digit of a number is 0 or 5. If 2x ⫺ 4 ⬍ 10. Hypothesis: it is Wednesday Conclusion: Jerri has aerobics class b. A conditional statement is a statement of the form If A. Hypothesis: it is Thursday Conclusion: you and Marylynn can watch a movie If it is Thursday. Susan is in school and she is in Find a counterexample for each statement. C: you can 1. H: a quadrilateral has equal sides. No valid conclusion because the number does not end end in 0 and never ends in 5. Conclusion: The sum of 4 and 8 is even. 7. You need to find only one counterexample for the statement to be false. then you will get the answer correct. 5. Consider 13 and 7. then a  3. 4 and 8 are even. The part of the statement immediately following the word then is called the conclusion. The two numbers are 4 and 8. 5. 6. 4. C: Karlyn goes to the movies. then you live in New York. then the quadrilateral is a square. A number that is divisible by 8 is also divisible by 4. then the number is divisible by 5 for the given conditions. If it is Wednesday. square is 49. then the number must be greater than six. If a number is divisible by 8. 13
7  20 However. C: run fast 2. then you can run fast. then x 4. a multiple of 4 need not 1. rules. 2. then x ⬍ 7. Hypothesis: 3a
2  11 Conclusion: a  3 If 3a
2  11. No valid conclusion. H: the area of a 4. 8. C: the figure is a rhombus. You could be born in with ᐉ ⫽ 5 and w ⫽ 6 6. If a quadrilateral has 4 right angles. H: you are a sprinter. 7. Hypothesis: 2x  4 10 Conclusion: x 7 Example 2 Identify the hypothesis and conclusion of each statement. If you are a sprinter. use a counterexample. then it might rain. If it is Monday.5) is greater than 15. New York and then live in California. then she is in math class. The number is a multiple of 4. If it is April. Therefore there is no valid conclusion. H: a number is divisible by 8. write no valid conclusion and explain why. then the quadrilateral is a rhombus. b. The number is 101. If you were born in New York. one example for which the conditional statement is false. C: you are in school 3. For a number a such that 3a ⫹ 2 ⫽ 11. Counterexample: If the problem is 475  5 and you press 475  5. To show that a conditional statement is false. The sum of two numbers is 20. 19
1. Deductive reasoning is the process of using facts. A quadrilateral with equal sides is a rhombus. then you are in school. If a valid conclusion does not follow. If you use a calculator for a math problem. Statements in this form are called if-then statements. If 12  4x  4. H: 12 ⫺ 4x ⫽ 4. then it is divisible by 2. H: it is Monday. If three times a number is greater than 15. then it is divisible by 4. Exercises Example 2 Provide a counterexample to this conditional statement. then their sum is even for the given conditions. If 3x  2  10. b. If a valid conclusion does not follow.5 is less than 6. Then write the statement in if-then form. 3(4) ⫺ 2 ⱕ 10. but 5. then the square has side length 7. a ⫽ 3. a. then Karlyn goes to the movies. You and Marylynn can watch a movie on Thursday. Identify the hypothesis and conclusion of each statement. Karlyn goes to the movies when she does not have homework. Conclusion: 120 is divisible by 5. a. If Karlyn does not have homework. The part of the statement immediately following the word if is called the hypothesis. 8. and 4
8  12. but 4 is not less than 4. If a quadrilateral has equal sides. If Susan is in school. Conditional Statements 1-7 NAME ______________________________________________ DATE © Glencoe/McGraw-Hill 38 Glencoe Algebra 1 9. C: it might rain Identify the hypothesis and conclusion of each statement. Example 1 Identify the hypothesis and conclusion of each statement. then Jerri has aerobics class. There is no way to determine the two numbers. a. then x  2. Then write the statement in if-then form. you will not get the correct answer. 12
8. then you and Marylynn can watch a movie.© ____________ PERIOD _____ Logical Reasoning Study Guide and Intervention Glencoe/McGraw-Hill Exercises A20 x⫽2 © Glencoe/McGraw-Hill 37 Glencoe Algebra 1 have homework. and 18
2 all equal 20. If a number is a square. write no valid conclusion and explain why. in 0 or 5 3. definitions. Logical Reasoning (continued) ____________ PERIOD _____ Study Guide and Intervention Deductive Reasoning and Counterexamples 1-7 NAME ______________________________________________ DATE Answers (Lesson 1-7) Glencoe Algebra 1 Lesson 1-7 . or properties to reach a valid conclusion.5. 25 is a square that is not history class. H: it is April. The number is 120. 4. A rectangle divisible by 2. then B. If the area of a square is 49. Example 1 Determine a valid conclusion from the statement If two numbers are even. 3(5. If a polygon has five sides. 3. Hector did not earn an A in science. If it is Saturday. Martina works at the bakery every Saturday. Then write the statement in if-then form. then they must be winning the game. it is early in the morning. C: Martina works at the bakery. Hector earned an A in science. Find a counterexample for each statement. If 6n
4 . 11. then n  7. conditional statement does not mention the number of hours Hector studied. If a valid conclusion does not follow. Ivan only runs early in the morning. Hector studied 10 hours for the science exam. H: it is Saturday. 6. C: it is a pentagon. The other team could have scored 101 points. A polygon that has five sides is a pentagon. C: it is early in the morning. H: Ivan is running. If Ivan is running. When 4⫺1⫽1⫺4 13. 8. then it is a pentagon. then he will earn an A in the class for the given condition. If the car will not start. then it holds for subtraction. No valid conclusion. 11–14. 4. Identify the hypothesis and conclusion of each statement. Hector scored 84 on the science exam. write no valid conclusion and explain why. Sample answers are given. If 2n
