Mathematics 11

1. Sets
    1.1 Introduction
    1.2 Sets and their Representations
    1.3 The Empty Set
    1.4 Finite and Infinite Sets
    1.5 Equal Sets
    1.6 Subsets
    1.7 Power Set
    1.8 Universal Set
    1.9 Venn Diagrams
    1.10 Operations on Sets
    1.11 Complement of a Set
    1.12 Practical Problems on Union and Intersection of Two Sets

2.Relations and Functions
    2.1 Introduction
    2.2 Cartesian Product of Sets
    2.3 Relations
    2.4 Functions

3.Trigonometric Functions
    3.1 Introduction
    3.2 Angles
    3.3 Trigonometric Functions
    3.4 Trigonometric Functions of Sum and Difference of Two Angles
    3.5 Trigonometric Equations

4.Principle of Mathematical Induction
    4.1 Introduction
    4.2 Motivation
    4.3 The Principle of Mathematical Induction

5.Complex Numbers and Quadratic Equations
    5.1 Introduction
    5.2 Complex Numbers
    5.3 Algebra of Complex Numbers
    5.4 The Modulus and the Conjugate of a Complex Number
    5.5 Argand Plane and Polar Representation
    5.6 Quadratic Equations

6.Linear Inequalities
    6.1 Introduction
    6.2 Inequalities
    6.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
    6.4 Graphical Solution of Linear Inequalities in Two Variables
    6.5 Solution of System of Linear Inequalities in Two Variables

7.Permutations and Combinations
    7.1 Introduction
    7.2 Fundamental Principle of Counting
    7.3 Permutations
    7.4 Combinations

8.Binomial Theorem
    8.1 Introduction
    8.2 Binomial Theorem for Positive Integral Indices
    8.3 General and Middle Terms

9.Sequences and Series
    9.1 Introduction
    9.2 Sequences
    9.3 Series
    9.4 Arithmetic Progression (A.P.)
    9.5 Geometric Progression (G.P.)
    9.6 Relationship Between A.M. and G.M.
    9.7 Sum to n terms of Special Series

10. Straight Lines
    10.1 Introduction
    10.2 Slope of a Line
    10.3 Various Forms of the Equation of a Line
    10.4 General Equation of a Line
    10.5 Distance of a Point From a Line

11. Conic Sections
    11.1 Introduction
    11.2 Sections of a Cone
    11.3 Circle
    11.4 Parabola
    11.5 Ellipse
    11.6 Hyperbola

12. Introduction to Three Dimensional Geometry
    12.1 Introduction
    12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space
    12.3 Coordinates of a Point in Space
    12.4 Distance between Two Points
    12.5 Section Formula

13. Limits and Derivatives
    13.1 Introduction
    13.2 Intuitive Idea of Derivatives
    13.3 Limits
    13.4 Limits of Trigonometric Functions
    13.5 Derivatives

14. Mathematical Reasoning
    14.1 Introduction
    14.2 Statements
    14.3 New Statements from Old
    14.4 Special Words/Phrases
    14.5 Implications
    14.6 Validating Statements

15. Statistics
    15.1 Introduction
    15.2 Measures of Dispersion
    15.3 Range
    15.4 Mean Deviation
    15.5 Variance and Standard Deviation
    15.6 Analysis of Frequency Distributions

16. Probability
    16.1 Introduction
    16.2 Random Experiments
    16.3 Event
    16.4 Axiomatic Approach to Probability

Appendix 1: Infinite Series
    A.1.1 Introduction
    A.1.2 Binomial Theorem for any Index
    A.1.3 Infinite Geometric Series
    A.1.4 Exponential Series
    A.1.5 Logarithmic Series

Appendix 2: Mathematical Modelling
    A.2.1 Introduction
    A.2.2 Preliminaries
    A.2.3 What is Mathematical Modelling

Answers

Supplementary Material