college algebra manual student lecture01

8/13/2019 College Algebra Manual Student Lecture01

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Video-based Supplemental Instruction

College AlgebraStudent Manual

July 2007 Edition

University of Missouri-Kansas CityThe College of Arts and Sciences

The Center for Academic Development


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VSI College Algebra Manual2007 Version

Sonny L. Painter, Assoc.VSI Coordinator and Curriculum DesignCenter for Academic DevelopmentUniversity of Missouri-Kansas City5100 Rockhill Road, SASS Building, Room 210Kansas City, MO 64110-2499(816) 235-1179

[email protected]://www.umkc.edu/cad/vsi

Copyrights by the Curators of the University of Missouri, 2007


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Table of Contents

p. I

ContentsSyllabus for Course .................................................................................................................. III

Suggested Homework ..............................................................................................................VI

Lecture 1: Numbers .................................................................................................................... 1

Lecture 2: The Language of Mathematics ............................................................................... 36

Lecture 3: The Powers that be - Exponents ............................................................................. 48

Lecture 4a: Polynomial Expressions ........................................................................................ 82Lecture 4b: Polynomial Expressions .................................................................................... 115

Lecture 5: More Numbers and Geometry .............................................................................. 146

Lecture 6: Graphs ................................................................................................................... 156

Lecture 7: Graphs ................................................................................................................... 174

Lecture 8: Graphs ................................................................................................................... 198

Lecture 9: Functions & Their Graphs ....................................................................................229

Lecture 10: Functions & Their Graphs .................................................................................258

Lecture 11: Functions & Their Graphs .................................................................................289

Lecture 12: Functions & Their Graphs ..................................................................................309



Lecture 15: Equations in One Variable .................................................................................. 366





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Table of Contents

p. II


Lecture 20: Inequalities in One Variable................................................................................ 455

Lecture 21: Inequalities in One Varialbe................................................................................ 475

Lecture 22: Inequalities in One Variable................................................................................ 494

Lecture 23: Polynomial & Rational Functions ...................................................................... 509

Lecture 24: Polynomial & Rational Functions ...................................................................... 533

Lecture 25: Locating the Zeros of a Polynomial Function ....................................................554

Lecture 26: Locating the Zeroes of a Polynomial Function .................................................. 582Lecture 27: Rational Functions .............................................................................................. 595

Lecture 28: Exponential Functions ........................................................................................625

Lecture 29: Logarithmic Functions ........................................................................................ 644

Lecture 30: Logarithmic Functions ........................................................................................ 663

Lecture 31: Exponential Functions ........................................................................................685

Lecture 32: Systems of Linear Equations .............................................................................. 700

Lecture 33- Systems of Linear Equations .............................................................................. 726

Lecture 34: System of Non-Linear Equations ....................................................................... 747

Lecture 35: Sequences ...........................................................................................................754

Lecture 36: Sequences ...........................................................................................................771

Lecture 37: Series & Induction .............................................................................................. 787

Lecture 38: The Binominal Theorem ....................................................................................804


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Syllabus

p. III

DESCRIPTION:VSI in Math 110 is a small group approach to College Algebra. This course uses video lectures of RichardDelaware with small group interactive discussions, problem solving practice, and directed study to learningalgebra effectively and ef ciently. You will have the opportunity to earn high grades in this rigorous class whileyou gain study strategies which transfer to similar classes.

LINKED COURSE: This course links College Algebra (Math 110) with Critical Thinking in the Arts and Sciences (A&S 103c.)Both courses carry 3 hours of college credit; therefore, by taking VSI in Math 110, you will receive 6 hourscredit. See also A&S 103c syllabus.

TEXTS:Sullivan and Sullivan, College Algebra: Enhanced with Graphing Utilities, 4th Ed. Prentice Hall, UpperSaddle River, NJ, 2000. ISBN #0-13-149104-0.

Note: 1st, 2nd, and 3rd Editions may also be used.

