# Welcome to MATH 103

This is a classic Face-to-Face class and we meet entirely in person. There will be no online discussions and if you have a question you can ask in class or email me at

I will post handouts and hyperlinks to videos for the class on this web page which is accessible through the URL http://math103.ml

Please bookmark (favorites) this URL in your browser so that you can easily return to it as the course progresses.

### So lets get started…

This is a fast paced mathematics course in an 8 week session.

I recommend you allocate approximately 20 hours per week to this course:

- Lecture = 6 hours per week
- Optional help session for one hour after each class = 2 hours per week
- Reading study, video watching, and homework = 12 hours per week or more if you are mathematically challenged

If you have a day job, I recommend that you enroll only in this course this session, because there will be a lot of homework. Unfortunately, UMUC is not enforcing the prerequisite for this course which is MATH012 and unprepared students may feel uncomfortable in this course. I give you this warning notification so you can properly allocate time for the course. The course has a common final exam for all UMUC sections worldwide. Therefore, I must remain on schedule to cover all topics.

Before the first class, I recommend that you print the latest updated version of the syllabus that can be found in the LEO classroom or here. Also print all Week 1 materials which are posted as PDF files below.

UMUC has moved to free online resources to support all courses and Will Tenney a UMUC faculty member has written a 433 page eBook titled ** Math for Today’s World**. The eBook is a work in progress and the latest version is available for free download in the LEO Course Resources. The eBook contains examples and exercises for each section that we will use for the course. Answers to all odd numbered exercises are in the appendix at the end of the book. You are required to do the specified exercises at the end of each section, which will be odd numbered problems so you can check your answers.

Please acquire the following items before the first class:

- Spiral notebook or ring binder for doing all homework
- Several pencils or better a 0.7mm mechanical pencil with soft HB graphite
- Good Eraser
- Buy a recommended multi-line display Scientific calculator:
**Texas Instrument TI-36X Pro**Reference Manual @ AAFES Price = $18.99- or Texas Instrument TI-30X IIS (solar) Reference Manual
- or Casio fx-300ES Plus Reference Manual
- or Casio fx-115 ES Plus Reference Manual

I recommend that you get started with Week 1 content today, by clicking Week 1 in the navigation bar above or scrolling down.

Robert Laurie

## Week 1: Number Theory and the Real Number System

This week we will be covering Number Theory and the Real Number System which is covered in Math103 eBook Chapter 1. The most important item to remember this week is the order of operation, which is described the acronym P E MD AS.

It is very important to do all assigned exercises in your homework notebook. Use enough paper to show the complete step-by-step process for each exercise. Chapter 1 is very important so that you have a firm foundation to build upon for the rest of the course. For the first week I have created a Chapter 1 Exercise Solutions handout, which provides more detail then the answer key in the appendix. The focus for the first four weeks of the course is Algebra and links to informative YouTube videos for the Algebra content are displayed below for each of these four weeks.

Please download and print the following before class this week:

- Print eBook Chapter 1 if desired. You need to view Chapter 1 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- Number Line Paper
- Computer Algebra versus Traditional Algebra Notation
- MATH 103 Slide Set 1: Section 1.1-1.2
- MATH 103 Slide Set 2: Section 1.3-1.4
- MATH 103 Slide Set 3: Section 1.5
- Chapter 1 Assignment Homework Exercises with my solutions to odd exercises. Due Monday Week 2.
- Section 1.1 all odd exercises (1 through 75)
- Section 1.2 all odd exercises (1 through 21)
- Section 1.3 exercises: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 103, 105, 107, 109
- Section 1.4 all odd exercises (1 through 45)
- Section 1.5 all odd exercises (1 through 75)

