Go BackMATHEMATICS - I(A)
MATHEMATICS - I(B)
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
- Determinants
- Adjoint and Inverse of a Matrix
- Consistency and Inconsistency of system of Simultaneous EquationsRank 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
- 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 Functions
- 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- IIIustrations
- 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
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
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