Chapter 13 Resource Masters
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1 Chapter 13 Resource Masters
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3 Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Stud Guide and Intervention Workbook Stud Guide and Intervention Workbook (Spanish) Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) Answers for Workbooks The answers for Chapter 13 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Spanish Assessment Masters Spanish versions of forms A and C of the Chapter 13 Test are available in the Pre-Algebra Spanish Assessment Masters ( ). Copright b 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 onl for classroom use; be provided to students, teacher, and families without charge; and be used solel in conjunction with Glencoe Pre-Algebra. An other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 77 rion Place Columbus, H 30 ISBN: Pre-Algebra Chapter 13 Resource Masters
4 CNTENTS Vocabular Builder...vii Lesson 13-1 Stud Guide and Intervention Skills Practice...73 Practice Reading to Learn Mathematics...73 Enrichment Lesson 13- Stud Guide and Intervention...73 Skills Practice Practice...70 Reading to Learn Mathematics...71 Enrichment...7 Lesson 13-3 Stud Guide and Intervention...73 Skills Practice...7 Practice...75 Reading to Learn Mathematics...7 Enrichment...77 Lesson 13- Stud Guide and Intervention...7 Skills Practice...79 Practice Reading to Learn Mathematics Enrichment...75 Lesson 13- Stud Guide and Intervention...75 Skills Practice Practice...70 Reading to Learn Mathematics...71 Enrichment...7 Chapter 13 Assessment Chapter 13 Test, Form Chapter 13 Test, Form A Chapter 13 Test, Form B Chapter 13 Test, Form C Chapter 13 Test, Form D Chapter 13 Test, Form Chapter 13 pen-ended Assessment Chapter 13 Vocabular Test/Review...77 Chapter 13 Quizzes 1 & Chapter 13 Quizzes 3 &...77 Chapter 13 Mid-Chapter Test Chapter 13 Cumulative Review...70 Chapter 13 Standardized Test Practice Standardized Test Practice Student Recording Sheet...A1 ANSWERS...A A3 Lesson 13-5 Stud Guide and Intervention Skills Practice...75 Practice Reading to Learn Mathematics...75 Enrichment iii
5 Teacher s Guide to Using the Chapter 13 Resource Masters The Fast File Chapter Resource sstem allows ou to convenientl file the resources ou use most often. The Chapter 13 Resource Masters includes the core materials needed for Chapter 13. These materials include worksheets, etensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Pre-Algebra TeacherWorks CD-RM. Vocabular Builder Pages vii-viii include a student stud tool that presents up to twent of the ke vocabular terms from the chapter. Students are to record definitions and/or eamples for each term. You ma suggest that students highlight or star the terms with which the are not familiar. When to Use Give these pages to students before beginning Lesson Encourage them to add these pages to their Pre-Algebra Stud Notebook. Remind them to add definitions and eamples as the complete each lesson. Stud Guide and Intervention Each lesson in Pre-Algebra addresses one or two objectives. There is one Stud Guide and Intervention master for each lesson. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Skills Practice There is one master for each lesson. These provide computational practice at a basic level. When to Use These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement. Practice There is one master for each lesson. These problems more closel follow the structure of the Practice and Appl section of the Student Edition eercises. These eercises are of average difficult. When to Use These provide additional practice options or ma be used as homework for second da teaching of the lesson. Reading to Learn Mathematics ne master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the contet of and relationships among terms in the lesson. Finall, students are asked to summarize what the have learned using various representation techniques. When to Use This master can be used as a stud tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students. Enrichment There is one etension master for each lesson. These activities ma etend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students perspectives on the mathematics the are learning. These are not written eclusivel for honors students, but are accessible for use with all levels of students. When to Use These ma be used as etra credit, short-term projects, or as activities for das when class periods are shortened. iv
