# Course

Course Summary
Credit Type:
Course
ACE ID:
ICCM-0005
Organization's ID:
MAT 105
Organization:
Location:
Online
Length:
Self-paced (180 days)
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 3 college algebra
Description

## Objective:

The course objective is to teach the fundamentals of college-level algebra, with a primary focus on functions. Students will discover early on what a function is and how this relates to equations; identify key concepts visually by being presented with a graph or algebraically, given the equation of the function; and learn several ways to approach the same question, through the use of different theorems and formulas such as the quadratic formula, completing the square, or the remainder theorem and the factor theorem to find the zeros of a function. The course ends with a basic introduction to sequences, series and combinatorics.

## Learning Outcomes:

• solve linear equations and inequalities, absolute value equations and inequalities, polynomial equations and inequalities, rational equations and inequalities, and systems of linear and nonlinear inequalities
• solve systems of equations in two and three variables using substitution, elimination, and matrices (Gaussian elimination, Gauss-Jordan elimination, and Cramer's Rule)
• find the domain and range of a function
• determine where a function is increasing or decreasing
• determine the symmetry of functions
• identify different types of functions (linear, quadratic, polynomial, rational, exponential, and logarithmic)
• determine the asymptotes, zeros, x and y intercepts of functions
• divide polynomials
• utilize the leading term test, the remainder theorem and the factor theorem
• decompose rational expressions into partial fractions
• graph equations of circles, ellipses and hyperbolas
• determine the general term and sum of an arithmetic and geometric sequence and series
• denote a sum using sigma notation
• determine the number of combinations or permutations of n objects taken k at a time
• identify maximum and minimum values of functions
• find the sum, difference, product and quotients of functions
• perform transformations of functions
• convert between logarithmic and exponential equations
• utilize the binomial theorem to expand a power of a binomial
• determine the theoretical probability of a situation

## General Topics:

• Distance and midpoint formulas, linear equations and inequalities, absolute value equations and inequalities, polynomial equations and inequalities, rational equations and inequalities, logarithmic equations, exponential equations, systems of equations and inequalities, Gaussian eliminations, Gauss-Jordan elimination, Cramer's rule, graphing functions, transformations of functions, zeros of functions, x and y intercepts of functions, domain and range of functions, maximum and minimum values of functions, increasing/decreasing intervals of functions, algebra of functions, leading term test, remainder theorem, factor theorem, rational zeros theorem, Descartes' rule of signs, partial fractions, circles, ellipses, hyperbolas, arithmetic sequence and series, geometric sequence and series, binomial theorem, combinations, permutations, and probability
Instruction & Assessment

## Instructional Strategies:

• Audio Visual Materials
• Lectures

• Examinations
• Quizzes

## Minimum Passing Score:

70%
Supplemental Materials

(ICCM-0002)
(ICCM-0006)
(ICCM-0007)