# Math Readiness Program Course Content

This page contains a brief description of the course content of the Math Readiness program at the University of Saskatchewan. The Math Readiness Course provides an overview of mathematical topics which are important for understanding calculus at the university level.

The course reviews relevant material from high school mathematics, approaching some topics from the perspective of their roles in calculus. Also introduced are a few topics which may be new to many students, such as natural logarithms.

## Math Readiness Courses and Registration

The Math Readiness course has been offered as a two-week summer course (generally held in August), a night course during the regular session (fall/winter) at the University of Saskatchewan, and as an Internet-based course. For more information about these program options, including how to register, please go to the Math Readiness course options page.

# Topics Covered in Math Readiness

## Working with Algebra

- overview of basic facts of algebra and algebraic techniques (including terminology and notation); in particular, rational expressions or "algebraic fractions"
- exponents and their properties (with complex expressions); the Binomial Theorem
- polynomials and polynomials in rational expressions: terminology, solving polynomial equations (includes the quadratic formula); factoring (including the Factor theorem); polynomial long division
- the real number line, interval notation, absolute value, and distance; intersection and union of sets
- solving polynomial, absolute value, and rational inequalities
- radicals and their properties; algebraic techniques for working with radicals
- real numbers as exponents and their properties; associated algebraic techniques

## Functions and Graphs

- review of the concepts of function and graph: interpreting notation; domain; graphing basic functions; piecewise-defined functions
- problem solving - including expressing one quantity as a function of another
- linear and quadratic functions: forms; properties; graphs; applications
- higher-degree polynomial functions and rational functions: forms; domain and graphs; special attributes (e.g. asymptotes); solving inequalities with graphs

## Basic Geometry

- facts about area, volume, etc. of geometric figures
- triangle geometry: similar triangles, Pythagorean theorem, distance formula
- Conic Sections (``analytic geometry''): circles, ellipses, parabolas, hyperbolas

## Trigonometry

- the unit circle; terminal points of arcs along the unit circle; p and special arcs along the unit circle
- definition of the trigonometric functions using coordinates of terminal point of an arc; special values of the trigonometric functions; properties of the trigonometric functions
- graphs of the basic trigonometric functions; domains; properties of the graphs
- angles in degrees; degree and radian measure; triangle trigonometry
- trigonometric identities; solving trigonometric equations and inequalities

## Exponential and Logarithmic Functions

- exponential functions: definition, domain, graphs, properties
- exponential base e; the exponential function f(x) = ex
- definition of logarithms; calculations involving logarithms; common and natural (base e) logarithms
- properties of logarithms
- using the properties of logarithms to rewrite expressions and to solve exponential and logarithmic equations
- logarithmic functions: form, domain, graph, properties
- using logarithmic properties to solve problems in applications such as exponential growth/decay

## Please Note

The Math Readiness Course is not a course in calculus, although some concepts from calculus might be discussed during the course. Math Readiness emphasizes the mathematical concepts and techniques which form the foundation of calculus. By helping students to improve their understanding of these basic ideas, we hope that they will be better able to make a smooth transition to university-level mathematics.

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For more information, contact Holly Fraser at the Department of Mathematics and Statistics, or Robb Larmer in the Centre for Continuing and Distance Education, University of Saskatchewan.

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**Holly Fraser**

Phone: (306) 966-2742 or (306) 966-2886

e-mail: holly.fraser@usask.ca

**Robb Larmer**

Phone: (306) 966-1739

e-mail: math.readiness@usask.ca