6 Assessment ptions The assessment masters in the Chapter 13 Resource Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Chapter Assessment Chapter Tests Form 1 contains multiple-choice questions and is intended for use with basic level students. Forms A and B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Forms C and D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with aes are provided for questions assessing graphing skills. Form 3 is an advanced level test with free-response questions. Grids without aes are provided for questions assessing graphing skills. All of the above tests include a freeresponse Bonus question. The pen-ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. A Vocabular Test, suitable for all students, includes a list of the vocabular words in the chapter and ten questions assessing students knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet. Intermediate Assessment Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and free-response questions. Continuing Assessment The Cumulative Review provides students an opportunit to reinforce and retain skills as the proceed through their stud of Pre-Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which ma appear on the standardized tests that the ma encounter. This practice includes multiplechoice, grid-in, and open-ended questions. Bubble-in and grid-in answer sections are provided on the master. Answers Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages This improves students familiarit with the answer formats the ma encounter in test taking. The answers for the lesson-b-lesson masters are provided as reduced pages with answers appearing in red. Full-size answer kes are provided for the assessment masters in this booklet. v
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8 13 Reading to Learn Mathematics Vocabular Builder This is an alphabetical list of ke vocabular terms ou will learn in Chapter 13. As ou stud this chapter, complete each term s definition or description. Remember to add the page number where ou found the term. Add these pages to our Pre-Algebra Stud Notebook to review vocabular at the end of the chapter. Vocabular Term Found on Page Definition/Description/Eample Vocabular Builder binomial b-nh-mee-uhl cubic function KY-bihk degree vii
9 13 Reading to Learn Mathematics Vocabular Builder (continued) Vocabular Term nonlinear function Found on Page Definition/Description/Eample polnomial PAHL-uh-NH-mee-uhl quadratic function kwah-drat-ihk trinomial tr-nh-mee-uhl viii
10 13-1 Stud Guide and Intervention Polnomials Polnomials are classified according to the number of terms the have. A monomial has one term, a binomial has two terms, and a trinomial has three terms. The eponent of a variable in a monomial must be a whole number, and the variable cannot be in the denominator or under a radical sign. Eample 1 Determine whether each epression is a polnomial. If it is, classif it as a monomial, binomial, or trinomial. a. 3 The epression is not a polnomial because 3 has a variable in the denominator. b. 3 a a 3 5a The epression is a polnomial with three terms, so it is a trinomial. A polnomial also has a degree. The degree of a polnomial is the same as that of the term with the greatest degree. The degree of a term is the sum of the eponents of its variables. Lesson 13-1 Eample Find the degree of each polnomial. a. 3 1 The greatest degree is, so the degree of the trinomial is. b. 10b c bc c 10b c has degree 1 or 3. bc has degree 1 1 or. c has degree. The greatest degree is 3, so the trinomial has degree 3. Eercises Determine whether each epression is a polnomial. If it is, classif it as a monomial, binomial, or trinomial. 1. 7q r 10. r 3. es; trinomial no es; binomial v w. a 5 b c es; monomial es; binomial es; trinomial Find the degree of each polnomial h p 3 p mn 5 mn m 1. Glencoe/McGraw-Hill 733 Glencoe Pre-Algebra