3 17. 5.© Logical Reasoning Skills Practice Glencoe/McGraw-Hill ____________ PERIOD _____ n⬎9 A21 © Glencoe/McGraw-Hill Glencoe Algebra 1 39 Glencoe Algebra 1 n ⫽ 7. H: a polygon has five sides. then Martina works at the bakery. If the basketball team has scored 100 points. 7. then it is out of gas. 12. not less than 17. 10. Hector scored an 86 on his science exam. 2n ⫹ 3 is equal to 17. Determine whether a valid conclusion follows from the statement If Hector scores an 85 or above on his science exam. The battery could be dead. Hector scored less than 85 on the exam. Hector did not earn an A in science. Answers 14. the 9. If the Commutative Property holds for addition. then n . 58. then there was a power outage. Then write the statement in if-then form. then mail is not delivered. he stays home from school. then it will not be refused. When Joseph has a fever. © Glencoe/McGraw-Hill 40 H: there is a reasonable offer. Identify the hypothesis and conclusion of each statement. The product is even. If the perimeter of a rectangle is 14 inches. 8. 2. H: H: it is raining. If two triangles are congruent. The product of the numbers is even. 6. Sample When h ⫽ 2. The product of two numbers is 12. C: it will not be refused. Perhaps someone accidentally unplugged it while cleaning. H: 6n ⫹ 4 ⬎ 58. 1-7 NAME ______________________________________________ DATE (Average) Logical Reasoning Practice ____________ PERIOD _____ x ⫽ 4. Two congruent triangles are similar. If 6h  7 5. and an area of 6 in2. write no valid conclusion and explain why. then he stays home from school. 3. 1-7 NAME ______________________________________________ DATE Answers (Lesson 1-7) Lesson 1-7 . 9. C: the meteorologist’s prediction was accurate 1. Glencoe Algebra 1 11. A rectangle with a length A rectangle has a length of 5 in. then 2x
3  11. then the meteorologist’s prediction was accurate. C: he stays home from school. and a width of 1 in. C: you are outdoors 2. H: it is Sunday. 9–10. 4. Determine whether a valid conclusion follows from the statement If two numbers are even. If x  4. 7–8. Then write the statement in if-then form. and a width of 2 in. 7. If it is Sunday. GEOMETRY For Exercises 9 and 10. then h  2. then they are similar. has a perimeter of 14 in. C: 2x ⫹ 3 ⫽ 11 but one of the numbers could be odd. Provide a counterexample to show the statement is false. C: mail is not delivered 1. use the following information. If the refrigerator stopped running. If Joseph has a fever. 10. H: Joseph has a fever. C: they are similar. If there is a reasonable offer. If you are hiking in the mountains. Sample answers are given. 9. then 6h ⫺ 7 ⫽ 5. then its area is 10 square inches. H: two triangles are congruent. of 6 in. Identify the hypothesis and conclusion of each statement. Identify the hypothesis and conclusion of each statement. answers are given. Find a counterexample for each statement. Two numbers are 8 and 6. then you are outdoors. then their product is even for the given condition. C: H: you are hiking in the mountains. If it is raining. such as 4 ⭈ 3.” Identify the hypothesis and conclusion of the statement. and so is not less than 5. State a condition in which the hypothesis and conclusion are valid. No valid conclusion. 5. ADVERTISING A recent television commercial for a car dealership stated that “no reasonable offer will be refused. If a valid conclusion does not follow. Sample answer: A valid conclusion is a statement that has to be true if you used true statements and correct reasoning to obtain the conclusion. You can prove that this statement is false in general if you can find one example for which the statement is false. Write hypothesis or conclusion to tell which part of the if-then statement is underlined.© Glencoe/McGraw-Hill A22 The heat was too high. Division is not an associative operation. What does the term valid conclusion mean? e. 6 ⫹ (4 ⭈ 2) ⱨ (6 ⫹ 4)(6 ⫹ 2) 6 ⫹ 8 ⱨ (10)(8) 14 ⫽ 80 3 5. For any numbers a and b. If our team wins this game. 1. a  b
b  a 6 ⫺ (4 ⫺ 2) ⱨ (6 ⫺ 4) ⫺ 2 6⫺2ⱨ2⫺2 4⫽0 1. How is logical reasoning helpful in cooking? Logical Reasoning Glencoe/McGraw-Hill 41 Glencoe Algebra 1 4. 2. Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-7 NAME ______________________________________________ DATE Enrichment ____________ PERIOD _____ © 2 62 ⫹ 62 ⱨ 64 36 ⫹ 36 ⱨ 1296 72 ⫽ 1296 6.75 2 6 ⫼ (4 ⫼ 2) ⱨ (6 ⫼ 4) ⫼ 2 1. Prove that the statement is false by counterexample. conclusion 1. Give a counterexample for the statement If a person is famous. You can make the equivalent verbal statement: subtraction is not a commutative operation. a  (b  c)
(a  b)  c 7. a  b  b  a. 73
37 4 4 Let a  7 and b  3. There was no television when Lincoln was alive. and c are any numbers. If 3x
7  13. the statement a  b  b  a is false. then x  2. If x is an even number. Subtraction is not an associative operation. Consider the following statement. Exercises 4 and 5 prove that some operations do not distribute. For the distributive property a(b
c)  ab
ac it is said that multiplication distributes over addition. a  (b
c)
(a  b)
(a  c) 3 ⫽ 0. a  (b  c)
(a  b)  c In each of the following exercises a. 8. then they will go to the playoffs. Division is not a commutative operation. Division does not distribute over addition. If it is Tuesday.5 6 ᎏ ⱨ ᎏ 2. 3. What are the two possible reasons given for the popcorn burning? Read the introduction to Lesson 1-7 at the top of page 37 in your textbook. See students’ work. but he was never on television. hypothesis b. 2. Helping You Remember Sample answer: President Abraham Lincoln was and still is famous. In general. Some statements in mathematics can be proven false by counterexamples. Addition does not distribute over multiplication. Counterexamples 1-7 NAME ______________________________________________ DATE Answers (Lesson 1-7) Glencoe Algebra 1 Lesson 1-7 . a
(bc)
(a
b)(a
