Mathematics 101 Transitional Mathematics
Course Information
Introduction
Welcome to Mathematics 101: Transitional Mathematics, a 0-university-science-credit course designed to review and hone the necessary mathematical skills required of students entering either pure or applied mathematics, any of the natural sciences, or any math-related programs of study.
Mathematics 101 is essentially a stepping stone to higher mathematical thinking. In this course, we begin with a fundamental observation that certain processes in our collective everyday world consist of intricate relationships between measurable but varying quantities. Many of these quantifiable interconnections can be modeled for further analysis using the notion of a ‘mathematical relation.’ Some of the mathematical relations we investigate are the polynomials, the rational functions, the exponentials, the logarithms, the trigonometric ratios and the conics sections. Each has made its mark variously in the worlds of medicine, engineering, architecture, finance, the natural sciences, the social sciences and numerous other applied disciplines.
Theoretically, when you have completed Mathematics 101, you will have been introduced to a world, even a cosmos, held together by mathematical certainties with room for approximation, perturbation, and a little bit of chaos. Practically, you should have acquired sufficient knowledge and skills to enroll in any introductory university-level mathematics or math-related course without undue background preparation. This course covers the Alberta Pure Mathematics 30 curriculum and is a preparatory course for Calculus courses, in particular.
This Course Information document contains information that you will need to complete Mathematics 101 successfully. Please read it carefully before you begin this course.
Course Objectives
After completing Mathematics 101, you should be able to:
- be able to demonstrate all the skills taught in an academic-stream senior high school Pure Mathematics curriculum; and
- be adequately prepared to enroll in introductory university-level mathematics or math-related courses.
Course Materials
Mathematics 101 is a fully online program using an e-text, an online text of tutorials and other online resources. It also has academic support.
eTextbook
Algebra and Trigonometry: Custom Edition for MATH 101, Athabasca University by Stewart, Redlin and Watson
Page numbers of the Custom Edition text are found at the bottom centre of each page. (The page numbers at the top left and right of the Custom Edition are the original page numbers of the Stewart et al. text from which it was made.)
- Answers to Practice Assignments: pp. 481–553
- Summary Sheets:
Formulas: pp. iv–vi after the Table of Contents at the beginning of the text
Formulas: pp. 568–570 after the Index at the end of the text - Symbols and Abbreviations: page viii after the Table of Contents
Student Solutions Manual for e-Textbook Exercises
Algebra and Trigonometry: Custom Edition for Math 101 by A. Bulman-Fleming
Online Text: AU Math Centre tutorials and practice (on selected topics)
To access the AU Math Centre tutorials, please log in with your AU Student ID and password.
To obtain access to the online practice Maple TA exercises, please subscribe to the AU Math Centre.
Course Information
Athabasca University, MATH 101 Course Information. Athabasca AB: Julie Peschke, 2014.
This Course Information provides essential information specific to the course, the course materials, and the procedures you should follow to complete the course successfully. Please read it through carefully before beginning your studies.
Study Guide
Athabasca University, MATH 101 Study Guide. Athabasca AB: Julie Peschke, 2014.
Forms
Forms to apply to write examinations, request extensions, and others you may need are available through your myAU Portal.
Calculator
Students are permitted to use scientific calculators for both examinations. However, no programmable calculators, computers, personal desktop assistants or other communication devices may be brought into either examination. If you have a graphing calculator, make certain that the memory has been cleared.
The Structure of Your Course
Mathematics 101 is divided into ten units.
Unit 1, “Preparatory Review of Number Theory, Planar Geometry, and Basic Algebra,” is designed to provide a review of fundamental mathematics skills and knowledge required of those planning to complete this program.
Unit 2, “Modeling the Real World: Algebra at Work,” introduces students to modeling techniques using basic algebraic expressions.
Unit 3, “Functions and Relations: Generally Speaking,” explores the concepts of a mathematical relation and a mathematical function, discussing their defining properties, how they can be visualized, how they can be combined, how they can be transformed and how they may be used to model real-world situations.
Unit 4, “Polynomials and Rational Functions,” discusses two of the most common functional relationships in the context of their defining properties, their geometric graphs, the solutions to their equations and inequalities and their applications to real-world situations.
