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.
Preliminary
Topics
Why
Do I Have to Take Algebra? Rounding (andsignificant
digits )Place
Value Roman Numerals
Number
Properties Number Bases Factoring Numbers LCM
and GCF Fractions
Converting
between Percents, Decimals, and Fractions Number
Types Set
Notation Geometric Formulas Absolute
Value Negative Numbers
Beginning
Algebra Topics
Variables Exponents:
basic rules Order of Operations Evaluation Polynomials Simplifying
with Parentheses Polynomials:
Adding & Subtracting Polynomials: Multiplying Simple
Factoring x + 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 Solving: Literal
Equations Ratio & Proportion Canceling
Units Translation :
How to translate age "
problems area/volume/perimeter " coin "
(money) problems distance " d = rt problems investment "I = Prt " mixture "
problems number "
(integer) problems work "
problems"Percent of" word problems Slope
of a straight line Slope
and Graphing
Graphing:
Linear Equations Slope
and y-intercept andStraight-line
equations y = mx + b )Intercepts Scatterplots
& Regressions Inequalities: Linear x < 4")Graphing:
Linear Inequalities y < 2x + 3")Graphing: Absolute
Value Solving: Absolute Value Equations Radicals (square roots, Exponents:
fractional Solving:
Radical Equations Graphing: Radical
Equations
Intermediate
Algebra Topics
Graphing:
Systems of Linear Inequalities Linear
Programming Inequalities:
Absolute Value Factoring
Quadratics Special Factoring Formulas Quadratic Formula Solving:
Quadratic Equations Graphing: Quadratic
Equations Quadratic
Word Problems
Inequalities:
Quadratic Solving
Systems: General Equations Functions Function
Notation Function
Transformations (direct, inverse, joint)Rational Roots
Test Remainder Theorem Factor
Theorem Synthetic Division
Descartes'
Rule of Signs Solving/Factoring Polynomials Finding
Polynomials from Their
Zeroes Polynomial Graphs circles ellipses solving
quadratics finding the vertex Sequences and Series
Advanced
Algebra Topics
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
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
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
Appendix
Mean,
Median, and Mode Box-and-Whisker Plots Stem-and-Leaf
Plots
Venn
Diagrams Calculators
Placement
Tests How Do I Compute My Grade? Books:
Reviews, etc.
...and
the beginnings of trig
Conventions Pythagorean
Theorem Greek Letters & Their
Names Radians
and Degrees Sectors,
Areas, and Arcs Basic Trigonometric
Ratios
Quadrants
and Angles Unit Circle Right-Triangle
Word Probs Angles of Elevation / Depr. Special
Angle Values Trig Functions &
Graphs
Advanced Trig
Graphs Trigonometric Identities Evaluating
Using Identities Proving Trig Identities Inverses
of Trig Ratios Solving Trig Equations
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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