c) 2 6⫼4ⱨ4⫼6 2 3 ᎏ ⫽ ᎏ 3. for any numbers a and b. Glencoe Algebra 1 6 ⫼ (4 ⫹ 2) ⱨ (6 ⫼ 4) ⫹ (6 ⫼ 2) 6 ⫼ 6 ⱨ 1. then that person has been on television. Write the verbal equivalents for Exercises 1. conclusion a. conclusion d.5 ⫹ 3 1 ⫽ 4. hypothesis c. Write a statement for each exercise that indicates this. 2. 3. Sample answers are given. then x  2 is an odd number. Substitute these values in the equation above. 5.5 4. and 3. I can tell you your birthday if you tell me your height. a2
a2
a4 Glencoe/McGraw-Hill 42 4. then it is raining. or the kernels heated unevenly. Write an example of a conditional statement you would use to teach someone how to identify an hypothesis and a conclusion. b. Tell how you know it really is a counterexample. dep: balance. Then describe what is happening in the graph.000). ind: age. 20). corresponds to the x-axis. 48). then the height decreases until the ball hits the ground. 1-8 NAME ______________________________________________ DATE Length (inches) Glencoe/McGraw-Hill Cost ($) © Value (thousands of $) Answers (Lesson 1-8) Lesson 1-8 . and the dependent variable is height. again increases. then it loses altitude until it falls to the ground. The car starts from a standstill. accelerates. dep: height. (4. Ind: time. Exercises The independent variable is time.000). 21). The height of the ball increases until it reaches its maximum value. 0 20 40 60 80 c. Identify the independent and the dependent variable. (0. ind: age. (4. y). Identify the independent and the dependent variable.000 16. Identify the independent and the dependent variable.000 14.000). and the y-value. Make a table showing the cost of buying 1 to 5 CDs. The table below represents the value of a car versus its age. (3.000). called the x-coordinate. Then describe what is happening in the graph.000 0 0 12 14 16 18 20 22 5 Glencoe Algebra 1 1 2 3 4 Age (years) c. 64) 1 16 Number of CDs a. a. (1. The input values are associated with the independent variable. Draw a graph that shows the relationship between the number of CDs and the total cost. Height The graph below represents the height of a football after it is kicked downfield. 14. (3. 18. (2. The graph represents the speed of a car as it travels to the grocery store. The account balance has an initial value then it increases as deposits are made. (2. The price increases steadily. (2.A23 ____________ PERIOD _____ Graphs and Functions Study Guide and Intervention Time © Time Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 43 Ind: time. The ball is hit a certain height above the ground.000 13. and the output values are associated with the dependent variable. Graphs can be used to represent many real-world situations. 23). 3. Exercises b. Price The graph below represents the price of stock over time. Identify the independent and dependent variables. 2. 0 20 Age (months) 1. Then describe what is happening in the graph. Example 2 1.000) b. Write the data as a set of ordered pairs. Time Time Time Glencoe Algebra 1 Height Account Balance (dollars) Speed The independent variable is time and the dependent variable is price. 32).000 18. (0. 20. then you will receive one CD of the same or lesser value free. Identify the independent and dependent variables. then increases. Identify the independent and dependent variable. Draw a graph showing the relationship between age and value. (4. Functions can be graphed without using a scale to show the general shape of the graph that represents the function. dep: length a. 23). The graph represents the height of a baseball after it is hit. (5. there is exactly one output for each input. (1. Write a set of ordered pairs representing the data in the table. then it falls. 48). It gains altitude until it reaches a maximum height. (1. The football starts on the ground when it is kicked. Ind: time. Input and output values are represented on the graph using ordered pairs of the form (x. The graph represents the balance of a savings account over time. Example 1 A function is a relationship between input and output values. The table below represents the length of a baby versus its age in months. Then describe what is happening in the graph. 16). and lastly goes to 0 as withdrawals are made. Draw Graphs You can represent the graph of a function using a coordinate system. 24) b. Then it slows down and stops. It then stays the same for a while. In a function. 16. The x-value. then travels at a constant speed for a while. dep: value Value ($) Age (years) 2. Identify the independent and dependent variable. or y-coordinate corresponds to the y-axis. Example A music store advertises that if you buy 3 CDs at the regular price of $16. (3. Write a set of ordered pairs representing the data in the table. Then describe what is happening in the graph. Draw a graph showing the relationship between age and length. Interpret Graphs 1-8 NAME ______________________________________________ DATE Graphs and Functions Study Guide and Intervention (continued) ____________ PERIOD _____ Total Cost ($) 2 32 3 48 4 48 5 64 © Length (inches) 1 21 2 23 3 23 4 24 Glencoe/McGraw-Hill 0 20 21 22 23 24 25 1 2 3 4 5 Age (months) c. 1 2 3 4 5 Number of CDs CD Cost 6 44 1 2 3 4 20. then falls again. 13. dep: speed. Then it rained moderately for a while before finally ending. LAUNDRY For Exercises 4–7. Write the ordered pairs the table represents. Describe what is happening in the graph. 1-8 NAME ______________________________________________ DATE Total Cost ($) Answers (Lesson 1-8) Glencoe Algebra 1 Lesson 1-8 . The graph below represents a student taking an exam. then pauses. Total Rainfall Number of Shirts independent : number of shirts. 9). Describe what is happening in the graph. Describe what is happening in the graph. (2. (4. Describe what is happening in the graph.50 0 4. reaches its maximum height. but then the firefighters contain the fire before extinguishing it. WEATHER During a storm. stays there for a while.50 18. nothing for 3 months. pauses again. $40. The graph below represents a puppy exploring a trail. (3. Use the data to predict the cost of subscribing for 9 months. use the table © Time The puppy goes a distance on the trail. ____________ PERIOD _____ 4 6 6 8 10 12 12 15 18 Glencoe Algebra 1 9 Time 3. 