Syllabus: Mathematics for Class 12 | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


CLASS-XII 
(202 4-2 5) 
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 Assessment 
20 
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. 
2. Inverse Trigonometric Functions 15 Periods 
Definition, range, domain, principal value branch.  Graphs 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. Operations 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).  Invertible matrices and proof of the uniqueness of 
inverse, if it exists; (Here all matrices will have real entries). 
2. Determinants 25 Periods 
Page 2


CLASS-XII 
(202 4-2 5) 
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 Assessment 
20 
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. 
2. Inverse Trigonometric Functions 15 Periods 
Definition, range, domain, principal value branch.  Graphs 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. Operations 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).  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), 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, chain rule, derivative of inverse trigonometric functions, 
???????? sin
-1
?? , cos
-1
?? and tan
-1
?? , 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. 
2. Applications of Derivatives                10 Periods 
Applications of derivatives: rate of change of quantities, increasing/decreasing functions, 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. 
?
dx
x
2
± a
2,
?
dx
vx
2
± a
2
, ?
dx
va
2
- x
2
, ?
dx
ax
2
+ bx + c
, ?
dx
vax
2 
+ ???? + ?? ?
px + q
ax
2
+ bx + c
dx, ?
px + q
vax
2+
bx + c
dx, ? va
2
± x
2
 dx, ?
v
x
2
- a
2
 dx 
      ?v????
2
+ ???? + ?? ???? ,     
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) 
5. Differential Equations       15 Periods 
Definition, order and degree, general and particular solutions of a differential equation. 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: 
Page 3


CLASS-XII 
(202 4-2 5) 
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 Assessment 
20 
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. 
2. Inverse Trigonometric Functions 15 Periods 
Definition, range, domain, principal value branch.  Graphs 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. Operations 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).  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), 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, chain rule, derivative of inverse trigonometric functions, 
???????? sin
-1
?? , cos
-1
?? and tan
-1
?? , 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. 
2. Applications of Derivatives                10 Periods 
Applications of derivatives: rate of change of quantities, increasing/decreasing functions, 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. 
?
dx
x
2
± a
2,
?
dx
vx
2
± a
2
, ?
dx
va
2
- x
2
, ?
dx
ax
2
+ bx + c
, ?
dx
vax
2 
+ ???? + ?? ?
px + q
ax
2
+ bx + c
dx, ?
px + q
vax
2+
bx + c
dx, ? va
2
± x
2
 dx, ?
v
x
2
- a
2
 dx 
      ?v????
2
+ ???? + ?? ???? ,     
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) 
5. Differential Equations       15 Periods 
Definition, order and degree, general and particular solutions of a differential equation. 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: 
dy
dx
+ py = q, where p and q are functions of x or constants.
d?? d?? + px = q, where p and q are functions of y or constants.
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. 
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, skew lines, shortest distance between two lines. Angle between two lines.
Unit-V: Linear Programming 
1. Linear Programming 20 Periods 
Introduction, related terminology such as constraints, objective function, optimization, 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 
1.  Probability         30 Periods 
Conditional probability, multiplication theorem on probability, independent events, total probability, 
Bayes’ theorem, Random variable and its probability distribution, mean of random variable. 
Page 4


CLASS-XII 
(202 4-2 5) 
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 Assessment 
20 
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. 
2. Inverse Trigonometric Functions 15 Periods 
Definition, range, domain, principal value branch.  Graphs 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. Operations 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).  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), 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, chain rule, derivative of inverse trigonometric functions, 
???????? sin
-1
?? , cos
-1
?? and tan
-1
?? , 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. 
2. Applications of Derivatives                10 Periods 
Applications of derivatives: rate of change of quantities, increasing/decreasing functions, 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. 
?
dx
x
2
± a
2,
?
dx
vx
2
± a
2
, ?
dx
va
2
- x
2
, ?
dx
ax
2
+ bx + c
, ?
dx
vax
2 
+ ???? + ?? ?
px + q
ax
2
+ bx + c
dx, ?
px + q
vax
2+
bx + c
dx, ? va
2
± x
2
 dx, ?
v
x
2
- a
2
 dx 
      ?v????
2
+ ???? + ?? ???? ,     
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) 
5. Differential Equations       15 Periods 
Definition, order and degree, general and particular solutions of a differential equation. 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: 
dy
dx
+ py = q, where p and q are functions of x or constants.
d?? d?? + px = q, where p and q are functions of y or constants.
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. 
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, skew lines, shortest distance between two lines. Angle between two lines.
Unit-V: Linear Programming 
1. Linear Programming 20 Periods 
Introduction, related terminology such as constraints, objective function, optimization, 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 
1.  Probability         30 Periods 
Conditional probability, multiplication theorem on probability, independent events, total probability, 
Bayes’ theorem, Random variable and its probability distribution, mean of random variable. 
MATHEMATICS (Code No. - 041) 
QUESTION PAPER DESIGN CLASS - XII 
(202 4-25) 
Time: 3 hours  Max. Marks: 80 
S. 
No. 
Typology of Questions 
Total 
Marks 
% 
Weightage 
1 
Remembering: Exhibit memory of previously learned material 
by recalling facts, terms, basic concepts, and answers. 
Understanding: Demonstrate understanding of facts and 
ideas by organizing, comparing, translating, interpreting, giving 
descriptions, and stating main ideas 
44 
55 
2 
Applying: Solve problems to new situations by applying 
acquired knowledge, facts, techniques and rules in a different 
way. 
20 25 
3 
Analysing : 
Examine and break information into parts by identifying 
motives or causes. Make inferences and find evidence to 
support generalizations 
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 
16 20 
Total 80 100 
1. No chapter wise weightage. Care to be taken to cover all the chapters
2. 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 in all the sections 
Note: For activities NCERT Lab Manual may be referred. 
INTERNAL ASSESSMENT 20 MARKS 
Periodic Tests ( Best 2 out of 3 tests conducted) 10 Marks 
Mathematics Activities   10 Marks 
Page 5


