Purple Math
Purplemath: Systems of Linear Inequalities
This Purplemath lesson describes how to solve a system of linear inequalities by graphing.
Purple Math
Purplemath: Variation Equations
Purplemath offers an extensive explanation of direct and inverse variation, containing several examples and real-world applications.
Purple Math
Purplemath: Introduction to Negative Numbers
This lesson from Purplemath.com reviews negative numbers and their operations. Number lines are used for demonstration.
Purple Math
Purplemath: Exponents: Basic Rules
At Purplemath.com, you can scroll down to the last lesson on the page to learn about radical exponents.
Purple Math
Purplemath: Number Types
This site explores the different types of numbers: natural numbers, whole numbers, integers, and rational and irrational numbers. Content includes some practice questions.
Purple Math
Purplemath: Factoring Numbers
Visit Purplemath.com for a lesson on finding the prime factorization of numbers. Numerous examples are worked through step by step.
Purple Math
Purplemath: Lessons and Tutoring: Reviews
An algebra teacher's treasure from Purplemath.com. This collection contains links to over 20 links for algebra lesson plans and other resources.
Purple Math
Purplemath: Exponential Functions: Introduction
Purplemath offers tables and graphs of various exponential functions for an exploration of how exponential functions behave from the real number domain. Compound interest problems are examined and the natural exponential is discussed...
Purple Math
Purplemath: Matrix Row Operations
Purplemath explains each of the elementary row operations and goes through explaining how each step is carried out and the common notation for each operation. The lesson ends with an example of how to solve an augmented matrix.
Purple Math
Purplemath: Finding the Next Number in a Sequence
This lesson explains how to find the terms of a sequence. The lesson explains how to determine a general formula for a sequence so as to be able to find any term in the sequence easily.
Purple Math
Purplemath: Remainder Theorem
Purplemath explains the Remainder Theorem and gives examples using synthetic division to evaluate, determine if a value is a solution/zero. The lesson contains a link to synthetic division and other related terms.
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: System of Equations Word Problems
This lesson gives numerous word problems with thier solutions for problems with systems of equations. Go to the third problem on the lesson, about half way down the page to find a problem with a quadratic system.
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: Factorials
A review of factorials in the areas of combinations, permutations, probability, and the Binomial Theorem is presented. Examples are worked out and explained, complete with graphing calculator steps.
Purple Math
Purplemath: Determinant Word Problems
Matrix determinants can be used to solve many algebra and geometry word problems. Among them: finding the area of a triangle, finding the area of a parallelogram, and finding the equation of a line between two points. These three...
Purple Math
Purplemath: Determinants
A complete lesson on matrix determinants is offered here. From explanation of what a determinant is to how to find the determinant of a 2x2 or 3x3 matrix. Steps are written in and shown for the student or teacher's use. Also provided are...
Purple Math
Purplemath: Cramer's Rule
Cramer's Rule for solving a system of equations is presented here using an example of a system in three variables with three equations. The "everything," approach of solving for all three variables is shown as well as the "selective,"...
Purple Math
Purplemath: Finding Quadratics From Their Zeroes
Students often have difficulty "working backwards" from the solution of a problem to its original question. Finding a polynomial, given its roots, is an example of a "working backwards" problem. Here are several examples using different...
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: Adding Polynomials
Demonstrates how to add polynomials using both the horizontal and vertical formats.
Purple Math
Purplemath: Place Value: Concepts
Explains and illustrates the thinking behind the concept of place value.
Purple Math
Purplemath: Roman Numerals
Explains the basic rules for writing numbers in Roman-numeral format.