Chapter 6 Resource Masters

Transcription

1 Chapter Resource Masters

2 CNSUMABLE WRKBKS 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) 0-0--X Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) Reading to Learn Mathematics Workbook ANSWERS FR WRKBKS The answers for Chapter of these workbooks can be found in the back of this Chapter Resource Masters booklet. StudentWorks This CD-RM includes the entire Student Edition tet along with the English workbooks listed above. TeacherWorks All of the materials found in this booklet are included for viewing and printing in the Glencoe Algebra TeacherWorks CD-RM. Glencoe/McGraw-Hill 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, teachers, and families without charge; and be used solel in conjunction with Glencoe Algebra. An other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: The McGraw-Hill Companies rion Place Columbus, H 0-0 ISBN: Glencoe Algebra Chapter Resource Masters

3 Contents Vocabular Builder vii Lesson - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Chapter Assessment Chapter Test, Form Chapter Test, Form A Chapter Test, Form B Chapter Test, Form C Chapter Test, Form D Chapter Test, Form Chapter pen-ended Assessment Chapter Vocabular Test/Review Chapter Quizzes & Chapter Quizzes & Chapter Mid-Chapter Test Chapter Cumulative Review Chapter Standardized Test Practice First Semester Test (Ch. ) Standardized Test Practice Student Recording Sheet A ANSWERS A A Lesson - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Glencoe/McGraw-Hill iii Glencoe Algebra

4 Teacher s Guide to Using the Chapter Resource Masters The Fast File Chapter Resource sstem allows ou to convenientl file the resources ou use most often. The Chapter Resource Masters includes the core materials needed for Chapter. 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 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 T USE Give these pages to students before beginning Lesson -. Encourage them to add these pages to their Algebra Stud Notebook. Remind them to add definitions and eamples as the complete each lesson. Stud Guide and Intervention Each lesson in Algebra addresses two objectives. There is one Stud Guide and Intervention master for each objective. WHEN T 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 T 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 T 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 T 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 T USE These ma be used as etra credit, short-term projects, or as activities for das when class periods are shortened. Glencoe/McGraw-Hill iv Glencoe Algebra

5 Assessment ptions The assessment masters in the Chapter Resources Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Chapter Assessment CHAPTER TESTS Form 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 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 Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of algebra concepts in various formats, which ma appear on the standardized tests that the ma encounter. This practice includes multiplechoice, grid-in, and quantitativecomparison questions. Bubble-in and grid-in answer sections are provided on the master. Answers Page A 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. Glencoe/McGraw-Hill v Glencoe Algebra

6 Reading to Learn Mathematics Vocabular Builder This is an alphabetical list of the ke vocabular terms ou will learn in Chapter. As ou stud the chapter, complete each term s definition or description. Remember to add the page number where ou found the term. Add these pages to our Algebra Stud Notebook to review vocabular at the end of the chapter. Vocabular Term Addition Propert of Inequalities Found on Page Definition/Description/Eample Vocabular Builder boundar compound inequalit Division Propert of Inequalities half-plane intersection Multiplication Propert of Inequalities (continued on the net page) Glencoe/McGraw-Hill vii Glencoe Algebra

7 Reading to Learn Mathematics Vocabular Builder (continued) Vocabular Term set-builder notation Found on Page Definition/Description/Eample Subtraction Propert of Inequalities union Glencoe/McGraw-Hill viii Glencoe Algebra

8 - Stud Guide and Intervention Solving Inequalities b Addition and Subtraction Solve Inequalities b Addition Addition can be used to solve inequalities. If an number is added to each side of a true inequalit, the resulting inequalit is also true. Addition Propert of Inequalities For all numbers a, b, and c, if a b, then a c b c, and if a b, then a c b c. The propert is also true when and are replaced with and. Eample Eample Solve. Then graph it on a number line. riginal inequalit Simplif. Add to each side. The solution in set-builder notation is { }. Number line graph: Solve a a. Then graph it on a number line. a a riginal inequalit a a a a Add a to each side. a Simplif. a a is the same as a. The solution in set-builder notation is {a a }. Number line graph: Lesson - 0 Eercises Solve each inequalit. Then check our solution, and graph it on a number line.. t. n. g n.. s Solve each inequalit. Then check our solution... 0.n 0.n 9. k 9k z. b b Define a variable, write an inequalit, and solve each problem. Then check our solution.. A number decreased b is less than.. The difference of two numbers is more than, and one of the numbers is.. Fort is no greater than the difference of a number and. Glencoe/McGraw-Hill Glencoe Algebra

9 - Stud Guide and Intervention (continued) Solving Inequalities b Addition and Subtraction Solve Inequalities b Subtraction Subtraction can be used to solve inequalities. If an number is subtracted from each side of a true inequalit, the resulting inequalit is also true. Subtraction Propert of Inequalities For all numbers a, b, and c, if a b, then a c b c, and if a b, then a c b c. The propert is also true when and are replaced with and. Eample Solve a a. Then graph it on a number line. a a riginal inequalit a a a a Subtract a from each side. a Simplif. a Subtract from each side. a Simplif. The solution is {a a }. Number line graph: Eercises Solve each inequalit. Then check our solution, and graph it on a number line.. t. n. h r r. q q Solve each inequalit. Then check our solution.. p p 0.. r 9. 9k k n n Define a variable, write an inequalit, and solve each problem. Then check our solution.. The sum of a number and is less than.. The sum of two numbers is at most, and one of the number is.. The sum of a number and is greater than or equal to. Glencoe/McGraw-Hill Glencoe Algebra

10 - Skills Practice Solving Inequalities b Addition and Subtraction Match each inequalit with its corresponding graph.. a. 0. b. 0. c. 0. d.. e. 0 0 Lesson - Solve each inequalit. Then check our solution, and graph it on a number line.. d. s 9 0. a 9. w k. 9 b Define a variable, write an inequalit, and solve each problem. Then check our solution.. A number decreased b 0 is greater than.. A number increased b is less than 9.. Seven more than a number is less than or equal to.. Twent less than a number is at least.. A number plus is at most. Glencoe/McGraw-Hill Glencoe Algebra

11 - Practice Solving Inequalities b Addition and Subtraction Match each inequalit with its corresponding graph.. a.. b.. c.. 9 d Solve each inequalit. Then check our solution, and graph it on a number line.. r ( ) n z 0. c Define a variable, write an inequalit, and solve each problem. Then check our solution.. The sum of a number and is no less than.. Twice a number minus is less than three times the number.. Twelve is at most a number decreased b.. Eight plus four times a number is greater than five times the number.. ATMSPHERIC SCIENCE The troposphere etends from the earth s surface to a height of miles, depending on the location and the season. If a plane is fling at an altitude of. miles, and the troposphere is. miles deep in that area, how much higher can the plane go without leaving the troposphere?. EARTH SCIENCE Mature soil is composed of three laers, the uppermost being topsoil. Jamal is planting a bush that needs a hole centimeters deep for the roots. The instructions suggest an additional centimeters depth for a cushion. If Jamal wants to add even more cushion, and the topsoil in his ard is 0 centimeters deep, how much more cushion can he add and still remain in the topsoil laer? Glencoe/McGraw-Hill Glencoe Algebra

12 - Reading to Learn Mathematics Solving Inequalities b Addition and Subtraction Pre-Activit How are inequalities used to describe school sports? Read the introduction to Lesson - at the top of page in our tetbook. Use the information in the graph to write an inequalit statement about participation in two sports. Reading the Lesson Rewrite our inequalit statement to show that 0 schools added both of the sports. Is the statement still true? Write the letter of the graph that matches each inequalit. Lesson -. a.. b.. c.. d Use the chart to write a sentence that could be described b the inequalit n n. Then solve the inequalit. Inequalities less than greater than at most at least fewer than more than no more than no less than less than or equal to greater than or equal to Helping You Remember. Teaching someone else can help ou remember something. Eplain how ou would teach another student who missed class to solve the inequalit. Glencoe/McGraw-Hill Glencoe Algebra