1-8 NAME ______________________________________________ DATE Total Cost ($) © (Average) Graphs and Functions Practice Time Time The student steadily answers questions. SAVINGS Jennifer deposited a sum of money in her account and then deposited equal amounts monthly for 5 months. Account Balance ($) 6. Height 1. Write the ordered pairs the table represents. 3). The graph below represents the height of a tsunami (tidal wave) as it approaches shore. After firefighters answer the call.50 5. 4. 18). use the table that shows the monthly charges for subscribing to an independent news server. 15).50 27. $24 6. and then resumed equal monthly deposits. FOREST FIRES A forest fire grows slowly at first. (12.50 9. it rained lightly for a while. Use the data to predict the cost for washing and pressing 16 shirts. 13.00 1 2 3 4 5 6 Number of Months Glencoe/McGraw-Hill 46 7. Identify the independent and dependent variables. the height of the wave increases more and more quickly. 22. (10. (4. 6).5) Total Cost ($) Number of Months INTERNET NEWS SERVICE For Exercises 4–6. Distance from Trailhead 2. Which graph represents this situation? B A B C As the tsunami approaches shore.5).00 13. ____________ PERIOD _____ Time Area Burned Time Area Burned Time © 1 4. (2. 9). Which graph represents this situation? C A B C The football is thrown upward from above the ground. Height 1.Glencoe/McGraw-Hill A24 Graphs and Functions Skills Practice Time Total Rainfall Time Total Rainfall Time 2 3 Total Cost ($) 0 3 6 9 12 15 18 21 2 4 6 8 10 12 14 Number of Shirts Glencoe/McGraw-Hill 45 7.50 2 9. (5. (8.00 22. and then stopped for a while. then resumes answering. resumes answering. Area Burned 3. Draw a graph of the data. Glencoe Algebra 1 Time 4. dependent: total cost 4. Draw a graph of the data. then poured heavily. (6. 18) 5.00 3 4 5 13. then rapidly as the wind increases. the fire grows slowly for a while. then goes back to the beginning of the trail. Sketch a reasonable graph of the account history. Number of Questions Answered 2.(1.50 18. and then falls downward until it hits the ground. goes ahead some more.00 22. stays there for a while. that shows the charges for washing and pressing shirts at a cleaners. The graph below represents the path of a football thrown in the air.5). 12). x comes before y. write the x value before the y value. Explain how the cumulative frequency column can be used to check a project like this one. tell what is meant by the terms dependent variable and independent variable. Which digit(s) appears least often? 7 48 4. Use the example below. 1. In the alphabet. The digits of  never form a pattern. How can real-world situations be modeled using graphs and functions? Graphs and Functions A25 x-axis x © Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 47 writing ordered pairs. 9 8 2 19 Frequency (Number) |||| |||| |||| |||| Frequency (Tally Marks) 0 Digit 2. the number of items being counted.14159 26535 89793 23846 69399 37510 58209 74944 86280 34825 34211 70679 09384 46095 50582 23172 84102 70193 85211 05559 26433 83279 50288 41971 59230 78164 06286 20899 82148 08651 32823 06647 53594 08128 34111 74502 64462 29489 54930 38196 ____________ PERIOD _____ 20 24 20 22 20 16 12 24 23 |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| || |||| |||| |||| |||| |||| |||| |||| | |||| |||| || |||| |||| |||| |||| |||| |||| |||| |||| |||| ||| 1 3 4 5 6 7 200 177 153 141 125 105 83 63 39 19 Cumulative Frequency Glencoe/McGraw-Hill 5. The numbers 25%. s the speed at which the vehicle is traveling is a function of the distance it takes to stop a motor vehicle d independent variable dependent variable 3. In your own words. Since d is a result of s. vertical axis y-axis a. Listed at the right are the first 200 digits that follow the decimal point of . Identify each part of the coordinate system. Use this fact to describe a method for remembering how to write ordered pairs. Which digit(s) appears most often? 2 and 8 Glencoe Algebra 1 3. The Digits of ␲ 1-8 NAME ______________________________________________ DATE Answers (Lesson 1-8) Lesson 1-8 . Glencoe Algebra 1 4. O origin y-axis 2. 50% and 75% represent the Read the introduction to Lesson 1-8 at the top of page 43 in your textbook. d is the dependent variable and s is the independent variable. The number  (pi) is the ratio of the circumference of a circle to its diameter. horizontal axis x-axis c. Reading the Lesson y ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-8 NAME ______________________________________________ DATE Enrichment © 3. It is a nonrepeating and nonterminating decimal. The last number should be 200. How many times would each digit appear in the first 200 places following the decimal point? 20 Solve each problem. Complete this frequency table for the first 200 digits of  that follow the decimal point. Suppose each of the digits in  appeared with equal frequency. Write another name for each term.© Glencoe/McGraw-Hill percent of blood flow to the brain and the numbers 0 through 10 represent the number of days after the concussion . Sample answer: Since x comes before y. coordinate system coordinate plane 1. when Helping You Remember Sample answer: The value of the dependent variable is a result of the value of the independent variable. b. 000. S. about 30% b. easily misunderstood.200 Example The circle graph at the right shows the number of international visitors to the United States in 2000.000 a. some graphs can be confusing. Describe the general trend in the graph.110. Source: Department of Energy HCFs. Public Schools 2. U. Source: The World Almanac 400 420 440 460 World Tourism Receipts 6 Students per Computer.S. Or they may be constructed to make one set of data appear greater than another set.. greenhouse gases emissions for 1999. Exercises b.S.6⬚. Exercises The values are difficult to read because the vertical scale is too condensed. and Sulfur Hexafluoride 2% Methane 9% Nitrous Oxide 6% U. Explain how the graph misrepresents the data.S. or 3. how many were from Mexico? 