Unit 5, “Exponential and Logarithmic Functions,” discusses these functions, which are inverses of one another, in the context of their defining properties, their geometric graphs, the solutions to their equations and inequalities and their applications to real-world situations.
Unit 6, “Trigonometry: As the Geometry of Angles in the Plane,” focuses on the trigonometric ratios in terms of the geometry of the Euclidean Plane.
Unit 7, “The Trigonometric Functions: Exemplars of Periodic Motion,” discusses the trigonometric ratios in terms of the geometry of the Cartesian Plane.
Unit 8, “Trigonometric Identities and Equations,” details various techniques to derive or prove trigonometric identities and to solve trigonometric equations, leading to applications of trigonometry in real-world situations.
Unit 9, “Solving Systems of Equations,” discusses the geometry behind systems of linear questions, the meaning of their simultaneous solutions, and methods for solving them.
Unit 10, “The Conics: A Special Case of Mathematical Relations,” introduces the conics sections in the context of their geometric properties, their equations, and how their forms have been utilized in architecture, engineering, medicine, and the sciences.
Each unit is divided into several sections, which involve readings from the e-textbook, the online tutorials, and exercises designed to ensure that you gain practice in the important mathematical concepts and techniques. The Student Solutions Manual that accompanies your e-textbook provides the detailed solutions for the recommended exercises and tests. There are review exercises and tests throughout which will allow you to judge your mastery of the material as you proceed through the course.
Study Schedule
Math 101 is a course designed to be completed in about twenty-four weeks. Students registered in the individualized-study version of the course are permitted to take up to six months, but we recommend following the twenty-four-week schedule suggested below, thereby keeping some time in reserve for unexpected delays or emergencies.
If you decide to follow the suggested study schedule, you should have no difficulty completing the course within your six-month contract. If you find yourself falling behind, contact your tutor to discuss the situation. You may also extend your course contract. However, there is a fee for this and you must apply for such extensions at least one month before your course end date. Also note that both examinations must be written within your six-month contract period (unless you have obtained an extension) and that there are deadlines concerning how soon you must apply to write examinations prior to the date on which you wish to write the examination. Extension deadlines and examination request deadlines are explained in the Student Manual. Check them carefully well before your contract end date. You may, of course, proceed more quickly than is suggested by this schedule.
Suggested Study Schedule
| Week | Activity | |
|---|---|---|
| 1 | Familiarize yourself with the homepage of MATH 101. | |
| Read the Student Manual and this Course Information carefully, and look over the other course materials. Contact your tutor, if he or she has not already contacted you. | ||
| Read Unit 0 of the Study Guide “The Stepping Stone to Higher Mathematics” and “Approaches to this Course: Customized to Suit Your Preferred Learning Style.” | ||
| Set up your study strategies and your study plan. | ||
| Read Unit 1 of the Study Guide, “Preparatory Review of Number Theory, Planar Geometry, and Basic Algebra.”
Brush up on the basic mathematics skills required for this course. |
||
| 2 | Read Unit 2: Modeling the Real World: Algebra at Work.
Read, study, and do as many exercises as possible or necessary. |
|
| 3 | Begin reading Unit 3: Functions and Relations: Generally Speaking.
Note: It is very important to understand the ins and outs of functions and relations. Success in the rest of the course will depend on a good grasp of the concepts introduced in this unit.
Read, study, and do as many exercises as possible or necessary. |
|
| 4 | Continue reading Unit 3.
Read, study, and do as many exercises as possible or necessary. |
|
| 5 | Finish reading Unit 3.
Read, study and do as many exercises as possible or necessary. |
|
| 6 | Begin reading Unit 4: Polynomials and Rational Functions.
Polynomial functions play much the same role in Function Theory as do the set of integers in Number Theory. They lay the foundations of much of the discourse around mathematical modeling of real-world situations. Read, study, and do as many exercises as possible or necessary. |
|
| 7 | Finish reading Unit 4.
Read, study, and do as many exercises as possible or necessary. Submit Assignment 1 (Units 1–4) to your tutor for marking. Apply for Midterm Exam. |
|
| 8 | Begin reading Unit 5: Exponential and Logarithmic Functions.
Read, study, and do as many exercises as possible or necessary. |
|
| 9 | Finish reading Unit 5.
