College of Marin Study Guide for Math 95 A,B - Pearson Learning ...

College of MarinStudy Guidefor Math 95 A,BRevised EditionTed Broomas, Ira G. Lansing, Jeannette WoodsRevision Editor—Dan AyerTo AccompanyBasic Mathematics, Tenth EditionBy Marvin L. Bittinger

Copyright © 2006, 2002 by College of Marin Department of MathematicsCopyright © 1999 by Addison Wesley, Inc.All rights reserved.Permission in writing must be obtained from the publisher before any part of this work may be reproduced or transmitted in any formor by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system.All trademarks, service marks, registered trademarks, and registered service marks are the property of their respective owners and areused herein for identification purposes only.Printed in the United States of America10 9 8 7 6 5 4 3 2 1ISBN 0-536-27023-62006360754SBPlease visit our web site at www.pearsoncustom.comPEARSON CUSTOM PUBLISHING75 Arlington Street, Suite 300, Boston, MA 02116A Pearson Education Company

ContentsMath 95A—Basic MathematicsLesson Page Title1 7 Operations on the Whole Numbers2 9 Multiplication and Division: Fractional Notation3 11 Addition and Subtraction: Fractional Notation4 13 Decimal Notation5 15 Ratio and ProportionFinal 16 Final Exam for Math 95AMath 95B—Intermediate MathematicsLesson Page Title6 24 Percent Notation7 26 Descriptive Statistics8 27 Geometry and Measures: Length and Area9 30 More on Measures10 32 The Real Number System11 34 Algebra: Solving Equations and ProblemsFinal 35 Final Exam for Math 95B44 Solutions to the Sample Finals1

2 Study Guide for Math 95A, BStudy Guide for Math 95A, BThe purpose of this Study Guide is to help you in learning the basic mathematical skillsand concepts that are taught in Math 95A, B.This Study Guide consists of 13 lessons. Use it with your textbook and be sure to do themargin exercises whenever the textbook tells you to do so. Each lesson of this StudyGuide tells you what pages to read in the textbook and which problems to do for homework.After you have completed each lesson, you will be ready to take a test on that lesson.Show your homework and sample test to your instructor or another staff member.At that point you will be given a test for a grade on that lesson. There is a final examafter the first five lessons and this will end Math 95A. There is also a final exam coveringthe last six lessons to end Math 95B.The textbook is Basic Mathematics, Ninth Edition, by Marvin Bittinger. It is a worktext,which means that you can do the problems in the textbook if you wish. When youread the text, be sure to have a pencil ready. It is important that you do the Margin Exercises.They accompany the reading. The Margin Exercises are a check to ensure youunderstand the concepts that are explained, and also to help you gain the necessaryskills one step at a time.The answers to the Margin Exercises are on pages A-1 to A-29 in the back of the textbook.Also, on these pages you will find the answers to the odd-numbered problems inthe exercise sets and all the problems for the Skill Maintenance Chapter Summary andReview Exercises, and Chapter Tests. The sample tests given in this Study Guide aresolved in detail in the back of this Study Guide. The homework problems should bechecked one at a time. The complete sample test should be worked before beingchecked. There are 16 videotapes available that introduce each section of the textbookand work some of the exercises. On the next page is a list of these videotapes by sectionnumber, content description, and which exercises are worked.

Video Index for Basic Mathematics,9th Edition Marvin BittingerThere are 16 videotapes that introduce the material in each section and work the followingtext exercises.VHSTape #RunTime9eSect #Section Title Presenter Exercises Used ExamplesUsed1 11:31 1.1 Standard Notation J. Penna 1, 3, 9, 23, 29, 41 71 13:49 1.2 Addition J. Penna 1, 11, 19, 31, 43 3, 41 08:06 1.3 Subtraction C. Vance 7, 15, 21, 29, 57 11 11:21 1.4 Rounding andEstimating; OrderB. Johnson 1, 5, 15, 29, 45 2, 3, 11, 121 13:00 1.5 Multiplication D. Ellenbogen 5, 15, 23, 37, 43 N/A2 13:52 1.6 Division C. Vance 5, 15, 19, 21, 23,25, 372 15:42 1.7 Solving Equations B. Johnson 15, 31, 41 2, 82 20:22 1.8 Applications andProblem Solving2 13:51 1.9 Exponential Notationand Order ofOperationsD. Ellenbogen 30, 49 N/AJ. Penna 1, 9, 21, 33 2, 4, 143 15:34 2.1 Factorizations P. Schwarzkopf 3, 7, 27, 31, 41, 45,59, 673 13:00 2.2 Divisibility B. Johnson 11, 15 1, 2, 3, 6, 8, 9,10, 11, 12, 13,19, 22, 24, 263 09:10 2.3 Fractions and FractionNotation3 05:25 2.4 Multiplication andApplicationsB. Johnson 1, 9, 35, 53, 55 8, 13C. Vance 1, 21, 31 1, 114 23:08 2.5 Simplifying M. Bittinger 23, 41, 43 3, 4, 64 16:28 2.6 Multiplying,Simplifying, andApplications4 13:05 2.7 Division andApplications5 14:26 3.1 Least CommonMultiples5 16:36 3.2 Addition andApplications5 19:34 3.3 Subtraction, Order,and ApplicationsJ. Penna 5, 25, 43, 51 1C. Vance 1, 3, 7, 11, 21, 33,37, 47P. Schwarzkopf 3, 7, 17, 41 81911M. Bittinger 4, 7, 33, 43 N/AM. Bittinger 25, 43, margin ex.155 08:51 3.4 Mixed Numerals B. Johnson 3, 31 4, 96 16:52 3.5 Addition andSubtraction UsingMixed Numerals;Applications6 12:58 3.6 Multiplication andDivision Using MixedNumerals;Applications6 09:16 3.7 Order of Operations;Estimation7 16:40 4.1 Decimal Notation,Order, and Rounding7 12:04 4.2 Addition andSubtraction2,6J. Penna 5, 25, 43 3, 8C. Vance 1, 3, 13, 17, 28C. Vance 7, 15, 19, 33, 37,43J. Penna 7, 13, 17, 25, 37,47123, 18J. Penna 13, 43 1, 4, 83

4 Study Guide for Math 95A, BVHSTape #RunTime9eSect #7 11:33 4.3 Multiplication C. Vance 7, 13, 17, 19, 49, 1557 11:19 4.4 Division C. Vance 15, 19, 37, 41, 43, 1598 18:32 4.5 Converting fromFraction Notation toDecimal NotationB. Johnson 5, 33, 49, 67 1, 7, 10, 178 08:20 4.6 Estimating C. Vance 9, 17, 19, 21, 23, 3258 21:01 4,7 Applications and P. Schwarzkopf 13, 29, 35 3Problem Solving9 11:51 5.1 Introduction to Ratios P. Schwarzkopf 13, 19, 23, 37, 39 N/A9 08:29 5.2 Rates and Unit Prices C. Vance 1, 5, 23 1,59 08:46 5.3 Proportions C. Vance 1, 5, 7, 11, 31, 41 19 13:39 5.4 Applications of P. Schwarzkopf 3, 11, 29 N/AProportions9 09:29 5.5 GeometricB. Johnson 3, 21 2Applications10 07:05 6.1 Percent Notation D. Ellenbogen 7, 21, 37, 49 N/A10 12:06 6.2 Percent and Fraction J. Penna 17, 31, 33, 39 5, 6Notation10 14:30 6.3 Solving PercentProblems UsingPercent EquationsM. Bittinger 9, 19 2, 1010 12:34 6.4 Solving PercentProblems UsingProportions11 19:38 6.5 Applications ofPercent11 20:10 6.6 Sales Tax,Commission, andDiscount11 14:36 6.7 Simple and CompoundInterest11 15:07 6.8 Interest Rates onCredit Cards andLoansD. Ellenbogen 5, 15 1, 9P. Schwarzkopf 3, 11, 29 4B. Johnson 23, 41 5J. Penna 11 1P. Schwarzkopf 1, 17 N/A12 13:45 7.1 Averages, Medians, B. Johnson 9, 13, 21 1, 6, 7, 10and Modes12 07:51 7.2 Tables and Pictographs B. Johnson 1, 7, 9 412 11:15 7.3 Bar Graphs and Line D. Ellenbogen 21, 23 5Graphs12 07:38 7.4 Circle Graphs B. Johnson 14 113 10:59 8.1 Linear Measures: C. Vance 3, 7, 21, 27, 35 1, 3American Units13 11:16 8.2 Linear Measures: The J. Penna 11, 13, 17, 19 1, 7Metric System13 10:44 8.3 Converting BetweenAmerican Units andMetric UnitsP. Scwharzkopf 3,9, 17, 21 513 10:17 8.4 Weight and Mass:Medical Applications13 12:22 8.5 Capacity: MedicalApplicationsSection Title Presenter Exercises Used ExamplesUsedB. Johnson 3, 25, 35, 39, 43,49B. Johnson 7, 11, 19, 25, 33,37, 41, 47, 5313 12:55 8.6 Time and Temperature J. Penna 7, 13, 15, 25, 29, 2, 123713 09:06 8.7 Converting Units of D. Ellenbogen 15, 25, 31 1, 3Area14 11:03 9.1 Perimeter J. Penna 7, 13 1, 61, 43

