CHAPTER I: MEASUREMENT OF ANGLES
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Revision of directed angle (+ve and –ve angles)
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angles in standard position
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angles in quadrant & quadrantal angles. Sexagesimal system
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relation between degree measure and radian measure. Theorem: Radian is a constant angle. Length of an arc of a circle (s = r. θ, θ is in radians) (without proof)
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Area of the sector of a circle A = ½ r2 . θ, θ is in radians (without proof)
CHAPTER II: TRIGONOMETRIC FUNCTIONS
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Trigonometric functions with the help of standard unit circle
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signs of trigonometric functions in different quadrants
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trigonometric functions of particular angles (0°, 30°, 45°, 60°, 90°, 180°, 270°, 360° )
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domain and range of trigonometric functions
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graphs of trigonometric functions
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Graph of y = a sin b xy = a cos bx
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trigonometric functions of negative angles
CHAPTER III: TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES
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trigonometric functions of sum and difference
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trigonometric functions of multiple angles (upto double and triple angles only)
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trigonometric functions of half angles
CHAPTER IV: FACTORIZATION FORMULAE
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Formulae for conversion of sum or difference into products
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formulae for conversion of product into sum or difference
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trigonometric functions of angles of a triangle
CHAPTER VI: STRAIGHT LINE
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Revision. Inclination of a line
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equation of lines parallel to coordinate axes
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revision of different forms of equations of a line
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other forms of equations of a line
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Theorem 1 : A general linear equation Ax + By+ C = 0
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provided A and B are not both zero
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always represents straight line. Theorem 2 : Every straight line has an equation of the form Ax +By + C = 0, where A, B and C are constants (without proof)
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Reduction of general equation of a line into normal form
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intersection of two lines
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condition for concurrency of three lines
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distance of a point from a line
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distance between two parallel lines
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equations of bisectors of angle between two lines
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equation of a straight line parallel to a given line
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equation of a straight line perpendicular to a given line
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equation of family of lines through the intersection of two lines
CHAPTER VII: CIRCLE AND CONICS
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parametric equations of standard equation
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Conics Napees – Intersection of Napees of a cone and Plane
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focus-directrix property of parabola
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standard equation (different forms of parabola)
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Application of conic section
CHAPTER IX: LINEAR INEQUATIONS
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Linear inequations in one variable – solution of linear inequation in one variable & graphical solution
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solutions of system of linear inequations in one variable
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Linear inequations in two variables – solution of linear inequation in one variable & graphical solution
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solution of linear inequations in two variables & graphical solution
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solutions of system of linear inequations in two variables
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Replacement of a set or domain of a set
PART - II
CHAPTER I: SETS, RELATIONS AND FUNCTIONS
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proper improper subset and their properties
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Relations – ordered pairs
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equality of ordered pairs
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Cartesian product of two sets
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No. of elements in the Cartesian product of two finite sets
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Cartesian product of the reals with itself
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codomain and range of a relation
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binary equivalence relation
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functions – function as a special kind of relation
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pictorial representation of a function
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codomain and range of a function
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types of functions - constant function
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modulus function,signum & greatest integer
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functions with their graphs
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sum difference product quotient of functions
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real valued function of the real variable
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domain and range of these functions
CHAPTER III: COMPLEX NUMBERS
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definitions –(real parts, imaginary parts, complex conjugates, modulus, argument)
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algebra of complex numbers – equality
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powers and square root of a complex number
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DeMoivre’s formula – (without proof)
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square root of a complex number
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properties of complex numbers – properties of addition of complex numbers 1) Closure Property 2) Commulative Law 3) Associative law 4) Existence of additive identity 5) Existence of additive inverse
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Properties of product of complex numbers –Existance of multiplicative identity – Existance of multiplicative inverse
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properties of conjugate & modulus of complex numbers
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Argand Diagram – representation of a complex number as a point in plane
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geometrical meaning of modulus and argument
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polar representation of complex numbers
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Fundamental theorem of algebra
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cube roots of unity – solution of quadratic equations in the complex number system
CHAPTER IV: SEQUENCES & SERIES
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Sum of first n terms of A.P
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geometric progression – introduction
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sum of the first ‘n’ terms
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(n terms from the end of G.P.) containing finitely many terms & sum to infinite terms
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H.P. as a special type of A.P
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Arithmetico-Geometric sequence
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sum of cube of first n natural numbers
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sum of cube of first n odd natural nos
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exponential & logarithmic series
CHAPTER V: PERMUTATIONS & COMBINATIONS
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when all r objects are distinct
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when all r objects are not distinct
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combinations – definition
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relations between permutations and combinations
CHAPTER VI: MATHEMATICAL INDUCTION AND BINOMIAL THEOREM
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Principle of mathematical induction
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binomial theorem – binomial theorem for positive integers
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properties of binomial coefficient with simple application
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binomial theorem for any index (without proof)
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particular cases of binomial theorem
CHAPTER VIII: DIFFERENTIATION
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geometrical significance of derivative
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physical significance (velocity as a rate of change of displacement)
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derivatives from first principle - of trigonometric functions
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rules of differentiation – derivative of sum
BETA