50.S. The graph below shows the U. companies over a 10-year period. public schools for the school years from 1995 to 1999. It would be more appropriate to let each unit on the vertical scale represent 1 student rather than 5 students and have the scale go from 0 to 12. These graphs may be mislabeled or contain incorrect data. PFCs. This gives the impression that $400 billion is a minimum amount spent on tourism.891.000 visitors. Graphs are very useful for displaying data. What would be a reasonable prediction for the percentage of imported steel used in 2002? general trend is an increase in the use of imported steel over the 10-year period. Analyze Data 1-9 NAME ______________________________________________ DATE Percent Glencoe/McGraw-Hill © Carbon Dioxide 82% Glencoe/McGraw-Hill The graph is misleading because the sum of the percentages is not 100%. Statistics: Analyzing Data by Using Tables and Graphs (continued) ____________ PERIOD _____ Study Guide and Intervention Misleading Graphs 1-9 NAME ______________________________________________ DATE Students © Billions of $ Answers (Lesson 1-9) Glencoe Algebra 1 Lesson 1-9 .000.1 2001
2
4. with slight decreases in 1996 and 2000.2
2. A line graph is useful to show how a data set changes over time.000  20%  10.6 1998 2000
1 1997 1999 % of Change Year (1st Qtr. Mexico 20% Canada 29% 1990 1994 1998 Year Source: Chicago Tribune Glencoe Algebra 1 1. If there were a total of 50. 1 2 3 4 5 Years since 1994 Source: The World Almanac 0 5 10 15 20 50 1995 1997 Year 1999 Glencoe Algebra 1 The graph is misleading because the vertical axis starts at 400 billion. The 1. b. What does the negative percent in the first quarter of 2001 indicate? Worker productivity a.____________ PERIOD _____ Statistics: Analyzing Data by Using Tables and Graphs Study Guide and Intervention A26 © Glencoe/McGraw-Hill 49 decreased in this period. 2000 Graphs or tables can be used to display data.891. If the percentage of visitors from each country remains the same each year. while a circle graph compares parts of a set of data as a percent of the whole set.178. The graph below shows the amount of money spent on tourism for 1998-99.000 visitors? 59.S. However. a. by country. Example The graph at the right shows the number of students per computer in the U. how many visitors from Canada would you expect in the year 2003 if the total is 59.) Worker Productivity Index Source: Chicago Tribune 0 10 20 30 40 Imported Steel as Percent of Total Used Source: TInet United Kingdom Japan 9% 10% Others 32% International Visitors to the U. Explain how each graph misrepresents the data. and lead to false assumptions. Which year shows the greatest percentage increase in productivity? 1998 2. The graph shows the use of imported steel by U. as compared to the productivity one year earlier. A bar graph compares different categories of data. Greenhouse Gas Emissions 1999 1.000  29%  17. Another section needs to be added to account for the missing 1%. The table shows the percentage of change in worker productivity at the beginning of each year for a 5-year period. gypsum. If B cannot scratch A. What percent of people chose a category other than action or drama? 24.5% Drama 30. how many would you expect to prefer drama? 305 7. how many chose action movies as their favorite? 180 graph that shows the percent of people who prefer certain types of movies. 7. If you want to know the exact number of people who preferred spaghetti over linguine in Survey 1.5% Leisure 4. making it appear that the tree grew much faster compared to its initial height than it actually did. then A’s hardness number is greater than B’s. 4. Suppose quartz will not scratch an unknown mineral. 1-9 NAME ______________________________________________ DATE Total Sales (thousands) © Tickets Sold (hundreds) Answers (Lesson 1-9) Lesson 1-9 .5% Action 45% 2002 CD Sales 6 Apatite 10 4 5 Fluorite 3 1 2 Talc Calcite Hardness Mineral Movie Preferences 3. the vertical axis should begin at 0. What is the hardness of the unknown mineral? at least 7 2. How many hours per day does Keisha spend at school? 9 h 1. How many hours does Keisha spend on leisure and meals? 3 h 2. If an unknown mineral scratches all the minerals in the scale up to 7. MOVIE PREFERENCES For Exercises 7–9. Describe the sales trend. Which one-year period shows the greatest growth in sales? SALES For Exercises 5 and 6. A fingernail has a hardness of 2. use the following information. because it gives exact numbers.5% 50 Survey 2 30 34 Fettuccine 20 28 Linguine Linguine Fettucine Spaghetti 0 5 10 15 20 25 30 35 40 45 50 Number of People Pasta Favorites The table. the table or the graph? Explain. Which mineral(s) will it scratch? talc.5% Meals 8% School 37. Describe why the graph is misleading. 10. How can the graph be redrawn so that it is not misleading? The vertical axis begins at 10. 52 11. linguine. then a steady increase to 2002.5% 8. 10 11 12 13 14 15 16 1 3 4 Years 5 6 Glencoe Algebra 1 2 Growth of Pine Tree 8. fettuccine. which is a better source. 