Mathematics 11 Mathematics 11

MATHEMATICS - I(A)
UNIT I: FUNCTIONS
  • Introduction
  • Ordered Pairs
  • Types of Function-Definitions
  • Real valued functions (Demain, Range and Inverse)
UNIT II: MATHEMATICAL INDUCTION
  • Introduction
  • Principles of Mathematical Induction and Theorems
  • Applications of Mathematical Induction
  • Problems on divisibility
UNIT III: MATRICES
  • Introduction
  • Scalar multiple of a matrix and multiplication of matrices
  • Transpose of a matrix
  • Determinants
  • Adjoint and Inverse of a Matrix
  • Consistency and Inconsistency of system of Simultaneous Equations
  • Rank of a Matrix
  • Solution of Simultaneous Linear Equations
UNIT IV: ADDITION OF VECTORS
  • Introduction
  • Vectors as a triad of real numbers
  • Some basic concepts Classification (Types) of Vectors
  • Sum (Addition) of Vectors
  • Scalar Multiplication of a vector
  • Angle between two non- zero vectors
  • Linear Combination of Vectors
  • Components of a vectors in Three Dimensions
  • Vector Equations of Line and Plane
UNIT V: PRODUCT OF VECTORS
  • Introduction
  • Scalar or dot product of two vectors-Geometrical interpretation
  • Orthogonal Projections
  • Properties of dot product
  • Expression for Scalar (dot) product
  • Angle between two vectors
  • Geometrical Vector methods
  • Vector equation of a plane -normal form
  • Angle between two planes
  • Vector product (cross product) of two vectors and properties
  • Vector product in (i, j, k) system
  • Vector Areas
  • Scalar triple product
  • Vector equation of a plane-different forms
  • Skew lines
  • Shortest distance- plane
  • Condition for coplanarity etc
  • Vector triple product-results
  • Solved Problems
UNIT VI: TRIGONOMETRIC RATIOS UPTO TRANSFORMATIONS
  • Introduction
  • Trigonometric ratios - variation - Graphs and periodicity
  • Trigonometric ratios of compound angles
  • Trigonometric ratios of multiple and sub- multiple angles
  • Sum and product transformation
UNIT VII: TRIGONOMETRIC EQUATIONS
  • Introduction
  • General solutions of trigonometric equations
  • Simple trigonometric equations-solutions
UNIT VIII: INVERSE TRIGONOMETRIC FUNCTIONS
  • Introduction
  • To reduce a trigonometric function into a bijective function
  • Graphs of Inverse trigonometric functions
  • Properties of inverse trigonometric functions
UNIT IX: HYPERBOLIC FUNCTIONS
  • Introduction
  • Definitions of Hyperbolic Function, graphs
  • Definitions of inverse Hyperbolic Functions and graphs
  • Additions formula of Hyperbolic Functions
UNIT X: PROPERTIES OF TRIANGLES
  • Introduction
  • Relation between the sides and angles of a triangle
  • Sine, cosine and Tangent Rules- Projection Rules
  • Half angle formulae and area of a triangle
  • Incircle and excircles of a triangle
MATHEMATICS - I(B)
UNIT I: LOCUS
  • Introduction
  • Definition of Locus- Illustrations
  • Equation of Locus-Problems connected to it
UNIT II: TRANSFORMATION OF AXES
  • Introduction
  • Transformation of axes-Rules, derivations and illustratiorts
  • Rotation of axes-Derivations-Illustrations
UNIT III: THE STRAIGHT LINE
  • Introduction
  • Revision of fundamental results
  • Straight line- Normal form-Illustrations
  • Straight line-Symmetric form
  • Straight line-Reduction into various forms
  • Intersection of two straight lines
  • Family of straight lines-Concurrent lines
  • Condition for Concurrent lines
  • Angle between two lines
  • Length of the perpendicular from a point to a line
  • Distance between two parallel lines
  • Concurrent lines- Properties related to a triangle
UNIT IV: PAIR OF STRAIGHT LINES
  • Introduction
  • Equations of a pair of lines passing through the origin Angle between a pair of lines
  • Condition for perpendicular and coincident lines
  • Bisectors of angles
  • Pair of bisectors of angles
  • Pair- of lines - Second degree general equation
  • Conditions for parallel lines- Distance between them
  • Point of intersection of pair of lines
  • Homogenising a second degree equation with a first degree equation in x and y
UNIT V: THREE DIMENSIONAL COORDINATES
  • Introduction
  • Coordinates
  • Section formula
  • Solved Problems
UNIT VI: DIRECTION COSINES AND DIRECTION RATIOS
  • Introduction
  • Direction cosines
  • Direction ratios
UNIT VII: THE PLANE
  • Introduction
  • Cartesian equation of a plane- Simple illustrations
UNIT VIII: LIMITS AND CONTINUITY
  • Introduction
  • Intervals and neighbourhoods
  • Standard limits
UNIT IX: DIFFERENTIATION
  • Introduction
  • Derivative of a function
  • Elementary properties
  • Trigonometric
  • Hyperbolic
  • Inverse Hyperbolic Functions- Derivatives
  • Methods of differentiation
  • Second Order Derivatives
UNIT X: APPLICATIONS OF DERIVATIVES INTRODUCTION
  • Introduction
  • Errors and approximations
  • Geometrical interpretation of the derivative
  • Equations of tangent and normal to a curve
  • Lengths of tangent, normal, subtangent and subnormal
  • Angle between two curves and condition for orthogonality of curves
  • Derivatives as a rate of change
  • Rolle’s Theorem and Lagrange’s Mean Valve Theorem
  • Increasing and Decreasing functions
  • Maxima and Minima