# UPG 020 - Math 1

## Course Description

This is the second of three courses designed to prepare you for university entrance. The course covers the properties of real numbers, a brief introduction to number theory, exponents and radicals, algebraic expressions, factoring, linear and quadratic equations, inequalities, system of linear equations, polynomials and their properties.

## Course Details

**Broad learning outcome:**

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

- Simplify and manipulate algebraic expressions.
- Use a variety of techniques to solve equations such as quadratic, radical, trigonometric, or rational.
- Use quadratics or other functions to model real world problems mathematically and interpret the solutions.
- Develop algebraic reasoning and number sense through the study of various relations and functions as well as sequences and series.
- Develop trigonometric reasoning through the study of rotational trigonometry, as well as obtuse or acute triangles.

**Supporting Learning Outcome Statements**

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

- Identify and differentiate the two types of sequences (arithmetic/geometric) and apply their properties to find the general term of the sequence, the sum of any number of terms of the sequence and series.
- Investigate infinite geometric sequences to determine if they are convergent or divergent.
- Convert entire radicals with rational coefficients or radicands to mixed radicals.
- Convert mixed radicals with rational coefficients or radicands to entire radicals.
- Add, subtract, multiply, and divide radicals.
- Solve radical equations.
- Identify and explain characteristics of graphs of quadratic functions such as: the vertex, maximum or minimum values, the intercepts, domain and range.
- Identify and explain the different forms of quadratic functions.
- Graph a quadratic function given its equation in any form.
- Determine the equation of a quadratic function given information that uniquely determines the function.
- Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using: factoring, completing the square, and the quadratic formula.
- Solve word problems that can be reduced to linear or quadratic equations.
- Determine equivalent forms of single-variable rational expressions with polynomial numerators, and denominators that are monomials, binomials or trinomials that can be factored.
- Determine the non-permissible values for the variable in single-variable rational expressions.
- Perform the operations of addition, subtraction, multiplication and division on single-variable rational expressions.
- Find and verify the solutions of rational equations that reduce to linear equations.
- Formulate and apply strategies to solve absolute value equations, radical equations, rational equations.
- Graph linear and quadratic inequalities in two variables.
- Solve systems of equations (in two variables) that have at least one quadratic equation using algebra and graphing.
- Identify and explain characteristics of reciprocal functions such as end behaviour and asymptotes.
- Graph linear and quadratic reciprocal functions.
- Demonstrate and understanding of rotational trigonometry using positive angles from 0 to 360 degrees.
- Analyze special triangles and how they are used to determine trigonometric ratios in exact form.
- Solve problems using the sine law and the cosine law.