11 13-1 Skills Practice Polnomials Determine whether each epression is a polnomial. If it is, classif it as a monomial, binomial, or trinomial. 1. 5g. z es; monomial es; trinomial no. r 9r 5. d 1. a 3 b a es; binomial es; binomial es; binomial 7. n. 17 c 9. a b 3 es; monomial no es; trinomial 10. m m a b c no es; trinomial es; trinomial h 15. u 5 u 3 u es; monomial es; binomial es; trinomial a 1 1 a 3 es; trinomial es; binomial no g 5 h es; monomial es; binomial es; monomial Find the degree of each polnomial ab. b c 3 c c 1. mn z k c de 3 c 5 d 3. a a k 3 3k b g abc ab 5c bc g h 5 gh Glencoe/McGraw-Hill 73 Glencoe Pre-Algebra
12 13-1 Practice Polnomials Determine whether each epression is a polnomial. If it is, classif it as a monomial, binomial, or trinomial. 1. 3n. v 9v 3. g h jk es; monomial es; binomial es; trinomial. b b 5. m 10. a b 9 no es; binomial es; binomial 7. 1 s. q 9. h h 1 no es; monomial es; trinomial 10. m n p es; trinomial es; trinomial no 13. 5w 7 t 1. 1 qr 15. p p p es; monomial es; binomial es; trinomial v k 5 es; trinomial es; binomial es; binomial c 5 c g h 7 es; monomial no es; monomial Lesson 13-1 Find the degree of each polnomial c c 5 c 3 c 9. ab 3 7. z r t t 3. 5a 3 a c c b 5 b k cde c e 3. wz w 5 z 39. g h gh METERLGY Summer simmer inde measures the discomfort level due to temperature and humidit. Meteorologists calculate this value b using a polnomial similar to The variable is the temperature in F and is the relative humidit epressed as a whole number. What is the degree of the polnomial? Glencoe/McGraw-Hill 735 Glencoe Pre-Algebra
13 13-1 Reading to Learn Mathematics Polnomials Pre-Activit How are polnomials used to approimate real-world data? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. How man terms are in the epression for the heat inde? 9 b. What separates the terms of the epression? plus and minus signs Reading the Lesson 1. See students work. Write a definition and give an eample of each new vocabular word. Vocabular Definition Eample 1. polnomial. binomial 3. trinomial. degree Helping You Remember 5. Notice that the words binomial, trinomial, and polnomial contain the same root nomial, but have different prefies. a. Find the definition of the prefi bi- in a dictionar. Write the definition. Eplain how it can help ou remember the meaning of binomial. Two; a binomial contains two terms. b. Find the definition of the prefi tri- in a dictionar. Write the definition. Eplain how it can help ou remember the meaning of trinomial. Three; a trinomial contains three terms. c. Find the definition of the prefi pol- in a dictionar. Write the definition. Eplain how it can help ou remember the meaning of polnomial. Man; a polnomial contains man terms. Glencoe/McGraw-Hill 73 Glencoe Pre-Algebra
14 13-1 Enrichment A Cross-Number Puzzle Use the clues at the bottom of the page to complete the puzzle. Write one digit in each bo. A B C D E F G H I J M K N L Lesson 13-1 P Q R S T U V W Across A for 5 B 3 for and 1 C ( 50) ( 15) for 0 E for 10 and 5 G for 3 and 7 I 10w 5 for w and 1 K 3 5 for 10 L ( ) (10 ) for M 3 1 for for 5 and Q ( ) ( 3) for 7 T ( 7) ( ) for 3 U for and V 7 1 for 10 W w w 7 for w 9 Down A ( 1) ( 3) for 5 B 7 for 1 D for 7 and 1 F 5(7w 3w) for w 10 H (z z 1) (z z ) for z J 0 for 10 and 10 K w w 3 for w L (3 0) (5 3) for 1 M 11 for 5 N for 10 and P ( 5) ( 11) for 3 R 5 10 for 1 S ( 75) + (10 ) for Glencoe/McGraw-Hill 737 Glencoe Pre-Algebra
