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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. |
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.
Top | Return
to Index
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