**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** .

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- CBSE Class 12 Mathematics Sample Papers
- CBSE Class 12 Mathematics Year Question Papers
- CBSE Class 12 Mathematics NCERT Solution
- CBSE Class 12 Mathematics Class Notes

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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

a matrix.

**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

identifiable).

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*

*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`

Topics Marks

Linear Programming 06

Relations and Functions 10

Probabiity 10

Algebra 13

Vectors and 3D geometry 17

Calculus 44

Total Marks 100

`Course Structure Period Wise`

Topics Periods

Linear Programming 12

Relations and Functions 22

Probabiity 18

Algebra 38

Vectors and 3D geometry 22

Calculus 68

Total Periods 180