### Direct Links to YouTube Videos:

- Prealgebra 7.1b - Changing Percents into Fractions5m
- Prealgebra 7.1c - Converting Percents and Decimals5m
- Prealgebra 7.1d - Changing a Fraction into a Percent6m
- Algebra 1 2.01a - The Commutative Property3m
- Algebra 1 2.01b - The Associative Property9m
- Algebra 1 2.03a - Addition of Real Numbers6m
- Algebra 1 2.03b - Adding Numbers with Different Signs6m
- Algebra 1 2.04a - Subtraction3m
- Algebra 1 2.04b - Distributing a Negative Sign9m
- Algebra 1 2.05a - The Distributive Property, Part 110m
- Algebra 1 2.05b The Distributive Property, Part 211m
- Algebra 1 2.06a - Properties of Multiplication11m
- Stand and Deliver (1/5) - All We Need is Ganas (1988)3m

Read and reflect on the topic of Math Anxiety which is described on the web page: math.about.com/od/reference/a/anxiety.htm

## Week 2: Algebra: Linear Equations and Inequalities

This week we will be covering the topics of Algebra of Linear Equations and Inequalities, which is covered in eBook Chapters 2 and 3.

Please download and print the following before class this week:

- Print eBook Chapter 2 and 3 if desired. You need to view Chapter 2 and 3 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- MATH 103 Slide Set 4: Chapter 2
- MATH 103 Slide Set 5: Chapter 3
- Answers to odd Exercises = 57 pages (from eBook Appendix)
- Tentative eBook Exercise Assignments
- Chapter 2 Assignment Exercises
- Section 2.1: 1, 5, 9, 13, 17, 21, 25, 27, 29
- Section 2.2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57
- Section 2.3: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37
- Section 2.4: 1, 3, 5, 7, 9, 11, 13, 15

- Chapter 3 Exercise Assignment
- Section 3.1: 1, 3, 5, 7, 13, 15
- Section 3.2: 1, 3, 7, 11, 13, 15
- Section 3.3: all odd exercises (1 through 21)
- Section 3.4: all odd exercises (1 through 45)
- Section 3.5: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 33

- Chapter 2 Assignment Exercises

### Direct Links to YouTube Videos:

- MathTV.com view topic list ALGEBRA > Simplifying Expressions.
- Mathematics and sex | Clio Cresswell | TEDxSydney 13m
- LucidEducation.com has some good links to Chapter 8 content.
- Algebra 1 6.1a - Simplifying - What You Can and Cannot Cancel5m
- Algebra Review 1.1 - Simplifying Expressions3m
- Algebra Review 1.2 - Simplifying Expressions2m
- Algebra Review 1.3 - Simplifying Expressions6m
- Algebra Review 2.2 - Solving Equations4m
- Algebra Review 2.3 - Solving Equations4m
- Algebra Review 2.4 - Solving Equations3m
- Algebra Review 9.1 - Fractional Equations4m
- Algebra Review 9.2 - Fractional Equations3m
- Algebra Review 9.3 - Fractional Equations5m
- Algebra Review 9.4 - Fractional Equations2m
- Prealgebra 7.1b - Changing Percents into Fractions5m
- Prealgebra 7.1c - Converting Percents and Decimals5m
- Prealgebra 7.1d - Changing a Fraction into a Percent6m
- Prealgebra 7.2a - Solving Percent Exercises - An Introduction9m
- Prealgebra 7.2b - How to Solve a Percent Exercise9m
- Prealgebra 7.3a - Solving Percent Applications6m
- Prealgebra 7.3b - Examples of Percentages in Calculations6m
- Prealgebra 7.3c - Real World Percentage Examples7m

Test 1 is scheduled for next week first class and will cover content from or eBook Chapters 1, 2, and 3. Test 1 is closed book, but you are permitted to bring in one half page of single sided handwritten notes that is 8.5 inches x 5.5 inches. I suggest you simply take a standard letter size paper and fold it in half. You can add to these notes in Test 2 and 3. You need to bring pencil, eraser, and calculator to Test 1. You may download and view Sample Test 1 available as a PDF file with answers attached.

## Week 3: Quadratic Equations, Graphing, and Functions

This week we will begin with Test 1, which will cover content from eBook Chapters 1, 2, and 3. Test 1 is closed book, but you are permitted to bring in one half page of handwritten notes on one side of an 8.5 inches x 5.5 inches area. I suggest you simply take a standard letter size paper and fold it in half. You can add to these notes for test 2 and 3. You may download and view Sample Test 1 available as a PDF file with answers attached.

