Class 12 Applied Maths Syllabus 2026-27

The class 12 applied maths syllabus 2026-27 for Subject Code 241 carries 80 marks for theory and 20 marks for internal assessment, spread across eight units. This page lists every unit with its exact marks weightage, the required spreadsheet practicals, the rule that prevents combining this subject with Mathematics (041), and the highest-weightage units you should prioritise — verified against the official CBSE curriculum document on 2026-07-13.

Verification and Subject Details

The details below are taken from the official Applied Mathematics (Code 241) curriculum document published for the 2026-27 session on the CBSE academic website. The paper is a single theory paper of 3 hours duration, with maximum marks of 80 for theory and 20 for internal assessment.

CBSE has designed this elective course specifically for students who intend to pursue Commerce, Economics, or Social Sciences at the university level — it is not a substitute for Core Mathematics (041) for students heading into Physical Sciences or Engineering. The complete curriculum document is available at cbseacademic.nic.in, and every figure on this page traces to that source.

Class 12 Applied Maths Syllabus 2026-27: Course Structure

The theory paper is split across eight units. Two units — Calculus (15 marks) and Financial Mathematics (15 marks) — together account for 30 of the 80 theory marks, so they deserve the bulk of your revision time. The exact unit-wise marks distribution is reproduced below from the official Grade XII table (per the CBSE curriculum document, page 10).

Paper duration: 3 Hours. Total marks (Theory + IA): 100.

Class 12 Applied Maths Unit-wise Topics

The eight units cover a mix of pure numerical methods, algebra, calculus, statistics, and applied finance. Below is the scope of each unit, summarised from the official curriculum so you know exactly what to study without guessing. You can deepen each topic through the Applied Mathematics notes on this site.

Unit I — Numbers, Quantification and Numerical Applications (11 marks)

• Modulo Arithmetic: modulus of an integer, modular addition and subtraction.
• Congruence Modulo: definition, solving problems using congruence modulo, equivalence class.
• Alligation and Mixture: rule of alligation, mean price of a mixture.
• Numerical Problems: boats and streams (upstream/downstream), pipes and cisterns, races and games.
• Numerical Inequalities: describing and solving numerical inequalities.

Unit II — Algebra (10 marks)

• Matrices and types of matrices; equality of matrices, transpose, symmetric and skew-symmetric matrices.
• Algebra of Matrices: addition, subtraction, multiplication of two matrices, scalar multiplication.
• Determinants: determinant of a square matrix, singular and non-singular matrices, the property \( |AB| = |A||B| \).
• Inverse of a matrix using cofactors; properties such as \( (AB)^{-1} = B^{-1}A^{-1} \) and \( (A^{-1})^{-1} = A \).
• Solving simultaneous equations (up to three variables, non-homogeneous) using the matrix method and Cramer’s rule.

Unit III — Calculus (15 marks, highest weightage)

• Derivatives up to second order, including differentiation of parametric functions and implicit functions.
• Application of Derivatives: rate of change of area and volume with respect to time or dimension.
• Marginal Cost and Marginal Revenue using derivatives.
• Increasing / Decreasing Functions in a given interval.
• Maxima and Minima using the first and second derivative tests; optimisation of cost, revenue, and profit.
• Integration as the reverse of differentiation; indefinite integrals by substitution, partial fraction, and by parts (non-trigonometric).
• Definite Integrals as area under the curve; application to consumer surplus and producer surplus.
• Differential Equations: order, degree, formation by eliminating arbitrary constants, solving by variable separable method only.

Unit IV — Probability Distributions (10 marks)

• Probability Distribution of discrete and continuous random variables.
• Mathematical Expectation as the expected value of a random variable.
• Variance and standard deviation of a random variable.
• Binomial Distribution: Bernoulli trials, the formula \( P(r) = {}^nC_r\, p^r q^{n-r} \), with \( \text{Mean} = np \), \( \text{Variance} = npq \), \( \text{S.D.} = \sqrt{npq} \).
• Poisson Distribution: conditions, the formula \( P(X) = \dfrac{\lambda^x e^{-\lambda}}{x!} \), with \( \text{Mean} = \text{Variance} = \lambda \).
• Normal Distribution: characteristics, total area under the curve = 1, standard normal variate \( Z = \dfrac{x – \mu}{\sigma} \).

