Maths 11th std

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Maths 11th std

Chapter 1 : Sets Relations and Functions


=> Sets, Relations and Functions: Introduction
=> Sets
=> Cartesian Product
=> Constants and Variables, Intervals and Neighbourhoods
=> Relations
=> Functions
=> Graphing Functions using Transformations
=> Exercise 1.1: Cartesian Product
=> Exercise 1.2: Relations
=> Exercise 1.3: Functions
=> Exercise 1.4: Graphing Functions using Transformations
=> Exercise 1.5: Choose the correct or the most suitable answer

Chapter 2 : Basic Algebra


=> Basic Algebra: Introduction
=> Real Number System
=> Absolute Value
=> Linear Inequalities
=> Quadratic Functions
=> Polynomial Functions
=> Rational Functions
=> Exponents and Radicals
=> Logarithm
=> Application of Algebra in Real Life
=> Exercise 2.1: Real Number System
=> Exercise 2.2: Absolute Value
=> Exercise 2.3: Linear Inequalities
=> Exercise 2.4: Quadratic Functions
=> Exercise 2.5: Quadratic Inequalities
=> Exercise 2.6: Polynomial Functions
=> Exercise 2.7: Method of Undetermined Coefficients
=> Exercise 2.8: Rational Functions
=> Exercise 2.9: Partial Fractions
=> Exercise 2.10: Graphical Representation of Linear Inequalities
=> Exercise 2.11: Exponents and Radicals
=> Exercise 2.12: Logarithm
=> Exercise 2.13: Choose the correct or the most suitable answer

Chapter 3 : Trigonometry


=> Trigonometry: Introduction
=> A recall of basic results
=> Radian Measure
=> Trigonometric functions and their properties
=> Trigonometric Identities
=> Trigonometric equations
=> Properties of Triangle
=> The Law of Sines or Sine Formula
=> Area of a triangle (Heron’s Formula )
=> Application to Triangle
=> Inverse Trigonometric Functions
=> Exercise 3.1: Basic results of Trigonometry
=> Exercise 3.2: Radian Measure
=> Exercise 3.3: Trigonometric functions and their properties
=> Exercise 3.4: Trigonometric Identities: Sum and difference identities or compound angles formulas
=> Exercise 3.5: Trigonometric Identities: Multiple angle identities and submultiple angle identities
=> Exercise 3.6: Trigonometric Identities: Product to Sum and Sum to Product Identities
=> Exercise 3.7: Trigonometric Identities: Product to Sum and Sum to Product Identities
=> Exercise 3.8: Trigonometric equations
=> Exercise 3.9: Area of a triangle (Heron’s Formula)
=> Exercise 3.10: Trigonometry Application to Triangle
=> Exercise 3.11: Inverse Trigonometric Functions
=> Exercise 3.12: Choose the correct or the most suitable answer

Chapter 4 : Combinatorics and Mathematical Induction


=> Combinatorics and Mathematical Induction: Introduction
=> Fundamental principles of counting
=> Factorials
=> Permutations
=> Combinations
=> Mathematical induction
=> Exercise 4.1: Factorials
=> Exercise 4.2: Permutations
=> Exercise 4.3: Combinations
=> Exercise 4.4: Mathematical induction
=> Exercise 4.5: Choose the correct or the most suitable answer

Chapter 5 : Binomial Theorem Sequences and Series


=> Binomial Theorem, Sequences and Series: Introduction
=> Binomial Theorem
=> Particular cases of Binomial Theorem
=> Finite Sequences
=> Finite Series
=> Infinite Sequences and Series
=> Exercise 5.1: Binomial Theorem
=> Exercise 5.2: Finite Sequences
=> Exercise 5.3: Finite Series
=> Exercise 5.4: Infinite Sequences and Series
=> Exercise 5.5: Choose the correct answer

Chapter 6 : Two Dimensional Analytical Geometry


=> Two Dimensional Analytical Geometry: Introduction
=> Locus of a point
=> Straight Lines
=> Angle between two straight lines
=> Pair of Straight Lines
=> Exercise 6.1: Locus of a point
=> Exercise 6.2: Straight Lines
=> Exercise 6.3: Angle between two straight lines
=> Exercise 6.4: Pair of Straight Lines
=> Exercise 6.5: Choose the correct answer

Chapter 7 : Matrices and Determinants


=> Matrices and Determinants : Introduction
=> Matrices
=> General form of a matrix
=> Types of Matrices
=> Equality of Matrices
=> Algebraic Operations on Matrices
=> Properties of Matrix Addition, Scalar Multiplication and Product of Matrices
=> Operation of Transpose of a Matrix and its Properties
=> Symmetric and Skew-symmetric Matrices
=> Determinants of Matrices of different order
=> Properties of Determinants
=> Application of Factor Theorem to Determinants
=> Product of Determinants
=> Relation between a Determinant and its Cofactor Determinant
=> Determinants: Area of a Triangle
=> Determinants: Singular and non-singular Matrices
=> Exercise 7.1: Matrices
=> Exercise 7.2: Determinants
=> Exercise 7.3: Application of Factor Theorem to Determinants
=> Exercise 7.4: Determinants: Area of a Triangle, Singular and non-singular Matrices
=> Exercise 7.5: Choose the correct answer