13 - Enrichment Triangle Inequalities Recall that a line segment can be named b the letters of its endpoints. Line segment AB (written as A B ) has points A and B for endpoints. The length of AB is written without the bar as AB. AB BC m A m B The statement on the left above shows that A B is shorter than B C. The statement on the right above shows that the measure of angle A is less than that of angle B. These three inequalities are true for an triangle ABC, no matter how long the sides. A a. AB BC AC b. If AB AC, then m C m B. c. If m C m B, then AB AC. B C Use the three triangle inequalities for these problems.. List the sides of triangle DEF in order of increasing length. D F 0 E. In the figure at the right, which line segment is the shortest? K 0 L J 0 M. Eplain wh the lengths cm, 0 cm, and 0 cm could not be used to make a triangle.. Two sides of a triangle measure in. and in. Between which two values must the third side be?. In triangle XYZ, XY, YZ, and XZ 9. Which is the greatest angle? Which is the least?. List the angles A, C, ABC, and ABD, in order of increasing size. C B D 9 A Glencoe/McGraw-Hill Glencoe Algebra

14 - Stud Guide and Intervention Solving Inequalities b Multiplication and Division Solve Inequalities b Multiplication If each side of an inequalit is multiplied b the same positive number, the resulting inequalit is also true. However, if each side of an inequalit is multiplied b the same negative number, the direction of the inequalit must be reversed for the resulting inequalit to be true. Multiplication Propert of Inequalities For all numbers a, b, and c, with c 0,. if c is positive and a b, then ac bc; if c is positive and a b, then ac bc;. if c is negative and a b, then ac bc; if c is negative and a b, then ac bc. The propert is also true when and are replaced with and. Eample Eample Solve. Solve k. riginal equation k riginal equation ( ) ( ) Multipl each side b ; change to. 9 Simplif. The solution is { 9}. Eercises k Multipl each side b. k 0 Simplif. The solution is {k k 0}. Lesson - Solve each inequalit. Then check our solution. n p... h. 0 m h. n 0. b... 0 g 9p n a Define a variable, write an inequalit, and solve each problem. Then check our solution.. Half of a number is at least.. The opposite of one-third a number is greater than 9.. ne fifth of a number is at most 0. Glencoe/McGraw-Hill 9 Glencoe Algebra

15 - Solve Inequalities b Division If each side of a true inequalit is divided b the same positive number, the resulting inequalit is also true. However, if each side of an inequalit is divided b the same negative number, the direction of the inequalit smbol must be reversed for the resulting inequalit to be true. For all numbers a, b, and c with c 0, Division Propert a b a b. if c is positive and a b, then ; if c is positive and a b, then ; c c c c of Inequalities a b a b. if c is negative and a b, then ; if c is negative and a b, then. c c c c The propert is also true when and are replaced with and. Eample Solve. riginal inequalit Divide each side b and change to. Simplif. The solution is { }. Eercises Stud Guide and Intervention (continued) Solving Inequalities b Multiplication and Division Solve each inequalit. Then check our solution.. g c. m. k. b. 0 n w 9. m 0. 0 p. n.. 0.0h p. 0 0h. n. Define a variable, write an inequalit, and solve each problem. Then check our solution.. Four times a number is no more than 0.. The opposite of three times a number is greater than.. Negative five times a number is at most 00. Glencoe/McGraw-Hill 0 Glencoe Algebra

16 - Skills Practice Solving Inequalities b Multiplication and Division Match each inequalit with its corresponding statement.. n 9 a. Three times a number is at most nine.. n 9 b. ne third of a number is no more than nine.. n 9 c. Negative three times a number is more than nine.. n 9 d. Three times a number is less than nine.. n 9 e. Negative three times a number is at least nine.. n 9 f. ne third of a number is greater than or equal to nine. Solve each inequalit. Then check our solution.. g. w 9. 0b 0 0. r s a p. p Lesson - t k.. z 90. m. h d c.. 0 Define a variable, write an inequalit, and solve each problem. Then check our solution.. Four times a number is greater than.. ne eighth of a number is less than or equal to.. Negative twelve times a number is no more than.. Negative one sith of a number is less than 9.. Eight times a number is at least. Glencoe/McGraw-Hill Glencoe Algebra

17 - Practice Solving Inequalities b Multiplication and Division Match each inequalit with its corresponding statement.. n a. Negative four times a number is less than five.. n b. Four fifths of a number is no more than five.. n c. Four times a number is fewer than five.. n d. Negative four times a number is no less than five.. n e. Four times a number is at most five.. n f. Four fifths of a number is more than five. Solve each inequalit. Then check our solution. a s.. h p 0. n. t. m. k 0 9. b c j v u. f Define a variable, write an inequalit, and solve each problem. Then check our solution.. Negative three times a number is at least.. Two thirds of a number is no more than 0.. Negative three fifths of a number is less than.. FLDING A river is rising at a rate of inches per hour. If the river rises more than feet, it will eceed flood stage. How long can the river rise at this rate without eceeding flood stage?. SALES Pet Supplies makes a profit of $.0 per bag on its line of natural dog food. If the store wants to make a profit of no less than $, how man bags of dog food does it need to sell? Glencoe/McGraw-Hill Glencoe Algebra

18 - Reading to Learn Mathematics Solving Inequalities b Multiplication and Division Pre-Activit Wh are inequalities important in landscaping? Read the introduction to Lesson - at the top of page in our tetbook. Would a wall bricks high be lower than a wall blocks high? Wh? Would a wall n bricks high be lower than a wall n blocks high? Eplain. Reading the Lesson. Write an inequalit that describes each situation. a. A number n divided b is greater than. b. Twelve times a number k is at least. c. A number divided b 0 is less than or equal to 0. Lesson - d. Three fifths of a number n is at most. e. Nine is greater than or equal to one half of a quantit m.. Use words to tell what each inequalit sas. a. n t b. c. Helping You Remember. In our own words, write a rule for multipling and dividing inequalities b positive and negative numbers. Glencoe/McGraw-Hill Glencoe Algebra

19 - Enrichment The Maa 'I'he Maa were a Native American people who lived from about 00 B.C. to about 00 A.D. in the region that toda encompasses much of Central America and southern Meico. Their man accomplishments include eceptional architecture, potter, painting, and sculpture, as well as significant advances in the fields of astronom and mathematics. The Maa developed a sstem of numeration that was based on the number twent. The basic smbols of this sstem are shown in the table at the right. The places in a Maan numeral are written verticall the bottom place represents ones, the place above represents twenties, the place above that represents 0 0, or four hundreds, and so on. For instance, this is how to write the number 99 in Maan numerals Evaluate each epression when v, w,,, and z. Then write the answer in Maan numerals. Eercise is done for ou. z v w z... v w. v. w z. vz. w(v z). vwz 9. z(w ) Tell whether each statement is true or false ( ) ( ). How are Eercises 0 and alike? How are the different? Glencoe/McGraw-Hill Glencoe Algebra

20 - Stud Guide and Intervention Solving Multi-Step Inequalities Solve Multi-Step Inequalities To solve linear inequalities involving more than one operation, undo the operations in reverse of the order of operations, just as ou would solve an equation with more than one operation. Eample Eample Solve. riginal inequalit Subtract from each side. Simplif. Add to each side. Simplif. Divide each side b. The solution is { }. Eercises Simplif. Solve a a. a a a a a a Subtract a from a a a 9 a 9 a 9 The solution is a a 9. Solve each inequalit. Then check our solution. q.. n 0 n. riginal inequalit each side. Simplif. Add to each side. Simplif. Divide each side b and change to. Simplif.. n n. d d. r r m m Lesson n n 0. Define a variable, write an inequalit, and solve each problem. Then check our solution.. Negative three times a number plus four is no more than the number minus eight.. ne fourth of a number decreased b three is at least two.. The sum of twelve and a number is no greater than the sum of twice the number and. Glencoe/McGraw-Hill Glencoe Algebra