15 13- Stud Guide and Intervention Adding Polnomials Add polnomials b combining like terms, which are monomials that contain the same variables to the same power. Eample Method 1 Add verticall. 7 1 ( ) Eercises Find each sum. Find ( 7 1) ( 5). Method Add horizontall. ( 7 1) ( 5) = ( ) 7 (1 5) = ( ) 1 3. w w + 3 ( ) w 5 5w w. d ( ) d 1 d 9. 5a a ( ) a 5 5a a 5 5. ( m 3) (7m 1). (9 3 1) ( 1) m (k k) (k 1). (5a ab) ( ab b ) k 1 5a 5ab b 9. (c 7) + (c 3c ) 10. ( ) ( ) 5c 3c (1h ) (h h ) 1. (10 5) ( 10 ) h h ( 1) ( 3 ) 1. ( p 3 ) (p p 3) 7 5 p 3 p p (3g 3g 5) (5g 3) 1. (5r ) ( r r 7) g 3g r r 1 Glencoe/McGraw-Hill 73 Glencoe Pre-Algebra
16 13- Skills Practice Adding Polnomials Find each sum. 1. 5q 7 ( ) q 7q 5 3. r 3r ( ) r r 1 r r 1 5. w 3w 3 ( ) w w 1 w w. 7f 10 ( ) f 3 5f 7. 9n 3n ( ) 3n 5 9n 5. c c ( ) c c 1 9c 3c 5 7. p p ( ) p p 5 p 3 9. m m 1 ( )m m 3 m m. 3v v ( ) v 7 3v v d 7d ( ) 5d d 10d d 11. (r 3) ( r r 1) 1. ( g g 5) (5g g 3) r r g Lesson ( m 9) (3m 3) 1. ( 7) (3 5) m (k k) (7k k ) 1. (a 3ab) (ab b ) k k a ab b 17. (5c 7) (3c c ) 1. ( ) ( ) 3c c ( h 3h ) (h h 3) 0. ( 1) ( 9 ) 3h h (g g 3) (g 5g). (b b 1) (b b 1) g 3g 3 b 3. ( 7 9) ( ). (7p 3 ) (p 5p 1) p 3 p 5p 3 Glencoe/McGraw-Hill 739 Glencoe Pre-Algebra
17 13- Practice Adding Polnomials Find each sum. 1. q 3 ( ) q 1q 1 3. r 11r ( ) 5r 3r 7 9r r 7 5. w w 7 ( )w 3w 9 1w 5w 7. 5p p ( ) 5p p m m 3 ( )m 9m 13m 15m 5. 9f 3 ( ) f 15 f 1. n 3n ( ) 3n 10 n 10. c 3c 15 ( ) 3c 3c 11 11c. 7v v ( ) 7v v 5 1v 3v d d 3 ( ) d d 3 d 9d 11. (r 9) ( r r 10) 1. (g 3g ) (g g 1) 3r r 19 7g 3g ( m 10) (5m 3) 1. ( 7) ( 5) 3m (3k 9k) (k k ) 1. (a 3ab) (ab b ) k 7k a ab b 17. (c ) (c c ) 1. (5 3) ( 9 ) c ( 3 5) ( 3) 0. ( 5p p 7) (p ) p p 9 1. (3ab a 1) (a ab 3). (rs 3 r) (5rs 3 7) 3ab a a ab 11rs 3 r 7 3. GEMETRY The lengths of the sides of a triangle are ( 5), (7 1), and. Find the perimeter of the triangle. Glencoe/McGraw-Hill 70 Glencoe Pre-Algebra
18 13- Reading to Learn Mathematics Adding Polnomials Pre-Activit How can ou use algebra tiles to add polnomials? Do the activit at the top of page 7 in our tetbook. Write our answers below. a. Write the polnomial for the tiles that remain. b. Find the sum of and 7 3 b using algebra tiles. 5 c. Compare and contrast finding the sums of polnomials with finding the sum of integers. The concept of the zero pairs is the same, but there are tiles that represent different terms in polnomials. Reading the Lesson 1. Draw a model that shows ( ) ( 3). Write the polnomial that shows the sum. 3 1 Lesson 13-. Show how to find the sum (5 ) ( ) both verticall and horizontall. Verticall Horizontall 5 (5 ) ( ) ( ) (5 ) ( ) 9 9 Helping You Remember 3. You have learned that ou can combine like terms. n the left below, write three pairs of monomials that have like terms. n the right below, write three pairs of monomials that have unlike terms. Eplain our answers. Sample answers are given. Like Terms Unlike Terms 1. 3a and 1a 1. and. b c and b c. 3mn and 3m n 3. 3 and 3 3. ab 3 and 5ab Glencoe/McGraw-Hill 71 Glencoe Pre-Algebra
19 13- Enrichment Adding Polnomials Can ou make a sentence using these words? A FRUIT TIME LIKE AN BUT FLIES BANANA ARRW LIKE FLIES Add the polnomials. Then find the word in the table at the right that corresponds to the sum. Read the words in order down the column to discover the hidden saing. Word 1. ( 3 ) (5 ) 11 TIME. ( 3 3 ) (5 ) 3 3 FLIES 3. ( ) ( ) LIKE. ( 3 ) (5 3 ) 3 AN 5. ( ) ( ) ARRW. (5 ) ( ) 5 BUT 7. ( ) ( ) FRUIT 3. (3 3 ) ( 3 ) FLIES A FRUIT TIME LIKE AN BUT FLIES BANANA ARRW LIKE FLIES 9. ( ) 3 3 LIKE 10. ( 3 3 ) ( 3 3 ) 3 A BANANA Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
20 13-3 Stud Guide and Intervention Subtracting Polnomials To subtract polnomials, subtract like terms. Eample Method 1 Eercises Subtract verticall. 3 ( ) Find each difference. Find ( 3 ) ( 1). Method Add the additive inverse of 1, which is ( 1)( 1) or 1. ( 3 ) ( 1) ( 3 ) ( 1) ( ) (3) ( 1) c 7 ( ) 3c 3 c 3. 9k k 5 ( ) k 5 k k 10. m 5 ( ) m 1 10m. 3z z ( ) 3z 5 3z z 5 5. ( r 3) (7r ). (f 7f 3) (f ) 13r 1 f 9f 7 7. (5n n) (3n 9). (a 5ab) ( ab 3b ) 5n 5n 9 a 7ab 3b 9. (g ) (5g g ) 10. ( 3) ( 3) g g Lesson (n 1) (n n 9) 1. (h h 1) (3h 7h ) n 1 h 5h ( 1) ( 1) 1. (p 5p 1) (p ) p 7p (q q) (q 3) 1. (v ) (7v v 5) 3q q 3 v v (u u ) (5u ) 1. (9b ) ( b b 9) u u 10b b 7 Glencoe/McGraw-Hill 73 Glencoe Pre-Algebra