Videotape Index for Basic Mathematics, 9th Edition5VHSTape #RunTime9eSect #14 14:33 9.2 Area J. Penna 7, 11, 31, 33, 35 1, 514 16:48 9.3 Circles B. Johnson 5, 17 2, 4, 614 12:56 9.4 Volume J. Penna 5, 11, 19, 21, 25 N/A14 13:21 9.5 Angles and Triangles C. Vance 1, 3, 25, 37, 39, 41 1, 2, 4, 514 14:51 9.6 Square Roots and thePythagorean TheoremJ. Penna 23, 27, 29, marginex 2515 18:42 10.1 The Real Numbers B. Johnson 13, 47 4, 8, 10, 2015 15:54 10.2 Addition of RealNumbers15 07:52 10.3 Subtraction of RealNumbers15 09:47 10.4 Multiplication of RealNumbers15 17:29 10.5 Division of RealNumbers and Order ofOperations16 21:26 11.1 Introduction toAlgebra16 07:52 11.2 Solving Equations:The Addition Principle16 08:13 11.3 Solving Equations:The MultiplicationPrinciple16 16:50 11.4 Using the PrinciplesTogether16 21:18 11.5 Applications andProblem SolvingSection Title Presenter Exercises Used ExamplesUsedC. Vance 9, 21, 23, 31, 41,55, 57, 67C. Vance 5, 17, 19, 35, 43,53, 671, 91, 2, 3, 4, 13,1911J. Penna 7, 37, 39 1, 4, 5C. Vance 21, 23, 25, 29, 33,43, 51, 85B. Johnson 5, 27, 45, 53 12, 17C. Vance 3, 13, 17, 29 2C. Vance 1, 19, 29, 35 3J. Penna 1, 27, 47 6B. Johnson 1, 7, 11, 25, 29, 33 21, 2, 3, 4, 21

Lesson 1: Whole NumbersProcedures1. Read Sect. 1.1, pp. 2–5Homework: Set 1.1, pp. 6–8 (Odd Numbered Problems).2. Read Sect. 1.2, pp. 9–12Homework: Set. 1.2, pp.13–14, 1–25 (Every Other Odd)., 27–35 (OddNumbered Problems).3. Read Sect. 1.3, pp. 15–19Homework: Set 1.3, pp. 20–21, 1–61 (Odd Numbered Problems).4. Read Sect. 1.4. pp. 22–26Homework: Set. 1.4, pp. 27–30, 1–67 (Odd Numbered Problems). 69–765. Read Sect. 1.5 pp. 31–36Homework: Set 1.5, pp. 37–39, 1–51(Odd Numbered Problems). 53–626. Read Sect. 1.6 pp. 40–47Homework: Set. 1.6, pp. 48–51, 1–75 (Odd Numbered Problems). 77–847. Read Sect. 1.7 pp. 52–55Homework: Set 1.7, pp. 56–57, 1–57 (Odd Numbered Problems). 59–688. Read Sect. 1.8 pp. 58–67Homework: Set 1.8, pp. 68–74, 1–61 (Odd Numbered Problems). 63–719. Read Sect. 1.9abc, pp. 75–79Note: If you have trouble remembering the sequence of operations, rememberinstead:“Please Excuse My Dear Aunt Sally”P is parentheses, E is exponents, M is multiplication, D is division, A is addition,S is subtraction. Don’t forget M and D are performed from left to right asthey appear in the problem. The same is true for A and S. For example, 18 ÷ 2 • 35 9 • 3 5 27. The division is to the left of the multiplication, so it is performedfirst. Another example is 8 2 2 1 3 5 6 1 3 5 9. The subtraction is to the left of theaddition, so it is performed first.Homework: Set 1.9abc, pp. 81–82, 1–57 (Odd Numbered Problems).10. Read Sect. 1.9d pp. 79–80Homework: Set 1.9d, pp. 82–83, 59–69 (Odd Numbered Problems). 71–8011. To get ready for the test on Lesson 1, do the Summary and Review for Chapter 1,pp. 84–86, 1–69. (Remember to check your answers). Notice that each problemis keyed to the section wherein that type of problem is presented.7

8 Study Guide for Math 95A, B12. The sample test is all the problems 1–47 of the Test: Chapter 1 on pages 87–88of your textbook. Time yourself to know how much time you should allow forthe actual test.13. Show your homework and sample test, then ask for the Lesson 1 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

Lesson 2: Fractions—Multiplication and DivisionProcedures1. Read Sect. 2.1, pp. 90–95Homework: Set 2.1, pp. 96–97, 1–87 (Odd Numbered Problems).2. Read Sect. 2.2, pp. 98–101Homework: Set 2.2, pp. 102–103, 1–35 (Odd Numbered Problems).3. Read Sect. 2.3, pp. 104–109Homework: Set 2.3, pp. 110–114, 1–75 (Odd Numbered Problems).4. Read Sect. 2.4, pp. 115–116Homework: Set 2.4ab, pp. 120, 1–35 (Odd Numbered Problems).5. Read Sect. 2.4c, pp. 117–119Homework: Set 2.4, pp. 120–121, 37–57 (Odd Numbered Problems).6. Read Sect. 2.5, pp. 122–126Homework: Set 2.5, pp. 127–128, 1–67 (Odd Numbered Problems).7. Read Sect. 2.6, pp. 129–130Homework: Set 2.6, pp. 131–134, 1–69 (Odd Numbered Problems).8. Read Sect. 2.7ab, pp. 135–137Homework: Set 2.7, pp. 141, 1–31 (Odd Numbered Problems).9. Read Sect. 2.7c, pp. 138–140Note: In Example 9, to go from step 1 to step 2, let us show you some intermediatesteps.4-- • x 34-- • x3-----------4--36--74--3------- • x 4--31 • xHomework: Set 2.7c, p. 142, 33–39 (odds).10. Read Sect. 2.7d, pp. 138–1406--7 ----- (divide both sides by 4 34-- )--36--74 --36 36 3 18 -- • -- So, x -- • -- ----- 7 47 4 28Homework: Set 2.7, pp. 142–143, 41–61 (Odd Numbered Problems).9-----149

10 Study Guide for Math 95A, B11. Do the Summary and Review exercises for Chapter 2, pp. 144–146, 1–83 (OddNumbered Problems).12. The sample test is all the problems 1–43 of the Test: Chapter 2 on pages 147–148of your textbook. Time yourself in order to know how much time to allot for theactual test.13. Show your homework and sample test, then ask for the Lesson 2 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

