MATHEMATICS - I(A)
UNIT I: FUNCTIONS
-
Types of Function-Definitions
-
Real valued functions (Demain, Range and Inverse)
UNIT II: MATHEMATICAL INDUCTION
-
Principles of Mathematical Induction and Theorems
-
Applications of Mathematical Induction
UNIT IV: ADDITION OF VECTORS
-
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
-
Scalar or dot product of two vectors-Geometrical interpretation
-
Properties of dot product
-
Expression for Scalar (dot) product
-
Angle between two vectors
-
Geometrical Vector methods
-
Vector equation of a plane -normal form
-
Vector product (cross product) of two vectors and properties
-
Vector product in (i, j, k) system
-
Vector equation of a plane-different forms
-
Condition for coplanarity etc
-
Vector triple product-results
UNIT VI: TRIGONOMETRIC RATIOS UPTO TRANSFORMATIONS
-
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
-
General solutions of trigonometric equations
-
Simple trigonometric equations-solutions
UNIT VIII: INVERSE TRIGONOMETRIC FUNCTIONS
-
To reduce a trigonometric function into a bijective function
-
Graphs of Inverse trigonometric functions
-
Properties of inverse trigonometric functions
UNIT IX: HYPERBOLIC FUNCTIONS
-
Definitions of Hyperbolic Function, graphs
-
Definitions of inverse Hyperbolic Functions and graphs
-
Additions formula of Hyperbolic Functions
UNIT X: PROPERTIES OF TRIANGLES
-
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
-
Definition of Locus- Illustrations
-
Equation of Locus-Problems connected to it
UNIT II: TRANSFORMATION OF AXES
-
Transformation of axes-Rules, derivations and illustratiorts
-
Rotation of axes-Derivations-Illustrations
UNIT III: THE STRAIGHT LINE
-
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
-
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
-
Equations of a pair of lines passing through the origin Angle between a pair of lines
-
Condition for perpendicular and coincident lines
-
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
UNIT VI: DIRECTION COSINES AND DIRECTION RATIOS
UNIT VIII: LIMITS AND CONTINUITY
-
Intervals and neighbourhoods
UNIT X: APPLICATIONS OF DERIVATIVES 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