21 - Solve Inequalities Involving the Distributive Propert When solving inequalities that contain grouping smbols, first use the Distributive Propert to remove the grouping smbols. Then undo the operations in reverse of the order of operations, just as ou would solve an equation with more than one operation. Eample Solve a (a ) (a ). a (a ) (a ) riginal inequalit a a a Distributive Propert 9a a Combine like terms. 9a a a a Add a to each side. a Combine like terms. a Subtract from each side. a 0 Simplif. a The solution in set-builder notation is {a a }. Eercises Stud Guide and Intervention (continued) Solving Multi-Step Inequalities Divide each side b and change to. Solve each inequalit. Then check our solution.. (t ). (d ) d. h (h ). 0 ( )..(.).. ( ). ( ) ( ) 0. (b ) b 9. (k ) ( k) 0. 0.( ) 0.( ). m (m ). n (n ) ( n). ( ). k ( k). n ( n) Define a variable, write an inequalit, and solve each problem. Then check our solution.. Twice the sum of a number and is less than.. Three times the sum of a number and si is greater than four times the number decreased b two.. Twice the difference of a number and four is less than the sum of the number and five. Glencoe/McGraw-Hill Glencoe Algebra

22 - Skills Practice Solving Multi-Step Inequalities Justif each indicated step.. t t a. t t ( ) b. t??. (k ) k 0 a. k k b. k 0 k 0 c. k??? Solve each inequalit. Then check our solution. d. b.. t. a.. j 0 9. f 9 0. p p 0. k k. ( m ). (w ) (w ). (q ) 0 Define a variable, write an inequalit, and solve each problem. Then check our solution. Lesson -. Four more than the quotient of a number and three is at least nine.. The sum of a number and fourteen is less than or equal to three times the number.. Negative three times a number increased b seven is less than negative eleven.. Five times a number decreased b eight is at most ten more than twice the number. 9. Seven more than five siths of a number is more than negative three. 0. Four times the sum of a number and two increased b three is at least twent-seven. Glencoe/McGraw-Hill Glencoe Algebra

23 - Practice Solving Multi-Step Inequalities Justif each indicated step.. () a. b. c.???. (h ) (h ) h h 0 a. h h h h h h b. h h c. h h d. h???? Solve each inequalit. Then check our solution. t. 9. u u 0. a w f 0.. h. h 9. (z ) (z ) 0. e (e ) (e ). n (n ) 0 Define a variable, write an inequalit, and solve each problem. Then check our solution.. A number is less than one fourth the sum of three times the number and four.. Two times the sum of a number and four is no more than three times the sum of the number and seven decreased b four.. GEMETRY The area of a triangular garden can be no more than 0 square feet. The base of the triangle is feet. What is the height of the triangle?. MUSIC PRACTICE Nabuko practices the violin at least hours per week. She practices for three fourths of an hour each session. If Nabuko has alread practiced hours in one week, how man sessions remain to meet or eceed her weekl practice goal? Glencoe/McGraw-Hill Glencoe Algebra

24 - Reading to Learn Mathematics Solving Multi-Step Inequalities Pre-Activit How are linear inequalities used in science? Read the introduction to Lesson - at the top of page in our tetbook. Then write an inequalit that could be used to find the temperatures in degrees Celsius for which each substance is a gas. Argon: Bromine: Reading the Lesson. What does the phrase undoing the operations in reverse of the order of operations mean?. Describe how checking the solution of an inequalit is different from checking the solution of an equation.. Describe how the Distributive Propert can be used to remove the grouping smbols in the inequalit ( ).. Is it possible to have no solution when ou solve an inequalit? Eplain our answer and give an eample. Lesson - Helping You Remember. Make a checklist of steps ou can use when solving inequalities. Glencoe/McGraw-Hill 9 Glencoe Algebra

25 - Enrichment Carlos Montezuma During his lifetime, Carlos Montezuma (? 9) was one of the most influential Native Americans in the United States. He was recognized as a prominent phsician and was also a passionate advocate of the rights of Native American peoples. The eercises that follow will help ou learn some interesting facts about Dr. Montezuma s life. Solve each inequalit. The word or phrase net to the equivalent inequalit will complete the statement correctl.. k 0. r 9 Montezuma was born in the state He was a Native American of the of?. Yavapais, who are a? people. a. k Arizona a. r Navajo b. k Montana b. r Mohawk c. k Utah c. r Mohave-Apache. 9. q Montezuma received a medical As a phsician, Montezuma's field of degree from? in 9. specialization was?. a. 9 Chicago Medical College a. q heart surger b. 9 Harvard Medical School b. q internal medicine c. 9 Johns Hopkins Universit c. q respirator diseases.. t t For much of his career, he maintained In addition to maintaining his medical a medical practice in?. practice, he was also a(n)?. a. 9 New York Cit a. t director of a blood bank b. Chicago b. t 0 instructor at a medical college c. 9 Boston c. t legal counsel to phsicians. a a 0. n n Montezuma founded, wrote, and Montezuma testified before a edited?, a monthl newsletter committee of the United States that addressed Native American Congress concerning his work in concerns. treating?. a. a Yavapai a. n appendicitis b. a Apache b. n asthma c. a Wassaja c. n 0 heart attacks Glencoe/McGraw-Hill 0 Glencoe Algebra

26 - Stud Guide and Intervention Solving Compound Inequalities Inequalities Containing and A compound inequalit containing and is true onl if both inequalities are true. The graph of a compound inequalit containing and is the intersection of the graphs of the two inequalities. Ever solution of the compound inequalit must be a solution of both inequalities. Eample Eample Graph the solution set of and Graph. Graph. Find the intersection. The solution set is { }. Eercises Solve using and. Then graph the solution set. and Graph the solution set of each compound inequalit. Graph. Graph. Find the intersection. The solution set is { }.. b and b. q. and 0. p. d and d. p 0 Solve each compound inequalit. Then graph the solution set.. w. p and Lesson - 0. n and n. d d d 0 Glencoe/McGraw-Hill Glencoe Algebra

27 - Inequalities Containing or A compound inequalit containing or is true if one or both of the inequalities are true. The graph of a compound inequalit containing or is the union of the graphs of the two inequalities. The union can be found b graphing both inequalities on the same number line. A solution of the compound inequalit is a solution of either inequalit, not necessaril both. Eample Solve a or a a. a or a a a a a a a a 0 a a Stud Guide and Intervention (continued) Solving Compound Inequalities 0 a a a The solution set is {a a }. Graph a. Graph a. Find the union. Eercises Graph the solution set of each compound inequalit.. b or b. q or q. or 0 0. p or p. d or d. or 0 Solve each compound inequalit. Then graph the solution set.. w or w 9. p or p 0 9. or 0. or 0 0. n or n n. a or a a Glencoe/McGraw-Hill Glencoe Algebra

28 - Skills Practice Solving Compound Inequalities Graph the solution set of each compound inequalit.. b or b 0. z and z. k and k. or 0 Write a compound inequalit for each graph Solve each compound inequalit. Then graph the solution set. 9. m and m 0. or 0 0. f and f. w 0 or w 9. b. p or p 0 Define a variable, write an inequalit, and solve each problem. Then check our solution. Lesson -. A number plus one is greater than negative five and less than three.. A number decreased b two is at most four or at least nine.. The sum of a number and three is no more than eight or is more than twelve. Glencoe/McGraw-Hill Glencoe Algebra

