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: 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.
Purple Math
Purplemath: Rounding Numbers
Reviews how to round numbers to a given place or number of decimal places.
Purple Math
Purplemath: Proportions: Introduction
Explains the basics and terminology of proportions.
Purple Math
Purplemath: Scatterplots and Regressions
Explains the purpose of scatterplots, and demonstrates how to draw them.
Purple Math
Purplemath: Simple Factoring
Demonstrates how to factor simple polynomial expressions such as "2x + 6".
Purple Math
Purplemath: Simplifying With Parentheses
Explains, with worked examples, how to simplify expressions which involve parentheses and variables, including how to take a negative through the parentheses.
Purple Math
Purplemath: Using Slope and Y Intercept to Graph Lines
Demonstrates, step-by-step and with illustrations, how to use slope and the y-intercept to graph straight lines.
Purple Math
Purplemath: Geometry Word Problems: Introduction
Introduces how to set up and solve simple geometric-figure word problems. Includes advice regarding formulas to memorize.
Purple Math
Purplemath: "Distance" Word Problems
Demonstrates how to set up and solve 'distance' problems using 'distance equals rate times time'.
Purple Math
Purplemath: Factoring Polynomials: How To
Demonstrates the steps involved in factoring a general polynomial, including using the Rational Roots Test and synthetic division. Shows how to "cheat" with a graphing calculator.
Purple Math
Purplemath: Operations on Functions
Demonstrates how to add, subtract, multiply, and divide functions. Includes an example of evaluation. Demystifies the notation.
Purple Math
Purplemath: Polynomial Graphs: End Behavior
Explains how to recognize the end behavior of polynomials and their graphs. Points out the differences between even-degree and odd-degree polynomials, and between polynomials with negative versus positive leading terms.
Purple Math
Purplemath: The Rational Roots Test
Demonstrates how to use the Rational Roots Test to list possible fractional solutions for polynomials.
Purple Math
Purplemath: Special Factoring: Differences of Squares
Demonstrates how to use the formula for finding the differences of squares, and warns against trying to factor a sum of squares.
Purple Math
Purplemath: Solving Quadratic Equations by Factoring
Demonstrates how to solve quadratics using factoring (that is/the Zero-Product Property). Provides worked examples/and warnings about common mistakes.
Purple Math
Purplemath: Solving Polynomials: How To
Demonstrates the steps involved in solving a general polynomial, including how to use the Rational Roots Test and synthetic division. Points out when using a graphing calculator can be very helpful.
Purple Math
Purplemath: Slant (Oblique)l Asymptotes
The functions and graphs of functions with oblique asymptotes are explained with a step-by-step description of how to find oblique asymptotes and gives examples.
Purple Math
Purplemath: Matrix Multiplication/the Identity Matrix
Definitions, examples, and detailed explanation of matrix multiplication and the identity matrix.
Purple Math
Purplemath: Solving Linear Equation With Parentheses; "No Solution" Equations
Learn how to solve linear equations with parenthesis and equations with no solutions. Please be aware that this is an ad heavy resource.
Curated OER
Y = (2/3)X 4
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...
Curated OER
Y = 2x + 3
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...