Lesson 3: Fractions—Addition and SubtractionProcedures1. Read Sect. 3.1, pp. 150–152 (to just before “Finding LCM’s Using Prime Factorization”).Note: Here is another example.Find the LCM of 8, 12 and 15.a. 15 is not a multiple of 8 or 12.b. Check multiples:2 • 15 30 Not a multiple of 8 or 12.3 • 15 45 Not a multiple of 8 or 12.4 • 15 60 Multiple of 12, but not of 8.5 • 15 75 Not a multiple of 8 or 12.6 • 15 90 Not a multiple of 8 or 12.7 • 15 105 Not a multiple of 8 or 12.8 • 15 120 Is a multiple of 8 and of 12.LCM 120.2. Read Sect. 3.1, pp. 152–155Homework: Set 3.1, pp. 156–157, 1–59 (Odd Numbered Problems).3. Read Sect. 3.2a, pp. 158–160Homework: Set 3.2, pp. 162, 1–35 (Odd Numbered Problems).4. Read Sect. 3.2b, pp. 161Homework: Set 3.2, pp. 163–164, 37–59 (Odd Numbered Problems).5. Read Sect. 3.3a, pp. 165–166Homework: Set 3.3, pp. 1–35 (Odd Numbered Problems).6. Read Sect. 3.3b, pp. 166–167Homework: Set 3.3, pp. 170, 37–59 (Odd Numbered Problems).7. Read Sect. 3.3cd, pp. 167–169Homework: Set 3.3, pp. 171–172, 61–75 (Odd Numbered Problems).8. Read Sect. 3.4a, pp. 173–175Homework: Set 3.4, pp. 177–178, 1–49 (Odd Numbered Problems).9. Read Sect. 3.4b, pp. 175–176Homework: Set 3.4, pp. 179, 51–73 (Odd Numbered Problems).10. Read Sect. 3.5a, pp. 180Homework: Set 3.5, pp. 185, 1–19 (Odd Numbered Problems).11. Read Sect. 3.5b, pp. 181–18211

12 Study Guide for Math 95A, BHomework: Set 3.5, pp. 185–186, 21–35 (Odd Numbered Problems).12. Read Sect. 3.5c, pp. 182–184Homework: Set 3.5, pp. 186–189, 37–75 (Odd Numbered Problems).13. Read Sect. 3.6a, pp. 190Homework: Set 3.6, pp. 196, 1–11 (Odd Numbered Problems).14. Read Sect. 3.6b, pp. 191Homework: Set 3.6, pp. 196, 13–23 (Odd Numbered Problems).15. Read Sect. 3.6c, pp. 192–195Note: Here is another exampleA car travels at 10 mph for 21-- hours. How far does it travel?21 mile1 mile1 mile. . . ?1 mile1 mile. . .. . .1 mile1 mile122 rows10 in each rowMiles perhourNumber of• =hoursTotal numberof milesSo, 10 • 2 1 2 --10 • 2 1 2= n10 5 2 • 5 • 5 2 5 • 5 25 ----- • -- ------------------- -- • ---------- ----- 25 miles1 2 2 • 1 2 1 1Homework: Set 3.6, pp. 197–200, 25–59 (Odd Numbered Problems).16. Read Sect. 3.7, pp. 201–204Homework: Set 3.7, pp. 205–208, 1–85 (Odd Numbered Problems).17. Do Summary and Review for Chapter 3, pp. 209–211, 1–63. (Odd NumberedProblems.)18. The sample test is all the problems 1–37 of the Test: Chapter 3 on pages 212–213of your textbook. Time yourself so that you know how much time to allot for theactual test.19. Show your homework and sample test, then ask for the Lesson 3 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

Lesson 4: Decimals—Addition and SubtractionProcedures1. Read Sect. 4.1a, pp. 218–220Note: The word and is used only for the decimal point and nowhere else!Homework: Set 4.1, pp. 225, 1–9 (Odd Numbered Problems).2. Read Sect. 4.1b, pp. 220–222Note: The word name for the decimal number indicates the denominator of thefraction.Examples1.9.3 is Nine and three tenths, so 9.393-----.102.59.25 is Fifty-nine and twenty-five hundredths,5925so, 59.25 -----------100Homework: Set 4.1, pp. 225–226, 11–41 (Odd Numbered Problems).3. Read Sect. 4.1cd, pp. 223–224Note: The second number line at the bottom of page 223 is an enlargement ofonly the portion between 0.3 and 0.4 in the first number line.Homework: Set 4.1, pp. 226–227, 43–99 (Odd Numbered Problems).4. Read Sect. 4.2ab, pp. 228–230Homework: Set 4.2, pp. 233–234, 1–47 (Odd Numbered Problems).5. Read Sect. 4.2c, pp. 231Homework: Set 4.2, pp. 234, 49–55 (Odd Numbered Problems).6. OPTIONAL: Read Sect. 4.2d, pp. 231–232Homework: Set 4.2, pp. 235, 57–67 (Odd Numbered Problems).13

Lesson 4: Decimals—Multiplication and DivisionProcedures1. Read Sect. 4.3a, pp. 236–238Homework: Set 4.3, pp. 241–242, 1–47 (Odd Numbered Problems).2. Read Sect. 4.3b, pp. 239–240Homework: Set 4.3, pp. 242–243, 49–71 (Odd Numbered Problems).3. Read Sect. 4.4a, pp. 244–245Homework: Set 4.4, p. 251, 1–13 (Odd Numbered Problems).4. Read Sect. 4.4a, pp. 246–248Homework: Set 4.4, pp. 251–252, 15–41 (Odd Numbered Problems).5. Read Sect. 4.4bc, pp. 248–250Homework: Set 4.4, pp. 252–254, 43–83 (Odd Numbered Problems).6. Read Sect. 4.5a, pp. 255–357Homework: Set 4.5, pp. 260, 1–357. Read Sect. 4.5b, pp. 257–258Homework: Set 4.5, 4.5, pp. 260–262, 37–658. Read Sect. 4.5c, pp. 259Homework: Set 4.5, pp. 262–263, 67–97 (Odd Numbered Problems).9. Read Sect. 4.6, pp. 264–266Homework: Set 4.6, pp. 267–269, 1–37 (Odd Numbered Problems).10. Read Sect. 4.7, pp. 270–277Homework: Set 4.7, pp. 278–284, 1–67 (Odd Numbered Problems).11. Do the Summary and Review for Chapter 4 on pp. 285–287, 1–77.12. The sample test is all the problems 1–53 of the Test: Chapter 4 on pages 288–290in your textbook. Time yourself to make sure you allot enough time for the actualtest.13. Show your homework and sample test, then ask for the Lesson 4 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Be sure you are ready for this test since everytest you take is averaged into your score for this lesson.14

Lesson 5: Ratio and ProportionProcedures1. Read Sect. 5.1, pp. 292–295Homework: Set 5.1, pp. 296–298, 1–51 (Odd Numbered Problems).2. Read Sect. 5.2, pp. 299–301Homework: Set 5.2, pp. 302–305, 1–41 (Odd Numbered Problems).3. Read Sect. 5.3a, pp. 306–307Homework: Set 5.3, pp. 311, 1–9 (Odd Numbered Problems).4. Read Sect. 5.3b, pp. 307–310Homework: Set 5.3, pp. 311–313, 1–57 (Odd Numbered Problems).5. Read Sect. 5.4, pp. 314–320Note: In setting up a proportion it is crucial to have both ratios in the samedirection. In Example 3 on page 315, for example, it would be wrong to write theproportion as8-----52since the ratio on the left represents tickets to cost while the ratio on the rightrepresents cost to tickets.Homework: Set 5.4, pp. 320–324, 1–47 (Odd Numbered Problems).6. Read Sect. 5.5, pp. 325–328Homework: Set 5.5, pp. 329–332, 1–39 (Odd Numbered Problems).7. Do the Summary and Review for Chapter 5 on pages 333–335, 1–35.8. The sample test is all the problems 1–23 of the Test: Chapter 5 on pages 336–337of your text book. Time yourself to ensure you allot enough time for the actualtest.9. Show your homework and sample test, then ask for the Lesson 5 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.90-----n15