29 - Practice Solving Compound Inequalities Graph the solution set of each compound inequalit.. e. 0 or 0. g or g. p Write a compound inequalit for each graph Solve each compound inequalit. Then graph the solution set. 9. k or k 0. n or n. h. c and c 0 Define a variable, write an inequalit, and solve each problem. Then check our solution.. Two times a number plus one is greater than five and less than seven.. A number minus one is at most nine, or two times the number is at least twent-four. METERLGY For Eercises and, use the following information. Strong winds called the prevailing westerlies blow from west to east in a belt from 0 to 0 latitude in both the Northern and Southern Hemispheres.. Write an inequalit to represent the latitude of the prevailing westerlies.. Write an inequalit to represent the latitudes where the prevailing westerlies are not located.. NUTRITIN A cookie contains 9 grams of fat. If ou eat no fewer than and no more than cookies, how man grams of fat will ou consume? Glencoe/McGraw-Hill Glencoe Algebra

30 - Reading to Learn Mathematics Solving Compound Inequalities Pre-Activit How are compound inequalities used in ta tables? Read the introduction to Lesson - at the top of page 9 in our tetbook. Eplain wh it is possible that Mr. Kell s income is $,0. Eplain wh it is not possible that Mr. Kell s income is $,00. Reading the Lesson. When is a compound inequalit containing and true?. The graph of a compound inequalit containing and is the of the graphs of the two inequalities.. When is a compound inequalit containing or true?. The graph of a compound inequalit containing or is the of the graphs of the two inequalities.. Suppose ou use ellow to show the graph of Inequalit # on the number line. You use blue to show the graph of Inequalit #. Write and or or in each blank to complete the sentence. a. The part that is green is the graph of Inequalit # Inequalit #. b. All colored parts form the graph of Inequalit # Inequalit #. Helping You Remember. ne wa to remember something is to connect it to something that is familiar to ou. Write two true compound statements about ourself, one using the word and and the other using the word or. Lesson - Glencoe/McGraw-Hill Glencoe Algebra

31 - Enrichment Some Properties of Inequalities The two epressions on either side of an inequalit smbol are sometimes called the first and second members of the inequalit. If the inequalit smbols of two inequalities point in the same direction, the inequalities have the same sense. For eample, a b and c d have the same sense; a b and c d have opposite senses. In the problems on this page, ou will eplore some properties of inequalities. Three of the four statements below are true for all numbers a and b (or a, b, c, and d). Write each statement in algebraic form. If the statement is true for all numbers, prove it. If it is not true, give an eample to show that it is false.. Given an inequalit, a new and equivalent inequalit can be created b interchanging the members and reversing the sense.. Given an inequalit, a new and equivalent inequalit can be created b changing the signs of both terms and reversing the sense.. Given two inequalities with the same sense, the sum of the corresponding members are members of an equivalent inequalit with the same sense.. Given two inequalities with the same sense, the difference of the corresponding members are members of an equivalent inequalit with the same sense. Glencoe/McGraw-Hill Glencoe Algebra

32 - Stud Guide and Intervention Solving pen Sentences Involving Absolute Value Absolute Value Equations When solving equations that involve absolute value, there are two cases to consider. Case : The value inside the absolute value smbols is positive. Case : The value inside the absolute value smbols is negative. Eample Eample Solve. Then graph the solution set. Write as or. or The solution set is {, }. The graph is shown below. 0 Eercises Write an inequalit involving absolute value for the graph. 0 Find the point that is the same distance from as it is from. units units 0 Solve each open sentence. Then graph the solution set. The distance from to is units. The distance from to is units. So, b. w. t p d For each graph, write an open sentence involving absolute value Lesson - Glencoe/McGraw-Hill Glencoe Algebra

33 - Absolute Value Inequalities When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving (or ) and two cases to consider for inequalities involving (or ). Remember that inequalities with and are related to intersections, while inequalities with or are related to unions. Eample Stud Guide and Intervention (continued) Solving pen Sentences Involving Absolute Value Solve a 0. Then graph the solution set. Write a 0 as a 0 and a 0. a 0 and a 0 a 0 a 0 a a a a If n, then n and n. If n, then n or n. Now graph the solution set. 0 a The solution set is a a. a Eercises Solve each open sentence. Then graph the solution set.. c f d. ( ) 9. r 0 0 For each graph, write an open sentence involving absolute value Glencoe/McGraw-Hill Glencoe Algebra

34 - Skills Practice Solving pen Sentences Involving Absolute Value Match each open sentence with the graph of its solution set.. a.. b.. c.. d Epress each statement using an inequalit involving absolute value. Do not solve.. The weatherman predicted that the temperature would be within of F.. Serena will make the B team if she scores within points of the team average of 9.. The dance committee epects attendance to number within of last ear s students. Solve each open sentence. Then graph the solution set.. s 9. c 0 0. n. t w. k For each graph, write an open sentence involving absolute value Lesson - Glencoe/McGraw-Hill 9 Glencoe Algebra

35 - Practice Solving pen Sentences Involving Absolute Value Match each open sentence with the graph of its solution set.. a.. b.. c.. d Epress each statement using an inequalit involving absolute value. Do not solve.. The height of the plant must be within inches of the standard -inch show size.. The majorit of grades in Sean s English class are within points of. Solve each open sentence. Then graph the solution set.. z 9. r 9. t 9 0. g 9 0 For each graph, write an open sentence involving absolute value FITNESS Taisha uses the elliptical cross-trainer at the gm. Her general goal is to burn 0 Calories per workout, but she varies b as much as Calories from this amount on an given da. What is the range of the number of Calories burned for Taisha s crosstrainer workout?. TEMPERATURE A thermometer is guaranteed to give a temperature no more than. F from the actual temperature. If the thermometer reads F, what is the range for the actual temperature? Glencoe/McGraw-Hill 0 Glencoe Algebra

36 - Reading to Learn Mathematics Solving pen Sentences Involving Absolute Value Pre-Activit How is absolute value used in election polls? Read the introduction to Lesson - at the top of page in our tetbook. What does the phrase margin of error mean to ou? In this poll, the number of people opposed to the ta lev ma be as high as or as low as. This can be written as the inequalit. Reading the Lesson Complete each compound sentence b writing and or or in the blank. Use the result to help ou graph the absolute value sentence. Absolute Value Sentence Compound Sentence Graph How would ou write the compound sentence or as an absolute value sentence? Helping You Remember. Recall that tells ou how man units the number is from zero on the number line. Eplain the meaning of n, n, and n b using the idea of the distance from to zero. Lesson - Glencoe/McGraw-Hill Glencoe Algebra

37 - Enrichment Precision of Measurement The precision of a measurement depends both on our accurac in measuring and the number of divisions on the ruler ou use. Suppose ou measured a length of wood to the nearest one-eighth of an inch and got a length of in. The drawing shows that the actual measurement lies somewhere 9 between in. and in. This measurement can be written using the smbol, which is read plus or minus. It can also be written as a compound inequalit. 9 in. in. m in. In this eample, in. is the absolute error. The absolute error is one-half the smallest unit used in a measurement. Write each measurement as a compound inequalit. Use the variable m.. in cm g. ft. 0. cm. in. For each measurement, give the smallest unit used and the absolute error... cm m. cm. in. m in. 9. in. m in mm m. mm Glencoe/McGraw-Hill Glencoe Algebra

38 - Stud Guide and Intervention Graphing Inequalities in Two Variables Graph Linear Inequalities The solution set of an inequalit that involves two variables is graphed b graphing a related linear equation that forms a boundar of a half-plane. The graph of the ordered pairs that make up the solution set of the inequalit fill a region of the coordinate plane on one side of the half-plane. Eample Graph. Graph. Since is the same as and, the boundar is included in the solution set and the graph should be drawn as a solid line. Select a point in each half plane and test it. Choose (0, 0) and (, ). 0 (0) ( ) 0 is false. is true. The half-plane that contains (, ) contains the solution. Shade that half-plane. Lesson - Eercises Graph each inequalit Glencoe/McGraw-Hill Glencoe Algebra