4. and corundum scratches the unknown. Explain how the graph misrepresents the data. showed a sharp increase in 2000.Glencoe/McGraw-Hill A27 ____________ PERIOD _____ Sleep 37. TICKET SALES For Exercises 10 and 11. Which mineral(s) will fluorite scratch? talc. What could be done to make the graph more accurate? vertical axis at 20 instead of 0 makes the relative sales for volleyball and track and field seem low. used as a guide to help identify minerals. MINERAL IDENTIFICATION For Exercises 1–4. use the table and bar graph that show the 3. then dipped in 1999. According to the graph. what is the hardness of the unknown? between 7 and 9 Gypsum 7 8 9 10 Orthoclase Quartz Topaz Corundum Diamond 0 2 4 6 8 1998 2000 Year Ticket Sales Comedy 14% Science Fiction 10% Glencoe Algebra 1 ll ll ll d ba ba Fiel yba et ot sk Fo k & olle a c V B a Tr 20 40 60 80 100 Foreign 0. the number of votes for spaghetti is twice the number of votes for which pasta in Survey 2? linguine The ranking is the same for both: spaghetti. Beginning the that compares annual sports ticket sales at Mars High. 6. Sales started off at about from 1999 to 2000 5.5. gypsum 1. use the line graph that shows CD sales at Berry’s Music for the years 1998–2002. use the bar graph 9. Of 1000 people at a movie theater on a weekend. If 400 people were surveyed. then B’s hardness number is less than or equal to A’s. use the circle graph 1-9 NAME ______________________________________________ DATE Height (ft) (Average) Statistics: Analyzing Data by Using Tables and Graphs Practice ____________ PERIOD _____ © Glencoe/McGraw-Hill Start the vertical axis at 0.5% Homework 12. use the line © Survey 1 Survey 2 5. Glencoe/McGraw-Hill Glencoe Algebra 1 Answers 51 To reflect accurate proportions. use the circle 6000 in 1998. Keisha’s Day Statistics: Analyzing Data by Using Tables and Graphs Skills Practice DAILY LIFE For Exercises 1–3. what is the ranking for favorite pasta in both surveys? 40 Survey 1 Spaghetti results of two surveys asking people their favorite type of pasta. PASTA FAVORITES For Exercises 4–8. In Survey 1. How many more people preferred spaghetti in Survey 2 than preferred spaghetti in Survey 1? 10 people PLANT GROWTH For Exercises 9 and 10. How many more people preferred fettuccine to linguine in Survey 1? 6 people 6. calcite The table shows Moh’s hardness scale. What percent of her day does Keisha spend in the combined activities of school and doing homework? 50% that shows the percent of time Keisha spends on activities in a 24-hour day. 10. If mineral A scratches mineral B. graph that shows the growth of a Ponderosa pine over 5 years. 9. A score at the 16th percentile means the score just above the lowest 16% of the scores. a score of 62 28th Glencoe/McGraw-Hill 10. while a stack of Al Gore’s votes would be 970 feet tall with your reaction to the graph shown in the introduction.© Glencoe/McGraw-Hill A28 Compare your reaction to the statement. are helpful when making predictions. 33rd percentile 66 1 2 5 6 7 8 7 6 4 3 1 95 90 85 80 75 70 65 60 55 50 45 2. 16% of the 50 scores is 8 scores. 90th percentile 86 3. The frequency is the number of people who had a particular score. A bar graph 1. are useful when showing how a set of data changes over time. a score of 50 6th Use the table above to find the percentile of each score. 58th percentile 71 Example 2 4. 80th percentile 81 5. Choose from the following types of graphs as you complete each statement. 42nd percentile 66 Use the table above to find the score at each percentile. Enrichment Percentiles 1-9 NAME ______________________________________________ DATE Read the introduction to Lesson 1-9 at the top of page 50 in your textbook. The percents in a circle graph can be used to display multiple sets of data in different categories Bar graphs at the same time. so the price rise appears steeper than it is. The 8th score is 55. There are 29 scores below 75. bar graph 200 225 250 275 300 1 2 3 4 Day 5 6 Glencoe/McGraw-Hill 53 7 Glencoe Algebra 1 graphs—parts of a pizza. a score of 85 90th © 8. A stack containing George W. Notice that no one had a score of 56 points. Line graphs c. Adding 4 scores to the 29 gives 33 scores. or data. Sample answer: circle Helping You Remember The first interval is from 0-200 and all other intervals are in units of 25. The score just above this is 56. See students’ work. Example 1 The table at the right shows test scores and their frequencies. Write a brief description of which presentation works best for you. Describe something in your daily routine that you can connect with bar graphs and circle graphs to help you remember their special purpose. starting at the lowest score and adding up. should always have a sum of 100%. What score is at the 16th percentile? 54 12. At what percentile is a score of 75? 6. a. line graph Line graphs circle graph circle graph b. A e. 2. Lesson 1-9 Why are graphs and tables used to display data? Statistics: Analyzing Data by Using Tables and Graphs Reading the Lesson © ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity 1-9 NAME ______________________________________________ DATE Price ($) Answers (Lesson 1-9) Glencoe Algebra 1 . a score of 58 16th 9. Sample answer: f. a score of 81 84th 11. Thus. 33 out of 50 is 66%. bar graphs—number of slices left in a loaf of bread 3. Stock Price compares different categories of numerical information. The cumulative frequency is the total frequency up to that point. 50 49 47 42 36 29 21 14 8 4 1 Cumulative Frequency Glencoe Algebra 1 Seven scores are at 75. a score of 75 is at the 66th percentile. the score at the 16th percentile is 56. Explain how the graph is misleading. So. The fourth of these seven is the midpoint of this group. Bush’s votes from Florida would be 970. d. compares parts of a set of data as a percent of the whole set.1 feet tall. a score of 77 72nd 7. 70th percentile 76 Frequency Score ____________ PERIOD _____ 1. B 12. A 20. C 10. B 18. 6. 8. B 11. B 4. C 2. C C A 9.Chapter 1 Assessment Answer Key Form 1 Page 55 1. C 3. D 4. Form 2A Page 57 (continued on the next page) © Glencoe/McGraw-Hill A29 Glencoe Algebra 1 . D 19. B 7. A 6. C 13. D 15. B B: 14. D 9. D 8. B 5. B 1. C D A B 17. A 14. D 11. C 16. A 10. B 13. C 7. 5. 12x  6 D Answers 3. B 12. Page 56 15. C 2. Chapter 1 Assessment Answer Key Form 2A (continued) Page 58 16. 17. A 9. 18. A 6. D 4. B 13. D 8. B B: A A30 8a 2 Glencoe Algebra 1 . C 3. 19. B 11. D 18. C 2. B: A C B D C 204 Form 2B Page 59 1. C 10. C 14. B 5. D 12. © Glencoe/McGraw-Hill Page 60 15. D 17. A 19. A 16. C 7. C 20. 20. (6.0 Weight (oz) Answers Substitution. Sample answer: 2 and 1. 17.0 8. Identity) 4  4 1 (Substitution) 1 (Mult. (8. C: I will attend football practice. 4. time. 3(14)  3(5). {2. 17y  7 15. temperature (8. 6 22. 6.80).M. 18 6.0 7. 5. 60 16. at 8 A. A31 5. 