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.
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
Digital course materials
Links to the following course materials will be made available in the course:
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
3e Algebra and Trigonometry: Custom Edition for Math 101,
taken from
Bulman-Fleming, A..2011. 3e Algebra and Trigonometry: Complete Solutions Manual. Cengage Learning
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.