39 - Solve Real-World Problems When solving real-life inequalities, the domain and range of the inequalit are often restricted to nonnegative numbers or to whole numbers. Eample BANKING A bank offers.% annual interest on regular savings accounts and % annual interest on certificates of deposit (CD). If Marjean wants to earn at least $00 interest per ear, how much mone should she deposit in each tpe of account? Let the amount deposited in a regular savings account. Let the amount deposited in a CD. Then is an open sentence representing this situation. Solve for in terms of riginal inequalit Subtract 0.0 from each side Divide each side b 0.0. Graph and test the point (0, 0). Since 0 0.(0) 000 is false, shade the half-plane that does not contain (0, 0). ne solution is (000, 000). This represents $000 deposited at.% and $,000 deposited at %. Eercises Stud Guide and Intervention (continued) Graphing Inequalities in Two Variables CD Account ($) Interest on Accounts Regular Savings Account ($). SCIAL EVENTS Tickets for the school pla cost $ per student and $ per adult. The school wants to earn at least $,00 on each performance. a. Write an inequalit that represents this situation. b. Graph the solution set. Adult Tickets Ticket Sales c. If 00 adult tickets are sold, what is the minimum number of student tickets that must be sold? Student Tickets. MANUFACTURING An auto parts compan can produce four-clinder engines or 0 V- engines per da. It wants to produce up to 00,000 engines per ear. a. Write an inequalit that represents this situation. b. Are there restrictions on the domain or range?. GEMETRY The perimeter of a rectangular lot is less than 00 feet. Write an inequalit that represents the amount of fencing that will enclose the lot. Glencoe/McGraw-Hill Glencoe Algebra

40 - Skills Practice Graphing Inequalities in Two Variables Determine which ordered pairs are part of the solution set for each inequalit.., {(, ), (, 0), (, 0), (, )}., {(, ), (, ), (, ), (, )} Lesson -., {(, ), (, ), (, ), (, )} Match each inequalit with its graph.. a. b.... c. d. Graph each inequalit Glencoe/McGraw-Hill Glencoe Algebra

41 - Practice Graphing Inequalities in Two Variables Determine which ordered pairs are part of the solution set for each inequalit.., {(, ), (, ), (, ), (, )}., {(, ), (, ), (, ), (, )}., {(, ), (, ), (, ), (, )} Match each inequalit with its graph.. 0 a. b c. d. Graph each inequalit MVING A moving van has an interior height of feet ( inches). You have boes in inch and inch heights, and want to stack them as high as possible to fit. Write an inequalit that represents this situation. BUDGETING For Eercises and, use the following information. Satchi found a used bookstore that sells pre-owned videos and CDs. Videos cost $9 each, and CDs cost $ each. Satchi can spend no more than $.. Write an inequalit that represents this situation.. Does Satchi have enough mone to bu videos and CDs? Glencoe/McGraw-Hill Glencoe Algebra

42 - Reading to Learn Mathematics Graphing Inequalities in Two Variables Pre-Activit How are inequalities used in budgets? Read the introduction to Lesson - at the top of page in our tetbook. What do and represent in the terms and? Lesson - Reading the Lesson. Complete the chart to show which tpe of line is needed for each smbol. Smbol Tpe of Line Boundar Part of Solution?. If a test point results in a false statement, what do ou know about the graph?. If a test point results in a true statement, what do ou know about the graph?. When can the origin not be used as a test point? Helping You Remember. The two-variable inequalities in this lesson can be solved for in terms of to get a sentence in slope-intercept form. It looks much like a slope-intercept equation, but it has an inequalit smbol instead of an equals sign. For eample, can be written as. Eplain how to graph an inequalit once it is written in slope-intercept form. Use the idea that greater can mean above and less can mean below. Glencoe/McGraw-Hill Glencoe Algebra

43 - Enrichment Using Equations: Ideal Weight You can find our ideal weight as follows. A woman should weigh 00 pounds for the first feet of height and additional pounds for each inch over feet ( feet 0 inches). A man should weigh 0 pounds for the first feet of height and additional pounds for each inch over feet. These formulas appl to people with normal bone structures. To determine our bone structure, wrap our thumb and inde finger around the wrist of our other hand. If the thumb and finger just touch, ou have normal bone structure. If the overlap, ou are small-boned. If the don t overlap, ou are large-boned. Small-boned people should decrease their calculated ideal weight b 0%. Large-boned people should increase the value b 0%. Calculate the ideal weights of these people.. woman, ft in., normal-boned. man, ft in., large-boned. man, ft in., small-boned. ou, if ou are at least ft tall For Eercises 9, use the following information. Suppose a normal-boned man is inches tall. If he is at least feet tall, then 0 represents the number of inches this man is over feet tall. For each of these inches, his ideal weight is increased b pounds. Thus, his proper weight ( ) is given b the formula ( 0) 0 or. If the man is large-boned, the formula becomes 0.0( ).. Write the formula for the weight of a large-boned man in slopeintercept form.. Derive the formula for the ideal weight ( ) of a normal-boned female with height inches. Write the formula in slope-intercept form.. Derive the formula in slope-intercept form for the ideal weight ( ) of a large-boned female with height inches.. Derive the formula in slope-intercept form for the ideal weight ( ) of a small-boned male with height inches. 9. Find the heights at which normal-boned males and large-boned females would weigh the same. Glencoe/McGraw-Hill Glencoe Algebra

44 NAME DATE PERID Chapter Test, Form SCRE Write the letter for the correct answer in the blank at the right of each question. For Questions 9, solve each inequalit.. A. { 0} B. { } C. { 0} D. { }.. t A. {t t } B. {t t } C. {t t } D. {t t }.. a A. {a a 0} B. {a a 0} C. {a a } D. {a a }. c. A. c c B. c c C. {c c } D. {c c }. Assessment. A. B. { } C. { } D. { }.. s A. {s s } B. {s s } C. {s s } D. {s s }.. t A. {t t } B. {t t } C. {t t } D. {t t }.. A. { 9} B. { } C. { 9} D. { }. 9. (d ) (d ) A. {d d 9} B. {d d } C. {d d } D. {d d } Si is at least four more than a number. Which inequalit represents this sentence? A. n B. n C. n D. n 0.. Which of the following is the graph of the solution set of m and m? A. B. 0 C. D.. 0. Which compound inequalit has the solution set shown in the graph? A. n B. n C. n D. n. Glencoe/McGraw-Hill 9 Glencoe Algebra

45 NAME DATE PERID Chapter Test, Form (continued). Which compound inequalit has the solution set shown in the graph? 0 A. or B. or C. or D. or.. Which of the following is the solution set of s 9 or s? A. {s s or s } B. {s s or s } C. {s s } D. {s s or s }.. Which of the following is the solution set of s? A. {, } B. { } C. {} D. {, }.. Solve b. A. {, } B. {, 0} C. {0, } D. {0}.. Solve. A. { } B. { } C. { } D. { }.. Which inequalit has the solution set shown in the graph? A. B. C. D.. 9. Which inequalit has the solution set shown in the graph? A. B. C. D. 9. (0, ) (, 0) 0. Juan s income consists of at least $,00 salar plus % commission on all of his sales. Which inequalit represents Juan s income in one ear? A.,00 B., C. 0.0(,00) D.,00 0. Bonus If 0, which integer does not satisf the inequalit B:? Glencoe/McGraw-Hill 0 Glencoe Algebra

