AOPS

Introduction to Algebra

 Syllabus

Syllabus

1 Follow the Rules

 1.1 Numbers

 1.2 Order of Operations

 1.3 When Does Order Matter?

 1.4 Distribution and Factoring

 1.5 Equations

 1.6 Summary


2 x Marks the Spot

 2.1 Expressions

 2.2 Arithmetic with Expressions

 2.3 Distribution, Subtraction, and Factoring

 2.4 Fractions

 2.5 Summary


3 One-Variable Linear Equations

 3.1 Solving Linear Equations I

 3.2 Solving Linear Equations II

 3.3 Word Problems

 3.4 Linear Equations in Disguise

 3.5 Summary


4 More Variables

 4.1 Evaluating Multi-Variable Expressions

 4.2 Still More Arithmetic

 4.3 Distribution and Factoring

 4.4 Fractions

 4.5 Equations

 4.6 Summary


5 Multi-Variable Linear Equations

 5.1 Introduction to Two-Variable Linear Equations

 5.2 Substitution

 5.3 Elimination

 5.4 Word Problems

 5.5 More Linear Equations in Disguise

 5.6 More Variables

 5.7 Summary


6 Ratios and Percents

 6.1 Basic Ratio Problems

 6.2 More Challenging Ratio Problems

 6.3 Conversion Factors

 6.4 Percent

 6.5 Percentage Problems

 6.6 Summary


7 Proportion

 7.1 Direct Proportion

 7.2 Inverse Proportion

 7.3 Joint Proportion

 7.4 Rate Problems

 7.5 Summary


8 Graphing Lines

 8.1 The Number Line and the Cartesian Plane

 8.2 Introduction to Graphing Linear Equations

 8.3 Using Slope in Problems

 8.4 Find the Equation

 8.5 Slope and Intercepts

 8.6 Comparing Lines

 8.7 Summary


9 Introduction to Inequalities

 9.1 The Basics

 9.2 Which Is Greater?

 9.3 Linear Inequalities

 9.4 Graphing Inequalities

 9.5 Optimization

 9.6 Summary


10 Quadratic Equations-Part 1

 10.1 Getting Started With Quadratics

 10.2 Factoring Quadratics I

 10.3 Factoring Quadratics II

 10.4 Sums and Products of Roots of a Quadratic

 10.5 Extensions and Applications

 10.6 Summary


11 Special Factorizations

 11.1 Squares of Binomials

 11.2 Difference of Squares

 11.3 Sum and Difference of Cubes

 11.4 Rationalizing Denominators

 11.5 Simon's Favorite Factoring Trick

 11.6 Summary


12 Complex Numbers

 12.1 Numbers, Numbers, and More Numbers!

 12.2 Imaginary Numbers

 12.3 Complex Numbers

 12.4 Summary


13 Quadratic Equations-Part 2

 13.1 Squares of Binomials Revisited

 13.2 Completing the Square

 13.3 The Quadratic Formula

 13.4 Applications and Extensions

 13.5 Summary


14 Graphing Quadratics

 14.1 Parabolas

 14.2 Circles

 14.3 Summary


15 More Inequalities

 15.1 Quadratic Inequalities

 15.2 Beyond Quadratics 

 15.3 The Trivial Inequality

 15.4 Quadratic Optimization

 15.5 Summary


16 Functions

 16.1 The Machine

 16.2 Combining Functions

 16.3 Composition

 16.4 Inverse Functions

 16.5 Problem Solving with Functions…

 16.6 Operations

 16.7 Summary


17 Graphing Functions

 17.1 Basics

 17.2 Transformations

 17.3 Inverse Functions Revisited

 17.4 Summary


18 Polynomials

 18.1 Addition and Subtraction

 18.2 Multiplication

 18.3 Summary


19 Exponents and Logarithms

 19.1 Exponential Functions

 19.2 Show Me the Money

 19.3 Interest-ing Problems

 19.4 What is a Logarithm?…

 19.5 Summary


20 Special Functions

 20.1 Radicals

 20.2 Absolute Value

 20.3 Floor and Ceiling

 20.4 Rational Functions

 20.5 Piecewise Defined Functions

 20.6 Summary


21 Sequences & Series

 21.1 Arithmetic Sequences

 21.2 Arithmetic Series

 21.3 Geometric Sequences

 21.4 Geometric Series

 21.5 Telescoping

 21.6 Summary


22 Special Manipulations

 22.1 Raising Equations to Powers

 22.2 Self-similarity

 22.3 Symmetry

 22.4 Summary