# UPG 010 - Math Fundamentals

## Course Description

This is the first of three courses designed to prepare you for university entrance. This course covers the properties of real numbers and number theory, exponents and radicals, algebraic expressions, expanding and factoring polynomials, functions, linear functions, systems of linear equations, and right-angled trigonometry. In terms of polynomial functions, this course will have an emphasis on functions of degree one (linear).

## Course Details

**Broad learning outcome:**

Upon completion of this course, successful students will be able to:

- Simplify and manipulate algebraic expressions.
- Solve linear equations and systems of equations.
- Develop algebraic reasoning and number sense through the study of number systems, exponents, radicals, and polynomial expressions.
- Use functions and relations to model real world problems mathematically and interpret the solutions.
- Develop graphical and algebraic reasoning through the study of relations and linear functions.
- Develop trigonometric reasoning through the study of right-angled trigonometry.

**Supporting learning outcome statements:**

Upon completion of this course, successful students will be able to:

- Demonstrate an understanding of the Real number system and which other systems are involved.
- Demonstrate an understanding of the power laws with integral and rational exponents.
- Represent powers that have rational exponents as radicals and vice versa.
- Change entire radicals to mixed radicals and vice versa (limited to radicands with whole numbers).
- Identify if an algebraic expression represents a polynomial, and determine the degree of a given polynomial.
- Find the product of polynomials (limited to monomials, binomials, and trinomials
**).** - Demonstrate and understanding of common factoring.
- Demonstrate and understanding of factoring trinomials of the form a
*x*²+ b*x*+ c, where a, b, and c are whole numbers. - Identify and factor perfect square trinomials.
- Identify and factor difference of squares.
- Examine different ways to represent a relation.
- Identify if a relation is a function or not.
- Determine the domain and range of relations and functions.
- Demonstrate an understanding of function notation.
- Identify and explain characteristics of the graphs of linear functions such as slope, intercepts, domain and range.
- Graph a linear function given its equation in any form.
- Determine the equation of linear functions when given the slope and y-intercept of the graph.
- Determine the equation of linear functions when given the slope and a point on the graph.
- Represent the equation of a linear function in the form a
*x*+ b*y*+ c = 0. - Solve problems that involve linear functions with parallel or perpendicular slopes.
- Identify and explain the slope as a rate of change.
- Solve systems of linear equations in two variables by graphing, and by algebra (substitution and elimination).
- Develop and apply the primary trigonometric ratios to solve problems involving right angled triangles.

## Notes

__Withdrawal Policy__

For a full refund to be issued, notice of withdrawal must be received ten calendar days or more prior to the start date of the course.

If notice of a student's withdrawal from a course is received less than ten calendar days prior to the start date or up to five days after the start date of the course, an administration fee of $100 will be applied to the refund amount.

Withdrawal notices received more than five days after the start date will not be issued a refund.