Mathematics Age 15 - 16

SETS

Introduction to Sets

Operations on Set

Venn Diagram

RELATIONS AND FUNCTIONS

Relations

Functions

Comparison of Relation and Function

Graphical Representation of a Function

TRIGNOMETRIC FUNCTIONS

Trignometric Identities

Addition and Subtration Formula

Multiple and Submultiple Formula

MATHEMATICAL INDUCTION

Mathematical Induction

COMPLEX NUMBERS

Complex Numbers

Solving Quadratic Equation

LINEAR INEQUATIONS

Linear Inequations

PERMUTATIONS AND COMBINATIONS

Permutations

Permutations Under Restriction

Combinations

Relation connecting Permutation and Combination

BINOMIAL THEOREM

Binomial Theorem

SEQUENCES AND SERIES

Introduction to Progression

Arithmetic Progression

Geometric Progression

Relation between AM and GM

STRAIGHT LINES

Area of a Triangle

Equation of a Straight Line in Different Forms

Orthocentre and Circumcentre

Distance of a Point from a Straight Line

CONIC SECTIONS

Circles

Parabola

Ellipse

Hyperbola

THREE DIMENSIONAL COORDINATE GEOMETRY

Distance Formula

Section Formula

Centroid

LIMITS AND DERIVATIVES

Limit of a Function

Derivative of a Function

Product Formula

Quotient Formula

Function of a Function Rule

MATHEMATICAL REASONING

Introduction to Mathematical Reasoning

Basic Logic Operators

Conditional and Biconditional Statements

Validations

STATISTICS

Measures of Central Tendency

Measures of Dispersion

PROBABILITY

Priliminaries of Probability

Classical Definition of Probability

Axiomatic Definition of Probability

Addition Theroem of Probability