CBSE class 12 Mathematics syllabus : Are You looking for new updated cbse syllabus ? Then you are in right place . Central Board Of Secondary Education which is normally known as CBSE has updated the mathematics curriculum for class 12 for session 2015-2016 . Each year CBSE make some changes in course structure . Sometimes they add some new topics or chapters or sometime they remove some topics . So , this year CBSE has made some changes in course outline and issued a new marking scheme with newly desinged mathematics question papers. We are presenting you the entire CBSE class 12 Mathematics syllabus for year 2015-2016 . You can simply download mathematics syllabus on clicking download button . Syllabus will be download in pdf format so, you will need a pdf reader to view this syllabus.
Note : All the student of class 12 are advised to download this latest updated cbse syllabus for mathematics of year 2015 even if they have downloaded the previous version of syllabus for session 2014-2015 .
Note : This syllabus is of exam which will be conducted in March 2016 .Download Here
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Mathematics Class 12 syllabus for session 2015-2016
UNIT I: RELATIONS AND FUNCTIONS
1. Relations and Functions (Periods 10)
Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto
functions, composite functions, inverse of a function. Binary operations.
2. Inverse Trigonometric Functions (Periods 12)
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.
Elementary properties of inverse trigonometric functions.
UNIT II: ALGEBRA
1. Matrices (Periods 18)
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric
and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple
properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication
of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square
matrices of order 2). Concept of elementary row and column operations. Invertible matrices and
proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants (Periods 20)
Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors
and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square
matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples,
solving system of linear equations in two or three variables (having unique solution) using inverse of
Mathematics Class 12 Syllabus
UNIT III: CALCULUS
1. Continuity and Differentiability (Periods 18)
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse
trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions.
Derivatives of loge
x and ex. Logarithmic differentiation. Derivative of functions expressed in parametric
forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof)
and their geometric interpretations.
2. Applications of Derivatives (Periods 10)
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals,
approximation, maxima and minima (first derivative test motivated geometrically and second derivative
test given as a provable tool). Simple problems (that illustrate basic principles and understanding of
the subject as well as real-life situations).
3. Integrals (Periods 20)
Integration as inverse process of differentiation. Integration of a variety of functions by substitution,
by partial fractions and by parts, only simple integrals of the type –
to be evaluated.
Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic
properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals (Periods 10)
Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses
(in standard form only), area between the two above said curves (the region should be cleraly
5. Differential Equations (Periods 10)
Definition, order and degree, general and particular solutions of a differential equation. Formation of
differential equation whose general solution is given. Solution of differential equations by method of
separation of variables, 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 functions of x or constants.
dx/dy + px = q, where p and q are functions of y or constants.
12th Mathematics Syllabus
UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors (Periods 10)
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, scalar triple product.
2. Three-dimensional Geometry (Periods 12)
Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar
and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle
between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.
Unit V: Linear Programming (Periods 12)
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 constrains).
Unit VI: Probability (Periods 18)
Multiplications theorem on probability. Conditional probability, independent events, total probability,
Baye’s theorem. Random variable and its probability distribution, mean and variance of haphazard
variable. Repeated independent (Bernoulli) trials and Binomial distribution.
Now you have got the latest revised syllabus of mathematics of class 12 for year 2015-2016 . Now You have to plan your time of study according to this mathematics curriculum i.e how much time you have to give to which topics , which topics is more important . which chapters take more or less time etc. For getting high marks inboard exam you must plan your study accordingly.
Detail analysis of Mathematics Course Structure
Analysing of course structure is very important for any student to do better in the exam . Good analysis can increase the marks of student . Here we are presenting the course outline of Mathematics syllabus.
Course Structure Marks Wise
Linear Programming 06
Relations and Functions 10
Vectors and 3D geometry 17
Total Marks 100
Course Structure Period Wise
Linear Programming 12
Relations and Functions 22
Vectors and 3D geometry 22
Total Periods 180