5 11.0. temperature is 87. Additive Identity. the 23. 1  (9  8)  7 Glencoe Algebra 1 . 4(5  1  20)  4(5  20) (Mult. 198  7 c. 3. 4 times n cubed plus 6 4.60). 9w  14w 2 14. (5. 87). 32 5. 27 13.0. 21.Chapter 1 Assessment Answer Key Form 2C Page 61 Page 62 1. 7.40) 25. 5(2x) 19. since 2  1  3 © Glencoe/McGraw-Hill 7 6 5 4 3 2 1 B: a.0 6. 10 Rate ($) 10. 0 18. 7 8. 4} between 1959–60 and 1969–70 The percent is decreasing slowly.0.80). H: It is Monday. Start the vertical axis at 0 and use tick marks at same-sized intervals. 3. 24.0. (1  9)  8  7 b. Inverse) 12. 7 20. n 2  34 2. (7. 9. 4. between 1960 and 1970 the percent decreased. Rate ($) 13. (3. 4} 9.0 4.0. 65 (2. between 1970 and 2000 the percent increased 7. score 22. 3. Robert is tired for the fourth game. 24.0 5. 20 6.0. H: It is a hot day. Sample answer: 1 and 3. {1. 3. 10(5)  3(5).  61 (Substitution) 6  1 (Mult. 23x  8 15.0. 5 times a number cubed plus 9 36 4. 1 11 game. 5. Multiplicative Inverse. 1. Start the vertical axis at 0 and show a break on the vertical axis between 0 and 100.50). Reflexive Property. 6(6  1  36)  6(6  36) (Mult. (4. 1. between 1990 and 2000 21. 2. 4.40) 11w 2  7z 2 14. Inverse) 12.60). 40 24. and (5.Chapter 1 Assessment Answer Key Form 2D Page 63 Page 64 1. 8 20. Sample answer: Between the first and third game Robert becomes comfortable with the lane. 2.0 2.0 Weight (oz) B: 2[(5  1)  4  1] 18. 4n 2 19. 10. 3 11. 6 8. 260 16. 3. 1 n  27 3 2. since 134 © Glencoe/McGraw-Hill A32 Glencoe Algebra 1 . C: We will go to the beach. Identity) 23. 6 5 4 3 2 1 0 17.70).0 3.0. ) 11. If a polygon has 5 sides. .5 million 20. H: A polygon has 5 sides. 3    2 3  0 (Subst.Chapter 1 Assessment Answer Key Form 3 Page 65 Page 66 2. if x  3 and y  2 then 2(3)  3(2) 2(2)  3(3) 19. Time B: © Glencoe/McGraw-Hill A33 10 Glencoe Algebra 1 . simplified 15. 105 16. The number of newspapers sold was steadily decreasing during the years 1990–1994. 40 Answers n 3  12 Time (hours per week) 1. Substitution. then it is called a pentagon. Iden.  68. six times a number squared divided by 5 4. 45 5. Inverse)  1 (Add. 9 2 (3  2)  (9  9) (Subst. Multi.  24. number of 23.1 million Sample answer: 21. 18. 1 2 4 17.  1 3 . 88 7. (2)(x)  (2)(3y)  (2)(2z). 1  8. Sample answer: Yes. Sample answer: Distance 13. 1 10. 200 6.. 42  2n 3. C: It is a pentagon.  1  0 (Mult. 20
55 4 –5 25 4 –2 18 7 –1 12 11 2– 9. 100 5 0 the vertical scale does not have tick-marks at same-sized intervals. Identity) 2x  6y  4z 15 Age Group 3 2 12.) 14. newspapers sold 24. 3  30a  33an 10 22. year. 25. No. conditional statements. graphs of functions. or no solution is given • Shows little or no understanding of most of the concepts of translating between verbal and algebraic expressions. • Written explanations are exemplary. 1 Nearly Unsatisfactory A correct solution with no supporting evidence or explanation • Final computation is correct. © Glencoe/McGraw-Hill A34 Glencoe Algebra 1 . • Uses appropriate strategies to solve problems. conditional statements. • Computations are mostly correct. • Graphs are mostly accurate. • Uses appropriate strategies to solve problems. and analyzing data in statistical graphs. open sentence equations. algebraic properties. • Computations are incorrect. • Written explanations are unsatisfactory. • Graphs may be accurate but lack detail or explanation. • Written explanations are satisfactory. and analyzing data in statistical graphs. accurate explanations • Shows thorough understanding of the concepts of translating between verbal and algebraic expressions. • Graphs are inaccurate or inappropriate. algebraic properties. • Graphs are accurate and appropriate. • Satisfies minimal requirements of some of the problems. and analyzing data in statistical graphs. • Written explanations are effective. • Satisfies all requirements of problems.Chapter 1 Assessment Answer Key Page 67. open sentence equations. 3 Satisfactory A generally correct solution. • Graphs are mostly accurate and appropriate. • Satisfies the requirements of most of the problems. • No written explanations or work is shown to substantiate the final computation. 2 Nearly Satisfactory A partially correct interpretation and/or solution to the problem • Shows an understanding of most of the concepts of translating between verbal and algebraic expressions. • Goes beyond requirements of some or all problems. conditional statements. and analyzing data in statistical graphs. • Does not satisfy requirements of problems. algebraic properties. • Computations are correct. algebraic properties. Open-Ended Assessment Scoring Rubric Score General Description Specific Criteria 4 Superior A correct solution that is supported by welldeveloped. graphs of functions. • Does not use appropriate strategies to solve problems. graphs of functions. 0 Unsatisfactory An incorrect solution indicating no mathematical understanding of the concept or task. open sentence equations. • No answer may be given. open sentence equations. conditional statements. • Computations are mostly correct. • May not use appropriate strategies to solve problems. graphs of functions. but may contain minor flaws in reasoning or computation • Shows an understanding of the concepts of translating between verbal and algebraic expressions. Since 23 is the sum of 20 and 3. yet the conclusion is false. then give a specific case in which the hypothesis is true. The student should explain that the Commutative Property and Associative Property allows the terms in the expression 18
33
82
67 to be moved and regrouped so that sums of consecutive terms are multiples of 10. A35 Glencoe Algebra 1 Answers 3a. then I will buy a sedan. the Multiplicative Property of Zero. and write the consequence in place of the blank in the statement If I do well in school. He jogs twice around the track. incorrect data being compared. Sample answer: 1