GRAPHING CALCULATORS: You will need a graphing calculator for this course. The most preferred models are the Texas Instruments TI-83(or TI-82), the Sharp EL-9600 (or EL-9300), or the Hewlett Packard HP-38G. Other calculators that are accept-able, but contain more features than you will need, are the TI-86 (or TI-85) and the Hewlett Packard HP-48G(or HP-48GX). Calculators that are not to be used, due to the advanced computer algebra systems they possess,are the Texas Instruments TI-89 or TI-92. COURSE CONTENT:

Unit 0 Basics: Remembrance of Things PastUnit 1 GraphsUnit 2 Functions and Their GraphsUnit 3 Equations and InequalitiesUnit 4 Polynomial and Rational FunctionsUnit 5 Exponential and Logarithmic FunctionsUnit 6 Systems of EquationsUnit 7 Some Discrete Topics

The Center for Academic Development at The University of Missouri-Kansas City presents

Video-based Supplemental Instruction inMath 110: College Algebra

Video Instructor: Richard Delaware ,UMKC Department of Mathematics and Statistics

Syllabus for Course


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Syllabus

p. IV

HOMEWORK:Assigned homework problems are your individual responsibility. Some, but not all of the assigned problemswill be looked at in class. It is to your bene t to work the suggested problems to ensure yourself of havinglearned the material. Quizzes in order to check for understanding may be given at the discretion of the

facilitator.

EXAMS:There will be in-class hour examinations (written by the instructor) and one 2-hour comprehensive nal exam(written by the UMKC Department of Mathematics and Statistics.) All exams are will be closed book andclosed notes. The most damaging exam score from Exams #1 5 will be dropped. Make-up exams willordinarily not be given.

The exam coverage will be as follows:

UMKC CAMPUS EXAMS HIGH SCHOOL EXAMS

Exam #1 Unit 0 Lectures 1-5 Exam #1 Unit 0 Lectures 1-5

Exam #2 Units 1 & 2 Lectures 6-14 Exam #2a Unit 1 Lectures 6-8

Exam #2b Unit 2 Lectures 9-14

Exam #3 Unit 3 Lectures 15-22 Exam #3 Unit 3 Lectures 15-22

Exam #4 Units 4 & 5 Lectures 23-31 Exam #4a Unit 4 Lectures 23-27

Exam #4b Unit 5 Lectures 28-31

Exam #5 Units 6 & 7 Lectures 32-38 Exam #5 Units 6 & 7 Lectures 32-38

FINAL Units 1 - 7 Lectures 4-38 FINAL Units 1 - 7 Lectures 4-38

Answers on exams must be supported by evidence on your paper that you understand the methods used to arriveat your solution. SHOW YOUR WORK!!! You will receive no credit for unsupported answers; however, thesupporting calculations may earn you substantial partial credit, even if you do not obtain the correct answer.

Graphing calculators may be used on Exams #1 - 5 ; however, they may not be used on the Final Exam .

The Final Exam is a combination of multiple choice questions and short answer and is common to all sections

of College Algebra offered on or off campus. An archive of previous nal exams for practice are given on theDepartment of Mathematics and Statistics website. It is to your bene t to work as many of these problems inmultiple choice format as possible.


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Syllabus

p. V

POINT DISTRIBUTION:

UMKC CAMPUS HIGH SCHOOL

Five Exams (100 pts each; drop lowest) 400 Seven Exams (100 pts each; drop lowest) 600Final Exam 100 Final Exam 100Total Possible 500 Total Possible 700

ROLE OF VIDEO COURSE INSTRUCTOR:The role of the course instructor is to:

- present lectures by video- prepare exams- supervise the grading of exams- assign content grade

ROLE OF VSI FACILITATOR:The role of the VSI facilitator is to:

- get you actively involved with the content- expect you to be prepared for each class session- plan a schedule with you which complements the syllabus- assist you as you develop the learning strategies necessary to master the content- assign written homework - assessment of knowledge through quizzes- prepare students for nal exam through review sessions and practice nals- monitor your progress/grade for the A&S 103c grade

ROLE OF VSI STUDENT:The role of the VSI student is to:

- come prepared to class- do homework nightly- participate in class (ask questions, work problems, talk & explain with peers)- understand that visitors will come to class to assist VSI staff as we educate the public about VSI

CONTACT:Center for Academic Development - VSI Program

University of Missouri - Kansas CitySASS Building, Room 2105100 Rockhill RoadKansas City, MO 64110(816) 235-1178http://www.umkc.edu/cad/vsi


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Suggested Homework

p. VI

Lecture Time Material Assignments(Second Edition)

Assignments(Third Edition)

Assignments(Fourth Edition)

