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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
|
Mean,
Median, and Mode
Box-and-Whisker Plots
Stem-and-Leaf
Plots |
|
Venn
Diagrams
Calculators
(what to look for, what to buy) |
|
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
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