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**CBSE Syllabus for Class 12 Mathematics 2019-20 Mathematics** is the study of numbers, shape, and patterns. Mathematics is not only important for success in life, but it is all around us. Mathematics is the science that deals with the logic of shape, quantity, and arrangement. myCBSEguide provides you latest Syllabus of Class 12 Mathematics is now available in **myCBSEguide mobile app.** The curriculum for March 2020 exams is designed by CBSE, New Delhi as per NCERT textbooks for the session 2019-20.

**CBSE Syllabus for class 12 Mathematics 2019-20**

## CBSE Syllabus Class 12 Mathematics

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 Biological science, Commerce or Computer Applications. The present revised syllabus has been designed in accordance with National Curriculum Framework 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.

**Objectives**

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

- to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.
- to feel the flow of reasons while proving a result or solving a problem.
- to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.
- to develop positive attitude to think, analyze and articulate logically.
- to 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.
- to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases.
- to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

**Class-12**

(2019-20)

(2019-20)

**One Paper Max Marks:80**

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

I. | Relations and Functions | 30 | 08 |

II. | Algebra | 50 | 10 |

III. | Calculus | 80 | 35 |

IV. | Vectors and Three – Dimensional Geometry | 30 | 14 |

V. | Linear Programming | 20 | 05 |

VI. | Probability | 30 | 08 |

Total | 240 | 80 | |

Internal Assesment | 20 |

**Unit-I**: **Relations and Functions**

**Relations and Functions**

**15 Periods**

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one andonto functions, composite functions, inverse of a function.**Inverse Trigonometric Functions**

**15 Periods**

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

**Unit-II: Algebra**

**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).- Determinants

**25 Periods**

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**

**Continuity and Differentiability**

**20 Periods**

Continuity and differentiability, derivative of composite functions, chain rule, derivative 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.**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).**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.**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).**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:

dydx+py=qdydx+py=q, where p and q are functions of x or constants.

dxdy+px=qdxdy+px=q, where p and q are functions of y or constants.

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

**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- two lines,
- two planes,
- a line and a plane. Distance of a point from a plan

**Unit-V: Linear Programming**

**Linear Programming**

20 Periods

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 (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

**Unit-VI: Probability**

**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.

**Prescribed Books:**

- Mathematics Part I – Textbook for Class XII, NCERT Publication
- Mathematics Part II – Textbook for Class XII, NCERT Publication
- Mathematics Exemplar Problem for Class XII, Published by NCERT
- Mathematics Lab Manual class XII, published by NCERT http://www.ncert.nic.in/exemplar/labmanuals.html

**Mathematics (Code No. – 041)**

Question Paper Design

Class – 12 (2019 – 20)

Question Paper Design

Class – 12 (2019 – 20)

**Time: 3 hours Max. Marks: 80**

S No. | Typology of Questions | Very Short AnswerObjective type (VSA) (1 Mark) | Short Answer-I (SA) (2 Marks | Short Answer-II (SA) (3 Marks) | Long Answer-II (LA) (4 Marks) | Total Mark | % Weightage (approx.) |
---|---|---|---|---|---|---|---|

1 | Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. | 4 | 1 | 1 | 1 | 16 | 20 |

2 | Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas | 6 | 2 | 3 | 1 | 28 | 35 |

3 | Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way | 6 | 2 | 1 | 1 | 20 | 25 |

4 | Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations | 4 | 1 | 1 | 1 | 16 | 20 |

Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. | |||||||

Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions | |||||||

Total | 20 ×× 1 =20 | 6 ×× 2 = 12 | 6 ×× 4 =24 | 4 ×× 6 = 24 | 80 | 100 |

**Question-Wise Break-up**

Type of Question | Mark per Question | Total No. of Questions | Total Marks |

VSA | 1 | 20 | 20 |

SA | 2 | 6 | 12 |

LA I | 4 | 6 | 24 |

LA II | 6 | 4 | 24 |

Total | 36 | 80 |

- No chapter wise weightage. Care to be taken to cover all the chapters
- Suitable internal variations may be made for generating various templates keeping the overall weightage to different form of questions and typology of questions same.

Choice(s):

There will be no overall choice in the question paper.

However, 33% internal choices will be given.

INTERNAL ASSESSMENT | 20 MARKS |
---|---|

Periodic Tests ( Best 2 out of 3 tests conducted) | 10 Marks |

Mathematics Activities | 10 Marks |

**Note:** For activities NCERT Lab Manual may be referred

**Conduct of Periodic Tests:**

Periodic Test is a Pen and Paper assessment which is to be conducted by the subject teacher. The format of periodic test must have questions items with a balance mix, such as, very short answer (VSA), short answer (SA) and long answer (LA) to effectively assess the knowledge, understanding, application, skills, analysis, evaluation and synthesis. The subject teacher will have the liberty of incorporating any other types of questions too. The modalities of the PT are as follows:

- Mode: The periodic test is to be taken in the form of pen-paper test.
- Schedule: In the entire Academic Year, three Periodic Tests in each subject may be conducted as follows:

Test | Pre Mid-Term | Mid-Term(PT-II) | Post Mid-Term (PT_III) |

Tentative Month | July-August | November | December-January |

This is only a suggestive schedule and schools may conduct periodic tests as per their convenience. The winter bound schools would develop their own schedule with similar time gaps between two consecutive tests.

- Average of Marks: Once schools complete the conduct of all the three periodic tests, they will convert the weightage of each of the three tests into ten marks each for identifying best two tests. The best two will be taken into consideration and the average of the two shall be taken as the final marks for PT.
- The school will ensure simple documentation to keep a record of performance
- Sharing of Feedback/Performance: The students’ achievement in each test must be shared with the students and their parents to give them an overview of the level of learning that has taken place during different periods. Feedback will help parents formulate interventions (conducive ambience, support materials, motivation and morale-boosting) to further enhance learning. A teacher, while sharing the feedback with student or parent, should be empathetic, non- judgmental and motivating. It is recommended that the teacher share best examples/performances with the class to motivate all learners.

**Assessment of Activity Work:**

Throughout the year any 10 activities shall be performed by the student from the activities given in the NCERT Laboratory Manual for the respective class ( XI or XII) which is available on the link: http://www.ncert.nic.in/exemplar/labmanuals.html A record of the same may be kept by the student. An year-end test on the activity may be conducted at the School Level.

The weightage are as under:

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