21 13-3 Skills Practice Subtracting Polnomials Find each difference ( ) 1 3. w w 1 ( ) w 3w w w d d ( ) d 3d d d 7. m 5m 3 ( ) 5m m 3 3m m 9. q q ( ) q 7q 9 q 9q 7. k ( ) k 9 k 17. c 7c ( ) c c 1 c c 3. 7n 3n ( ) n 3n 1 n 1. d 3d ( ) d d 1 d v v ( ) v v 7v 9v 11. (r 10r 3) ( r r 1) 1. (7k k ) (k 3k 3) r 9r 5k k (a 9) (a ) 1. ( 11 7) ( 3 ) a a (k 3k) (k 7k 1) 1. (5a ab) (ab 3b ) k k 1 5a 3b 17. (5u 7) (3u u ) 1. (m mn) (3mn n ) u u 13 m mn n 19. (h 3h ) (h h 3) 0. ( 1) ( 9 ) 5h (g 3g 3) (g g 5). (b b 1) (b b 1) 5g g b 3. (a 9a 10) (a a ). (r 7r) (3r r 7) a r 9r 7 Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
22 13-3 Practice Subtracting Polnomials Find each difference ( ) j j ( ) j 9 j j 7j 5. d d ( ) d 3d 7d m m 13 ( ) 7m m 3 m m 1 9. q 3q ( ) 3q q 9q 7q. k 3 ( ) 7k 5k 9. c 5c 3 ( ) c 5c 1 c 10c. n 3n 10 ( ) n 3n 3n 1. d 3d ( ) d 3d v v ( ) v 9v 3 v v (n n ) ( n 3n 1) 1. (3k 9k) (k 1) n n 5k 9k (k 7) (k 11) 1. (9 ) (3 ) k k 15. (k 1) (k k 9) 1. (k kb) (5kb b ) k 3 k kb b Lesson (3u 9) (u 1u ) 1. (5m mn) (mn n ) u 1u 11 5m mn n 19. (h h 5) (h 3h 7) 0. ( ) ( ) 11h (g 3g ) (g g ). (b 3 b ab) (b 3 3b 5) 5g g b ab 5 3. PLS A swimming pool is (w 1) feet long and (w 1) feet wide. How much longer is the length than the width? w w ft Glencoe/McGraw-Hill 75 Glencoe Pre-Algebra
23 13-3 Reading to Learn Mathematics Subtracting Polnomials Pre-Activit How is subtracting polnomials similar to subtracting measurements? Do the activit at the top of page 7 in our tetbook. Write our answers below. a. What is the difference in degrees and the difference in minutes between the two stations? degrees,.1 minutes b. Eplain how ou can find the difference in latitude between an two locations, given the degrees and minutes. Subtract the degrees and subtract the minutes. c. The longitude of Station 1 is and the longitude of Station 5 is. Find the difference in longitude between the two stations. 9 3 Reading the Lesson 1. Show how to find the difference (3 ) ( 7) b aligning like terms and b adding the additive inverse. Like Terms Additive Inverse 3 3 ( ) 7 ( ) Which method do ou prefer? Wh? Answers will var. Helping You Remember 3. a. You have learned to subtract polnomials b adding the additive inverse. Look up inverse in the dictionar. What is its definition? How does this help ou remember how to find the additive inverse? pposite; ou change each sign to the opposite and then add instead of subtract. b. Write the additive inverses of the polnomials in the table below. Polnomial Additive Inverse Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
24 13-3 Enrichment Polnomials with Fractional Coefficients Polnomials ma have fractional coefficients in some or all of the terms. Computation with these tpes of polnomials is done in the same wa as with whole-number coefficients. Add or subtract. Write all coefficients as fractions. 1. Add 3 5 and From ,take Add 3 3, 7 7, and Subtract from Add to Add and Lesson From 1 3 3,take Subtract 1 1 from Add and Subtract 3 1 from Glencoe/McGraw-Hill 77 Glencoe Pre-Algebra
25 13- Stud Guide and Intervention Multipling a Polnomial b a Monomial The Distributive Propert can be used to multipl a polnomial b a monomial. Eample 1 Find 7( ). 7( ) 7() 7() 5 Eample Eercises Find ( 5 )( ). ( 5 )( ) ( ) 5( ) ( ) 3 10 Find each product. 1. 5(7 ). (3h ) 3. 9(q ) h 9q 7. (d ) 5. (g 5)( ). 7( 7) d 1 g (n 3n 9). (a ab b )5 9. r(r 9) n n 1 5a 10ab 5b r 9r 10. (b )( b) 11. (3 ) 1. (k 9)(k ) b 3 b 3 k 3 9k 13. m(m 1) 1. p(7p ) 15. ( 3h)( h) m m 7p p 3h h 1. w(w w 3) 17. ab(a b) 1. (7 ) w 3 w 3w a b ab (m mn n)m 0. (5 1) 1. 10u(u 5) m 3 m n mn 10 10u 50u. (5r r)( 3r) 3. z(z 7). 5b (b ) 15r 3 r 1z 5z 30b 3 10b 5. p (p 3p). (5v v )( v) 7. 3 (3 ) p 1p 3 10v 3 v v m(m n) 9. (gh 3h)( 3gh) 30. 5a(a 3ab b) m 1mn g h 9gh 10a 15a b 5ab Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
