Purple Math
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: 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: 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.
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Purplemath: Graphing Quadratic Functions: Introduction
The most basic quadratic is y = x2. The general technique for graphing quadratics is the same as for graphing linear equations. The quadratics graph as curvy lines (called "parabolas"), rather than the straight lines generated by linear...
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Purplemath: Graphing Trigonometric Functions
This resource explains how to relate constants in trigonometric function to amplitudes, vertical shifts, periods, and horizontal or phase shifts with the help of many solved examples for various trigonometric functions.
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Purplemath: How Can 0.9999 = 1?
This resource discusses the relationship between '0.999' and '1' and provides various proofs of their equality.
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Purplemath: Greek Letters and Their Names
When you are working with geometry and trigonometry, you will see a lot of Greek letters. It will be helpful to know how the names of these letters are spelled and pronounced.
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Purplemath: How Do I Compute My Grade?
Demonstrates how to figure out what you need on the Final to pass your course, given a typical grading scheme.
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Purplemath: Linear Programming: Introduction
Linear programming is a part of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources. Linear...
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Purplemath: Logarithmic Word Problems
Logarithmic word problems generally involve evaluating a given logarithmic equation at a given point, and solving for a given variable; they're pretty straightforward. This resource contains worked examples to demonstrate the reasoning...
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Purplemath: Partial Fraction Decomposition: General Techniques
Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions. This reference material demonstrates the...
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Purplemath: Reducing Fractions
Any number, divided by itself, is just 1. Use this fact when reducing fractions. This resource helps you learn about how to reduce fractions. It has few worked out examples with detailed explanations.
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Purplemath: Minors and Cofactors: Expanding Along a Row
A "minor" is the determinant of the square matrix formed by deleting one row and one column from some larger square matrix. To find the determinant of the matrix A, you have to pick a row or a column of the matrix, find all the cofactors...
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Purplemath: Number Bases: Introduction & Binary Numbers
The process of converting between different number bases is actually fairly simple, but the thinking behind it can seem a bit confusing at first. And while the topic of different bases may seem somewhat pointless to you, the rise of...
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Purplemath: Functions: Domain and Range
Discusses the domain and range of a function, and how to find the domain and range from a list of points or from a graph.
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Purplemath: Converting Between Radians and Degrees
Describes degrees and radians with respect to angles, the reason for the invention and use of radians, and how to convert between radians and degrees.
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Purplemath: Graphing Rational Functions: Introduction
To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then sketch in the graph. Once you get the swing of things, rational functions are actually fairly simple to graph. This resources provides...
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Purplemath: Practical Algebra Lessons
Pre-algebra and algebra lessons, from negative numbers through pre-calculus. Grouped by level of study. Lessons are practical in nature informal in tone, and contain many worked examples and warnings about problem areas and probable...
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Purplemath: Practical Algebra Lessons
Pre-Algebra and algebra lessons, from negative numbers through Pre-Calculus. Grouped by level of study. Lessons are practical in nature, informal in tone, and contain many worked examples and warnings about problem areas and probable...