0  1. then rides his bike straight home. The student should write an equation that represents the Additive Identity Property. The student should provide any logical consequence to doing well in school. the Multiplicative Identity Property. Additive Identity Property . the following sample answers may be used as guidance in evaluating open-ended assessment items. The solution set is the set of values for the variable in an open sentence that makes the open sentence true. The student should also name the property that is illustrated. Thus. and tick marks not being the same distance apart or having different sized intervals. 9% Homework 13% Extra Curricular Activities 32% Sleep 17% Other 29% School 6b. then ________. Label the vertical axis as distance and the horizontal axis as time. two times x plus 1 4a. He rides to his high school which is a bit closer to his house. graphs constructed to make one set of data appear greater than another set. and 7 and 3. numbers being omitted on an axis but no break shown. I bought a station wagon. 2. The boy rides his bike to the post office to drop off a letter. 3c. 1b. Sample answer: A set of data that describes what percent of your day you use for different activities. 1a. Sample answer: the quotient of x x1 minus 1 and 2. The student should write a conditional statement in if-then form. Ways in which a bar graph can be misleading include: graphs being mislabeled. The student should explain that a replacement set is a set of possible values for the variable in an open sentence.Chapter 1 Assessment Answer Key Page 67. the Distributive Property allows the product of 7 and 23 to be found by calculating the sum of the products of 7 and 20. Sample answer: If I buy a car. Open-Ended Assessment Sample Answers In addition to the scoring rubric found on page A34. or the Multiplicative Inverse Property. after the first step of addition the remaining sums are easier to accomplish. Sample answer: 2x
1. 3b. Sample answer: The distance a boy is from his home as a function of time.   2 4b. 5. 18
33
82
67  18
82
33
67 Commutative (
)  (18
82)
(33
67) Associative (
)  100
100 Addition  200 Addition © Glencoe/McGraw-Hill 6a. 490 2. simplified 1. 8 7. then the dog will have a bath. 1960 and 1970 5. Sample answer: A replacement set is a set of numbers from which replacements for a variable may be chosen. 3  2(3  2) (Substitution) 3  2  3 (Substitution) 3 2 1 (Mult. variable Quiz (Lessons 1-1 through 1-3) Page 69 1. 12 is divisible by 2 C 5. 3x 3 3.00 0. © Glencoe/McGraw-Hill A36 Glencoe Algebra 1 . 1. range Quiz (Lessons 1-8 and 1-9) Page 70 11. 686 4. then B. Multiplicative Property of Zero. equation 3. domain 8. Cost ($) A conditional statement is a statement of the form If A. 4. the data does not represent a whole set.50 Cost (dollars) Quiz (Lessons 1-4 and 1-5) Page 69 1. 84  6 2. power 2. 9x 2 5.8 h 4. {3. inequality 10. 9. Inverse) 3. 1. If the dog is dirty. the product of 3 and n squared plus 1 sentence 5. Sample answer: 12.50 0 5 10 Length of call (minutes) 15 length of call. No. 11 10. 7 9. 35 30 25 20 15 10 5 0 1 2 3 4 5 Number of Tickets 3. 4.Chapter 1 Assessment Answer Key Vocabulary Test/Review Page 68 1. 42 8. 0 2 [3  (10  8)] 2. 22x  8 3. H: The dog is dirty. C: The dog will have a bath. 1 6. solving an open 4. Like terms 6. coefficient 7. 1. cost 2. 5. 625 4. function 5. 6} Quiz (Lessons 1–6 and 1–7) Page 70 1. where A and B are statements. A 7. D Part II Sample answer: {0. {0.Chapter 1 Assessment Answer Key Mid-Chapter Test Page 71 Cumulative Review Page 72 Part I 1.) (Mult. Iden. 4. 11n 13. 1} 11. 3. 5. Inv. 18 times p 11. 12 3. Glencoe Algebra 1 . 2x  6 6. 2. 4 12. 6(10)  6(2).04 4. D 136 2. 18 10. 1} 9. (Mult. x squared minus 5 Sample answer: 12. four times m squared plus two 7.) 13. 5} 10. 13b  2b 2 © Glencoe/McGraw-Hill Time 15.5% 16. 22 9. 11y  3 A C B 5. {4. Distance 14. about 2% Sample answer: 10. 1  6 5. A37 Answers 8. 72 14. C 6. 11 8. 1. / .Chapter 1 Assessment Answer Key Standardized Test Practice Page 74 Page 73 1. 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 16. A B C D 19. E F G H 7. A B C D 17. 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 H D © Glencoe/McGraw-Hill A38 Glencoe Algebra 1 . A B C D 5 2 . 11. E F G H 3. / . A B C D 12. 5 6 . 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 15. E F G H 9. . 7 . . / . / . A B C D 18. 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 1 1 8 8 . . . E F G A B C D 6. / . A B C D 2. 7 5 H 5. 13. / . / . A B C D 10. 4. E A F B G C . / . A B C D 8. 14. Documents Similar To Glenco Algebra 1 Chapter 1Skip carouselcarousel previouscarousel nextAlgebra 2Glencoe - Algebra 1Glencoe Algebra, chapter 2Pre AlgebraHonAlg2AnsKeyMath Answers and WbGlencoe Mathematics Algebra IGeometry Home Practice WorkbookChapter 10 Hw Coterminal Angles Glencoe Algebra II glencoe algebra practice wsGlencoe Pre Algebra Study Guide Answer KeyGlen McGrow math worksheetsPre Algebra Glencoe Workbok -Answers on Page EndAlgebra I_Solutions Manualalgebra 8-1studyguideWord Problem Practicea2c1rmGlencoe Math Practice GoodMaths Word Problems and SolutionsPre-Algebra Homework BookAlgebra Word ProblemsAlg2 Homeworkalg2sgialg1snbseGlencoe Algebra2Algebra 2Beginning Algebra6th Grade Math WorkbookMath Word Problems and SolutionsAlgebra 1Footer MenuBack To TopAboutAbout ScribdPressOur blogJoin our team!Contact UsJoin todayInvite FriendsGiftsLegalTermsPrivacyCopyrightSupportHelp / FAQAccessibilityPurchase helpAdChoicesPublishersSocial MediaCopyright © 2018 Scribd Inc. .Browse Books.Site Directory.Site Language: English中文EspañolالعربيةPortuguês日本語DeutschFrançaisTurkceРусский языкTiếng việtJęzyk polskiBahasa indonesiaSign up to vote on this titleUsefulNot usefulMaster Your Semester with Scribd & The New York TimesSpecial offer for students: Only $4.99/month.Master Your Semester with a Special Offer from Scribd & The New York TimesRead Free for 30 DaysCancel anytime.Read Free for 30 DaysYou're Reading a Free PreviewDownloadClose DialogAre you sure?This action might not be possible to undo. Are you sure you want to continue?CANCELOK