26 13- Skills Practice Multipling a Polnomial b a Monomial Find each product. 1. (k 7). (5h 3)3 3. 9(q 7) k 15h 9 1q 3. (v 1)( ) 5. (5h ). 3(1 ) 3v 0h (9d 3). 5(5n 9) 9. ( ) 3d 1 5n (5 3) 11. ( 9)9 1. 7(c c 5) c 5c g(g 5) 1. b(9b ) 15. ( 7) g 5g 9b b 7 1. (j 1)( j) 17. c(c ) 1. h(h ) j j c c h h 19. (k )( k) 0. p(3p ) 1. a(a ) k k 3p p a a. r(r 7r) 3. ( 1). ab(3ab a) r 3 7r 3 3a b a b 5. ( 3 ). (gh h)( g) 7. ( ) 3 g h gh 3. v(3v 9) 9. (u )( 5u) 30. b(b ) 1v 5v 5u 0u b b 31. 7d(5d 9) 3. (w )w 33. a(7a ) 35d 3d w w 7a a 3. ( )( ) 35. s(s 1) 3. m(m 7) 3 s s m 7m 37. k (k 3) 3. c(7c 3c ) 39. 7mn(m mn n) k 3 3k 7c 3 3c c 7m n 1m n mn Lesson a(a ab b) 1. ( )( ). u(7u uv v ) a a b ab 3 5u 3 1u v 3uv Glencoe/McGraw-Hill 79 Glencoe Pre-Algebra
27 13- Practice Multipling a Polnomial b a Monomial Find each product. 1. 5(3k ). (3h ) 3. (q ) 15k 0 h 1 q. (3v 5)( 7) 5. 11(d 7). (1c ) 1v 35 d 77 9c 7. (5g 10)( 5). (5p 10) 9. 9(3f f 1) 5g 50 10p 0 7f 1f (w 5) 11. (r 3 3r)( ) 1. (3 7) 0w 1.5 3r 3 r n(7n 3) 1. (u 15)( u) 15. h(h ) 7n 3n u 15u h h 1. ( 3)( ) 17. a(a ) 1. (5p 15)( p) 3 a a 5p 15p 19. d( 5d 1) 0. g(1.g 10) 1. m(0.9m 0.5) 5d d 1.g 10g 0.9m 3 0.5m. (q 3 5q q)( q) 3. k 3 (7k k ). ab(10a b 3a) q 5q 3 q 7k 7 k 5 k 3 10a 3 b 3a b 5. (5 ). n( m 1mn ) 7. (gh g h)( g ) n mn 1mn 3 g 3 h g g h. (0q )( q) 9. 1k(k 5) 30. (9p 7)( 3p ) 0q q k 70k 7p 3 1p 31. (0.c 1)( 1.5c ) 3..5n(n ) 33. ( 10) 0.3c 3 1.5c n 3 5n h (h 3 h 7h ) 35. ( 3 9)( ) 3. gh(g gh 3h ) 10h 5 5h 35h 3 0h 3 1 g 3 h g h 1gh a(a 5ab a) 3. ( 3 )( 7) 39. 5c (cd d 1) 0a 3 50a b 0a c 3 d 5c d 5c 0. Find the area of a porch that is 3 feet wide and 9 feet long. 1 7 ft Glencoe/McGraw-Hill 750 Glencoe Pre-Algebra
28 13- Reading to Learn Mathematics Multipling a Polnomial b a Monomial Pre-Activit How is the Distributive Propert used to multipl a polnomial b a monomial? Do the activit at the top of page 3 in our tetbook. Write our answers below. a. Write an epression that represents the area of the rectangular region outlined on the photo. w (w 5) b. Recall that ( 1) () (1) b the Distributive Propert. Use this propert to simplif the epression ou wrote in part a. w 5w c. The Grande Arche is approimatel w feet deep. Eplain how ou can write a polnomial to represent the volume of the hollowed-out region of the building. Then write the polnomial. Use the Distributive Propert to multipl w 5w b w; w 3 5w. Reading the Lesson 1. Draw a model that shows the product ( ). Write the polnomial that shows the product. See students work.. Eplain the Distributive Propert and give an eample of how it is used to multipl a polnomial b a monomial. Sample answer: Multipl each number inside the parentheses b the number outside the parentheses. (3 ) (3) () Helping You Remember 3. Distribute is a common word in the English language. a. Find the definition of distribute in a dictionar. Write the definition that most closel relates to this lesson. to deliver to members of a group b. Eplain how this definition can help ou remember how to use the Distributive Propert to multipl a polnomial b a monomial. The number outside the parentheses is distributed to each number inside. Lesson 13- Glencoe/McGraw-Hill 751 Glencoe Pre-Algebra
29 13- Enrichment Polnomials and Volume The volume of a rectangular prism can be written as the product of three polnomials. Recall that the volume equals the length times the width times the height. The two prisms at the right represent the cube of and the cube of. Multipl to find the volume of each prism. Write each answer as an algebraic epression ( ) or. 5.. ( ) or ( ) or 3 ( ) or 3 Multipl, then add to find each volume. Write each answer as an algebraic epression ( ) ( ) 3 3 ( ) ( ) or 3 or 3 3 ( ) or Glencoe/McGraw-Hill 75 Glencoe Pre-Algebra
