An Ordered Listing of the 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.
While the structure of the Purplemath lessons lends itself to many topical orderings, the following is one possible lesson sequence. To do your self-study, follow this sequence by working down the left-hand column, then the middle column, and finally the right-hand column of each section, proceeding through the sections from the top of the page to the bottom.
Switch to the alphabetical listing
Preliminary Topics
- Why Do I Have to
- Placement Tests
- Rounding
- Place Value
- Roman Numerals
- Number Properties
(Distributive, Associative, Commutative, etc.)
- Number Bases
(binary, octal, etc.) - Factoring Numbers
- LCM and GCF
- Fractions
- (and fraction division: why does flip-n-multiply work?)
Beginning Algebra Topics
- Variables
- Exponents: Basic Rules
- Order of Operations
- Evaluation
- Polynomials
- (Definitions & "like terms")
- Simplifying with Parentheses
- Polynomials: Adding
- Polynomials: Multiplying
- Simple Factoring
- such as "2x + 6 = 2(x + 3)
- Exponents: Negative
- Simplifying with Exponents
- Scientific Notation
- Engineering Notation
- Polynomials: Dividing
- x,y-Plane (plotting points, etc)
- Midpoint Formula
- Distance Formula
- Solving Linear Equations
Translation: How to translate word problems from English into math
Slope and y-intercept
(and their meaning in word problems)
- Straight-Line Equations
- such as "y = mx + b"
- x- and y-Intercepts
- Scatterplots & Regressions
- Solving Linear Inequalities
- such as "2x < 4"
- Graphing Linear Inequalities
- such as "y < 2x + 3"
- Graphing Absolute-
- Solving Absolute-
- Radicals (square roots,
- cube roots, etc)
- Exponents: Fractional
- Solving Radical Equations
- Graphing Radical Equations
Intermediate Algebra Topics
Advanced Algebra Topics
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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