# UPG 105 - Math 1

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## Course Description

This is the first of two 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 qua-dratic equations, inequalities, system of linear equations, polynomials and their properties.

## Course Details

### Broad Learning Outcome:

Upon successful completion of the Math 1 course, students will be able to simplify and manipulate algebraic expressions and solve basic equations such as linear, quadratic, rational and those involving radical expressions.

### Supporting Learning Outcome Statements

Upon successful 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.
- Demonstrate an understanding of powers with real number bases (excluding base 0).
- Explain and apply the exponent laws for powers of numbers and for variables with rational exponents.
- Examine the nature of relations with an emphasis on functions.
- Represent and analyze quadratic, polynomial and rational functions,
- Perform operations on algebraic expressions.
- Find the product of polynomials.
- Divide an integral polynomial by a monomial/binomial.
- 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.
- Determine the equation of a line, given information that uniquely determines the line.
- Solve problems using slopes of parallel lines and perpendicular lines.
- Describe a function in terms of ordered pairs, a rule, in word or equation form, a graph.
- Use function notation to evaluate and represent functions.
- Determine the domain and range of a relation from its graph.
- Determine the following characteristics of the graph of a linear function, given its equation: intercepts slope, domain, range.
- Classify numbers as natural, whole, integer, rational or irrational, and show that these number sets are nested within the real number system.
- Solve systems of linear equations, in two variables: algebraically (elimination and substitution) and graphically.
- Solve word problems that can be reduced to linear or quadratic equations.
- Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using:
- Factoring, completing the square, and the quadratic formula.
- Perform operations on functions and compositions of functions.
- Formulate and apply strategies to solve absolute value equations, radical equations, rational equations.
- Graph linear inequalities, in two variables.

## Prerequisites

Successful completion of Pure Math 10, 10C or equivalent course.