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Unit Plan
Purple Math

Purplemath: Composition of Functions: Composing With Sets of Points

For Students 9th - 10th
An in-depth lesson that explains the notation and terminology of function composition, and demonstrates how to use composition. Successive pages look at composing functions at points, composing functions with functions, word problems...
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Unit Plan
Purple Math

Purplemath: Conics: Hyperbolas

For Students 9th - 10th Standards
A three-part tutorial that discusses the basic terms, definitions, and formulas related to hyperbolas.
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Unit Plan
Purple Math

Purplemath: Evaluation: Evaluating Expressions, Polynomials, and Functions

For Students 9th - 10th
Demonstrates evaluation (or 'plug-n-chug'), and points out common usage and mistakes.
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Handout
Purple Math

Purplemath: Complex Numbers: Introduction

For Students 9th - 10th Standards
This website provides an in-depth lesson on complex numbers. You learn about simplifying, adding, and multiplying complex numbers by viewing example problems that are worked through step-by-step. Continue on to pages 2 and 3 which...
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Handout
Purple Math

Purplemath: Sequences and Series: Terminology and Notation

For Students 9th - 10th
Explains the basic terminology and notation of sequences and series, including summation symbols, subscripts, and indices.
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Activity
Purple Math

Purplemath: Polynomials: Definition and Evaluation

For Students 9th - 10th Standards
A great lesson on polynomials is found at this Purplemath resource. Provides a clear definition of what a polynomial is, tells how to tell what the different degrees of a polynomial are, and how to simplify polynomials by combining like...
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Handout
Purple Math

Purplemath: Graphing Exponential Functions: Intro

For Students 9th - 10th Standards
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.
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Activity
Purple Math

Purplemath: Adding & Subtracting Rational Expressions: Introduction

For Students 9th - 10th Standards
Finding common denominators is no problem with Purplemath. Use this lesson to learn how to add and subtract rational expressions with these great examples.
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Handout
Purple Math

Purplemath: Binomial Theorem: Formulas

For Students 9th - 10th Standards
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...
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Handout
Purple Math

Purplemath: Function Notation & Evaluating at Numbers

For Students 9th - 10th Standards
Presents a lesson on function notation. Includes interactive widget for evaluating functions.
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Unit Plan
Purple Math

Purplemath: Simplifying Expressions With Exponents

For Students 9th - 10th Standards
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.
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Handout
Purple Math

Purplemath: Converting Units

For Students 6th - 8th Standards
This resource provides a description and examples of how to convert between two units.
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Handout
Purple Math

Purplemath: The Order of Operations: Pemdas

For Students 9th - 10th
Gives a detailed explanation of how the order of operations works. Explains how to use the PEMDAS acronym (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) to remember the correct order. Includes lots of example...
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Handout
Purple Math

Purplemath: Square Roots: Introduction & Simplification

For Students 9th - 10th Standards
Purplemath offers a well-described definition of radicals and square roots. The lesson is very easy to understand. Many examples.
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Handout
Purple Math

Purplemath: Completing the Square: Solving Quadratic Equations

For Students 9th - 10th Standards
Purplemath gives several examples which clearly show the process of completing the square to find the maximum and minimum solutions to a quadratic equation.
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Activity
Purple Math

Purplemath: Converting Between Decimals, Fractions, and Percents

For Students 9th - 10th
Scroll down to just below the middle of the lesson for an in-depth lesson on converting fractions to percents. Works through numerous examples step by step and shows what happens when the "decimal expansion" doesn't end when converting.
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Graphic
Purple Math

Purplemath: Solving Inequalities: An Overview

For Students 9th - 10th Standards
A discussion on how to solve linear and nonlinear inequalities is presented. Both the Test Method and the Factor Method of checking positive/negative intervals are included as part of the discussion.
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Handout
Purple Math

Purplemath: Set Notation

For Students 9th - 10th Standards
This resource explains concepts related to set notation and gives examples for each.
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Unit Plan
Purple Math

Purplemath: Basic Triangle Values

For Students 9th - 10th
This Purplemath lesson explains a simple pictorial way to remember basic reference angle values.
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Handout
Purple Math

Purplemath: Distance Formula

For Students 9th - 10th Standards
A concise presentation of a lesson showing how the Distance Formula is really just the Pythagorean Theorem, and how it can be used to find the distance between two sets of coordinates.
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Handout
Purple Math

Purplemath: Functions Versus Relations

For Students 9th - 10th Standards
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.
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Handout
Purple Math

Purplemath: The Meaning of Slope and Y Intercept in Context of Word Problems

For Students 9th - 10th Standards
This resource contains a lesson on the slope and y-intercept of a line and how to interpret them in word problems.
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Unit Plan
Purple Math

Purplemath: Composition of Functions: Composing Functions With Functions

For Students 10th - 12th Standards
Explanations and examples of composing functions with functions.
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Handout
Purple Math

Purplemath: Solving Literal Equations

For Students 9th - 10th Standards
Provides a lesson on solving literal equations, explains how they are similar to solving linear equations, and works through numerous examples showing how different types of literal equations are solved.