After Test 1, we will continue with eBook Chapter 4 covering the important topic of Quadratic Equations to include polynomial operations, factoring, and the Quadratic Formula.

A quadratic equation is a polynomial equation of the second degree, having the general form:

The letters *a*, *b* and *c* are called coefficients: *a* is the coefficient of *x ^{2}*,

*b*is the coefficient of

*x*, and

*c*is the constant coefficient. A quadratic equation has two solutions (i.e., solutions for the unknown term

*x*). In some cases, these solutions can have the same value. The values of the solutions can be computed using the quadratic formula as shown below:

For example, the solutions of the quadratic equation

can be determined by first substituting 2 for *a*, -14 for *b*, and 20 for *c* in the quadratic forumula

and then solving the expression, which gives the solutions of the equation as *x* = 5 and *x* = 2.

As the week progresses we will cover eBook Chapter 5.1 covering Cartesian coordinate graphing and functions. You will plot points, lines, and functions on graph paper.

Please download and print the following before class this week:

- Print eBook Chapter 4 and 5 if desired. You need to view Chapter 4 and 5 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- X-Y Graph Paper 4 per sheet and PRINT 10 copies to bring to class
- MATH 103 Slide Set 6: Chapter 4
- MATH 103 Slide Set 7: Chapter 5.1-3
- Class Notes: Quadratic Equation AC-Method class smart board file
- Tentative eBook Exercise Assignments
- Chapter 4 Exercise Assignment
- Section 4.1: 1, 5, 9, 13, 17, 21, 25, 29, 33
- Section 4.2: 3, 7, 11, 15, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 83, 85
- Section 4.3: 1, 5, 9, 13, 17

- Chapter 5 Exercise Assignment
- Section 5.1: 1, 3, 5, 7, 9, 11, 13, 17, 21, 27, 29, 31, 33, 35, 39

- Chapter 4 Exercise Assignment

**Geogebra** is a freeware graphing program that can be downloaded and installed from www.geogebra.org. It is helpful to to be able to graph various mathematical functions using graphing software and to check your homework solutions.

- Download and Install Geogebra to your computer
- Geogebra Web Java App executable in a browser
- My Geogebra video tutorial available here

### Direct Links to YouTube Videos:

- Prealgebra 10.1a - Introduction to Polynomials6m
- Prealgebra 10.1b - Evaluating Polynomials6m
- Prealgebra 10.2a - Adding and Subtracting Polynomials9m
- Prealgebra 10.2b - Adding and Subtracting Polynomials8m
- Prealgebra 10.3a - Multiplying Exponents9m
- Prealgebra 10.3b - Raising an Exponent to a Power6m
- Prealgebra 10.3c - Raising a Product to a Power6m
- Prealgebra 10.4a - Multiplying Monomials8m
- Prealgebra 10.4b - Multiplying a Monomial and a Polynomial7m
- Prealgebra 10.4c - Multiplying Binomials6m
- Prealgebra 10.4d - Multiplying Binomials FOIL Method5m
- Prealgebra 10.4e - Multiplying Binomials6m
- Prealgebra 10.5a - Factoring Polynomials8m
- Prealgebra 10.5b - Factoring Polynomials7m
- Prealgebra 10.5c - Factoring Polynomials11m
- Algebra Review 4.1 - Factoring5m
- Algebra Review 4.2 - Factoring6m
- Prealgebra 9.3a - The Rectangular Coordinate System9m
- Prealgebra 9.3b - Coordinates in Two Dimensions9m
- Prealgebra 9.3c - Plotting Points in Two Dimensions8m
- Prealgebra 9.4a - Equations with Two Variables10m
- Prealgebra 9.4b - Ordered Pair Solutions to Equations5m

The ac-Method is a very systematic factoring method that allows you to factor trinomial mathematical expressions. Once you understand how to use the ac-method you can usually find the factors much quicker than FOIL. I found several videos on youtube.com covering the ac-Method. Try working out the exercises illustrated in these videos to understand the step-by-step factoring process. Then try it on homework exercises. If you find a different video that is helpful and easy to understand please email me and provide a hyperlink.

