Algebra - Laws - Basic

• Algebraic equations - Simplification
• Algebra - Basic concepts - Errors and approximations

• Units - Conversions and scientific notations

Number theory

• Divisibility - Properties
• Division algorithm

• Numbers - Properties
• GCD - Euclid's algorithm

• Prime number - Definition and properties
• Composite numbers
• Divisors - Total number and their sum
• Prime number - Properties

• Congruence - Properties
• Congruence - Linear

Indices - Laws - Basic

• Indices - First law
• Indices - Second law
• Indices - Third law
• Indices - Fourth law
• Indices - Fifth law
• Indices - Laws - Applications

Rational fractions - Proper and improper

• Partial fractions - Factors - Non repeated linear
• Partial fractions - Factors - Repeated and non repeated linear
• Partial fractions - Factors - Non repeated irreducible
• Partial fractions - Factors - Repeated, non repeated irreducible

Mathematical induction - Induction set

• Mathematical induction - Principles
• Mathematical induction - Examples

Surds - Classification & properties

• Surds - Properties - Examples

• Surds - Square root - Properties
• Surds - Square root - Examples

• Surds - Cube root - Examples

Logarithms - Common and natural

• Logarithms - Product to sum form
• Logarithms - Division to difference form
• Logarithms - Exponent to product form
• Logarithms - Equality of components
• Logarithms - Change of base - Rule

• Logarithms - Characteristics theorems
• Logarithms - Mantissa and antilogarithms
• Logarithms - Characteristics and mantissa - Examples

• Logarithms - Sign
• Logarithms - Inequalities

• Logarithms - Applications - Numerical calculations
• Logarithms - Applications - Other calculations

Progression - Types

• Progression - Arithmetic - General term
• Progression - Arithmetic - General term - From end
• Progression - Arithmetic - Sum of n terms
• Progression - Arithmetic - Mean
• Sum to n terms of the special series - involving natural numbers

• Progression - Geometric - Mean

• Progression - Harmonic - Mean

• Progression - Problems involving triangles
• Progression - Arithmeticogeometric - nth term
• Progression - Arithmeticogeometric - Sum of n terms

Exponential series - Expansion of e^x for real x

• Exponential series - Limit problems
• Exponential theorem

• Exponential series - General term
• Exponential series - Coefficient of x^n
• Exponential series - Sum

Logarithmic Series

• Logarithmic Series - Proving problems
• Logarithmic series - Sum
• Logarithmic series - Coefficient of x^n

Quadratic equations - Roots

• Quadratic equations - Roots - Real and distinct
• Quadratic equations - Roots - Real and equal
• Quadratic equations - Roots - Imaginary

• Quadratic inequations - Examples
• Quadratic inequations - Domain and range

Equations - Higher degree

• Cubic equations - Roots in AP
• Cubic equations - Roots in GP
• Cubic equations - Roots in HP

• Equations - Higher degree - Symmetric functions of roots
• Equations - Higher degree - Irrational roots
• Equations - Biquadratic - Roots
• Equations - Cubic - Roots - Cardon's method

• Equations - Higher degree - Roots with multiplicity 'r'
• Equations - Higher degree - Real roots
• Equations - Higher degree - Imaginary roots

Polynomial functions and equations

• Roots of an equation
• Descarte's rule of signs
• Newton's theorem
• Synthetic division

Linear inequalities

• Solution of linear inequalities in one variable
• Solution of linear inequalities in two variables