Go BackPART - II
Mathematics 11 Mathematics 11
CHAPTER I: MEASUREMENT OF ANGLES
- Revision of directed angle (+ve and –ve angles)
- zero angle
- straight angle
- angles in standard position
- coterminal angles
- angles in quadrant & quadrantal angles. Sexagesimal system
- circular system
- 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)
- Area of the sector of a circle A = ½ r2 . θ, θ is in radians (without proof)
CHAPTER II: TRIGONOMETRIC FUNCTIONS
- Trigonometric functions with the help of standard unit circle
- signs of trigonometric functions in different quadrants
- trigonometric functions of particular angles (0°, 30°, 45°, 60°, 90°, 180°, 270°, 360° )
- domain and range of trigonometric functions
- periodicity of functions
- fundamental identities
- graphs of trigonometric functions
- Graph of y = a sin b xy = a cos bx
- trigonometric functions of negative angles
CHAPTER III: TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES
- Introduction
- trigonometric functions of sum and difference
- trigonometric functions of multiple angles (upto double and triple angles only)
- trigonometric functions of half angles
CHAPTER IV: FACTORIZATION FORMULAE
- Introduction
- Formulae for conversion of sum or difference into products
- formulae for conversion of product into sum or difference
- trigonometric functions of angles of a triangle
CHAPTER V: LOCUS
- Introduction
- Definition and equation of locus
- points of locus
- shift of the origin
CHAPTER VI: STRAIGHT LINE
- Revision. Inclination of a line
- slope of a line
- equation of lines parallel to coordinate axes
- intercepts of a line
- revision of different forms of equations of a line
- slope-point form
- slope-intercept form
- two point form
- double intercept form
- other forms of equations of a line
- parametric form
- normal form
- general form
- Theorem 1 : A general linear equation Ax + By+ C = 0
- provided A and B are not both zero
- simultaneously
- 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)
- Reduction of general equation of a line into normal form
- intersection of two lines
- parallel lines
- perpendicular lines
- identical lines
- condition for concurrency of three lines
- angle between lines
- distance of a point from a line
- distance between two parallel lines
- equations of bisectors of angle between two lines
- family of lines
- equation of a straight line parallel to a given line
- equation of a straight line perpendicular to a given line
- equation of family of lines through the intersection of two lines
CHAPTER VII: CIRCLE AND CONICS
- Revision
- standard equation
- centre-radius form
- diameter form
- general equation
- parametric equations of standard equation
- Conics Napees – Intersection of Napees of a cone and Plane
- introduction
- focus-directrix property of parabola
- ellipse
- hyperbola
- parabola
- standard equation (different forms of parabola)
- parametric equations
- ellipse
- standard equation
- hyperbola
- standard equation
- parametric equations
- Application of conic section
CHAPTER VIII: VECTORS
- Definition
- magnitude of a vector
- free and localized vectors
- types of vectors
- zero vector
- unit vector
- equality at vectors
- negative of a vector
- collinear vectors
- coplanar vectors
- coinitial vectors
- like and unlike vectors
- scalar multiple of a vector
- triangle law
- parallelogram law
- polygon law
- properties of addition of vectors
- three dimensional co-ordinate geometry
- coordinate axes & coordinate planes in space
- co-ordinates of a point in space
- distance between two points in a space
- unit vectors along axes
- position vector of a point in a space
- product of vectors
- properties
- properties
- simple applications
- work done by force
- resolved part of a force
- moment of a force
CHAPTER IX: LINEAR INEQUATIONS
- Linear inequations in one variable – solution of linear inequation in one variable & graphical solution
- solutions of system of linear inequations in one variable
- Linear inequations in two variables – solution of linear inequation in one variable & graphical solution
- solution of linear inequations in two variables & graphical solution
- solutions of system of linear inequations in two variables
- Replacement of a set or domain of a set
- Transposition
CHAPTER X: DETERMINANTS
- Revision
- determinant of order three
- definition
- expansion
- properties of determinants
- minors & co-factors
- applications of determinants
- condition of consistency
- area of a triangle
- Cramer’s rule for system of equations in three variables
CHAPTER XI: MATRICES
- Introduction
- concepts
- notations, order
- zero matrix
- row matrix
- column matrix
- square matrix
- determinant of a square matrix
- diagonal matrix
- scalar matrix
- identity matrix
- triangular matrices
- singular & non-singular matrices
- transpose of a matrix
- symmetric & skew symmetric matrices
- operations on matrices – equality
- addition
- subtraction
- multiplication of a matrix by a scalar
- simple properties
- multiplication of matrices – definition
- properties of matrix multiplication
- properties of transpose of a matrix - (A’)’ = A, (KA)’ = KA’, (AB)’ = B’A'
PART - II
CHAPTER I: SETS, RELATIONS AND FUNCTIONS