1 1 Introduction none none none

1 11 Sets of Objects and Natural Numbers

p.18 # 1-10,13-20 p.18 # 1-10,13-20 p.18 # 1-10,13-20

1 20 Integers, Rational Numbersand Irrational Numbers

p.19 # 31-32 p.19 # 31-32 p.19 # 31-32

1 24 Real Numbers p.45 # 1-20 p.45 # 1-20 p.45 # 1-20

1 8 Real Numbers, cont. p.46 # 21-50 p.46 # 21-50 p.46 # 21-50

1 11 Real Numbers, cont. p.18 # 21-30 p.18 # 21-30 p.18 # 21-30

2 Language of Mathematics

3 12 Integer Exponents p.65 # 1-4 p.65 # 1-4 p.65 # 1-4

3 31 Operations with IntegerExponents

p.65 # 5-20; p.151 #1-19,21-42

p.65 # 5-20; p.151 # 1-19,21-42

p.65 # 5-20; p.151 # 1-19,21-42

3 13 Square Roots; A Pair ofEqual Factors

p.153 # 1-5; p.158 #1-10; p.42 # 21-50

p.153 # 1-5; p.158 # 1-10; p.42 # 21-50

p.153 # 1-5; p.158 # 1-10; p.42 # 21-50

3 12 Nth Roots and RationalExponents

p.158 # 11-30 p.158 # 11-30 p.158 # 11-30

3 21 Operations With RationalExponents

p.165 # 1-27; p.168# 1-31

p.165 # 1-27; p.168 #1-31

p.165 # 1-27; p.168 # 1-31

4a 21 What is a Polynomial?;Adding and Subtracting

p.65 # 21-53 p.70 #1-43

p.65 # 21-53 p.70 # 1-43 p.65 # 21-53 p.70 # 1-43

4a 19 Multiplying Polynomials p.78 # 1-60 p.78 # 1-60 p.78 # 1-60

4a 20 A Common Error andHandy Polynomial Products

none none none

4a 27 Un-Multiplying (Factoring)Polynomials

p.83 # 1-54; p.90 #1-69

p.83 # 1-54; p.90 # 1-69 p.83 # 1-54; p.90 # 1-69

4a 10 Completing a PerfectSquare

p.90 # 1-33 usingcomplete the square

p.90 # 1-33 using com- plete the square

p.90 # 1-33 using completethe square

4b 24 Dividing Polynomials:Rational Expressions

p.96 # 21-36 p.96 # 21-36 p.96 # 21-36

5 19 Beyond Real Numbers:

Complex Numbers

p.176 # 1-47 p.176 # 1-47 p.176 # 1-47

5 20 Some Area Formulas andThe Pythagorean Theorem

p.180 # 1-26 p.180 # 1-26 p.180 # 1-26

6 12 Rectangular coordinates p.10 # 1-8 p. 97 # 1-8 p. 97 # 11-18

6 18 Distance btwn points p.12 # 21-44 p. 98 # 21-44 p. 98 # 31-54

6 7 Midoint of segment p.13 # 49-58 p. 98 # 49-58 p. 98 # 55-64

6 18 Graphing device

7 26 Graphs of Equations p.28 # 47-56; p.26 #11-21

p.108 # 1-6; p.109 #19-22

p.110 # 77-80

Suggested Homework


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Suggested Homework

p. VII

7 12 Intercepts p.27 # 31-46parts(a) p.108 # 7-18 p. 224 # 11-22parts(b)

7 15 Symmetry of Graphs p.26 # 1-10,31-46parts(b), 57-75

p. 262 # 1-34 p. 224 # 11-22parts(c )

7 34 De ning Slope p.79 # 1-22 p. 176 # 1-12 p. 176 # 7-18

8 23 Lines & their Equations p.80 # 23-26,31-42,55-85,93-99

p. 177 # 27-30, # 35-46 p. 177 # 33-36, # 41-52

8 12 Parallel Lines p.80 # 27-28,43-48 p. 177 # 31, 32, 47-52 p. 177 # 37, 38, 53-58

8 14 Perpendicular Lines p.80 # 29,30,49-54 p. 177 # 33, 34, 53-58 p. 177 # 39, 40, 59-64

8 28 Circles & their Equations p.88 # 1-38,43-44 p. 184 # 1-24 p. 185 # 5-30

8 18 Exercises Explained on tape on tape on tape

9 27 Central Idea manual, p.110 # 1-12 manual manual

9 20 Language and Notation manual manual manual

9 20 More on Domains p.112 # 49-62 p. 210 # 33-46 p. 217 # 47-609 17 Notation Practice p.110 # 13-20 p. 210 # 13-20 p. 217 # 39-46

10 26 Visualizing Functions:Graphs of (x,f(x)) pairs

p.111 # 37-48,75-78 p. 211 # 47,48, p. 212 #61-66

p. 224 # 9, 10, p. 225 # 23-28

10 23 Increasing and DecreasingFunctions

p.173 # 9-24, 67-70 p. 273 # 1-6, # 11-20part(c )

p. 237 # 11-16, # 21-28part(c)