46 NAME DATE PERID Chapter Test, Form A SCRE Write the letter for the correct answer in the blank at the right of each question. For Questions 9, solve each inequalit.. A. { } B. { 9} C. { 9} D. { }.. m A. m m B. m m C. m m D. m m.. n 9 n A. {n n 9} B. {n n 9} C. {n n 9} D. n n 9. t. A. {t t } B. {t t } C. {t t } D. {t t }. Assessment. d A. d d B. d d C. d d D. d d...z A. {z z } B. {z z } C. {z z } D. {z z }.. w w 0 A. {w w } B. {w w } C. {w w } D. {w w }.. v v A. v v B. v v C. v v D. v v. 9. r (r ) A. {r r 9} B. {r r 9} C. {r r 9} D. {r r 9} The sum of two consecutive integers is at most. What is the greatest possible value for the greater integer? A. B. C. D. 0.. Which of the following is the graph of the solution set of or? A. B. 0 C. D Glencoe/McGraw-Hill Glencoe Algebra

47 NAME DATE PERID Chapter Test, Form A (continued). Which compound inequalit has the solution set shown in the graph? 0 A. n B. n C. n or n D. n.. Which of the following is the solution set of t 0? A. {t t } B. {t t } C. {t t and t } D. {t t or t }.. Which of the following is the graph of the solution set of t t or t t? A. B. 0 C. D.. 0. Which of the following is the solution set of? A. {} B. {, 0} C. { 0, } D. {0}.. The graph below represents the solution set of which inequalit? 0 A. w B. w C. w D. w.. Which of the following is the solution set of? A. or > B. { or } C. D. or.. Which ordered pair is part of the solution set of the inequalit? A. (, ) B. (, ) C. (, ) D. (, ). 9. Which inequalit is graphed at the right? A. B. C. D Taka is planning to bu a new coat and new shoes. He has saved $. Which inequalit represents this situation if represents the cost of a coat and represents the cost of the shoes he bus? 0 0 A. B. C. D. 0. Bonus Solve ( n ) n. B: (0, ) (, ) Glencoe/McGraw-Hill Glencoe Algebra

48 NAME DATE PERID Chapter Test, Form B SCRE Write the letter for the correct answer in the blank at the right of each question. For Questions 9, solve each inequalit.. w A. {w w } B. {w w } C. {w w } D. {w w }.. A. B. C. D... A. B. { } C. { } D. { }. m. A. {m m } B. {m m } C. {m m } D. {m m }. Assessment. s A. {s s 9} B. {s s 9} C. {s s 9} D. {s s 9}...t. A. {t t.} B. {t t.} C. {t t.} D. {t t.}.. z z A. {z z } B. {z z } C. {z z } D. {z z }.. b b A. {b b } B. {b b } C. {b b } D. {b b }. 9. 9r (r ) A. {r r } B. r r C. {r r } D. r r The sum of two consecutive integers is at most. What is the largest possible value for the lesser integer? A. B. C. D. 0.. Which of the following is the graph of the solution set of 0 or? A. B. 0 C. D Glencoe/McGraw-Hill Glencoe Algebra

49 NAME DATE PERID Chapter Test, Form B (continued). Which compound inequalit has the solution set shown in the graph? 0 A. B. C. or D... Which of the following is the solution set of? A. { } B. { } C. { or } D. { }.. Which of the following is the graph of the solution set of a a or a a? A. B. 0 C. D.. 0. Which of the following is the solution set of 9? A. {, } B. { } C. {} D. {, }.. The graph below represents the solution set of which inequalit? 0 A. 0 0 B. 0 0 C. 0 0 D Which of the following is the solution set of? A. or B. { is a real number} C. or D. { }.. Which ordered pair is part of the solution set of the inequalit? A. (, ) B. (, ) C. (, ) D. (, ). 9. Which inequalit is graphed? A. B. C. D Alicia is planning to bu a new baseball glove and a new baseball bat with at most $9. Which inequalit represents this situation if represents the cost of a glove and represents the cost of the bat she bus? 0 0 A. 9 B. 9 (, ) C. 9 D Bonus Solve ( ) ( ) 0. B: (0, ) Glencoe/McGraw-Hill Glencoe Algebra

50 NAME DATE PERID Chapter Test, Form C SCRE Solve each inequalit. Then graph our solution on a number line n. 9 For Questions and, solve each inequalit.. t.. z.. Define a variable, write an inequalit, and solve:. The sum of and a number is no greater than. Assessment Solve each inequalit.. b.. t r a ( p ) ( p ) p...(c ). 0.c. For Questions, solve each compound inequalit. Then graph the solution set.. w and w. 0. n or n.. b or. 0 Glencoe/McGraw-Hill Glencoe Algebra

51 NAME DATE PERID Chapter Test, Form C (continued). Define a variable, write an inequalit and solve. Felicita s. bank charges $.0 per month plus $0.0 per check. How man checks does she write if her bank charges are alwas between $.0 and $.00? Solve each open sentence. Then graph the solution set Solve each open sentence.... w. For Questions and, graph each inequalit EXPENSES Camille has no more than $0.00 to spend each. week for lunch and bus fare. Lunch costs $.00 each da, and bus fare is $0. each ride. Write an inequalit for this situation. Can Camille bu lunch times and ride the bus times in one week? Bonus Graph the solution set of the compound inequalit B:. Glencoe/McGraw-Hill Glencoe Algebra

52 NAME DATE PERID Chapter Test, Form D SCRE Solve each inequalit. Then graph our solution on a number line m. 9 For Questions and, solve each inequalit.. s.. k.. Define a variable, write an inequalit, and solve:. is greater than a number plus. Assessment Solve each inequalit.. h 9.. z.. 9..k. 9. m f 0.. t t.. ( w ) (w )...9..( ). For Questions, solve each compound inequalit. Then graph the solution set.. w and w. 0. w or w or. 0 Glencoe/McGraw-Hill Glencoe Algebra

53 NAME DATE PERID Chapter Test, Form D (continued). Define a variable, write an inequalit and solve. Jose s bank. charges $. per month plus $0.0 per check. How man checks does he write if his bank charges are alwas between $. and $.? Solve each open sentence. Then graph the solution set. 9. z w 0. 0 Solve each open sentence.... c. For Questions and, graph each inequalit SHPPING Matthew is shopping for shoes and socks. He. has $.00 to spend. The shoes he likes cost $.00, and the socks cost $.00. Write an inequalit for this situation. Can Matthew bu pairs of shoes and pairs of socks? Bonus Graph the solution set of the compound inequalit B: or. Glencoe/McGraw-Hill Glencoe Algebra

54 NAME DATE PERID Chapter Test, Form SCRE Solve each inequalit. Then graph our solution on a number line.. m (.)... t ( ). Define a variable, write an inequalit, and solve each problem.. Negative three sevenths plus a number is at least.. Assessment. A number less is greater than the sum of twice the. number and. Solve each inequalit... w.. t 9.. b b.. ( ) ( ) ( ) 9. Define a variable, write an inequalit, and solve each problem. 0. Raul plans to spend $.00 on two shirts and a pair of 0. jeans. He bought the two shirts for $9.9 each. How much can he spend on the jeans?. The sum of two consecutive positive even integers is at. most. What are the possible pairs of integers?. Susan makes 0% commission on her sales. She also. receives a salar of $,00. How much must she sell to receive a total income between $,00 and $,900? Glencoe/McGraw-Hill 9 Glencoe Algebra

55 NAME DATE PERID Chapter Test, Form (continued) Solve each compound inequalit, and graph the solution set.. m 0 and (m ) m.. n or n.. ( ) ( ) 0. For Questions, solve each open sentence. Then graph the solution set Graph DGS Each afternoon Maria walks the dogs at a local pet 0. shelter for up to hours. Maria spends minutes walking a large dog and minutes walking a small dog. Write an inequalit for this situation. If Maria walked 9 dogs in one afternoon, what is the greatest number of large dogs that she could have walked that afternoon? Bonus If 0, determine if the compound inequalit, B: and, is true or false. Eplain our reasoning. Glencoe/McGraw-Hill 90 Glencoe Algebra