Read, study, and do as many exercises as possible or necessary. Go to the section of the Study Guide entitled “Midterm Exam Preparation.” Study for Midterm (based on Units 1–5). |
|
| 10 | Finish reviewing for Midterm (based on Units 1–5).
Write Midterm Exam. |
|
| 11 | Begin reading Unit 6: Trigonometry: As the Geometry of Angles in the Plane.
Read, study, and do as many exercises as possible or necessary. |
|
| 12 | Finish reading Unit 6.
Read, study, and do as many exercises as possible or necessary. |
|
| 13 | Begin reading Unit 7: The Trigonometric Functions: Exemplars of Periodic Motion.
Read, study, and do as many exercises as possible or necessary. |
|
| 14 | Finish reading Unit 7.
Read, study, and do as many exercises as possible or necessary. Submit Assignment 2 (Units 5–7) to your tutor for marking. |
|
| 15 | Begin reading Unit 8: Trigonometric Identities and Equations.
Read, study, and do as many exercises as possible or necessary. |
|
| 16 | Finish reading Unit 8.
Read, study, and do as many exercises as possible or necessary. |
|
| 17 | Begin reading Unit 9: Solving Systems of Equations.
Read, study, and do as many exercises as possible or necessary. |
|
| 18 | Finish reading Unit 9.
Read, study, and do as many exercises as possible or necessary. |
|
| 19 | Begin reading Unit 10: The Conics: A Special Case of Mathematical Relations.
Read, study, and do as many exercises as possible or necessary. |
|
| 20 | Continue reading Unit 10.
Read, study and do as many exercises as possible or necessary. Apply for Final Exam. Request Transcripts. |
|
| 21 | Finish reading Unit 10.
Read, study, and do as many exercises as possible or necessary. Submit Assignment 3 (Units 8–10) to your tutor for marking. |
|
| 22 | Go to the section of the Study Guide entitled “Final Exam Preparation.”
Study for Final Exam (comprehensive but emphasis on Units 6–10). |
|
| 23 | Finish reviewing for Final Exam (comprehensive but emphasis on Units 6–10). | |
| 24 | Go to the section of the Study Guide entitled “Au revoir.”
Write Final Exam. |
Student Evaluation
Your final grade in Mathematics 101 is based on the grades you achieve in three assignments, a midterm examination, and a final examination.
Assignments
The three course assignments, each worth 10% of your final grade, are designed to challenge you. They will contain only problems that you can solve using the skills and knowledge you will have acquired while working through the course, but you may need to combine knowledge and skills in unexpected ways. Access the assignments through the course home page.
Note: Assignments will not be accepted for marking if submitted after the course contract end date.
Midterm Exam
The midterm examination is worth 30% of your final grade and will cover material presented in Units 1–5 of the course.
The midterm examination will be a supervised examination conducted in a manner consistent with the examination policy described in the Athabasca University Calendar. The examination will consist of problems similar in nature to those presented in the unit tests and the relevant assignments.
Final Exam
The final examination is worth 40% of your final grade and will cover material presented throughout the entire course but with an emphasis on Units 6–10.
The final examination will be a supervised examination conducted in a manner consistent with the examination policy described in the Athabasca University Calendar. The examination will consist of problems similar in nature to those presented in the unit tests and the assignments.
What You May Bring into the Exam Room
Both midterm and final examinations are closed-book examinations. No formula sheets will be provided with either exam. However, in each case, you are allowed to bring into the examination room two 8 1/2 × 11-inch summary sheets, which may include formulas, personal notes, or both. You must turn these sheets in with the examination before leaving the examination room. The sheets may be annotated on both sides.
You should also bring a scientific calculator to each examination. However, no programmable calculators, computers, personal desktop assistants or other communication devices may be brought into either examination. If you have a graphing calculator, make certain that the memory has been cleared.
Passing Grade
To pass this course, you must achieve a mark of at least 40% on (a) the midterm examination, and a mark of at least 50% on each of the following: (b) the final examination, and (c) the composite course grade.
Supplemental Exams
Students who do not achieve a minimum passing grade of at least 40% on the midterm examination or at least 50% on the final examination will be allowed to write one supplemental for each examination.
For further information, please see the section of the Student Manual titled “Procedures for Applying for and Writing Examinations.”