Chapter 8 : Vector Algebra I


=> Vector Algebra: Introduction
=> Scalars and Vectors
=> Representation of a vector and types of vectors
=> Algebra of Vectors
=> Position vectors
=> Resolution of Vectors
=> Direction Cosines and Direction Ratios
=> Product of Vectors
=> Scalar product and Properties of Scalar Product
=> Vector Product and Properties of Vector Product
=> Exercise 8.1: Position vectors
=> Exercise 8.2: Direction Cosines and Direction Ratios
=> Exercise 8.3: Scalar product and Properties of Scalar Product
=> Exercise 8.4: Vector Product and Properties of Vector Product
=> Exercise 8.5: Choose the correct answer

Chapter 9 : Differential Calculus Limits and Continuity


=> Differential Calculus - Limits and Continuity
=> The calculation of limits
=> One sided limits: left-hand limit and right-hand limit
=> Theorems on limits
=> Infinite Limits
=> Limits at infinity
=> Limits of rational functions
=> Applications of limits
=> Sandwich Theorem
=> Two special Trigonometrical limits
=> Some important other limits
=> Continuity - Differential Calculus
=> Examples of functions Continuous at a point
=> Algebra of continuous functions
=> Removable and Jump Discontinuities - Differential Calculus
=> Exercise 9.1: One sided limits: left-hand limit and right-hand limit
=> Exercise 9.2: Theorems on limits
=> Exercise 9.3: Applications of limits
=> Exercise 9.4: Some important limits
=> Exercise 9.5: Algebra of continuous functions, Removable and Jump Discontinuities
=> Exercise 9.6: Choose the correct answer

Chapter 10 : Differential Calculus Differentiability and Methods of Differentiation


=> Differential Calculus- Differentiability and Methods of Differentiation
=> The concept of derivative
=> The tangent line problem - The concept of derivative
=> Velocity of Rectilinear motion - The concept of derivative
=> The derivative of a Function - The concept of derivative
=> One sided derivatives (left hand and right hand derivatives) - The concept of derivative
=> Differentiability and Continuity
=> Differentiation Rules
=> Derivatives of basic elementary functions - Differentiation Rules
=> Examples on Chain Rule (Differentiation Rules)
=> Implicit Differentiation
=> Logarithmic Differentiation
=> Substitution method - Differential Calculus
=> Derivatives of variables defined by parametric equations
=> Differentiation of one function with respect to another function
=> Higher order Derivatives
=> Exercise 10.1: Differentiability and Continuity
=> Exercise 10.2: Derivatives of basic elementary functions - Differentiation Rules
=> Exercise 10.3: Examples on Chain Rule (Differentiation Rules)
=> Exercise 10.4: Higher order Derivatives
=> Exercise 10.5: Choose the correct answer

Chapter 11 : Integral Calculus


=> Integral Calculus: Introduction
=> Newton Leibnitz Integral
=> Basic Rules or Formula of Integration
=> Integrals of the Form (ax + b)
=> Properties of Integrals
=> Simple applications of Integral Calculus
=> Methods of Integration
=> Decomposition Methods of Integration
=> Decomposition by Partial Fractions - Integration Method
=> Integration Method of substitution or change of variable
=> Important Results of Integral Calculus
=> Integration by parts
=> Bernoulli’s formula for Integration by Parts
=> Integrals of the form e pow(ax) cos bx and e pow(ax) sin bx
=> Integration of Rational Algebraic Functions
=> Exercise 11.1: Basic Rules or Formula of Integration
=> Exercise 11.2: Integrals of the Form (ax + b)
=> Exercise 11.3: Properties of Integrals
=> Exercise 11.4: Simple applications of Integral Calculus
=> Exercise 11.5: Decomposition by Partial Fractions - Integration Method
=> Exercise 11.6: Important Results of Integral Calculus
=> Exercise 11.7: Bernoulli’s formula for Integration by Parts
=> Exercise 11.8: Integrals of the form e pow(ax) cos bx and e pow(ax) sin bx
=> Exercise 11.9: Integrals of the form e pow(ax) cos bx and e pow(ax) sin bx
=> Exercise 11.10: Integration of Rational Algebraic Functions (Type I,II)
=> Exercise 11.11: Integration of Rational Algebraic Functions (Type III)
=> Exercise 11.12: Integration of Rational Algebraic Functions (Type IV)
=> Exercise 11.13: Choose the correct answer

Chapter 12 : Introduction to Probability Theory


=> Introduction to Probability Theory
=> Basic definitions for Probability Theory
=> Finite sample space - Probability Theory
=> Classical definition (A priori) of probability (Bernoulli’s principle of equally likely)
=> Axiomatic approach to Probability
=> Odds - Probability Theory
=> Some basic Theorems on Probability
=> Conditional Probability
=> Total Probability of an event
=> Bayes’ Theorem
=> Exercise 12.1: Odds - Probability Theory
=> Exercise 12.2: Some basic Theorems on Probability
=> Exercise 12.3: Conditional Probability
=> Exercise 12.4: Bayes Theorem
=> Exercise 12.5: Choose the correct answer

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