Unit 1:
Sets, Relations And Functions
Sets and their representation; Union, intersection and
complement of sets and their algebraic properties; Power set; Relation,
Types of relations, equivalence relations, functions; One-one, into and
onto functions, composition of functions.
Unit 2:
Complex Numbers and Quadratic Equations
Complex numbers as ordered pairs of reals, Representation
of complex numbers in the form a+ib and their representation in a plane,
Argand diagram, algebra of complex numbers, modulus and argument (or
amplitude) of a complex number, square root of a complex number,
triangle inequality, Quadratic equations in real and complex number
system and their solutions. Relation between roots and coefficients,
nature of roots, formation of quadratic equations with given roots.
Unit 3:
Matrices And Determinants
Matrices, algebra of matrices, types of matrices,
determinants and matrices of order two and three. Properties of
determinants, evaluation of determinants, area of triangles using
determinants. Adjoint and evaluation of inverse of a square matrix using
determinants and elementary transformations, Test of consistency and
solution of simultaneous linear equations in two or three variables
using determinants and matrices.
Unit 4:
Permutations And Combinations
Fundamental principle of counting, permutation as an
arrangement and combination as selection, Meaning of P (n,r) and C
(n,r), simple applications.
Unit 5:
Mathematical Induction
Principle of Mathematical Induction and its simple applications.
Unit 6:
Binomial Theorem And Its Simple Applications
Binomial theorem for a positive integral index, general
term and middle term,properties of Binomial coefficients and simple
applications.
Unit 7:
Sequences And Series
Arithmetic and Geometric progressions, insertion of
arithmetic, geometric means between two given numbers. Relation between
A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3.
Arithmetico – Geometric progression.
Unit 8:
Limit, Continuity And Differentiability
Real valued functions, algebra of functions, polynomials,
rational, trigonometric, logarithmic and exponential functions, inverse
functions. Graphs of simple functions.Limits, continuity and
differentiability. Differentiation of the sum, difference, product and
quotient of two functions. Differentiation of trigonometric, inverse
trigonometric, logarithmic, exponential, composite and implicit
functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean
Value Theorems. Applications of derivatives: Rate of change of
quantities, monotonic increasing and decreasing functions, Maxima and
minima of functions of one variable, tangents and normals.
Unit 9:
Integral Calculus
Integral as an anti derivative. Fundamental integrals
involving algebraic, trigonometric, exponential and logarithmic
functions. Integration by substitution, by parts and by partial
fractions. Integration using trigonometric identities.Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form
Evaluation of simple integrals of the type:
Unit 10:
Differential Equations
Ordinary differential equations, their order and degree.
Formation of differential equations. Solution of differential equations
by the method of separation of variables, solution of homogeneous and
linear differential equations of the type
Unit 11:
Coordinate Geometry
Cartesian system of rectangular coordinates 10 in a plane,
distance formula, section formula, locus and its equation, translation
of axes, slope of a line, parallel and perpendicular lines, intercepts
of a line on the coordinate axes.Straight lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.
Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point(s) of tangency.
Unit 12:
Three Dimensional Geometry
Coordinates of a point in space, distance between two
points, section formula, direction ratios and direction cosines, angle
between two intersecting lines. Skew lines, the shortest distance
between them and its equation. Equations of a line and a plane in
different forms, intersection of a line and a plane, coplanar lines.
Unit 13:
Vector Algebra
Vectors and scalars, addition of vectors, components of a
vector in two dimensions and three dimensional space, scalar and vector
products, scalar and vector triple product.
Unit 14:
Statistics And Probability
Measures of Dispersion: Calculation of mean, median, mode
of grouped and ungrouped data calculation of standard deviation,
variance and mean deviation for grouped and ungrouped data.
No comments:
Post a Comment