Cumulative Lesson: Final Exam for Math 95ACongratulations, you have completed all your lesson tests for the first module Math95A of the Arithmetic course. The only remaining task for you to complete is the finalexamination. This will demonstrate that you have mastered the material contained in thefirst five lessons of this Study Guide.ObjectivesWhen you have completed the final exam, you will be able to:1. Say you have mastered the material in Lessons 1–5.2. Receive a grade in Math 95A.Procedures1. Read through your past homework assignments and redo as many problems asneeded to make sure you feel that you are comfortable with all the material.2. Redo your sample tests from the first five lessons.3. Do the Cumulative Review for Chapters 1–5, pp. 338–340, 1–47.4. The sample test is Cumulative Lesson: Sample Final for Math 95A given onpages 18–23 of this Study Guide. Be sure to time this test and allow enough timefor yourself during the real examination. If you take this test during the designatedday of finals week you will be restricted to a time limit of 3 hours. Duringthe regular class time you can take the entire continuous period for which themath lab is open.5. Show your sample test to a staff member and ask for the final for Math 95A. Ifyou use scratch paper number the problems in sequence and staple your scratchpaper to your test before you turn it in. Be sure you are ready for this test sinceyou can take it only once and it counts for 35% of your course grade.16

Cumulative Lesson: Sample Final for Math 95AThis is a very close representation for the actual final exam, so be sure you can workthese problems easily.1. Write a word name for 5742.2. Add: 356 491 3. Subtract: 625 3274. Round to the nearest hundred: 90798535. Multiply: 6. Divide: 48 48993 9367. Solve: 13 x 42 8. Find your new balance, if you write checks of$45, $78, and $32 from a balance of $246.9. Evaluate: 9 3 10. Simplify: 15 ÷ 3 • 2 ÷ (10 8)17

18 Study Guide for Math 95A, B11. Find the prime factorization of 156.12. You will be asked to state one of the divisibility rules for 2, 3, 4, 5, 9, or 10.13. Identify the numerator and the denominator for11----- .2014. Multiply:7 2----- • --13 315. Write an equivalent expression with the denominator of 45 for5-- .31816. Simplify: ----- 17. Multiply and simplify:2410-----213• --48 418. Divide and simplify: ----- -- 19. Solve:15 54-- • x 605220. How many -- -cup sugar bowls can be filled from 16 cups of sugar?3

Cumulative Lesson: Sample Final for Math 95A 1921. Find the LCM of 24, 36, and 12.22. Add and simplify:3-----203 --4723. A student walked --3mile alone, and then walked -- mile with a friend. How fardid the student walk?643 1124. Subtract and simplify: -- ----- 25. Solve: x -----4 20301-----1026. Convert 52-- to fractional notation.3Add or subtract and write a mixed numeral for the answer:2 7 8 --27. 28. 35 8 --4 1 5 --23 5 --

20 Study Guide for Math 95A, BMultiply or divide and write a mixed numeral for the answer:29. 8 • 2 5 30.6 --20 3 1 5 --31. Write a word name for 23.9.32. Convert to fractional notation (do not simplify): 8.2133. Convert to decimal notation:92--------.10034. Round 809.4732 to the nearest tenth.35. Round 809.4732 to the nearest thousandth.36. Add: 0.34 3.5 0.127 768 37. Subtract: 100 0.3438. Solve: 3.205 x 22.456

Cumulative Lesson: Sample Final for Math 95A 2139. A man bought a hat for $16.99 and paid for it with a $20 bill. How much changewas there?40. How much did you spend if you wrote checks for $176.20, $141.87, and $38.82?41. Multiply: 0.04 6.3 42. Convert from dollars to cents: $28.88.43. Divide: 3.2 27.2 44. Solve: 4.2 • x 39.06Convert to decimal notation:1745. -----46.207--6

22 Study Guide for Math 95A, B47. Estimate by rounding to the nearest tenth: 2.678 0.44548. What is the cost of 8 pairs of socks at $4.95 each?49. A car went 250 miles in 4 hours. How far did it go in 1 hour?50. Write fractional notation for the ratio of 4 to 5.51. Solve:18-----4x-----1052. Find the rate as a ratio of distance to time: 120 miles, 3 hours53. An 8-pound chicken contains 36 servings. What is the ratio in servings perpound?

Cumulative Lesson: Sample Final for Math 95A 2354. A car travels 800 miles in 3 days. At this rate, how many miles will it travel in 15days? (Set up a proportion, then solve.)55. If 7 tickets cost $45.50, what is the cost of 17 tickets? (Set up a proportion, thensolve.)

Lesson 6: PercentProcedures1. Are you officially enrolled in Math 95B? If not have your instructor sign an addcard and turn it into the Admissions Office.Read Sect. 6.1ab, pp. 342–344 up to and including Example 4.Homework: Set 6.1, pp. 346–347, 1–33 (Odd Numbered Problems).2. Read Sect. 6.1b, pp. 344–345Note: In the first example, another way to see how to convert from a decimal toa percent is to first change to a fraction:Homework: Set 6.1, pp. 347–348, 35–61 (Odd Numbered Problems).3. Read Sect. 6.2a, pp. 349–351Homework: Set 6.2, pp. 354, 1–35 (Odd Numbered Problems).4. Read Sect. 6.2b, pp. 351–353Homework: Set 6.2, pp. 355–357, 37–95 (Odd Numbered Problems).5. Read Sect. 6.3, pp. 358–362Homework: Set 6.3, pp. 363–364, 1–45 (Odd Numbered Problems).6. Read Sect. 6.4a, pp. 365–367Homework: Set 6.4, pp. 369 1–67. Read Sect. 6.4b, pp. 367–368Homework: Set 6.4, pp. 369–370, 7–45 (Odd Numbered Problems).8. Read Sect. 6.5a, pp. 371–373Homework: Set 6.5, pp. 379–381, 1–19 (Odd Numbered Problems).9. Read Sect. 6.5b, pp. 374–378Homework: Set 6.5, pp. 381–384, 21–63 (Odd Numbered Problems).10. Read Sect. 6.6, pp. 385–389Homework: Set 6.6, pp. 390–393, 1–59 (Odd Numbered Problems).11. Read Sect. 6.7, pp. 394–3973810.38 -------- 38 -------- 38%100 100Homework: Set 6.7, pp. 398–400, 1–45 (Odd Numbered Problems).12. Do the Summary and Review exercises for Chapter 6, pp. 410–412, 1–33.24

Lesson 6: Percent 2513. The sample test is all the problems 1–20 on pages 413–414 of your textbook.Time yourself to ensure you allot enough time for the actual test.14. Show your homework and sample test, then ask for the Lesson 6 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

Lesson 7: Data Analysis, Graphs, and PredictionsProcedures1. Read Sect. 7.1, pp. 416–421Homework: Set 7.1, pp. 424–426, 1–35 (Odd Numbered Problems).2. Read Sect. 7.2a, pp. 427–428Homework: Set 7.2, pp. 431–433, 1–25 (Odd Numbered Problems).3. Read Sect. 7.2b, 429–430Homework: Set 7.2, pp. 433–435, 27–51 (Odd Numbered Problems).4. Read Sect. 7.3ab, pp. 436–438Homework: Set 7.3, pp. 442–444, 1–31 (Odd Numbered Problems).5. Read Sect. 7.3cd, pp. 438–441Homework: Set 7.3 445–447, 33–57 (Odd Numbered Problems).6. Read Sect. 7.4, pp. 448–450Homework: Set 7.4, pp. 451–453, 1–17 (Odd Numbered Problems).7. So the Summary and Review for chapter 7, pp. 454–457, 1–53 (Odd NumberedProblems).8. The sample test is all the problems 1–31 of the Test: Chapter 7, pp. 458–461.Time yourself to ensure that you allot enough time to complete the actual test.9. Show your homework and sample test, then ask for the Lesson 7 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.26

Lesson 8: Measures of Length and AreaProcedures1. Read Sect. 8.1, pp. 466–470Homework: Set 8.1, pp. 470–471, 1–47 (Odd Numbered Problems).2. Read Sect. 8.2, pp. 472–477Homework: Set 8.2, pp. 478–479, 1–61 (Odd Numbered Problems).3. Read Sect. 8.3, pp. 480–481Homework: Set 8.3, p. 482, 1–39 (Odd Numbered Problems).4. Read Sect. 9.1, pp. 516–518Homework: Set 9.1, pp. 519–520, 1–31 (Odd Numbered Problems).Note: Here are two more examples.Example 1 A framed painting measures 24 in. by 36 in. The painting itself measures20 in. by 32 in. Find the area of the frame.36 in.24 in.32 in.20 in.An easy way to do this problem is to find the area of the whole thing (frame andpainting) and subtract out the area of the painting.Area of PaintingPlus Frame Area ofPaintingArea ofFrame(24 36) (20 32) n864 640 224 in. 227

