Purple Math
Purplemath: Introduction to Matrices / Matrix Size
Purplemath gives the fundamentals of matrices. Begins with linear equations of three variables and shows the corresponding matrix. Discusses the augmented and coefficient matrix formed from the equation. The size of a matrix and special...
Purple Math
Purplemath: Basic Log Rules / Explanding Logarithmic Expressions
Purplemath gives both a formal and informal discussion of log rules with exercises. Examples include expanding, simplifying, and evaluating logarithms. Changing the base of a logarithm is also discussed with examples.
Purple Math
Purplemath: Solving Logarithmic Equations: Solving From the Definition
This Purplemath lesson teaches students to solve logarithmic equations. There are many examples and links to solving with exponentials and calculator considerations at the top of the lesson.
Purple Math
Purplemath: Change of Base
This section of a Purplemath lesson gives the formula for a change of base with several examples. The lesson gives examples of typical problems involving changing the base of logarthims including: evaluating, converting to another base;...
Purple Math
Purplemath: Binomial Theorem: Formulas
The Binomial Theorem is a process of expanding a binomial that is being raised to a large power. All steps needed to perform the process on a graphing calculator are listed. The concepts of factorials and Pascal's Triangle -- both key to...
Purple Math
Purplemath: Graphing Linear Equations: T Charts
A nice tutorial on how to graph linear equations. Goes through the process step by step and gives numerous examples.
Purple Math
Purplemath: Fractional (Rational) Exponents
A good explanation of rational exponents and how to compute with them.
Purple Math
Purplemath: Conics: An Overview
Introduces the basics of conics in algebra, including a flow-chart for determining which sort of conic is represented by a given equation.
Purple Math
Purplemath: Basic Trigonometric Ratios: Examples
Demonstrates how to use trig ratios to do simple solving of triangles.
Purple Math
Purplemath: Conics: Parabolas: Introduction
This reference material introduces the terms and equations related to parabolas in the context of conics. Also, relates concepts to previously-learned material and shows how to 'read' from the 'conics' form of the parabola equation.
Purple Math
Purplemath: Graphing Exponential Functions: Intro
An in-depth lesson which teaches you how to graph exponential equations. Examples are worked through step by step and explained in detail for different exponential equations.
Purple Math
Purplemath: Function Notation & Evaluating at Numbers
Presents a lesson on function notation. Includes interactive widget for evaluating functions.
Purple Math
Purplemath: Simplifying Expressions With Exponents
A detailed look at how to simplify expressions with exponents and how to apply the rules for exponents. Lots of examples included. The third page provides an interactive widget to use for simplifying expressions with exponents.
Purple Math
Purplemath: Functions Versus Relations
This lesson offers a thorough explanation of functions, domain and range, and how to find them. Includes multiple example problems and graphs. Great review tool for Algebra students.
Purple Math
Purplemath: Composition of Functions: Composing Functions With Functions
Explanations and examples of composing functions with functions.
Purple Math
Purplemath: Slope of a Straight Line
This lesson on slope explains the slope concepts, demonstrates how to use the slope formula, shows how to find slope in horizontal and vertical lines, and how to use slope to find whether the lines through the pairs of points are...
Purple Math
Purplemath: Graphing Logarithmic Functions: Intro
This lesson details graphing logarithmic functions. The lesson explains the relationship between the graph of the logarithm and its inverse. The site gives examples of logarithmic graphs of base 2, 3, and e. Shifts in logarithmic graphs...
Purple Math
Purplemath: Function Notation: Even and Odd
A lesson on function notation contains a section on even and odd functions. An explanation is given on how to algebraically determine if a function is even or odd, along with example problems.
Purple Math
Purplemath: Graphing Absolute Value Functions
Introduces the basic technique for graphing absolute-value functions, and illustrates a common mistake.
Purple Math
Purplemath: Basic "Percent Of" Word Problems
Demonstrates how to set up and solve 'percent of' word problems such as 'What percent of 16 is 5?'.
Purple Math
Purplemath: Trigonometric Functions and Their Graphs
Explains the horizontal forms of trigonometric graphs by showing how they relate to the circular graphs.
Purple Math
Purplemath: Geometric Formula Review
Need to freshen up on your geometric formulas? This explanation focuses on some basic formulas that should be committed to memory such as area, volume, perimeter, and more.
Purple Math
Purplemath: "Coin" Word Problems
This site demonstrates how to solve 'coin' word problems, given relationships between the types of coins.
Purple Math
Purplemath: General Polynomials
Confused about graphing or just need a refresher? This explanation focuses on graphing higher-power polynomials along with radical functions, rational functions, and piecewise functions. Plenty of examples are included.