MATHEMATICS - I(A)
UNIT I: FUNCTIONS
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Types of Function-Definitions
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Real valued functions (Demain, Range and Inverse)
UNIT II: MATHEMATICAL INDUCTION
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Principles of Mathematical Induction and Theorems
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Applications of Mathematical Induction
UNIT IV: ADDITION OF VECTORS
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Vectors as a triad of real numbers
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Some basic concepts Classification (Types) of Vectors
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Sum (Addition) of Vectors
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Scalar Multiplication of a vector
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Angle between two non- zero vectors
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Linear Combination of Vectors
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Components of a vectors in Three Dimensions
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Vector Equations of Line and Plane
UNIT V: PRODUCT OF VECTORS
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Scalar or dot product of two vectors-Geometrical interpretation
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Properties of dot product
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Expression for Scalar (dot) product
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Angle between two vectors
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Geometrical Vector methods
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Vector equation of a plane –normal form
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Vector product (cross product) of two vectors and properties
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Vector product in (i,j,k) system
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Vector equation of a plane-different forms
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Condition for coplanarity etc
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Vector triple product-results
UNIT VI: TRIGONOMETRIC RATIOS UPTO TRANSFORMATIONS
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Trigonometric ratios – variation – Graphs and periodicity
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Trigonometric ratios of compound angles
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Trigonometric ratios of multiple and sub- multiple angles
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Sum and product transformation
UNIT VII: TRIGONOMETRIC EQUATIONS
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General solutions of trigonometric equations
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Simple trigonometric equations-solutions
UNIT VIII: INVERSE TRIGONOMETRIC FUNCTIONS
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To reduce a trigonometric function into a bijective function
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Graphs of Inverse trigonometric functions
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Properties of inverse trigonometric functions
UNIT IX: HYPERBOLIC FUNCTIONS
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Definitions of Hyperbolic Functions
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Definitions of inverse Hyperbolic Functions and graphs
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Additions formula of Hyperbolic Functions
UNIT X: PROPERTIES OF TRIANGLES
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Relation between the sides and angles of a triangle
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Sine, cosine and Tangent Rules- Projection Rules
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Half angle formulae and area of a triangle
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Incircle and excircles of a triangle
MATHEMATICS - I(B)
UNIT I: LOCUS
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Definition of Locus- IIIustrations
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Equation of Locus-Problems connected to it
UNIT II: TRANSFORMATION OF AXES
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Transformation of axes-Rules
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Derivations and illustratiorts
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Rotation of axes-Derivations - Illustrations
UNIT III: THE STRAIGHT LINE
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Revision of fundamental results
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Straight line- Normal form - Illustrations
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Straight line-Symmetric form
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Straight line-Reduction into various forms
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Intersection of two straight lines
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Family of straight lines-Concurrent lines
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Condition for Concurrent lines
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Length of the perpendicular from a point to a line
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Distance between two parallel lines
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Concurrent lines- Properties related to a – triangle
UNIT IV: PAIR OF STRAIGHT LINES
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Equations of a pair of lines passing through the origin Angle between a pair of lines
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Condition for perpendicular and coincident lines
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Pair of bisectors of angles
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Pair- of lines - Second degree general equation
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Conditions for parallel lines- Distance between them
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Point of intersection of pair of lines
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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
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Intervals and neighbourhoods
UNIT X: APPLICATIONS OF DERIVATIVES INTRODUCTION
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Errors and approximations
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Geometrical interpretation of the derivative
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Equations of tangent and normal to a curve
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Angle between two curves and condition for orthogonality of curves
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Derivatives as a rate of change
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Rolle’s Theorem and Lagrange’s Mean Valve Theorem
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Increasing and Decreasing functions
BETA
