Algebra

Definition

Algebra can essentially be considered as doing computations similar to that of arithmetic with non-numerical mathematical objects.

Topics

Manipulating Equations

• Rearranging Equations
• Substitution
• Expanding Brackets
• Factorising Expressions
• Polynomial Division

Solving Equations

• Solving Linear Equations in One Variable
• Solving Quadratic Equations
• The Quadratic Formula
• Completing the Square
• Solving Cubic Equations
• Solving Inequalities
• Simultaneous Equations
• The Fundamental Theorem of Algebra

Fractions

• Fractions
• Partial Fractions

Powers, Logarithms and Factorials

• Powers
• Logarithms
• Factorials

Complex Numbers

• Complex Arithmetic
• Modulus and Argument
• Polar Form and De Moivre's Theorem
• Complex Roots of Polynomials
• Euler's Formula and Euler's Identity