The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like engineering, physical and Bioscience, commerce or computer applications. The present revised syllabus has been designed in accordance with National Curriculum Frame work 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on application of various concepts.
|One Paper||Time: Three Hours||Marks: 100|
|Unit I||Relations and Functions||10||28|
|Unit IV||Vectors Algebra and Three-Dimensional Geometry||17||25|
|Unit V||Linear Programming||06||15|
Types of relations : (Empty, universal, identity, reflexive, symmetric, antisymmetric and transitive relations in a set) Equivalence relation and equivalence class in a set.
Types of functions : (injective, surjective and bijective functions) Composition of functions Invertible function Binary operation.
(domain, co-domain, range (principal value branches) and graphs of inverse trigonometric functions) Properties of inverse trigonometric functions.
Concept of a matrix and its notation and order.
Types of matrices (row, column, square, diagonal, scalar identity and zero matrices) Equality of matrices, Operation on matrices (addition of matrices, multiplication of a matrix by a scalar, multiplication of matrices)
Properties of matrix addition, scalar multiplication of a matrix and multiplication of matrices Transpose of a matrix symmetric and skew symmetric matrices. Elementary row and column operations of a matrix. Invertible matrices.
Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, Area of a trianglee, Minors and co-factors, Adjoint and inverse of a matrix. Applications of Determinants and matrices.
Continuity, differentiability, derivative of composite functions, (chain rule), Derivatives of implicit function, Exponential and logarithmic functions and its differentiation, Logarithmic differentiation, derivatives of functions in parametric forms, second order, derivative, Roll’s and Lagrange’s mean value theorem (without proof) and their geometrical interpretations.
Rate of Change of quantities, increasing and decreasing functions, tangents and normals, approximation, maxima and minima.
Integration as an inverse process of differentiation. Integration by substitution, Integration using trigonometric identies. Integration by partial fractions and integration by parts. Evaluation of the integrals of the type–
Area under simple curves
Area between two curves.
Concepts of differential equation, concept of order and degree of a differential equation. General and particular solutions of a differential equation. Formation of a differential equation whose premitive is given. Solution of differential equation with variables separable, solution of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type.
dy/dx + Py = Q , where P and Q are constants or functions of x only.
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.
Direction cosines/ ratios of a line joining two points. Cartesian and vectors equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. fa-angle-double-right between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.