CLASS-XII 
(202 4-2 5) 
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 Assessment 
20 
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. 
2. Inverse Trigonometric Functions 15 Periods 
Definition, range, domain, principal value branch.  Graphs 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. Operations 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).  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), 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, chain rule, derivative of inverse trigonometric functions, 
???????? sin
-1
?? , cos
-1
?? and tan
-1
?? , 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. 
2. Applications of Derivatives                10 Periods 
Applications of derivatives: rate of change of quantities, increasing/decreasing functions, 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. 
?
dx
x
2
± a
2,
?
dx
vx
2
± a
2
, ?
dx
va
2
- x
2
, ?
dx
ax
2
+ bx + c
, ?
dx
vax
2 
+ ???? + ?? ?
px + q
ax
2
+ bx + c
dx, ?
px + q
vax
2+
bx + c
dx, ? va
2
± x
2
 dx, ?
v
x
2
- a
2
 dx 
      ?v????
2
+ ???? + ?? ???? ,     
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) 
5. Differential Equations       15 Periods 
Definition, order and degree, general and particular solutions of a differential equation. 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: 
dy
dx
+ py = q, where p and q are functions of x or constants.
d?? d?? + px = q, where p and q are functions of y or constants.
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. 
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, skew lines, shortest distance between two lines. Angle between two lines.
Unit-V: Linear Programming 
1. Linear Programming 20 Periods 
Introduction, related terminology such as constraints, objective function, optimization, 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 
1.  Probability         30 Periods 
Conditional probability, multiplication theorem on probability, independent events, total probability, 
Bayes’ theorem, Random variable and its probability distribution, mean of random variable. 
MATHEMATICS (Code No. - 041) 
QUESTION PAPER DESIGN CLASS - XII 
(202 4-25) 
Time: 3 hours  Max. Marks: 80 
S. 
No. 
Typology of Questions 
Total 
Marks 
% 
Weightage 
1 
Remembering: Exhibit memory of previously learned material 
by recalling facts, terms, basic concepts, and answers. 
Understanding: Demonstrate understanding of facts and 
ideas by organizing, comparing, translating, interpreting, giving 
descriptions, and stating main ideas 
44 
55 
2 
Applying: Solve problems to new situations by applying 
acquired knowledge, facts, techniques and rules in a different 
way. 
20 25 
3 
Analysing : 
Examine and break information into parts by identifying 
motives or causes. Make inferences and find evidence to 
support generalizations 
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 
16 20 
Total 80 100 
1. No chapter wise weightage. Care to be taken to cover all the chapters
2. 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 in all the sections 
Note: For activities NCERT Lab Manual may be referred. 
INTERNAL ASSESSMENT 20 MARKS 
Periodic Tests ( Best 2 out of 3 tests conducted) 10 Marks 
Mathematics Activities   10 Marks 
Conduct of Periodic Tests: 
Periodic Test is a Pen and Paper assessment which is to be conducted by the respective 
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. 
Depending on the nature of subject, the subject teacher will have the liberty of incorporating 
any other types of questions too. The modalities of the PT are as follows: 
a) Mode: The periodic test is to be taken in the form of pen-paper test.
b) Schedule: In the entire Academic Year, three Periodic Tests in each subject may be
conducted as follows:
Test Pre Mid-term (PT-I) 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. 
c) 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.
d) The school will ensure simple documentation to keep a record of performance as
suggested in detail circular no.Acad-05/2017.
e) 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 of IA with the class to motivate all learners.