Purple Math
Purplemath: Trigonometric Functions and Their Graphs
Explains the horizontal forms of trigonometric graphs by showing how they relate to the circular graphs.
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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.
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Purplemath: "Coin" Word Problems
This site demonstrates how to solve 'coin' word problems, given relationships between the types of coins.
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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.
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Purplemath: Completing the Square: Deriving the Quadratic Formula
View examples on completing the square and deriving the quadratic formula. The key to solving by completing the square is "practice, practice, practice". By so doing, the process will become more "automatic", and you'll be much more...
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Purplemath: Conics: Ellipses: Introduction
Introduces the basic terms, variables, and equations for ellipses, and discusses their physical properties.
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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.
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Purplemath: Adding and Subtracting Matrices
Demonstrates how to add and subtract matrices, explains why the addition or subtraction sometimes can't be done, and gives an example of how matrix addition is used in homework problems.
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Purplemath: Basic Trigonometric Ratios: Examples
Demonstrates how to use trig ratios to do simple solving of triangles.
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Purplemath: "The Bible Says Pi = 3"
Shows how a simple reading from the Bible proves that the Judeo-Christian value of 'pi' is about 3.14 and not 3.
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Purplemath: Angles of Inclination and Declination
Explains the terminology for angles of elevation, depression, inclination, and declination. Demonstrates how to 'translate' exercises into triangles and equations.
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Purplemath: "Mixture" Word Problems
Demonstrates, step-by-step and with examples, how to set up and solve 'mixture' word problems.
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Purplemath: "Number" Word Problems
Demonstrates, step-by-step and with illustrations, how to set up and solve 'number' problems.
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Purplemath: "Work" Word Problems
Explains the "trick" to "work" word problems (such as two people painting a room, or two pipes filling a tank), and demonstrates how to set up and solve these exercises.
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Purplemath: "Investment" Word Problems
Demonstrates in a systematic way how to set up and solve 'investment' word problems.
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Purplemath: Quadratic Word Problems: Projectile Motion
Launching a rocket up into the air, throwing a textbook down off a rooftop, or tossing a baseball out to someone in center field are all examples of projectile motion and quadratic word problems. Situations like these are explored here,...
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Purplemath: Solving Linear Inequalities: Introduction and Formatting
This resource demonstrates how to solve linear inequalities step-by-step and shows four different solution formats/notations viz. inequality notation, set notation, interval notation, and the last "notation" which is more of an...
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Purplemath: Numerical Approximation of Zeroes: The Midpoint Method
Explains the reasoning and methodology for the process of numerically approximating the zeroes of a non solvable polynomial.
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Purplemath: Metric Units & Converting Between Them
This resource demonstrates how to convert between various sizes of metric units quickly and easily. Metric units are very nice to work with, since they are all multiples of ten (or a hundred, or one-tenth, etc) of each other. You can...
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Purplemath: Conventions
A "convention" is "just the way a thing is done!". This reference material lists some common conventions (notational assumptions) for geometry and trigonometry.
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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.
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Purplemath: Function Transformations
Generally, translation involves only moving the graph around. Squeezing or stretching a graph is more of a "transformation" of the graph. But these two topics are usually taught at the same time, and usually under the same name. Just be...
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Purplemath: Formatting Math as Text: Common Algebraic Notation
Math can look so pretty, all nicely formatted in the textbook. But when you go to e-mail your instructor with a question, or post your question to a math tutoring forum, you can end up with a mess or with something that totally doesn't...
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Purplemath: Graphing Overview: Straight Lines
This resource provides an overview of graphing for various types of functions, instruction on graphing straight lines and also, includes advice on common mistakes made by students.