28 Study Guide for Math 95A, BExample 2 Find the area of this polygon.5 cm9 cm15 cm6 cm20 cmOne way to find the area is to draw dashed lines to complete the rectangle.9 cm5 cm15 cm(96) cm = 3 cm6 cm20 cmThe area of the L-shaped region is the area of the large rectangle minus the areaof the small rectangle.Area of L-shaped region (20 9) (15 3) 180 45 135 cm 2A second way to do the problem is to divide the region into smaller rectangles.5 cm3 cm A15 cm6 cm B6 cm20 cmArea ofL-shaped Region Area ofRectangle AArea ofRectangle B(5 3) (20 6) 15 120 135 cm 25. Read Sect. 9.2ab, pp. 521–525Homework: Set 9.2, pp. 527–528, 1–33 (Odd Numbered Problems).6. Read Sect. 9.2c, pp. 525–526Homework: Set 9.2, pp. 529–531, 35–67 (Odd Numbered Problems).

Lesson 8: Measures of Length and Area 297. Read Sect. 9.3, pp. 532–536Homework: Set 9.3, pp. 537–540, 1–41 (Odd Numbered Problems).8. Read Sect. 9.6ab, pp. 560–561Homework: Set 9.6, pp. 565, 1–27 (Odd Numbered Problems).9. Read Sect. 9.6cd, pp. 561–564Homework: Set 9.6, pp. 565–568, 29–65 (Odd Numbered Problems).Note: You are only required to give exact answers–not approximations.10. Do the Summary and Review for Chapter 8 on pp. 510–511, 1–12 and theSummary and Review for Chapter 9 on pp. 569–571, 1–21, and 42–50.11. The sample test is all the problems 1–8 of the Test: Chapter 8 on p. 513, andproblems 1–10, 28–34 of the Test: Chapter 9 on pp. 574–576 of your textbook.Time yourself to ensure you allot enough time for the actual test.12. Show your homework and sample test, then ask for the Lesson 8 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

Lesson 9: More on MeasuresProcedures1. Read Sect. 9.4a, pp. 541–542; Sect. 8.5a, pp. 493–495Note: A cube has sides of equal length.A liter can also be represented by a cube with each edge measuring 10 cm.10 cm10 cm10 cmThe volume of this cube is:10 cm 10 cm 10 cm 1000 cm 3Homework: Set pp. 546, 1–7 (Odd Numbered Problems).Set. 8.5, pp. 496–497, 1–35 (Odd Numbered Problems).2. Read Sect. 8.5b, p. 495Homework: Set 8.5, pp. 497–498, 37–65 (Odd Numbered Problems).3. Read Sect. 9.4b, pp. 542–543Homework: Set 9.4, p. 547, 9–13 (Odd Numbered Problems).4. Read Sect. 9.4c, pp. 543–544Homework: Set 9.4, p. 547, 15–19 (Odd Numbered Problems).5. Read Sect. 9.4de, pp. 544–545Homework: Set 9.4, pp. 548–550, 21–49 (Odd Numbered Problems).6. Read Sect. 8.4ab, pp. 484–487; Sect. 8.6a, p. 499Homework: Set 8.4, pp. 489–490, 1–41 (Odd Numbered Problems).Set 8.6, pp. 502, 1–21 (Odd Numbered Problems).7. Read Sect. 8.6b, pp. 500–502Homework: Set 8.6, pp. 502–504, 23–61 (Odd Numbered Problems).8. Read Sect. 8.7, pp. 505–507Homework: Set 8.7, pp. 508–509, 1–39 (Odd Numbered Problems).9. Read Sect. 9.5, pp. 551–556Homework: Set 9.5, pp. 557–559, 1–57 (Odd Numbered Problems).10. Do the Summary 1and Review for Chapter 8, pp. 510–49, 13–49. Do theSummary and Review for Chapter 9, pp. 571–573, 22–41.30

Lesson 9: More on Measures 3111. The sample test is problems 9–29 of the Test: Chapter 8 on pages 513–514 ofyour textbook, and problems 11–34 of the Test: Chapter 9 on pages 574–576 ofyour textbook. Be sure to time yourself to ensure that you allot enough time totake the actual exam.12. Show your homework and sample test, then ask for the Lesson 9 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

Lesson 10: The Real Number SystemProcedures1. Read Sect. 10.1abc, pp. 582–585Homework: Set 10.1, p. 588, 1–23 (Odd Numbered Problems).2. Read Sect. 10.1de, pp. 585–587Homework: Set 10.1, p. 589, 25–69 (Odd Numbered Problems).3. Read Sect. 10.2a, pp. 590–592Homework: Set 10.2, p. 594, 1–53 (Odd Numbered Problems).4. Read Sect. 10.2b, pp. 592–593Homework: Set 10.2, p. 595, 55–77 (Odd Numbered Problems).5. Read Sect. 10.3, pp. 596–598Note: There is a way to explain subtraction of integers on the number line. Thedifferences, a b, is obtained as follows:Start at b and move toward a. If you move toward the right, the difference is positive.If you move toward the left, the difference is negative.In other words, a b is the directed distance from b to a.Example 1 8 3 ?5 units right7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9So 8 3 5 (Of course, you already knew that!)Example 2 5 (2) ?7 units right7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9So, 5 (2) 7Example 3 2 5 ?7 units left7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9So, 2 5 732

Lesson 10: The Real Number System 33Example 4 3 8 ?5 units left7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9So, 3 8 5Example 5 4 (6) ?2 units right7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9So, 4 (6) 26. Read Sect. 10.4, pp. 602–603Note: It is important that you learn the shortcut method shown at the top ofpage 597. Once you know it, then every subtraction problem is easily changed toaddition.Homework: Set 10.4, pp. 604–605, 1–69 (Odd Numbered Problems).7. Read Sect. 10.5a, pp. 606–607Homework: Set 10.5, p. 613, 1–208. Read Sect. 10.5bc, pp. 607–609Homework: Set 10.5, p. 613, 21–39 (Odd Numbered Problems).9. Read Sect. 10.5de, pp. 609–612Homework: Set 10.5, pp. 613–615, 41–97 (Odd Numbered Problems).10. Do the Summary and Review for Chapter 10 on pp. 616–618, 1–47.11. The sample test is all the problems 1–32 of the Test: Chapter 10 on pages 619–620 of your textbook. Be sure to time yourself to ensure you allot enough time totake the actual test.12. Show your homework and sample test, then ask for the Lesson 10 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.

34 Study Guide for Math 95A, BLesson 11:Algebra: Equations, Problem Solving, and ExponentsProcedures1. Read Sect. 11.1a, pp. 622–624Homework: Set 11.1, p. 629, 1–102. Read Sect. 11.1b, pp. 624–627Homework: Set 11.1, p. 629, 11–29 (Odd Numbered Problems).3. Read Sect. 11.1c, pp. 627–628Homework: Set 11.1, pp. 629–630, 31–45 (Odd Numbered Problems).4. Read Sect. 11.1d, p. 628Homework: Set 11.1, p. 630, 47–71 (Odd Numbered Problems).5. Read Sect. 11.2, pp. 631–632Homework: Set 11.2, pp. 633–634, 1–57 (Odd Numbered Problems).6. Read Sect. 11.3, pp. 635–637Homework: Set 11.3, 1–49 (Odd Numbered Problems).7. Read Sect. 11.4ab, pp. 640–645 Up to and including Example 6.Homework: Set 11.4, pp. 647–648, 1–43 (Odd Numbered Problems).8. Read Sect. 11.4b, pp. 642–644Homework: Set 11.4, pp. 648–649, 45–579. Read Sect. 11.4c, pp. 645–646Homework: Set 11.4, pp. 649–650, 59–8910. Read Sect. 11.5a, pp. 651–652Homework: Set 11.5, p. 661, 1–711. Read Sect. 11.5b, pp. 653–660, 9–49 (Odd Numbered Problems).12. Do the Summary and Review for chapter 11, pp. 666–668, 1–46.13. The sample test is all the problems 1–25 of the Test: Chapter 11 on pages 669–670 of your textbook. Time yourself to be sure you allot enough time for theactual test.14. Show your homework and sample test, then ask for the Lesson 11 test. If you usescratch paper, number your problems in sequence and staple your scratch paperto your test before you turn it in. Make sure your scratch paper is clear and easyto read. Be sure you are ready for this test since every test you take is averagedinto your score for this lesson.34