56 NAME DATE PERID Chapter pen-ended Assessment SCRE Demonstrate our knowledge b giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justif our answers. You ma show our solution in more than one wa or investigate beond the requirements of the problem.. Solve 0n (n ) n. Eplain each step in our solution.. Draw a line on a coordinate plane so that ou can determine at least two points on the graph. a. Write an inequalit to represent one of the half planes created b the line. b. Determine if the solution set of the inequalit written for part a includes the line or not. Eplain our response.. Let b. Describe how ou would determine if ab a. Assessment. a. Eplain wh the solution set for is {, }. b. Determine if the open sentence and the compound inequalit or have the same solution set.. ARCHITECTURE An architect is designing a house for the Frazier famil. In the design, she must consider the desires of the famil and the local building codes. The rectangular lot on which the house will be built is feet long, and 90 feet wide. a. The building codes state that one can build no closer than 0 feet to the lot line. Write an inequalit to represent the possible widths of the house along the 90-foot dimension. Solve the inequalit. b. The Fraziers requested that the rectangular house contain no less than 00 square feet and no more than 00 square feet of floor space. If the house has onl one floor, use the maimum value for the width of the house from part a, and eplain how to use an inequalit to find the possible lengths. c. The Fraziers have asked that the cost of the house be about $,000 and are willing to deviate from this price no more than $0,000. Write an open sentence involving an absolute value and solve. Eplain the meaning of the answer. Glencoe/McGraw-Hill 9 Glencoe Algebra

57 NAME DATE PERID Chapter Vocabular Test/Review SCRE Addition Propert of Inequalities boundar compound inequalit Division Propert of Inequalities half-plane intersection Multiplication Propert of Inequalities set-builder notation Subtraction Propert of Inequalities union Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.. The Addition Propert of Inequalities states that if the. same number is added to each side of a true inequalit, the resulting inequalit is true.. An inequalit defines the boundar or edge for each. half-plane.. A compound inequalit containing and is true if one or both. of the inequalities is true.. According to the Division Propert of Inequalities, if each. side of a true inequalit is divided b the same positive number, the direction of the inequalit smbol must be reversed so that the resulting inequalit is also true.. The solution set for an inequalit that contains two. variables consists of man ordered pairs which fill a region on the coordinate plane called a half-plane.. The graph of a compound inequalit containing and is the. intersection of the graphs of the two inequalities.. The Division Propert of Inequalities states that if each. side of a true inequalit is divided b the same negative number, the resulting inequalit is also true.. Set-builder notation is a wa of writing a solution set.. 9. If the same number is subtracted from each side of a true 9. inequalit, the resulting inequalit is also true. 0. The graph of a compound inequalit containing and is the 0. union of the graphs of the two inequalities. In our own words. Eplain how to use the Multiplication Propert of Inequalities to solve the inequalit. Glencoe/McGraw-Hill 9 Glencoe Algebra

58 NAME DATE PERID Chapter Quiz (Lessons and ) SCRE Solve each inequalit. Then graph our solution on a number line.. n. 0. w 9. 0 For Questions and, solve each inequalit.. r. m.. Define a variable, write an inequalit, and solve:. A number decreased b is at least.. Assessment Solve each inequalit. m.. 9 r.. n 9...w.. 0. STANDARDIZED TEST PRACTICE Which inequalit does not have the solution { }? A. B. 9. C. D. 0. NAME DATE PERID Chapter Quiz (Lesson ) SCRE For Questions, solve each inequalit.. d ( ) ( ) ( ).. t (t 9) (t ).. Define a variable, write an inequalit, and solve. The sum. of a number and three is less than nineteen less the number. Glencoe/McGraw-Hill 9 Glencoe Algebra

59 NAME DATE PERID Chapter Quiz (Lessons and ) SCRE. Solve. Then graph the solution set.. 0. Solve the compound inequalit or.. Then graph the solution set. 0. Define a variable, write an inequalit and solve.. Eight times a number is between and 0.. Solve... Write an open sentence involving absolute value for this. graph. 0 NAME DATE PERID Chapter Quiz (Lesson ) SCRE. From the set {(0, ), (, ), (, ), (, )}, which ordered. pairs are part of the solution set for 0? For Questions and, graph each inequalit.... ( ).. CLTHING Rita plans to spend at most $0.00 on a new. wardrobe. The skirts she wants to bu cost $ each, and the blouses cost $ each. Write an inequalit that represents the number of skirts and blouses Rita can bu. Can Rita bu skirts and blouses? Glencoe/McGraw-Hill 9 Glencoe Algebra

60 NAME DATE PERID Chapter Mid-Chapter Test (Lessons through ) SCRE Part I Write the letter for the correct answer in the blank at the right of each question. For Questions, solve each inequalit.. r A. r r B. r r C. r r D. r r.. 0 A. { } B. { } C. { } D. { }.. m ( m) (m ) m A. {m m } B. m m 9 C. {m m } D. m m 9. Assessment. Four less than three times a number is at most five. Which of the following describes the number? A. an number less than B. an number greater or equal to C. an number less than or equal to D. an number less than or equal to. Part II Solve and check each inequalit... t.. v. Define a variable, write an inequalit, and solve each problem.. For a package to qualif for a certain postage rate, the. sum of its length and girth cannot eceed inches. If the girth is inches, how long can the package be?. The minimum dail requirement of vitamin C for. -ear-olds is at least 0 mg per da. An average-sized apple contains mg of vitamin C. How man apples would a person have to eat each da to satisf this requirement? Glencoe/McGraw-Hill 9 Glencoe Algebra

61 NAME DATE PERID Chapter Cumulative Review (Chapters ). Simplif ( ) ( ). (Lesson ).. Name the set or sets of numbers to which the real number. 0 belongs. (Lesson ). Solve. (Lesson ).. State whether the percent of change is a percent of increase. or a percent of decrease. Then find the percent of change. (Lesson ) original: new:. Epress the relation {(, ), (, ), (, ), (, 0)} as a. mapping. Then write the inverse of the relation. (Lesson ). Determine whether the sequence,, 0, is an. arithmetic sequence. If it is, state the common difference. (Lesson ). Find the slope of the line that passes through (, 0) and. (, ). (Lesson ). The Lopez famil drove miles in hours. Write a direct. variation equation for the distance driven in an time. How far can the Lopez famil drive in hours? (Lesson ) 9. Write an equation of a line that passes through (, ) 9. with slope. (Lesson ) 0. Draw a scatter plot of the relation, and determine what 0. relationship eists, if an, in the data. (Lesson ) {(, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (9, )} 9 X Y 9. Solve r. Then graph the solution. (Lesson ). 0. Solve u. (Lesson ).. Define a variable, write a compound inequalit, and solve. the problem. (Lesson ) Seven less than twice a number is greater than or less than or equal to.. Solve. Then graph the solution set. (Lesson ). 0 Glencoe/McGraw-Hill 9 Glencoe Algebra

