# CBSE Class 12 Maths Syllabus :

CBSE Class 12 Maths Syllabus which has cover all the units such as : Relation and Function, Algebra, Calculus, Vector and three – Dimensional Geometry, Linear Programming, Probability

NCERT Books are also provided on our website refer the link www.CBSEmaths4u.com/ncert

## MATHEMATICS (Code No. 041)

The CBSE Class 12 Maths Syllabus has undergone changes from time to time in accordance with growth of the subject and emerging the 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 Framework 2005 and as per guidelines given in FocusGroup 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.

## Objectives

The broad objectives of teaching Mathematics at senior school stage intend to help the students to:-

- Develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics
- Acquire knowledge and critical understanding, particularly by way of motivation and visualisation, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.
- Develop interest in the subject by participating in related competitions. to acquaint students with different aspects of Mathematics used in daily life. to develop an interest in students to study Mathematics as a discipline
- Feel the flow of reasons while proving a result or solving a problem
- Develop positive attitude to think, analyse and articulate logically
- Apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method
- Develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases

## COURSE STRUCTURE

#### One Paper (Time: 3 hrs.)

Max Marks: 100

Units | Unit Name | No. of Periods | Marks |
---|---|---|---|

I. | Relation and Function | 30 | 10 |

II. | Algebra | 50 | 13 |

III. | Calculus | 80 | 44 |

IV. | Vector and three – Dimensional Geometry | 30 | 17 |

V. | Linear Programming | 20 | 06 |

VI. | Probability | 30 | 10 |

Total | 240 | 100 |

#### Unit-I: Relations and Functions-

**1. Relations and Functions** (15 Periods)

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** (15 Periods)

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

#### Unit-II: Algebra-

**1. Matrices (25 Periods)
**Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. 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 (25 Periods)**

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors 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 (20 Periods)
**Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. 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 interpretation.

**2. Applications of Derivatives (10 Periods)
**Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in 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 (20 Periods)
**Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them:-

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

**5. Differential Equations (15 Periods)
**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 solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

**Unit-IV:Vectors and Three-Dimensional Geometry **

**1. Vectors (15 Periods)**

Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. 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. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

**2. Three – dimensional Geometry (15 Periods)
**Direction cosines and direction ratios of a line joining two points.Cartesian equation 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 (20 Periods)
**Introduction, related terminology such as constraints, objective function, optimisation, 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(bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

**Unit-VI: Probability**

**1. Probability (30 Periods)
**Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

**Prescribed Books:**

1) Mathematics Textbook for Class XI, NCERT Publications

2) Mathematics Part I – Textbook for Class XII, NCERT Publication

3) Mathematics Part II – Textbook for Class XII, NCERT Publication

4) Mathematics Exemplar Problem for Class XI, Published by NCERT

5) Mathematics Exemplar Problem for Class XII, Published by NCERT

## QUESTION PAPER DESIGN CLASS – XII (2017-18)

**Time 3 Hours (Max. Marks: 100)**

**Typology of Questions:**

**1. Remembering:
**(knowledge based simple recall questions, to know specific facts, terms,

**concepts, principles, or theories, Identify, define, or recite, information)**

VSA (1 mark) : 2 questions

SA (2 marks) : 2 questions

LA-I (4 marks) : 2 questions

LA-II (6 marks) : 1 questions

Total Questions : 7 questions

Total Marks : 20 Marks

Percent Weightage: 20%

**2. ** **Understanding:
**(Comprehension – to be familiar with meaning and to understand

**conceptually, interpret, compare, contrast, explain, paraphrase information)**

VSA (1 mark) : 1 question

SA (2 marks) : 3 questions

LA-I (4 marks) : 4 questions

LA-II (6 marks) : 2 questions

Total Questions : 10 questions

Total Marks : 35 Marks

Percent Weightage: 35%

**3. ** **Application:
**(Use abstract information in concrete situation, to apply knowledge to new

**situations, Use given content to interpret a situation, provide an example, or solve a problem)**

VSA (1 mark) : 1 question

SA (2 marks) : 0 questions

LA-I (4 marks) : 3 questions

LA-II (6 marks) : 2 questions

Total Questions : 6 questions

Total Marks : 25 Marks

Percent Weightage: 25%

**4. ** **High Order Thinking Skills:
**(Analysis & Synthesis: Classify, compare, contrast, or

**differentiate between different pieces of information, Organize and/or integrate unique pieces of information from a variety of Sources.**

VSA (1 mark) : 0 question

SA (2 marks) : 3 questions

LA-I (4 marks) : 1 questions

LA-II (6 marks) : 0 question

Total Questions : 4 questions

Total Marks : 10 Marks

Percent Weightage: 10%

**5. Evaluation:
**(Appraise, judge, and/or justify the value of worth of a decision or outcome, or

**to predict outcomes based on values)**

VSA (1 mark) : 0 question

SA (2 marks) : 0 question

LA-I (4 marks) : 1 question (value based)

LA-II (6 marks) : 1 question

Total Questions : 2 questions

Total Marks : 10 Marks

Percent Weightage: 10%

## Question – wise Break – up:

Type of Question | Marks per question | Total no. of questions | Total Marks |
---|---|---|---|

VSA | 1 | 4 | 4 |

SA | 2 | 8 | 16 |

LA – I | 4 | 11 | 44 |

LA – II | 6 | 6 | 36 |

Total | 29 | 100 |

No chapter wise weightage. Care to be taken to cover all the chapters.

**Choice(s):
**There will be no overall choice in the question paper, 30% internal

**choices will be given in 4 marks and 6 marks questions.**

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