Cumulative Lesson: Final Exam for Math 95BCongratulations, you have completed all your lesson tests for the second module Math95 B of the Arithmetic course. The only remaining task for you to complete is the finalexamination. This will demonstrate that you have mastered the material contained in thelast six lessons of this Study Guide.ObjectivesWhen you have completed the final exam, you will be able to:1. Say you have mastered the material in Lessons 6–11.2. Receive a grade in Math 95B.Procedures1. Read through your past homework assignments, and redo as many problems asneeded to make sure you feel that you are comfortable with all the material.2. Redo your sample tests from the last six lessons.3. Do the Cumulative Review for Chapters 1–11, pp. 671–676, 1–123.4. Do the following as a sample test for the final exam:The sample test is Cumulative Lesson: Sample Final for Math 95B given onpages 36–43 of this Study Guide. Time yourself on this test to ensure you allotenough time to take the actual exam. If you take this test during the designatedday of finals week you will be restricted to a time limit of 3 hours. During theregular class times you can take the entire continuous period for which the mathlab is open.5. Show your sample test to a staff member and ask for the final for Math 95B. Ifyou use scratch paper number the problems in sequence and staple your scratchpaper to your test before you turn it in. Be sure you are ready for this test sinceyou can take it only once and it counts for 35% of your course grade.35

36 Study Guide for Math 95A, BCumulative Lesson: Sample Final for Math 95BThis is a very close representation for the actual final exam, so be sure you can workthese problems easily.1. a. Find decimal notation for 0.18%.b. Find percent notation for 0.334.52. Find percent notation for -- .83. Find fractional notation for 16.6%.4. $39 is what percent of $50?5. 70% of what is 14?6. What is 76% of 90? (Use a proportion.)

Cumulative Lesson: Sample Final for Math 95B 377. A mix consists of three products a, b, and c. There is 1800 lb of product a, 1500 lbof product b, and 700 lb of product c. What percent is product c?8. The amount in an account increased from $200 to $216. What was the percent ofincrease?9. The sales-tax rate is 8.25%. What is the total price of a product with a purchaseprice of $248?10. The sales tax is $48 on a purchase of $960. What is the sales-tax rate?37

38 Study Guide for Math 95A, B11. If the rate of discount is 15% and the amount of discount is $65.70, find the saleprice.12. Find the amount in an account with a principal of $400 at 7% for one year, ifinterest is compounded semiannually.13. For the set {8, 7, 15, 15, 15, 12}, find the:a. average b. median c. mode14. Find the grade-point average for two courses. One is a 12-unit course with agrade of B, and the other is a 4-unit course with a grade of C.

Cumulative Lesson: Sample Final for Math 95B 3915. To get a B, a student must have an average of 80. The previous scores were 80,74, 81, and 75. What is the lowest score that the student can get on the last testand still get a B?See the graph on page 451 of your textbook for problems 16–18. Suppose thefamily has a monthly income of $2000.16. Which item accounts for the greatest expense?17. How much is spent for transportation?18. What percent would be spent on medical care and personal care combined?19. A survey is conducted to determine which of two math problems students enjoymost. They solved both problems giving each a rating from 1 to 10. From theseresults, which was best?Problem A6, 8, 10, 77, 9, 9, 85, 10, 9, 109, 4, 7, 6Problem B10, 9, 9, 68, 8, 10, 78, 7, 4, 37, 8, 10, 9

40 Study Guide for Math 95A, B20. How many inches are there in 7 yards?21. Complete the following: 98 cm _____________________ m22. Complete the following: 7.44 m _____________________ hm23. Find the perimeter of the rectangle that is 5 ft by 10 ft.24. Find the area of the square that is 22 feet on a side.25. How much would it cost to carpet a 15 ft by 20 ft room, if the carpet costs $18.50per square foot?26. Find the area of the triangle that has a height of 8 cm and a base of 15 cm.27. Find the area of the trapezoid that has a height of 8 feet and the lengths of theparallel sides are 6 feet and 20 feet.28. Find the circumference of the circle with a radius of 7 meters. (Use the fractionalrepresentation for .)

Cumulative Lesson: Sample Final for Math 95B 4129. Find the area of the circle with a diameter of 32 feet. (Use the decimal representationfor .)30. Simplify:36131. In a right triangle, find the length of side a if side b is 18 and side c is 30.32. Complete the following: 1 gal _____________________ oz33. Find the volume of a cube 18 yards on a side.34. The diameter of the base of a circular cylinder is 14 yards. The height is 220yards. Find the volume of the cylinder. Use as a fraction.35. Complete the following: 8 kg _____________________ cg36. Complete the following: 2 wk _____________________ hr37. Convert 86F to Celsius.

42 Study Guide for Math 95A, B38. Complete the following: 22 yd 2 _____________________ ft 239. Find angle ACB:A35C25B40. Is 3 4 or 4 3?41. Find |7|.42. Add: 10 643. Find the opposite, or additive inverse, of 24.44. Subtract: 8 (2)45. Simplify: 31 (28) (14) 1746. Multiply: 8 • (2)47. Multiply: 7 • (21) • 1348. Divide:72----------949. Simplify: 9 ÷ (3) 16 ÷ 850. Multiply: 7( y 2)

Cumulative Lesson: Sample Final for Math 95B 4351. Factor: 32 4y52. Collect like terms: 41x 90 60x 2Solve using the addition principle. Then check.53. x 6 8 54. x 7 21Solve using the multiplication principle, then check.55. 2x 10 56.3--x 274Solve:57. 7x 2 54 58. 5 2x 3x 7x 2559. Translate to an algebraic expression.c less than 960. Seventeen less than four times a number is two hundred eleven. Find the number.(Translate to an algebraic equation, then solve.)

Solutions to the Sample FinalsCumulative Lesson: Sample Final for Math 95AThere are text references in front of each problem on this final. For example, [1.1]means Chapter 1, Section 1 of your textbook.[1.1] 1. Write a word name for 5742.Five thousand seven hundred forty-two[1.2] 2. Add: 356 491 [1.3] 3. Subtract: 625 327356 491 847 625 327 298[1.4] 4. Round to the nearest hundred: 90799100[1.5] 5. Multiply: 853 [1.6] 6. Divide: 9365188 798,40825590767700798408[1.7] 7.13 x 42x 42 13x 29[1.8] 8. Find your new balance, if you write checks of $45, $78, and $32 from abalance of $246.Let x the new balance if $.x 246 (45 78 32) 246 155 $91[1.9] 9. Evaluate: 9 3 [1.9] 10. Simplify: 15 ÷ 3 • 2 ÷ (10 8)9 • 9 • 9 81 • 9 729 15 ÷ 3 • 2 ÷ 2 5 • 2 ÷ 2 10 ÷ 2 5[2.1] 11. Find the prime factorization of 156.156 2 • 78 2 • 2 • 39 2 • 2 • 3 • 13[2.2] 12. You will be asked to state one of the divisibility rules for 2, 3, 4, 5, 9, or10.Look on pages 109–112 of your textbook for the divisibility rules.[2.3] 13. Identify the numerator and the denominator for11----- .The numerator is 11 and the denominator is 20.10248 489948000900009996320102 R 344