30 13-5 Stud Guide and Intervention Linear and Nonlinear Functions Linear functions have constant rates of change. Their graphs are straight lines and their equations can be written in the form m b. Nonlinear functions do not have constant rates of change and their graphs are not straight lines. Eample 1 Determine whether each equation represents a linear or nonlinear function. a. 9 This is linear because it can be written as 0 9. b. This is nonlinear because the eponent of is not 1, so the equation cannot be written in the form m b. Tables can represent functions. A nonlinear function does not increase or decrease at a constant rate. Eample Determine whether each table represents a linear or nonlinear function. a. As increases b. b, increases 0 7 b. The rate of change is 5 1 constant, so 5 75 this is a linear 5 9 function Eercises As increases b 5, decreases b a greater amount each time. The rate of change is not constant, so this is a nonlinear function. Determine whether each equation or table represents a linear or nonlinear function. Eplain Linear; equation can. Nonlinear; equation cannot be written as 1 3. be written in the form m b ( 1) Nonlinear; equation. 9 5 Linear; equation can be cannot be written in the form m b. written as Linear; rate of 1 1 change is 1 constant. 3 7 Nonlinear; rate of change is not constant. Lesson 13-5 Glencoe/McGraw-Hill 753 Glencoe Pre-Algebra
31 13-5 Skills Practice Linear and Nonlinear Functions Determine whether each graph, equation, or table represents a linear or nonlinear function. Eplain Nonlinear; the graph is a curve.. 1 Linear; equation can be written as Linear; equation can be written as 0. Linear; the graph is a straight line Nonlinear; equation cannot be written in the form m b.. 5 Linear; equation can be written as 5. Nonlinear; the graph is a curve.. Linear; equation can be written as Nonlinear; equation cannot be written in the form m b Nonlinear; equation cannot be written in the form m b Linear; equation can be written as Nonlinear; equation cannot be written in the form m b Linear; rate of change is constant Nonlinear; rate of change is not constant Linear; rate of change is constant. Glencoe/McGraw-Hill 75 Glencoe Pre-Algebra
32 13-5 Practice Linear and Nonlinear Functions Determine whether each graph, equation, or table represents a linear or nonlinear function. Eplain Nonlinear; the graph is a curve Linear; equation can be written as Nonlinear; equation cannot be written in the form m b. Linear; the graph is a straight line Nonlinear; equation cannot be written in the form m b.. Nonlinear; equation cannot be written in the form m b. Linear; the graph is a straight line Linear; equation can be written as Nonlinear; equation cannot be written in the form m b Linear; rate of change is constant Linear; rate of change is constant Nonlinear; rate of change is not constant. 13. GEMETRY The graph shows how the area of a square increases as the perimeter increases. Is this relationship linear or nonlinear? Eplain. Nonlinear; the graph is not a straight line. Area Perimeter Lesson 13-5 Glencoe/McGraw-Hill 755 Glencoe Pre-Algebra
33 13-5 Reading to Learn Mathematics Linear and Nonlinear Functions Pre-Activit How can ou determine whether a function is linear? Do the activit at the top of page 7 in our tetbook. Write our answers below. a. Write an epression to represent the area of the deck. (0 ) or 0 b. Find the area of the deck for widths of,, 10, 1, and 1 feet. 1 ft, 19 ft, 00 ft, 19 ft, 1 ft c. Graph the points whose ordered pairs are (width, area). Do the points fall along a straight line? Eplain. No; the connected points fall along a curve. Area Reading the Lesson 1 3. See students work Width Write a definition and give an eample of each new vocabular phrase. Vocabular Definition Eample 1. nonlinear function. quadratic function 3. cubic function Helping You Remember. You have learned about linear and nonlinear functions. Nonlinear functions include quadratic functions and cubic functions. Below, write three equations that represent each tpe of function given. For the nonlinear functions, include at least one quadratic function and one cubic function. Sample answers are given. Linear Nonlinear Glencoe/McGraw-Hill 75 Glencoe Pre-Algebra
