CBSE Class 12 Applied Mathematics Syllabus 2026-27

Applied Mathematics

Subject Code – 241

Classes XII

Secondary School Education prepares students to explore future career options after graduating from schools. Mathematics is an important subject that helps students to choose various fields of their choices. Mathematics is widely used in higher studies as an allied subject in the field of Economics, Commerce, Social Sciences and many others. It has been observed that the syllabus of Mathematics in senior secondary grades meant for science subjects may not be appropriate for the students who wish to pursue Commerce or Social Science-based subjects in university education. By keeping this in mind, one more elective course in the mathematics syllabus is developed for Senior Secondary classes with an aim to provide students relevant experience in Mathematics that can be used in fields other than Physical Sciences.

This course is designed to develop substantial mathematical skills and methods needed in other subject areas. Topics covered in two years aim to enable students to use mathematical knowledge in the field of business, economic and social sciences. It aims to promote appreciation of mathematical power and simplicity for its countless applications in diverse fields. The course continues to develop mathematical language and symbolism to communicate and relate everyday experiences mathematically. In addition, it reinforces the logical reasoning skills of formulating and validating mathematical arguments, framing examples, finding counterexamples. It encourages students to engage in mathematical investigations and to build connections within mathematical topics and with other disciplines. The course prepares students to use algebraic methods as a means of representation and as a problem-solving tool. It also enables students to interpret two-dimensional geometrical figures using algebra and to further deduce properties of geometrical figures in a coordinate system. The course content will help students to develop a sound understanding of descriptive and inferential statistics which they can use to describe and analyze a given set of data and to further make meaningful inferences out of it. Data based case studies from the field of business, economics, psychology, education, biology and census data will be used to appreciate the power of data in contemporary society.

It is expected that the subject is taught connecting concepts to the applications in various fields. The objectives of the course areas are as follows:

Course Objectives:

• To develop an understanding of essential mathematical and statistical concepts that are relevant to areas such as business, economic and social sciences.
• To enable students to interpret real-life situations into structured numerical, algebraic and graphical representations for analysis and decision making.
• To develop ability to organise, analyse and interpret data, and to draw meaningful conclusions in practical contexts.
• To strengthen logical thinking and reasoning by engaging students in problem-solving situations that require nuance understanding of qualification and relative change.
• To develop clarity in mathematical communication, including the ability to justify solutions, examine assumptions and validate results.

To help students recognise connections between mathematics and other disciplines, and to use these connections meaningfully.

Grade XII (2026-27)

Number of Paper: 1

Time: 3 Hours

Max Marks: 80

No. Units Marks

1 Numbers, Quantification and Numerical 11

Applications Ш Algebra 10

Ш Calculus 15

IV Probability Distributions 10

V Inferential Statistics 05

VI Time-based data 06

VII Financial Mathematics 15

VIII Linear Programming 80

Total 80

Internal Assessment 20

CLASS-XII

SI. Contents Learning Outcomes: Notes / Explanation

No. Students will be able to UNIT – 1 NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS Numbers & Quantification 1.1 Modulo Arithmetic Define modulus of an integer Definition and meaning

Introduction to modulo

using arithmetic modular operator

rules Modular addition and

subtraction

1.2 Congruence Modulo • Define congruence modulo Definition and meaning

Solution using congruence

problems modulo

Equivalence class

1.3 Alligation and Understand rule of the Meaning and Application of

Mixture alligation to produce а rule of alligation

Mean price of a mixture

Determine the mean price of

a mixture

Apply rule of allegation

1.4 Numerical Problems | Solve real life problems mathematically Boats and Streams Distinguish between Problems based on speed

(upstream and upstream and downstream of stream and the speed of

downstream) • Express the problem in the boat in still water

form of an equation Pipes and Cisterns Determine the time taken by Calculation of the portion of

the tank filled or drained by

empty the tank the pipe(s) in unit time

Races and Games • Compare the performance of Calculation of the time

taken/ distance covered /

distance speed of each player

1.5 Numerical Describe the basic concepts Comparison between two

Inequalities of numerical inequalities statements/situations

• Understand write which can be compared numerically Application of the techniques of numerical solution of algebraic inequations

UNIT-2 ALGEBRA 2.1 Matrices and types Define matrix • The entries, rows and

of matrices Identify different kinds of columns of matrices

• Present a set of data in a

order of matrices matrix form

2.2 Equality of matrices, Determine equality of two Examples of transpose of

Transpose of a matrices matrix

matrix, Symmetric Write transpose of given A square matrix as a sum of

and Skew symmetric matrix symmetric and skew

matrix Define symmetric and skew symmetric matrix

symmetric matrix Observe that diagonal

elements of skew

symmetric matrices are

always zero

2.3 Algebra of Matrices Perform like operations • Addition and Subtraction

on addition & subtraction of matrices

Multiplication of matrices

(It can be shown to the

students that Matrix

multiplication is similar to

scalar with matrix multiplication of two

polynomials)

Multiplication of a matrix

with a real number

2.4 Determinants Find determinant of a square Singular matrix, Non-

matrix singular matrix

|AB|=|A||B|

Simple problems to find

determinant value

2.5 Inverse of a matrix Define the inverse of a Inverse of a matrix using

square matrix cofactors

• If A and B are invertible

matrices square matrices of same

size,

i) <math>(AB)^{-1} = B^{-1}A^{-1}</math>

ii) <math>(A^{-1})^{-1} = A</math>

iii) <math>(A')^{-1} = (A^{-1})'</math>

2.6 Solving system of Solve of the system • Solution of system of

simultaneous simultaneous equations simultaneous equations

equations using using up to three variables only

matrix method and (non- homogeneous

Cramer's rule i) Cramer's Rule equations)

ii) Inverse of coefficient matrix

Formulate real life problems

into of a system simultaneous linear

equations and solve it using

these methods