10 19 Local Maximums and LocalMinimums

p. 173 # 67-70 p. 273 # 7-10, p. 274 #21-24, # 51-58

p. 237 # 17-20, p. 238 # 29-32, # 42-52

10 20 Even and Odd Functions p. 173 # 9-24 part c,41-52

p. 273 # 11-20part(d), p.274 # 37-48

p. 237 # 21-28part(d), p. 238# 33-44

11 21 Library of Important Func-

tions

manual, p.172 # 1-8 manual, p. 283 # 1-8 manual, p. 263 # 9-16

11 20 Piecewise De ned Func -tions

p.174 # 25-28, 55-62 p. 283 # 19-28 p. 263 # 29-38

11 11 Some Exercises Explained p.177 # 79-82

12 14 Graphing Techniques: Ver-tical Shifts

p.189 # 19-20, 29-32 p. 296 Exercise 3.4 p. 275 Section 2.7

12 14 Graphing Techniques: Hori-zontal Shifts


12 13 Graphing Techniques:Vertical Compressions andStretches

p. 189 # 23, 37-40 p. 296 Exercise 3.4 p. 275 Section 2.7

12 15 Graphing Techniques: Hori-zontal Compressions andStretches

p. 189 # 24, p. 296 Exercise 3.4 p. 275 Section 2.7

12 17 Graphing Techniques: Re-ections Across the Axes


12 8 Putting it all Together p.188 # 1-12, 25-28 p. 296 Exercise 3.4 p. 275 Section 2.7

12 6 Putting it all Together p.188 #47-66, 69-74 p. 296 Exercise 3.4 p. 275 Section 2.7

12 12 Putting it all Together p. 296 Exercise 3.4 p. 275 Section 2.7

12 12 Putting it all Together p. 296 Exercise 3.4 p. 275 Section 2.7

13 17 Algbra of Functions p.198 #1-12 p. 306 #1-10





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Suggested Homework

p. VIII

13 24 A New Operation p.198 #13-60 p. 307 #31-44 p. 402 # 11-20

15 18 Solving Equations with aGraphing Device and IVT


p.253 #63-68 p. 397 # 63-68 p. 380 # 73-78



15 23 Solving Linear Equations:The Linear Formula

p. 38 #1-42 p. 110 # 29-48

15 13 Solving Non-linear Equa-

tions that lead to linearequations

p. 110 # 49-76

16 12 Solving Quadratic Equa-tions: Factoring or Graph-ing

p. 121 # 11-44

16 12 Complex Reminder and thePrinciple Square Root

p. 262 #1-69 p. 406 #1-44 p. 132 # 9-46

16 50 Solving Quadratic Equa-tions: Quadratic Formula &Discriminant

p.137 #13-24 p. 126 #77-94, p. 406#65-70

p. 122 # 45-62, p. 122 #75-80

17 7 Some Linear & QuadraticExercises Explained

manual manual manual

17 15.5 Some Linear & QuadraticExercises Explained

manual Tape 18 manual Tape 18 manual Tape 18

19 14 Solving Radical Equa-tions

p.38 #43-58 p. 147 # 1-30 p. 139 # 9-46

19 15 Solving Equations Qua-dratic in Form

p. 148 # 31-62 p. 139 # 47-78

19 7 Solving Factorable Equa-tions

p. 125 # 37-60

20 20 Properties of Inequalities p. 64 #17-30, 75-84 p. 160 #29-42 p. 160 #39-52

20 17 Solving Inequalities ingeneral

20 19 Solving Linear Inequalities p. 64 #31-60 p. 160 #43-72 p. 160 #53-8221 17 Solving Quadratic Inequali-

ties p.299 #1-15 p. 372 #1-16 p. 365 #3-18

21 5 Solving Higher-DegreePolynomial Inequalities

p.299 #16-39 p. 372 #17-36 p. 372 #19-34

21 27 Solving Rational Inequali-ties

p.299 #37-58 p. 372 #37-58 p. 372 #35-56

22 12.5 When Absolute Value Ap- pears: Equations

p.38 #61-72 p. 148 #63-84 p. 139 #79-100





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22 17 When Absolute Value Ap- pears: Inequalities

p.64 #61-74 p. 161 #73-92 p. 161 #83-102

22 15 More Exercises Explained practice problems23 20 Degree 2: Quadratic Func-

tions p. 137 #25-32,37-54 p. 235 #1-8 p. 312 #11-18

23 16 Graphing Quadratic Func-tions

p. 235 #13-30 p. 312 #19-34

23 23 Graphing Quadratic Func-tions

24 8 Degree n: General Poly-nomial Functions

p. 219 #1-9 p. 329 #1-16 p. 331 #23-36

24 16 Special Case: Power Func-tions and their Graphs

p.230 #17-35

24 42 Graphing General Polyno-mial Functions

25 13 How MANY Zeros areThere?

p. 269 #1-15 p. 396 #11-22 p. 379 #21-32

25 13 How Many Zeros areREAL?