45 Study Guide for Math 95A, B[2.4] 14. Multiply:7 • 2------------- 13 • 314-----397 2----- • --13 35[2.5] 15. Write an equivalent expression with the a denominator of 45 for -- .35--35--315• -----1575-----4518[2.5] 16. Simplify: -----[2.6] 17. Multiply and simplify:2410-----213• --418-----242 • 3 • 3------------------- 2 • 4 • 33--410 3----- • --21 42 • 5 3---------- • ---------- 3 • 7 2 • 25-----14[2.7] 18. Divide and simplify:8-----154 --58-----154 2 • 2 • 2 5 -- ------------------- • ---------- 5 3 • 5 2 • 22--3[2.7] 19. Solve:4-- • x 6055-- 4 4 5 -- • x55 4 • 15 -- [ 60]; x -- • ------------- 7544 12[2.7] 20. How many -- -cup sugar bowls can be filled from 16 cups of sugar?Let x the number of sugar bowls.[3.1] 21. Find the LCM of 24, 36, and 12.24 2 • 2 • 2 • 3; 36 2 • 2 • 3 • 3; 12 2 • 2 • 3; LCM 2 • 2 • 2 • 3 • 3 or 72[3.2] 22. Add and simplify:323 2 • 8-- • x 16; x -- • ---------- ; x 3 • 8 so x 24 sugar bowls.32 13-----203 --43-----203 --43 3 5 3 15 18 ----- -- • -- ----- ----- ----- 20 4 5 20 20 209-----10[3.2] 23. A student walked73-- mile alone, and then walked --64mile with a friend.How far did the student walk?Let x the number of miles the student walked.7 3 7 2 3 3 14 9 23x -- -- -- • -- -- • -- ---------------- ----- miles or 1 11 ----- miles.126 4 6 2 4 3 12 12

Solutions to the Sample Finals 46[3.3] 24. Simplify:3--41 -----203--45• --51 -----2015 1 14 ---------------- ----- 20 207-----101[3.3] 25. Solve: x -----301-----10x1 1 1 3 1 3 1 2 ----- ----- ----- • -- ----- ------------- ----- 10 30 10 3 30 30 301-----152[3.4] 26. Convert 5 -- to fractional notation.5 2 3 --3 • 5 2 15 2 --------------------- ---------------- 3 3Add or subtract and write a mixed numeral for the answers:[3.5] 27. is the same as 3 5 8 --4 1 5[3.5] 28. -- 15 13 1 -- 3 -- -- 3 6 55 55 --so we have 2 3 5 -- 2 3 5 -- 2 3 5 -- 2 3 5 --Multiply or divide and write a mixed numeral for the answer:[3.6] 29. 8 • 22 7 8 --5--6[3.6] 30. 20 ÷ 3[4.1] 31. Write a word name for 23.9.Twenty-three and nine tenths317-----32 7 8 -- 35 8 -- 5 12 ----- 5 1 4 -- 6 1 88 2 --8 • 2 5 6 -- 8 17 ----- 8 17 2 • 4 • 17 68 • -- • ----- ---------------------- ----- 22 2 36 1 6 1 • 2 • 3 3--1--520 3 1 16 20 5 4 • 5 • 5 255 -- 20 ----- ----- • ----- ------------------- ----- 6 1 45 1 16 1 • 4 • 4 4--[4.1] 32. Convert to fractional notation (do not simplify): 8.211 3 5 --8.21821--------10092[4.1] 33. Convert to decimal notation: -------- .10092-------- 0.92100

47 Study Guide for Math 95A, B[4.1] 34. Round 809.4732 to the nearest tenth.809.4732 809.5[4.1] 35. Round 809.4732 to the nearest thousandth.809.4732 809.473[4.2] 36. Add: 0.34 3.5 0.127 7680.340 3.500 0.127 768.000 771.967[4.2] 37. Subtract: 100 0.34100.00 0.34 99.66[4.2] 38. Solve: 3.205 x 22.456x 22.456 3.205 19.251[4.7] 39. A man bought a hat for $16.99 and paid for it with a $20 bill. How muchchange was there?Let x the change in $. x 20 16.99 20.00 16.99 $3.01[4.7] 40. How much did you spend if you wrote checks for $176.20, $141.87, and$38.82?Let x amount spent in $. x 176.20 141.87 38.82 $356.89[4.3] 41. Multiply: [4.3] 42. Convert from dollars to cents:0.04 6.3 0.252 $28.88 28.88 • 100 cents 2888 ¢[4.4] 43. Divide:8.5[4.4] 44. Solve:3.2 27.2.025.6.0x 1.6.08.5 1.6.0Convert to decimal notation:4.2 • x 39.0639.06------------ 9.34.217[4.5] 45. -----[4.5] 46.207--617 5----- • --20 585-------- 0.85100[4.6] 47. Estimate by rounding to the nearest tenth: 2.678 2 0.4452.678 0.445 2.7 0.4 2.3[4.7] 48. What is the cost of 8 pairs of socks at $4.95 each?Let x cost of 8 pairs in $. x 8 • 4.95 $39.601.166 7.00 1.16

Solutions to the Sample Finals 48[4.7] 49. A car went 250 miles in 4 hours. How far did it go in 1 hour?Let x the distance in miles the car went in one hour.x miles 250 miles250---------------- ----------------------- ; 4x 1 • 250; x -------- 62.5 miles1 hour 4 hours4[5.1] 50. Write fractional notation for the ratio of 4 to 5.The ratio of 4 to 5 4--5[5.3] 51. Solve18-----4x-----104 • x 10 • 18; 4x 180; x 180-------- 454[5.2] 52. Find the rate as a ratio of distance to time: 120 miles, 3 hours120 milesRatio of distance to time ----------------------- 40 mph3 hours[5.2] 53. An 8-pound chicken contains 36 servings. What is the ratio in servingsper pound?Ratio in servings per pound 36 servings---------------------------8 pounds 4.5 servings per pound[5.4] 54. A car travels 800 miles in 3 days. At this rate, how many miles will ittravel in 15 days? (Set up a proportion, then solve.)Let x the distance in miles the car traveled in 15 days.x miles------------------15 daysx800 miles ----------------------- ; 3x 15 • 800; 3x 12,000;3 days12,000--------------- 4000 miles3[5.4] 55. If 7 tickets cost $45.50, what is the cost of 17 tickets? (Set up a proportion,and then solve.)Let x the cost of 17 tickets in $.7 tickets-------------------45.5017 tickets773.50 ---------------------- ; 7x 17 • 45.50; x --------------- $110.50$ x7

49 Study Guide for Math 95A, BCumulative Lesson: Sample Final for Math 95BThere are text references in front of each problem on this final. For example, [6.1]means Chapter 6, Section 1 of your textbook.[6.1] 1. a. Find decimal notation for 0.18%.0.18% 0.18 • 0.01 0.0018[6.1] 1. b. Find percent notation for 0.334.0.334 0.334 • 100% 33.4%5[6.2] 2. Find percent notation for -- .85-- • 100%8500--------% 62.5% or 62 1 28--%[6.2] 3. Find fractional notation for 16.6%.16.6% 16 2 3 --% 16 • 3 2 50 50 1 ------------------------ % -----% ----- • -------- 3 3 3 100[6.3] 4. $39 is what percent of $50?Let x the number in percent.3939 x% • 50; 39 x 0.01 • 50; 39 0.50 x; x --------- 78; 78%0.50[6.3] 5. 70% of what is 14?Let x the number.1470% • x 14; 0.70 • x 14; x --------- 20; 200.70[6.4] 6. What is 76% of 90? (Use a proportion.)76--------100Let x the number.x -----; 76 • 90 100 • x; 6840 100x; x 68.4; 68.490[6.5] 7. A mix consists of three products a, b, and c. There is 1800 lb of product a,1500 lb of product b, and 700 lb of product c. What percent is product c?We need to solve “700 is what percent of (1800 1 1500 1 700)?”.Let x the percent of the total mix that is product c.1--6700 x% • 4000; 700 x • 0.01 • 4000; 700 40x; x700--------4035-----; 17 1 22--%