62 NAME DATE PERID Standardized Test Practice (Chapters ) Part I: Multiple Choice Instructions: Fill in the appropriate oval for the best answer.. Evaluate [ ()] [(9) ]. (Lesson ) A. B. C. D.. A B C D. If a person s birthda is in Januar, what are the odds that it is between the 0th and the 9th, inclusivel? (Lesson ) E. 0 F. G. H. 0.. How man liters of a 0% saline solution must be added to liters of a 0% saline solution to obtain a % saline solution? (Lesson 9) A. 0 L B. L C. L D. L. E A F B G C H D Assessment. The currenc echange rate between the U.S. and Canada in 999 could be modeled b the equation d.9c where d represents the number of U.S. dollars and c represents the number of Canadian dollars. Solve the equation for Canadian dollar amounts of $, $, $, and $0. (Lesson ) E. {(,.9), (,.9), (,.), (0, 9.) F. {(,.), (, ), (,.), (0, 0)} G. {(, 0.), (,.), (,.), (0,.)} H. {(,.9), (,.9), (,.9), (0,.9)}. E F G H. If a line passes through (0, ) and has a slope of, what is the equation of the line? (Lesson ) A. B. C. D.. A B C D. If r is the slope of a line, and s is the slope of a line perpendicular to that line, what is the relationship between r and s? (Lesson ) E. There is no relationship. F. r s G. r s H. r. s E F G H. Which inequalit does not have the solution {t t }? (Lesson ) t A. t B. t C. D. t. A B C D. Solve r ( r) (r ). (Lesson ) E. r r F. {r r } G. {r r } H. r r 9. E F G H 9. Write a compound inequalit for the graph. (Lesson ) 0 A. and B. or C. or D. and 9. A B C D Glencoe/McGraw-Hill 9 Glencoe Algebra

63 NAME DATE PERID Standardized Test Practice (continued) Part : Grid In Instructions: Enter our answer b writing each digit of the answer in a column bo and then shading in the appropriate oval that corresponds to that entr. 0. Find the th term of the arithmetic sequence 0..,,,,,.... (Lesson ). If when, find when. (Lesson ) For Questions and, determine the value that is missing.. The solution set is {n n } for the.. inequalit n. (Lesson ). If a, then a or a 9. (Lesson ) / /... / / / /... / / Part : Quantitative Comparison Instructions: Compare the quantities in columns A and B. Shade in A if the quantit in column A is greater; B if the quantit in column B is greater; C if the quantities are equal; or D if the relationship cannot be determined from the information given. Column A Column B the percent of change if the percent of change if. original: 0 new: 0. original: new: 9 A B C D (Lesson ) The slope of the line The slope of an line. perpendicular to... A B C D (Lesson ).. A B C D (Lesson ) Glencoe/McGraw-Hill 9 Glencoe Algebra

64 NAME DATE PERID First Semester Test (Chapters ) For Questions 0, write the letter for the correct answer in the blank at the right of each question.. Evaluate v (n s) if n, s, and v. SCRE A. 0 B. C. D... Simplif 9a a a a. A. a 9a B. a C. a a D. a a.. Identif the conclusion of the statement. If the oven works properl, then we will learn how to cook. A. The oven works properl. B. The oven is new. C. I alread know how to cook. D. We will learn how to cook... Evaluate if. Assessment A. 9 9 B. C. 9 D The land areas in square miles of the 9 zip codes in Guam are listed below. Use a stem-and-leaf plot to determine which measure of central tendenc is equal to A. mean B. median C. mode D. frequenc.. Name the set of numbers to which the real number 9 does not belong. A. rational number B. integer C. irrational number D. natural number.. Translate the sentence into an equation. Twelve times a number r is the same as two times the sum of r and p. A. r (r p) B. r r p C. r (r p) D. r r p.. Solve h 0. A. B. 0 C. 0 D.. 9. Solve (a ) (a ). A. B. C. D The surface area A of a sphere is A r where r is the radius of the sphere. What is the radius, rounded to the nearest tenth, of a ball with surface area equal to square inches? A.. in. B.. in. C.. in. D.. in. 0. Glencoe/McGraw-Hill 99 Glencoe Algebra

65 NAME DATE PERID First Semester Test (continued) (Chapters ). The coordinates of the vertices of rectangle MNP are M(, ), N(, ), (, 0), and P(, ). If the rectangle is reflected over the -ais, which point below has the correct coordinates? A. M (, ) B. N (, ) C. (, 0) D. P (, ).. The graph of the line is the graph of which equation? A. B. C. D... If f(), find f(a ). A. a B. a C. a D. a.. The average rate of change for the combined population of San Diego, California and Tijuana, Meico was 0.0 million people per ear from 990 to 000. If the 000 population was about million, what was the approimate 990 population? Source: Time Magazine A.. million B..9 million C.. million D.. million.. A line passes through (, ) and (, ). Which equation does not represent the line? A. ( ) ( ) B. 0 C. ( ) ( ) D... Write the slope-intercept form of an equation for the line that passes through (, 0) and is parallel to the graph of. A. B. C. D... Solve r r. A. {r r } B. {r r } C. {r r } D. {r r }.. Solve h. A. {h h } B. {h h } C. {h h } D. {h 0 h }. 9. Which graph represents the solution of n? A. B. 0 C. D Which ordered pair is not a solution of? A. (, ) B. (, ) C. (, ) D. (, ) 0. Glencoe/McGraw-Hill 00 Glencoe Algebra

66 NAME DATE PERID First Semester Test (continued) (Chapters ). Evaluate ab c if a, b, and c.. c. Find the solution set for 9 if the replacement set. is {,,,,,}.. Name the propert used in the equation n 0. Then. find the value of n.. Simplif.( ).( )... Find a countereample for the statement. If ou visit an. art galler, then ou will see a painting b Monet.. Name the coordinates of the. points graphed on the number line. 0 Assessment. Simplif ( ) (u)(v) uv... Evaluate uv if u., v, and w.. w 9. A card is selected at random from a standard deck of 9. cards. What are the odds against selecting a heart? 0. Solve the following problem b working backward. A father 0. made a batch of cookies. His son ate four and gave si to a friend. Two of his daughters ate half of the remaining cookies. The father was left with thirteen cookies. How man cookies did the father make? For Questions and, solve each equation.... ( ). m. State whether the percent of change is a percent of increase. or a percent of decrease. Then find the percent of change. original: 0 new: 0. Two airplanes leave Phoeni at the same time and fl in. opposite directions. ne plane travels 0 miles per hour faster than the other. After hours the are 00 miles apart. What is the rate of the slower plane?. Identif the transformation as a reflection,. translation, dilation, or rotation. Glencoe/McGraw-Hill 0 Glencoe Algebra

67 NAME DATE PERID First Semester Test (continued) (Chapters ). Epress the relation shown in the. graph as a set of ordered pairs. Then write the inverse of the relation.. Graph... Write an equation for the nth term of the arithmetic. sequence,,, 9,. 9. Ms. rtiz paid $ for 0 gallons of gasoline. Write a direct 9. variation equation relating the cost of gasoline C to the number of gallons purchased n. 0. Find the slope, -intercept, and -intercept of the line 0. represented b the equation.. Find the value of r so that the line through (, ) and (r, ). has a slope perpendicular to the graph of. For Questions and, use the table that shows UV indices and humidities for cities on a Jul da. UV Inde 0 Humidit Forecast (Percent) 0 9. Use a scatter plot to determine what relationship, if an,. eists in the data.. Write the slope-intercept form of an equation for a line of. fit. For Questions and, solve each inequalit... t 9 t. ( ) ( ).. Solve 9 or. Then graph the solution set.. 0. Solve u.. Glencoe/McGraw-Hill 0 Glencoe Algebra

68 NAME DATE PERID Standardized Test Practice Student Record Sheet (Use with pages of the Student Edition.) Part Multiple Choice Select the best answer from the choices given and fill in the corresponding oval. A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D 9 A B C D Part Short Response/Grid In Solve the problem and write our answer in the blank. For Questions and, also enter our answer b writing each number or smbol in a bo. Then fill in the corresponding oval for that number or smbol. 0 (grid in) / / / / Answers (grid in) Part Etended Response Record our answers for Questions 9 on the back of this paper. Glencoe/McGraw-Hill A Glencoe Algebra