Course Title: Advanced Algebra
Course Level: Level 2
Course Description: The course will include a review and strengthening of skills in linear and quadratic functions. Polynomial, exponential, and logarithmic functions will be discussed as well as topics in Matrix Algebra. There will be an introduction to trigonometric functions and the graphs of the sine and cosine curves. The course will conclude with a preview to counting principles and probability.
Pre-requisites: Successful completion of Algebra II & Trigonometry
Student Learning Outcomes:
“Students will be able to…”
- Solve linear equations and linear inequalities.
- Solve quadratic functions by factoring, the quadratic formula, and a graphing calculator.
- Multiply, divide and factor polynomial functions.
- Solve exponential and logarithmic equations.
- Use the definition of a function to solve inverse functions.
- Understand matrix algebra and apply matrices to systems of equations.
- Implement the use of technology such as a graphing calculator.
Methods of Assessment:
Class lectures include question and answer discussions between instructor and students.
Written homework assignments are given daily including a review the next class day.
Students demonstrate their knowledge at the white board.
Weekly exams/quizzes are given.
Homework Notebook/folders are graded every interim and quarter.
Material for Course:
Textbook - Applied College Algebra (Houghton Mifflin)
Pen or pencil
Houghton Mifflin Textbook Site
Scope & Sequence:
- Set of Numbers
- Union & Intersection of Sets
- Absolute Value and Distance
- Interval Notation
- Order of Operations
- Properties of Real Numbers
- Simplifying Variable Expressions
Integer Exponents and Scientific Notation
- Properties of Exponents
- Introduction to Scientific Notation
- Operations on Numbers in Scientific Notation
Introduction to Polynomials
- Standard form of a polynomial
- Addition & Subtraction of Polynomials
- Multiplication of Polynomials
- Division of Polynomials
Factoring of polynomials
Rational Exponents and Radicals
Equations & Inequalities
- Linear Equations
- Quadratic Equations
- Rational Equations
- Polynomial Equations
- Absolute Value Equations
- Radical Equations
- Linear and Absolute Value Inequalities
Introduction to Functions
- Rectangular Coordinate and Graphs
- Relations and Functions
- Properties of Linear Functions
- Linear Models
- Quadratic Equations
Properties of Functions
- Algebra of Functions
- Inverse Functions
Polynomial and Rational Functions
- The Remainder Theorem and Factor Theorem
- Polynomial Functions of Higher Degree
Exponential and Logarithmic Functions
- Exponential Functions and Their Applications
- Logarithmic Functions and their Applications
- Working with Logarithms
- Exponential and Logarithmic Equations
Systems of Linear Equations
- Systems of Linear Equations in Two Variables
- The Algebra of Matrices
- The Inverse of a Matrix