25 17 How many Zeros are POSI-TIVE? NEGATIVE?

p. 253 #11-27

25 22 WHERE (on what interval)are all the Real Zeros?

p. 396 #23-28 p. 379 #33-38

25 5 How Can You Geuss theLocations of Real Zeros?

25 21 How Can You REDUCEthe Number of Real Zeros?

26 15 Strategy & Tools: A PartialChecklist

p. 253 #29 - 45

27 15 General Rational Functions p. 287 p. 354 p. 344

27 18 What is an Asymptote?

27 26 Finding Asymptotes ofRational Functions

27 11 Finding Asymptotes ofRational Functions

p. 287 p. 354 p. 344

27 20 Graphing Rational Func-tions

28 15 One-to-One Functions p. 320 p. 429 p. 416

28 27 Exponential Functions &Their Graphs

p. 331 p. 441 #11-36 p. 431 #29-52

28 8 The Natural ExponentialFunction

29 24 Inverse Functions p. 321 p. 430 #21-54 p. 417 #37-70

29 24 Logarithmic Functions andTheir Graphs

p. 343 p. 454 #53-84 p. 445 #67-90





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Suggested Homework

p. X

29 4 Natural Logarithmic Func-tion

30 17 Properties of Logarithms p. 354 p. 465 #25-58 p. 456 #31-64

30 15 All Logarithms are Natural(or Common)

30 21 Solving Logarithmic Equa-tions

p. 361 p. 471 Exercise 6.5 p. 461 Section 4.6

31 15 Solving Exponential Equa-tions


31 Models

32 20 Systems of Linear Equa-tions in General

p. 410 p. 520 # 1-4

32 21 Solving A System of 2 or 3Linear Equations in 2 or 3Variables

p. 418 p. 521 #9-30, p. 527#3-16

p. 516 #17-40, #41-54

33 30 Some Exercises Explained

34 15 Solving A System of 2 Non-Linear Equations in 2Variables

p. 652 p. 750 #21-30 p. 641 #27-44

35 30 In nite Sequences: Func -tions with Domain N

p. 506 p. 622 #1-12, #21-34 p. 659 #17-28, #37-50

35 8 Factorial Symbol: ! p. 659 #11-16

35 17 Adding the First n Terms ofa Sequence

p. 506 p. 623 #35-44, #55-66 p. 659 #51-60, #71-82

36 19 Arithmetic Sequences p. 513 p. 630 Exercise 8.2 p. 667 Section 7.236 31 Geometric Sequences p. 527 p. 640 Exercise 8.3 p. 675 Section 7.3

37 26 Geometric Series and TheirIn nite Sums

p. 640 Exercise 8.3 p. 675 Section 7.3

38 11 The Binomial Coef cientSymbol


38 19 Pascals Triangle p. 541

38 32 The Binomial Theorem:How to expand (x+a)^n

p. 653 Exercise 8.5 p. 687 Section 7.5





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Lecture 1: Numbers Preview Activity Sets of Objects Process Activity (1) Real Numbers

Process Activity (2) The Real Line: Distance Between Points Review Activity


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Preview Activity

p. 2

1. When you thing of numbers, there are many terms used to describe numbers. Makea list of terms usually associated with numbers.


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Process Activity1. List the prime factors of the following numbers:

a.) 128

b.) 93

c.) 250

d.) 359

2. Classify which set of number the following numbers belong to:

a.) 1.1

b.)

c.)

d.)

(1)

2756

13

16


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Process Activity1. Graph on a number line the following inequalities:

a.) x 25

b.) 1 13 5< x .

c.) > > x

d.) 10 15 x

2. Describe the number line in interval notation.

a.)

b.)

c.)

d.)

-3 3 -3

-3 3 -3 3

(2)


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Review Activity1. Give ve examples of each type of number.

a.) Integers:

b.) Rational Numbers:

c.) Natural Naumbers:

d.) Real Numbers:

e.) Irrational Numbers:

2. Graph on a number line the following inequalities and write in interval notation.

a.) x 5

b.) 1 14 < x

c.)13

3> > x

d.) x 2

college algebra manual student lecture01

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