**MATHEMATICS SYLLABUS FOR CLASS 12[CBSE]**

INSTRUCTIONS

i. All questions are compulsory.

ii. Questions number 1 to 12 one of 3 marks each.

Questions number 13 to 22 one of 4 marks each.

Questions number 23 to 26 one of 6 marks each.

iii. There will be no over all choice. There will be internal choices in any two questions of 3 marks each, any two questions of 4 marks and any two questions of 6 marks each (Total of six internal choices).

iv. Use of calculator is not permitted. However each your may ask for logarithmic and statistical tables, if required.

ii. Questions number 1 to 12 one of 3 marks each.

Questions number 13 to 22 one of 4 marks each.

Questions number 23 to 26 one of 6 marks each.

iii. There will be no over all choice. There will be internal choices in any two questions of 3 marks each, any two questions of 4 marks and any two questions of 6 marks each (Total of six internal choices).

iv. Use of calculator is not permitted. However each your may ask for logarithmic and statistical tables, if required.

**QUESTIONWISE DISTRIBUTION OF MARKS (XII CLASS) FOR 2008**

Unit Topic | Sub-Topic | 3 Marks | 4 Marks | 6 Marks | Total Marks | Unit Total |

I Relations and Functions | Relations and Functions Inverse Trigonometric Functions | 2 - | - 1 | - - |
6
4
| 10 |

II Algebra | Matrices Determinants | 1 - | 1 - | - 1 | 7 6 | 13 |

III Calculus | Continuity and differentiability Applications of derivatives Integrals Applications ofintegrals Differential equations | 2 1 2 - 1 | 1 1 2 - 1 | - - - 1 - | 10 7 14 6 7 | 44 |

IV Vectors and three dimensional geometry | Vector... Three dimensional geometry | 1 - | 1 1 | - 1 | 7 10 | 17 |

V Linear Programming | Linear Programming | - | - | 1 | 6 | 6 |

VI Probability | Probability | 2 | 2 | - | 10 | 10 |

Total no. of ques. | 12 | 10 | 4 | 100 | 100 | |

Total Marks. | 36 | 40 | 24 | 100 | 100 |

CLASS XII

One Paper Time : 3 Hours

100 marks

CLASS XII

One Paper Time : 3 Hours

100 marks

**Unit I: Relations and Functions**

1. Relations and Functions :

1. Relations and Functions :

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and on to functions, composite functions, inverse of a function. Binary

operations.

**2. Inverse Trigonometric Functions:**

Defination, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

**Unit II: Algebra**

1. Matrices:

1. Matrices:

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 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 :**

Determinant of a square matrix (up to 3 (X) 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.

**Unit-III: Calculus**

**1. Continuity and Differentiability:**

(Periods 18)

Continutiy and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept

of exponential and logarithmic functions, and their derivative.Logarithmic differentiation. Derivative of functions expressed in parametric forms, Second order

derivatives. Rolle's and Lagrange 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& 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. Intergration of a variaty of functions by subsitution, by partial fractions and by parts, only simple integrals of the type

to be evaluated.

Definite intergrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite intergrals and evaluation of definte integrals.

**4. Applications of the Integrals:**

Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).

**5. Differential Equations :**

Defination, 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 = p(x) y = q(x), where p(x) and q(x) are functions of x. dx

Unit -IV : Vectors and Three-Dimensional Geometry

Unit -IV : Vectors and Three-Dimensional Geometry

**1. Vectors:**

Vectors and scalars, maguitude 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

.

**2. Three - dimensional Geometry :**

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**

**1. Linear Programming:**

Introduction, definition of 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, optional feasible solutions (up to three non-trivial constrain:)

**Unit VI Probability**

**1. Probability :**

Multiplication 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.

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