, MATHEMATICS
Visit https://telegram.me/booksforcbse for more books.
MTG Learning Media (P) Ltd.
New Delhi | Gurugram
, Price : ` 200
Edition : 2022
Published by : MTG Learning Media (P) Ltd., New Delhi
Corporate Office : Plot 99, Sector 44 Institutional Area, Gurugram, Haryana-122 003
Phone : 0124 - 6601200 Web: mtg.in Email:
Registered Office : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110 029
Information contained in this book has been obtained by mtg, from sources believed to be reliable. Every effort has been made to
avoid errors or omissions in this book. In spite of this, some errors might have crept in. Any mistakes, error or discrepancy noted may
be brought to our notice which shall be taken care of in the next edition. It is notified that neither the publishers nor the author or seller
will be responsible for any damage or loss of action to anyone, of any kind, in any manner, therefrom.
© MTG Learning Media (P) Ltd. Copyright reserved. No part of this publication may be reproduced, stored in a retrieval system or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission
of the Publisher.
All disputes subject to Delhi jurisdiction only.
Visit www.mtg.in for buying books online.
, SYLLABUS
MATHEMATICS (Code No. 041)
COURSE STRUCTURE, CLASS XII (2021 - 22)
TERM - II
Time : 2 Hours Max Marks : 40
S. No. Units Marks
III. Calculus 18
IV. Vectors and Three Dimensional Geometry 14
VI. Probability 8
Total 40
Internal Assessment 10
Total 50
Unit-III : Calculus dy/dx = f(y/x). Solutions of linear differential equation of the type:
1. Integrals dy/dx+py = q,where p and q are functions of x or constant.
Integration as inverse process of differentiation. Integration of a Unit-IV : Vectors and Three Dimensional Geometry
variety of functions by substitution, by partial fractions and by 4. Vector Algebra
parts, Evaluation of simple integrals of the following types and Vectors and scalars, magnitude and direction of a vector. Direction
problems based on them. cosines and direction ratios of a vector. Types of vectors (equal,
dx dx dx dx dx unit, zero, parallel and collinear vectors), position vector of a point,
∫ x 2 ± a2 , ∫ 2 2
,∫
2 2
,∫
ax 2 + bx + c
,∫
2
,
negative of a vector, components of a vector, addition of vectors,
x ±a a −x ax + bx + c
multiplication of a vector by a scalar, position vector of a point
px + q px + q
∫ ax 2 + bx + c dx, ∫ dx , ∫ a2 ± x 2 dx , ∫ x 2 − a 2 dx dividing a line segment in a given ratio. Definition, Geometrical
ax 2 + bx + c
Interpretation, properties and application of scalar (dot) product
Fundamental Theorem of Calculus (without proof).Basic properties of vectors, vector (cross) product of vectors.
of definite integrals and evaluation of definite integrals. 5. Three Dimensional Geometry
2. Applications of Integrals Direction cosines and direction ratios of a line joining two points.
Applications in finding the area under simple curves, especially Cartesian equation and vector equation of a line, coplanar and
lines, parabolas; area of circles /ellipses (in standard form only) (the skew lines, shortest distance between two lines. Cartesian and
vector equation of a plane. Distance of a point from a plane.
region should be clearly identifiable).
3. Differential Equations
Unit-VI : Probability
Definition, order and degree, general and particular solutions 6. Probability
of a differential equation. Solution of differential equations by Conditional probability, multiplication theorem on probability,
method of separation of variables, solutions of homogeneous independent events, total probability, Bayes’ theorem, Random
differential equations of first order and first degree of the type: variable and its probability distribution.
Internal Assessment 10 Marks
Periodic Test 5 Marks
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva 5 Marks
Visit https://telegram.me/booksforcbse for more books.
MTG Learning Media (P) Ltd.
New Delhi | Gurugram
, Price : ` 200
Edition : 2022
Published by : MTG Learning Media (P) Ltd., New Delhi
Corporate Office : Plot 99, Sector 44 Institutional Area, Gurugram, Haryana-122 003
Phone : 0124 - 6601200 Web: mtg.in Email:
Registered Office : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110 029
Information contained in this book has been obtained by mtg, from sources believed to be reliable. Every effort has been made to
avoid errors or omissions in this book. In spite of this, some errors might have crept in. Any mistakes, error or discrepancy noted may
be brought to our notice which shall be taken care of in the next edition. It is notified that neither the publishers nor the author or seller
will be responsible for any damage or loss of action to anyone, of any kind, in any manner, therefrom.
© MTG Learning Media (P) Ltd. Copyright reserved. No part of this publication may be reproduced, stored in a retrieval system or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission
of the Publisher.
All disputes subject to Delhi jurisdiction only.
Visit www.mtg.in for buying books online.
, SYLLABUS
MATHEMATICS (Code No. 041)
COURSE STRUCTURE, CLASS XII (2021 - 22)
TERM - II
Time : 2 Hours Max Marks : 40
S. No. Units Marks
III. Calculus 18
IV. Vectors and Three Dimensional Geometry 14
VI. Probability 8
Total 40
Internal Assessment 10
Total 50
Unit-III : Calculus dy/dx = f(y/x). Solutions of linear differential equation of the type:
1. Integrals dy/dx+py = q,where p and q are functions of x or constant.
Integration as inverse process of differentiation. Integration of a Unit-IV : Vectors and Three Dimensional Geometry
variety of functions by substitution, by partial fractions and by 4. Vector Algebra
parts, Evaluation of simple integrals of the following types and Vectors and scalars, magnitude and direction of a vector. Direction
problems based on them. cosines and direction ratios of a vector. Types of vectors (equal,
dx dx dx dx dx unit, zero, parallel and collinear vectors), position vector of a point,
∫ x 2 ± a2 , ∫ 2 2
,∫
2 2
,∫
ax 2 + bx + c
,∫
2
,
negative of a vector, components of a vector, addition of vectors,
x ±a a −x ax + bx + c
multiplication of a vector by a scalar, position vector of a point
px + q px + q
∫ ax 2 + bx + c dx, ∫ dx , ∫ a2 ± x 2 dx , ∫ x 2 − a 2 dx dividing a line segment in a given ratio. Definition, Geometrical
ax 2 + bx + c
Interpretation, properties and application of scalar (dot) product
Fundamental Theorem of Calculus (without proof).Basic properties of vectors, vector (cross) product of vectors.
of definite integrals and evaluation of definite integrals. 5. Three Dimensional Geometry
2. Applications of Integrals Direction cosines and direction ratios of a line joining two points.
Applications in finding the area under simple curves, especially Cartesian equation and vector equation of a line, coplanar and
lines, parabolas; area of circles /ellipses (in standard form only) (the skew lines, shortest distance between two lines. Cartesian and
vector equation of a plane. Distance of a point from a plane.
region should be clearly identifiable).
3. Differential Equations
Unit-VI : Probability
Definition, order and degree, general and particular solutions 6. Probability
of a differential equation. Solution of differential equations by Conditional probability, multiplication theorem on probability,
method of separation of variables, solutions of homogeneous independent events, total probability, Bayes’ theorem, Random
differential equations of first order and first degree of the type: variable and its probability distribution.
Internal Assessment 10 Marks
Periodic Test 5 Marks
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva 5 Marks
