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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 text he is using, may benefit.
While the structure of the Purplemath lessons lends
itself to many topical orderings, the following is one possible lesson sequence. Follow this sequence
by working down the left-hand, then middle, and then right-hand columns of each section, proceeding through
the sections from the top of the page to the bottom.
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Preliminary Topics |
Why Do I Have
to
Take Algebra?
Rounding
(and
significant
digits)
Number Properties
(Distributive, Commutative,
Associative, etc.)
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Number Bases
(binary, hexadecimal, etc.)
Factoring
Numbers
LCM and
GCF
Fractions
Converting
between Percents, Decimals, and Fractions
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Number Types
(natural, integer, real, etc.)
Set Notation
Geometric
Formulas
Absolute Value
Negative
Numbers
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Beginning Algebra Topics |
Variables
Exponents: basic rules
Order of Operations
Evaluation
Polynomials
(definitions
& "like terms")
Simplifying
with Parentheses
Polynomials:
Adding &
Subtracting
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
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Solving: Linear
Equations
Solving: Literal Equations
Ratio
& Proportion
Canceling Units
Translation: How to translate
word problems from English
into math
"age" problems
"area/volume/perimeter"
geometry
problems
"coin" (money) problems
"distance" d = rt
problems
"investment"
simple interest I = Prt
"mixture" problems
"number" (integer) problems
"work" problems
"Percent of"
word problems
Slope
of a straight line
Slope and Graphing
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Graphing: Linear
Equations
Slope
and y-intercept and
their meaning
in word
problems)
Straight-line equations
(y = mx + b)
Intercepts
Scatterplots & Regressions
Inequalities:
Linear
(such as "2x < 4")
Graphing: Linear Inequalities
(such as "y <
2x + 3")
Graphing: Absolute Value
Solving:
Absolute Value Equations
Radicals (square
roots,
cube roots, etc.)
Exponents: fractional
Solving:
Radical Equations
Graphing: Radical Equations
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Intermediate Algebra Topics
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Graphing: Systems of Linear
Inequalities
Linear
Programming
Inequalities: Absolute Value
Factoring Quadratics
Special
Factoring Formulas
(different of square, sums
and differences
of cubes)
Quadratic Formula
Solving:
Quadratic Equations
Graphing: Quadratic Equations
Quadratic Word Problems
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Inequalities: Quadratic
Solving Systems: General Equations
Functions
Function Notation
Function
Transformations
Variation (direct, inverse, joint)
Rational Roots
Test
Remainder Theorem
Factor
Theorem
Synthetic Division
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Descartes' Rule of Signs
Solving/Factoring
Polynomials
Finding Polynomials
from
Their
Zeroes
Polynomial Graphs
Completing the Square:
circles
ellipses
solving quadratics
finding
the vertex
Sequences and Series
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Advanced Algebra Topics
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Complex Fractions
Rational
Expressions:
Simplifying
Adding
Rational Expressions
Multiplying Rational
Expressions
Asymptotes
Graphing:
Rational Equations
Solving: Rational Equations
Complex Numbers
Partial-Fraction
Decomposition
Composition of Functions
Inverse Functions
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Exponentials
Graphing
Exponential Equations
Solving Exponential Equations
Logarithms
Log Rules
Graphing: Logarithmic
Equations
Solving: Logarithmic
Equations
Exponential &
Logarithmic
word problems
Systems
of Linear Equations
Systems-of-equations word
problems
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Matrix Definitions
Matrix
Addition / Subtraction
Matrix Multiplication
Matrix
Row Operations
Matrix Inversion
Determinants
Minors and Cofactors
Cramer's Rule
Determinant Word Problems
Next Number in a Sequence
Factorials
Binomial Theorem
Induction
Proofs
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Appendix
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Mean, Median,
and Mode
Box-and-Whisker Plots
Stem-and-Leaf
Plots |
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Venn Diagrams
Calculators
(what to look for, what to
buy) |
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Placement Tests
How Do I Compute My Grade?
Books:
Reviews, etc. |
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...and the beginnings
of trig
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Conventions
Pythagorean
Theorem
Greek Letters & Their Names
Radians and Degrees
Sectors,
Areas, and Arcs
Basic Trigonometric Ratios
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Quadrants and Angles
Unit
Circle
Right-Triangle Word Probs
Angles
of Elevation / Depr.
Special Angle Values
Trig
Functions & Graphs
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Advanced Trig Graphs
Trigonometric
Identities
Evaluating Using Identities
Proving
Trig Identities
Inverses of Trig Ratios
Solving
Trig Equations
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Please note that the above is only one of many equally-valid
lesson orderings, and should not be regarded as "the" lesson sequence. You may benefit
as much or more by studying the lessons in a different order. Let your own needs be the final judge.
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