A background with solid basic mathematical skills up to and including either an academic-stream grade 11 level or an applied mathematics grade 12 level of expertise, or their equivalents. Students looking for a basic mathematics refresher are advised to request access to the AU Math Centre through the Math Site. It is a self-study program with opportunities for self-assessment and, upon request, is available at no extra cost for AU students.

Students must use a calculator capable of performing logarithms and exponents. A graphing calculator capable of plotting graphs is also desirable, but not necessary. To ease communication with a tutor, it is desirable that each student have an e-mail account.

Students who successfully complete this course may obtain credit, in many universities and colleges across Canada, for having completed the equivalent of an academic-stream grade 12 high school mathematics program. Please check with your post-secondary institution.

Overview

Mathematics 101 is intended for students who wish to upgrade their mathematics skills before or while attending a post-secondary institution. Students who successfully complete Mathematics 101 are generally permitted to pursue courses and programs that would otherwise require Pure Mathematics 30 as a prerequisite or corequisite.

From a background of using algebra and algebraic methods to solve mathematics problems, this course then introduces the concept of a ‘function’ of one or more variables. We first study certain important properties of functions, discover how they can be transformed and consider different ways of working with them numerically (in practical terms), algebraically (in abstract theoretical terms) and geometrically (by visual representations). From there, we discuss a variety of kinds or families of functions which are used to represent and solve real-world situations. In short, we may think of MATH 101 as an introductory course in mathematical modeling.

Outline

Unit 1: Preparatory Review of Number Theory, Planar Geometry and Basic Algebra

Unit 2: Modeling the Real World: Algebra at Work

Unit 3: Functions and Relations: Generally Speaking

Unit 4: Polynomials and Rational Functions

Unit 5: Exponential and Logarithmic Functions

Unit 6: Trigonometry: as the Geometry of Angles in the Plane

Unit 7: The Trigonometric Functions: Exemplars of Periodic Motion

Unit 8: Trigonometric Identities and Equations

Unit 9: Solving Systems of Equations

Unit 10: The Conics: a Special Case of Mathematical Relations

Objectives

After completing this course, you should be able to

understand the role of functions and algebraic expressions in modeling the real world; to be able to create mathematical models of real life situations using various kinds of functions; and to be capable of solving practical problems using these models.

understand, define, describe, and give examples of mathematical relations and mathematical functions, including what their domains, ranges and values are in a given context. Particular families of functions studied in this program include the polynomials, the exponential functions, the logarithmic functions, the radical functions, the rational functions, the trigonometric functions, and the conic relations.

plot the graphs of the above-mentioned functions and know what information can be deduced by looking at the geometric graphs of a function in a context.

perform algebraic operations (addition, subtraction, multiplication, division, exponentiation, composition and inversion) on various functions, including the ability to apply and recognize both rigid and non-rigid transformations on them.

solve equations and inequalities involving various functions, including the ability to factor them into irreducible components and use identities when necessary.

understand and be able to compute three basic ways of measuring angles – in degrees, in radians, and as trigonometric ratios, namely the sine, the cosine, the tangent, the cosecant, the secant and the cotangent of a given angle;

recognize and be able to prove some trigonometric identities, including certain geometric relationships in circles, triangles and quadrilaterals in the plane;

know the geometric definitions of a parabola, an ellipse, a circle and a hyperbola; to recognize the standard and general forms of their equations; and to be able to compute their constituent parts and graph them in the plane;

Evaluation

To receive credit in MATH 101, you must achieve a grade of at least 40 percent on the midterm exam, at least 50 percent on the final examination, and a course composite grade of at least D (50 percent).

The midterm and final examinations are closed book exams but each student may bring into each exam TWO 8 ½ inch x 11 inch sheets of formulas or personal notes (annotated on both sides) and a scientific or graphing calculator with all memory cleared.

Activity

Weight

3 Assignments (10% each)

30%

Midterm Exam (Units 1-5)

30%

Final Examination (Units 1-10)

40%

Total

100%

To learn more about assignments and examinations, please refer to Athabasca University’s online Calendar.

Materials

Algebra and Trigonometry: Custom Edition for MATH 101, Athabasca University, selections taken from Stewart, J., Redlin, L., & Watson, S..2012. Algebra and Trigonometry: Third Edition. Cengage Learning (eText)

3e Algebra and Trigonometry: Custom Edition for Math 101, taken from Bulman-Fleming, A..2011. 3e Algebra and Trigonometry: Complete Solutions Manual. Cengage Learning (eText)

Apart from the e-texts listed above, the online course materials also include a Student Manual, a Course Information document, a Study Guide, copies of all Assignments, and direct access to the AU Math Centre audio-visual tutorials.

Other Resources

All other learning resources will be available online.

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized study counterparts.