## Week 4: Graphing Functions and 2-Variable Equations

This week we will finish eBook Chapter 5 covering the following topics:

- Graphing Linear Equations: eBook Section 5.2
- Solving Systems of Linear Equations: eBook Section 5.3
- Quadratic Functions: eBook Sections 5.4
- Exponential Functions: eBook Sections 5.5
- Logarithmic Functions: eBook Sections 5.6

Please download and print the following before class this week:

- Print eBook Chapter 5 if desired. You need to view Chapter 5 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- X-Y Graph Paper 4 per sheet
- Earth Quake and Trajectory Exercises
- MATH 103 Slide Set 8: Chapter 5.4-6
- Tentative eBook Exercise Assignments
- Chapter 5 Exercise Assignment
- Section 5.1: 1, 3, 5, 7, 9, 11, 13, 17, 21, 27, 29, 31, 33, 35, 39
- Section 5.2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49
- Section 5.3: 1, 3, 5, 7, 9, 13, 17, 21, 25, 29, 33, 35, 37, 39
- Section 5.4: 1, 5, 9, 13, 17, 19, 21, 23
- Section 5.5: 1, 5, 9, 13, 15, 17
- Section 5.6: 1, 5, 9, 13, 17, 21, 23

- Chapter 5 Exercise Assignment

**Geogebra** is a freeware graphing program that can be downloaded and installed from www.geogebra.org. It is helpful to to be able to graph various mathematical functions using graphing software and to check your homework solutions.

- Download and Install Geogebra to your computer
- Geogebra Web Java App executable in a browser
- My Geogebra video tutorial available here
- Geogebra Quickstart Guide
- Linear Equation in Slope-Intercept Form :: Geogebra File
- Graph of Quadratic Equation in Standard form :: Geobebra File
- Graph of Exponential and Logarithm Equations :: Geogebra File

**Test 2** is scheduled for next week first class, and will cover content since the last test in sections from eBook Chapters 4 and 5. Test 2 is closed book, but you are permitted to bring in one page of single sided handwritten notes that is 8.5 inches x 11 inches. You need to bring pencil, eraser, and calculator to Test 2. You may download Sample Test 2 which I used in class last year.

### Direct Links to YouTube Videos:

- Prealgebra 9.4b - Ordered Pair Solutions to Equations5m
- Prealgebra 9.4c - Graphing Linear Equations, Part 110m
- Prealgebra 9.4d - Graphing Linear Equations, Part 29m
- Prealgebra 9.4e - Horizontal and Vertical Lines6m
- Algebra 2 2.01c - Graphing Functions and the Vertical Line Test10m
- Algebra 2 2.01d - Function Notation5m

## Week 5: Financial Mathematics

**Test 2** will be at the beginning of first class, so do not be late. It will cover content since Test 1. Test 2 is closed book, but you are permitted to bring in one page of single sided handwritten notes that is 8.5 inches x 11 inches. You need to bring pencils, eraser, and calculator to Test 2. You may download and try this Sample Test 2 which I used in class previously.

Financial Mathematics will be the topic this week and after Test 2 we will begin to discuss eBook Chapter 6 covering the following financial mathematics topics:

- 6.1 Simple Interest
- 6.2 Compound Interest
- 6.3 Annuities
- 6.4 Mortgages

Please download and print the following before class this week:

- Print eBook Chapter 6 if desired. You need to view Chapter 6 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- MATH 103 Slide Set 9: Chapter 6
- Formula Sheet
- Tentative eBook Exercise Assignments
- Chapter 6 Exercise Assignment
- Section 6.1: 1, 5, 9, 13, 17, 21, 25, 29, 33
- Section 6.2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 39, 43
- Section 6.3: 1, 3, 5, 7, 9, 11, 13
- Section 6.4: 1, 3, 5, 7, 9, 11, 13

