Course Introduction
In Advanced Algebra, you will build on your foundation of basic algebra to be able to solve increasingly complex problems. You will learn to solve equations beyond the familiar 2x – 5(2x + 3) = 13 to equations that model more interesting real-life applications. You will make use of the graphing calculator, which will be available for your use. It is assumed that each of you is planning on taking Pre-Calculus or Statistics/Trigonometry, and has aspirations for college or technical training beyond high school. This course it not designed to be easy, nor is it a place to simply get a third math credit. Approaching this class with a minimum of determination and effort sets you up for frustration, failure and a waste of 10,080 minutes of your time.

Topics covered and intended learning outcomes

Algebra Review

• Use the Distributive Property and and other methods to simply and solve linear equations
• Use the Pythagorean Theorem to find unknown sides of right triangles and to determine if a given triangle is a right triangle
• Solve equations involving squaring and square roots
• Graph linear equations and inequalities
• Find the equation of a line given sufficient information
• Add, subtract, and multiply polynomials
• Factor a monomial from a polynomial
• Factor trinomials and differences of squares
• Simplify expressions using the laws of exponents
• Solve problems involving percent increase and decrease, and simple interest

Functions

• Be able to determine if a relation is a function and describe its domain and range
• Add, subtract, multiply and divide functions
• Evaluate and simplify composite functions
• Find and use inverse functions
• Determine if a function is 'one-to-one'

Linear Equations and Inequalities

• Use linear equations to solve application problems
• Solve one-variable absolute value equations and inequalities and graph their solutions on a number line
• Graph linear functions and inequalities, and absolute value functions and inequalities, on the coordinate plane
• Graph piece-wise linear functions, and write piece-wise linear functions from graphs

Matrices

• Store data in matrices, and interpret data stored in matrices
• Add, subtract and multiply matrices, use scalar multiplication, and solve application problems involving these operations
• Use matrices to perform dilation and translation of figures on the coordinate plane
• Find the inverse of a matrix, and use it to solve a matrix equation involving multiplication
• Use matrices to describe networks and directed networks
• Use matrices to encode and decode messages
• Use dominance matrices to determine the winner in a non-tournament league

Systems of Equations and Inequalities

• Solve a system of two equations using graphing, elimination, substitution or a matrix equation
• Solve a system of three equations using elimination, substitution or a matrix equation
• Graph a system of linear inequalities
• Use system of two or three variable to solve application problems involving, but not limited to, pricing, mixtures, relative speeds, and investments

Variation

• Use direct, inverse and joint and combined variation to solve problems either from variation statements or from data
• Use the Fundamental Theorem of Variation to determine the effect on the output from a change to the input of a variation function

Quadratic Equations and Complex Numbers

• Solve quadratic equations by graphing, factoring, completing the square and the Quadratic Formula
• Convert between vertex form and standard form of quadratic equation
• Use the vertex form of a real-life quadratic function to determine maximum values
• Graph numbers on the complex plane and find their absolute value
• Simplify imaginary and complex numbers and expressions using addition, subtraction, multiplication and division

Polynomials

Exponents and Logarithms

Trigonometry

Linear Programming

Miscellaneous Topics

• Determine theoretical and experimental probabilities
• Use the counting principles, permutations and combinations to anwer probability questions
• Use changes in functions to describe horizontal and vertical shifts on the coordinate plane
• Find best-fit lines for linear and quadratic data using algebraic and electronic means
• Visually inspect a scatterplot to determine a negative or positive trend and a strong or weak correlation
• Be able to graph points and planes on a three-dimensional coordinate system