34 13-5 Enrichment David R. Hedgle African-American mathematician David R. Hedgle, Jr. (1937 ) solved one of the most difficult problems in the field of computer graphics how to program a computer to show an three-dimensional object from a given viewpoint just as the ee would see it. Hedgle s solution helped researchers in aircraft eperimentation. Hedgle received an M.S. in Mathematics from California State Universit in 1970 and a Ph.D. in Computer Science from Somerset Universit in England in 19. Hedgle has received numerous national achievement awards. Polnomials in three variables are needed to describe some three-dimensional objects. Each variable represents one of the three dimensions: height, width, and depth. P 1 : z 10 z 19 P : z 3 5z 1. Add the polnomials P 1 and P.. Subtract the polnomials, P 1 from P z 7z 1 z 1 7 3z 17 If the polnomials above were each set equal to zero, the would form equations describing two different spheres in three-dimensional space, or 3-space. The coordinate plane ou studied in Chapter represents two-space.you described most lines in that plane b an equation in two variables. Each point on a line could be written as an ordered pair of numbers (, ). Each point on an figure in 3-space can be written as an ordered triple of numbers (,, z). B z 1 D C G 3. What are the values of,, and z for point A in the diagram? 1,, z. Give the ordered triple representing each of the points B through G in the diagram. B (1, 0, ), C(0,, ), D (0, 0, ), E (1,, 0), F (1, 0, 0), G (0, 0, 0) F E A (1,, ) Lesson 13-5 Glencoe/McGraw-Hill 757 Glencoe Pre-Algebra
35 13- Stud Guide and Intervention Graphing Quadratic and Cubic Functions To graph a quadratic or cubic function, make a table of values and then plot the points. Eample 1 3 Graph = Eercises Graph each function Glencoe/McGraw-Hill 75 Glencoe Pre-Algebra
36 13- Skills Practice Graphing Quadratic and Cubic Functions Graph each function Lesson Glencoe/McGraw-Hill 759 Glencoe Pre-Algebra
37 13- Practice Graphing Quadratic and Cubic Functions Graph each function WINDWS A window maker has 5 feet of wire to frame a window. ne side of the window is feet and the other side is 9 feet. a. Write an equation to represent the area A of the window. A 9 b. Graph the equation ou wrote in part a A 10 1 c. If the area of the window is 1 square feet, what are the two possible values of? 3 and Glencoe/McGraw-Hill 70 Glencoe Pre-Algebra
38 13- Reading to Learn Mathematics Graphing Quadratic and Cubic Functions Pre-Activit How are functions, formulas, tables, and graphs related? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. The volume of cube V equals the cube of the length of an edge a. Write a formula to represent the volume of a cube as a function of edge length. V a 3 b. Graph the volume as a function of edge length. (Hint: Use values of a like 0, 0.5, 1, 1.5,, and so on.) Lesson 13- V Volume Edge Length a Reading the Lesson 1. Write a quadratic function. Eplain what makes it a quadratic function and what its graph would look like. Sample answer: 5; This is a quadratic function because it has the form a b c, a 0. It is a parabola.. Write a cubic function. Eplain what makes it a cubic function and what its graph would look like. Sample answer: 3 3 ; This is a cubic function because it has the form a 3 b c, a 0. It is similar in appearance to 3,onl shifted up two units and increasing more rapidl. Helping You Remember 3. You have learned to graph quadratic and cubic functions. Make a list of the steps ou use to graph the two functions. Make a table of values. Plot the ordered pairs. Connect the points with a curve. Glencoe/McGraw-Hill 71 Glencoe Pre-Algebra
39 13- Enrichment Translating Quadratic Graphs When a figure is moved to a new position without undergoing an rotation, then the figure is said to have been translated to the new position. The graph of a quadratic equation in the form ( b) c is a translation of the graph of. Start with a graph of. Slide to the right units. ( ) Then slide up 3 units. ( ) The following equations are in the form c. Graph each equation. 1. = + 1. = + 3. = The following equations are in the form ( b).graph each equation.. = ( 1) 5. = ( 3). = ( + ) Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
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