- Set – Revision
- subset
- proper improper subset and their properties
- union
- intersection
- disjoint sets
- empty set
- finite & infinite sets
- equal sets
- equivalent sets
- universal set
- Venn diagrams
- complement of a set
- difference of two sets
- power set
- Relations – ordered pairs
- equality of ordered pairs
- Cartesian product of two sets
- No. of elements in the Cartesian product of two finite sets
- Cartesian product of the reals with itself
- definition of relation
- pictorial diagrams
- domain
- codomain and range of a relation
- one-one
- many-one
- binary equivalence relation
- functions – function as a special kind of relation
- pictorial representation of a function
- domain
- codomain and range of a function
- equal functions
- types of functions - constant function
- identity function
- one-one function
- onto function
- into function
- even & odd functions
- polynomial function
- rational function
- modulus function,signum & greatest integer
- exponential function
- logarithmic function
- functions with their graphs
- sum difference product quotient of functions
- scalar multiplication
- composite function
- inverse function
- binary operations
- real valued function of the real variable
- domain and range of these functions
CHAPTER II: LOGARITHMS
- Introduction
- definition
- properties
- laws of logarithms
- change of base
- characteristics & mantissa – method of finding characteristics
- method of finding mantissa
- method of finding antilogarithm
CHAPTER III: COMPLEX NUMBERS
- Introduction
- need for complex numbers
- definitions –(real parts, imaginary parts, complex conjugates, modulus, argument)
- algebra of complex numbers – equality
- addition
- subtraction
- multiplication
- division
- powers and square root of a complex number
- higher powers of i
- DeMoivre’s formula – (without proof)
- square root of a complex number
- 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
- Properties of product of complex numbers –Existance of multiplicative identity – Existance of multiplicative inverse
- properties of conjugate & modulus of complex numbers
- Argand Diagram – representation of a complex number as a point in plane
- geometrical meaning of modulus and argument
- polar representation of complex numbers
- Fundamental theorem of algebra
- cube roots of unity – solution of quadratic equations in the complex number system
- cube roots of unity
CHAPTER IV: SEQUENCES & SERIES
- Sum of first n terms of A.P
- properties of A.P
- geometric progression – introduction
- general term
- sum of the first ‘n’ terms
- (n terms from the end of G.P.) containing finitely many terms & sum to infinite terms
- properties of G.P
- H.P. as a special type of A.P
- Means – arithmetic mean
- geometric mean
- harmonic mean
- Arithmetico-Geometric sequence
- special series
- sum of cube of first n natural numbers
- sum of cube of first n odd natural nos
- exponential & logarithmic series
CHAPTER V: PERMUTATIONS & COMBINATIONS
- factorial notation
- permutations
- when all r objects are distinct
- when all r objects are not distinct
- circular permutations
- combinations – definition
- properties
- relations between permutations and combinations
CHAPTER VI: MATHEMATICAL INDUCTION AND BINOMIAL THEOREM
- Principle of mathematical induction
- simple applications
- binomial theorem – binomial theorem for positive integers
- general term
- particular term
- properties of binomial coefficient with simple application
- binomial theorem for any index (without proof)
- particular cases of binomial theorem
CHAPTER VII: LIMITS
- Introduction of concept
- meaning of x→a,the limit of a function
- fundamental theorem on limits
- algebra of limits – standard limits
- without proof
- limits at infinity – concepts
- simple problems
CHAPTER VIII: DIFFERENTIATION
- Definition : derivative
- derivative at a point
- geometrical significance of derivative
- physical significance (velocity as a rate of change of displacement)
- derivatives from first principle - of trigonometric functions
- logarithmic functions
- algebraic functions
- exponential functions
- rules of differentiation – derivative of sum
- difference
- product and quotient
CHAPTER IX: INTEGRATION
- Definition of integration as antiderivative
- geometrical interpretation of indefinite integrals
- algebra of integrals – integrals of some standard functions
- rules of integration
CHAPTER X: STATISTICS
- Measures of dispersion – range
- quartile & quartile deviation (for grouped and ungrouped data)
- comparison of two frequency distributions with same mean
- mean deviation about mean
- mean deviation about median (for grouped & ungrouped data)
- variance
- standard deviation
- effect of change of origin and scale on variance and standard deviation
- combined variance and standard deviation
- co-efficient of variation
CHAPTER XI: PROBABILITY
- axiomatic definition of probability
- mutually exclusive and exhaustive events
- mutually exclusive events
- addition theorem – for any two events A and B
- Result on complementary events. Conditional probability – definition
- multiplication theorem
- independent events
- odds in favour and against
BETA