- Chapter 6 Exercise Assignment

### Direct Links to YouTube Videos:

- Prealgebra 7.1b - Changing Percents into Fractions5m
- Prealgebra 7.1c - Converting Percents and Decimals5m
- Prealgebra 7.1d - Changing a Fraction into a Percent6m
- Prealgebra 7.2a - Solving Percent Exercises - An Introduction9m
- Prealgebra 7.2b - How to Solve a Percent Exercise9m
- Prealgebra 7.3a - Solving Percent Applications6m
- Prealgebra 7.3b - Examples of Percentages in Calculations6m
- Prealgebra 7.3c - Real World Percentage Examples7m

## Week 6: Probability Theory

Probability Theory will be covered this week, with applications to situation analysis, risk tolerance, and gambling. We will be covering the following topics described in eBook Chapter 7 section numbers:

- 7.1 Counting Rules
- 7.2 Probabilities
- 7.3 Complement Rule and Addition Rule
- 7.4 Multiplication Rule and Conditional Probabilities

Please download and print the following before class this week:

- Print eBook Chapter 7 if desired. You need to view Chapter 7 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- MATH 103 Slide Set 10: Chapter 7.1-2
- MATH 103 Slide Set 11: Chapter 7.3-4
- Formula Sheet is same as last week
- Tentative eBook Exercise Assignments
- Chapter 7 Exercise Assignment
- Section 7.1: 1, 3, 5, 7, 9, 11, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49
- Section 7.2: 1, 3, 5, 9, 11, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61
- Section 7.3: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49
- Section 7.4: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69

- Chapter 7 Exercise Assignment

Rolling two Dice program:

**Test 3** is scheduled for next week, and will cover content since the last test in sections from eBook Chapters 6 and 7. Test 3 is closed book, but you are permitted to bring in the Formula Sheet. You need to bring pencils, eraser, and calculator to Test 3. You may download Sample Test 3 which I used in class last year and practice.

## Week 7: Statistics

**Test 3** will be at the beginning of first class, so do not be late. It will cover content from eBook Chapters 6 and 7. Test 3 is closed book, but you are permitted to bring in the Formula Sheet. You need to bring pencils, eraser, and calculator to Test 3. An example test for Test 3 with answers can be viewed here.

Statistics will be the topic this week after Test 3. The Statistics content is in eBook Chapter 8.

Please download and print the following before class this week:

- Print eBook Chapter 8 if desired. You need to view Chapter 8 content in class so you could view on paper, a notebook computer, iPad, or Kindle tablet device in class.
- MATH 103 Slide Set 12: Chapter 8
- Formula Sheet is same as last week
- z-Score Tables
- Tentative eBook Exercise Assignments
- Chapter 8 Exercise Assignment
- Section 8.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
- Section 8.2: 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 37, 39, 41, 43
- Section 8.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
- Section 8.4: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65
- Section 8.5: 1, 3, 5, 7, 9, 11

- Chapter 8 Exercise Assignment

Your calculator may have a Statistics (STAT) mode that would do the standard deviation calculation after all data values are entered with frequencies. Please consult your Calculator User Manual below:

- Texas Instrument TI-36X Pro Reference Manual
- Texas Instrument TI-30X II Reference Manual
- Casio fx-300ES Plus Reference Manual
- Casio fx-115 ES Plus Reference Manual

## Week 8: Week 8: Final Exam Time

The Final Exam is the last class of the term. The Final Exam is comprehensive and any material covered in this eight week course may be on the Final Exam. The Final Exam is closed book, but you are permitted to bring in pencils, eraser, calculator, Formula Sheet and z-Score Tables. An example Final Exam and Answers can be downloaded and viewed here.

Please bring your notebook contining homework, which I will examine for borderline grade cases. Please bring your Tests 1, 2, and 3 to me during the final exam time. I re-examine these tests when determining final grades if you are within a few points of the next grade in the course.

I hope you feel are more comfortable with mathematics after taking this course and you will find it a useful skill when you apply it in life situations. It is your best critical thinking skill to help you make financial decisions. Mathematics is the basis of technology development and understanding physical sciences.

I would appreciate if you can do the Course Evaluation in LEO.

Thank you for your participation in the class this term.