Index of Purplemath's Lessons
The Purplemath lessons have been written so that they may be studied in whatever manner the student finds most useful. Different textbooks cover different topics in different orders. The Purplemath lessons try not to assume any fixed ordering of topics, so that any student, regardless of the textbook being, may benefit.
Below, Purplemath's lessons are listed in groups according to the general meanings of "beginning", "intermediate", and "advanced" algebra. If you are not sure where to find your topic, please try the "Search" box above.
Switch to a listing of the lessons "in study order"
Preliminary Topics
- Absolute Value
- Converting between Decimals, Fractions, and Percents
- Factoring Numbers
- Fractions
- Fraction Division: Why does flip-n-multiply (that is, "Keep, Change, Flip") work?
- Geometric Formulas
- LCM and GCF
- Metric Conversions
- Negative Numbers
- Number Bases
(binary, octal, etc.) - Number Properties
(Distributive, Associative, Commutative, etc.)
- Number Types
(natural, integer, real, etc.) - Place Value
- Roman Numerals
- Rounding (and significant digits)
- Set Notation
Beginning Algebra Topics
- Canceling Units
- Distance Formula
- Engineering Notation
- Evaluation
- Exponents:
- Graphing Overview
- Graphing Absolute Value
- Graphing Linear Equations
- Graphing Radical Equations
- Graphing Linear Inequalities
(of the form "y < 2x + 3") - Inequalities Overview
(three solution methods) - Intercepts
- Midpoint Formula
- Order of Operations
- Polynomials
(definitions & "like terms") - Polynomials: Adding & Subtracting
- Polynomials: Multiplying
- Polynomials: Dividing
- Radicals
(square roots, cube roots, rationalizing denominators, etc.) - Ratio & Proportion
- Scatterplots & Regressions
- Scientific Notation
- Simple Factoring
like "2x + 6 = 2(x + 3)" - Simplifying with Exponents
- Simplifying with Parentheses
- Slope of a straight line
- Slope and Graphing
- Slope and y-intercept
(their meaning in the context of word problems) - Solving Absolute Values
- Solving Linear Inequalities
(such as "2x < 4") - Equations
- Solving Linear Equations
- Solving Literal Equations
- Solving Radical Equations
- Straight-line equations
(y = mx + b) - Variables
- x,y-Plane
(plotting points, etc.)
Intermediate Algebra Topics
- Quadratic Formula
- Sequences and Series
- Solving Polynomials
- Solving Quadratic Equations
- Solving Systems of Non-Linear Equations
- Special Factoring Formulas (difference of squares, sums and differences of cubes, etc.)
- Symmetry
- Synthetic Division
- Variation (direct, inverse, & joint)
- Vertical Line Test
Advanced Algebra Topics
Solving Word Problems
Translation: How to translate word problems from English into mathematical equations
- "age" word problems
- "area/volume/perimeter"
geometry word problems - "coin" (money) problems
- "distance"
d = rt word problems - "investment"
simple interest I = Prt - "mixture" problems
- "number" (integer) problems
- "work" problems
- Determinant Word Problems
- Exponential and Logarithmic word problems
- "Percent of" word problems
(including increase / decrease problems) - Quadratic word problems
(including projectile motion) - Systems-of-equations word problems
Appendix
Formatting Math as Text
(how to type math when e-mailing or posting questions on tutoring forums)
...and the beginnings of trig
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