Solutions to the Sample Finals 50[6.5] 8. The amount in an account increased from $200 to $216. What was the percentof increase?The amount of increase is ($216 $200) $16We need to solve "$16 is what percent of $200?".Let x the percent of increase.16 x • % • 200; 16 x • 0.01 • 200; 16 2x; x 8; 8%[6.6] 9. The sales-tax rate is 8.25%. What is the total price of a product with a purchaseprice of $248?The total price is purchase price plus the sales tax.Let x the total price in $.x 248 8.25% • 248; x 248 20.46 268.46; $268.46[6.6] 10. The sales tax is $48 on a purchase of $960. What is the sales-tax rate?We need to solve “$48 is what percent of $960?”.Let x the sales-tax rate.48 x • % • 960; 48 x • 0.01 • 960; 48 9.6x; x 5; 5%[6.6] 11. If the rate of discount is 15% and the amount of discount is $65.70, findthe sale price.Let x the original price in $, and let x 65.70 the sale price in $. Rate of discounttimes the original price equals the amount of discount.0.15 x 65.70; x 65.70 ÷ 0.15 438; so x 65.70 $372.30[6.7] 12. Find the amount in an account with a principal of $400 at 7% for one year,if interest is compounded semiannually.1For the first 6 months, the amount is $400 $400 • 0.07 • -- $414.1For the full year, the amount would be $414 $414 • 0.07 • -- $428.49[7.1] 13. For the set {8, 7, 15, 15, 15, 12}, find thea. average b. median c. mode228 7 15 15 15 12--------------------------------------------------------------------- 7, 8, 12, 15, 15, 1561572----- 12612 15------------------- 13.5215[7.1] 14. Find the grade-point average for two classes. One is a 12-unit class with agrade of B, and the other is a 4-unit class with a C.12 • 3 4 • 2 44GPA --------------------------------- ----- 2.7512 4 16

51 Study Guide for Math 95A, B[7.1] 15. To get a B, a student must have an average of 80. The previous scoreswere 80, 74, 81, and 75. What is the lowest score that the student can get on the lasttest and still get a B?Let x the score on the last test.80 74 81 75 x--------------------------------------------------------- 80; 310 x 5 • 80; x 400 310 905See the graph on page 397 of your textbook for problems 16–18. Suppose the familyhas a monthly income of $2000.[7.4] 16. Which item accounts for the greatest expense?The item that accounts for the greatest expense is food at 28%.[7.4] 17. How much is spent for transportation?Let x the amount spent for transportation is 10% of monthly income.x 10% of $2000 0.10 • 2000 $200 is spent for transportation.[7.4] 18. What percent would be spent on medical and personal care combined?Since 12% if spent on medical care and 2% on personal care, 12% 2% 14% would be spent on medical care and personal care combined.[7.1] 19. (See problem 2 on p. 405.) Find the average of the ratings for A (7.75) andthe average for B (7.687). The students preferred problem A.[8.1] 20. How many inches are there in 7 yards?7 yards-----------------13 feet 12 inches• -------------- • ---------------------- 252 inches1 yard 1 foot[8.2] 21. Complete the following: 98 cm __________________ m98 cm--------------1[8.2] 22. Complete the following: 7.44 m __________________ hm7.44 m----------------11 m• ----------------- 0.98 m100 cm1 hm• -------------- 0.0744 hm100 m[8.3] 23. Find the perimeter of the rectangle that is 5 ft by 10 ft.Let P the perimeter in ft.P 2L 2W; P 2 • 10 2 • 5 30 feet[9.1] 24. Find the area of the square that is 22 feet on a side.Let A the area in sq ft.A s • s 22 • 22 484 square feet[9.1] 25. How much would it cost to carpet a 15 ft by 20 ft room, if the carpet costs$18.50 per square foot?Let A the area in sq ft.A L • W 15 • 20 300 square feetC the cost in $.C $18.50---------------- • 300 sq ft $5550sq ft

Solutions to the Sample Finals 52[9.2] 26. Find the area of the triangle that has a height of 8 cm and a base of 15 cm.1 1Let A the area in sq cm. A -- bh -- • 15 • 8 60 sq cm[9.2] 27. Find the area of the trapezoid that has a height of 8 feet and the lengths ofthe parallel sides are 6 feet and 20 feet.Let A the area in sq ft.[9.3] 28. Find the circumference of the circle with a radius of 7 meters. (Use thefractional representation for p.)Let C the circumference in m. C 2pr 2 •22 ----- • 44 meters77[9.3] 29. Find the area of the circle with a diameter of 32 feet. (Use the decimalrepresentation for .)The radius, r, is one-half the diameter.21A --h b2r 32 ÷ 2 16 feetLet A the area in sq ft. A r 2 (16) 2 3.14 • 256 803.84 ft 221 ( B) -- • 8 • ( 6 20) 104 ft 22[9.6] 30. Simplify:361361 19 • 19 19[9.6] 31. In a right triangle, find the length of side a if side b is 18 and side c is 30.a 2 b 2 c 2 ; a 2 (18) 2 (30) 2 ; a 2 324 900; a 2 576; a 24[9.4] 32. Complete the following: 1 gal __________________ oz1 gal1 gal-----------14 qt 2 pt 16 oz• --------- • -------- • ------------ 128 oz1gal 1 qt 1 pt[9.4] 33. Find the volume of a cube 18 yards on a side.Let V the volume in cubic yards. V s 3 (18) 3 5832 yd 3[9.4] 34. The diameter of the base of a circular cylinder is 14 yards. The height is220 yards. Find the volume. Use p as a fraction.The radius, r, is one-half the diameter.r 14 ÷ 2 7 yardsLet V the volume in cu yd. V r 2 22h ----- ( 7) 2 220 33,880 yd 37[9.4] 35. Complete the following: 8 kg __________________ cg8 kg8 kg----------11000 g 100 cg• ---------------- • --------------- 800,000 cg1 kg 1 g[9.4] 36. Complete the following: 2 wk __________________ hr2 wk2 wk-----------17 days 24 hr• --------------- • ------------ 336 hr1 wk 1 day

53 Study Guide for Math 95A, B[8.6] 37. Convert 86F to Celsius.868F55 • 4 -- ( 86 32) ---------- 308C99[8.7] 38. Complete the following: 22 yd 2 __________________ ft 222 yd 2 22 yd 2 9 ft --------------- • ------------2 198 ft 21 1 yd 2[9.5] 39. Find angle ACBA35C25B180 (35 25) 120[10.1] 40. Is 3 4 or 4 3?3 4[10.1] 41. Find |7|.|7| 7[10.2] 42. Add: 10 610 6 4[10.2] 43. Find the opposite, or additive inverse, of 24.The opposite, or additive inverse, of 24 is 24.[10.3] 44. Subtract: 8 (2)8 (2) 8 2 6[10.3] 45. Simplify: 31 (28) (14) 1731 (28) (14) 17 31 28 14 17 59 3 62[10.4] 46. Multiply: 8 • (2)8 • (2) 16[10.4] 47. Multiple: 7 • (21) • 137 • (21) • 13 147 • 13 1911[10.5] 48. Divide:72---------- 8972----------9[10.5] 49. Simplify: 9 ÷ (3) 16 ÷ 89 ÷ (3) 16 ÷ 8 3 2 1[11.1] 50. Multiply: 7(y 2)7(y 2) 7 • y (7) • (2) 7y 14

Solutions to the Sample Finals 54[11.1] 51. Factor: 32 4y32 4y 4 • 8 4y 4(8 y)[11.1] 52. Collect like terms: 41x 90 60x 241x 90 60x 2 (41 60)x (90 2) 19x 88Solve using the addition principle. Then check.[11.2] 53. x 6 8 [11.2] 54. x 7 21x 8 6 14x 21 7 14Solve using the multiplication principle. Then check.[11.3] 35. 2x 10 [11.3] 56.3--x 274xSolve:10 ---------- 5x2[11.4] 57. 7x 2 54 [11.4] 58. 5 2x 3x 7x 257x 54 2 5 2x 4x 257x 56 4x 2x 25 5x[11.5] 59. Translate to an algebraic expression.c less than 9c less than 9 9 c[11.5] 60. Seventeen less than four times a number is two hundred eleven. Find thenumber. (Translate to an algebraic equation, then solve.)Let x the number4 27 -- • ----- 4 • 9 363 15620 ---------- 82x 20; x ----- 10724x 17 211; 4x 211 17; 4x 228; x 228--------4 57 is the number