Unit V — Inferential Statistics (05 marks)

• Population and Sample: representative vs non-representative sample, simple random sampling and systematic random sampling (sample size less than 100).
• Parameter and Statistics: conceptual relationship, limitations of generalising from sample to population, Central Limit Theorem (conceptual only).
• t-Test: framing Null and Alternate hypothesis, degree of freedom, testing a null hypothesis for one small group sample.

Unit VI — Time-based data (06 marks)

• Time Series as chronological data; components — secular trend, seasonal variation, cyclical variation, irregular variation.
• Univariate time series analysis: fitting a straight-line trend and estimating the value.
• Methods of measuring trend: moving average method and method of least squares.

Unit VII — Financial Mathematics (15 marks, joint-highest weightage)

• Perpetuity and Sinking Funds: concept, calculation, and the difference between a sinking fund and a savings account.
• Valuation of Bonds: coupon rate, maturity rate, current price, present value approach.
• EMI calculation: flat-rate method and reducing-balance method.
• Compound Annual Growth Rate (CAGR): meaning, difference from annual growth rate, formula-based calculation.
• Linear method of Depreciation: cost, residual value, useful life of an asset, advantages and disadvantages.

Unit VIII — Linear Programming (08 marks)

• Introduction and terminology: decision variable, constraints, objective function, optimisation, non-negative constraints.
• Mathematical formulation of an LPP up to three non-trivial constraints.
• Different types of LPP: manufacturing problem, diet problem, and similar real-world cases.
• Graphical method: corner-point method for the optimal solution of an LPP in two variables.
• Feasible and infeasible regions and solutions; bounded and unbounded regions; optimal feasible solution.

The full topic-level breakdown for every unit is also visible through the Class 12 notes hub, which organises the same content into chapter-wise study material.

Exam Pattern and Assessment Scheme

The Class XII Board Examination covers the entire syllabus of Class 12 as prescribed for each subject (per the official curriculum document, page 13). Marks are awarded on a 9-point grading system from A-1 (top 1/8th of passed candidates) down to E (Essential Repeat).

The board places all passed students in a rank order and then allocates each grade to one-eighth of the cohort.

The Board explicitly states that the question papers will move away from textbook-driven assessment and will include more questions based on real-life situations, requiring students to apply, analyse, evaluate, and synthesise information. The detailed design of the question paper is not included in the curriculum document itself; it is released separately with the sample question paper

later in the academic year. The Board examination will, however, test according to the weightage allocated to each unit shown in the course structure table above.

Practical Work and Internal Assessment

The 20 marks for internal assessment are earned through spreadsheet-based practical work and a project. The official curriculum document (page 18) lists the following suggested spreadsheet practicals for Class XII — these are not generic; they map directly to the units in the theory paper.

Spreadsheet practicals required for Class 12 Applied Maths

1. Plot the graphs of functions on Excel and study the graph to find the point of maxima/minima.
2. Probability and dice roll simulation — a direct application of Unit IV (Probability Distributions).
3. Matrix multiplication and the inverse of a matrix on Excel — applies Unit II (Algebra).
4. Stock Market data sheet on Excel — applies Unit VII (Financial Mathematics) and Unit VI (Time-based data).
5. Collect data on weather, price, inflation, and pollution; analyse the data and make meaningful inferences.
6. Collect data from newspapers on traffic, sports activities, and market trends; use Excel to study future trends.

Suggested project topics (selected from the official list)

• Use of prime numbers in coding and decoding of messages.
• Stock price movement and predicting stock market trends.
• Linear method of depreciation models for assets.
• Weather prediction (prediction of monsoon from past data).
• Risk assessments by insurance firms from collected data.
• Vehicle registration data correlated with pollution and the number of accidents.
• Predicting the outcome of an election using exit poll data.
• Analysis of a cricketer’s career graph (batting average / bowling average).

The full list of 25 suggested projects is given on page 18 of the curriculum document. The practical record and the project together carry the 20 internal-assessment marks — keep the spreadsheet file with all working data ready for the examiner.

Deletions and Changes in the Syllabus

Checked against the official Applied Mathematics curriculum document for the 2026-27 session: no deleted chapters or removed topics are explicitly listed in the official PDF. The eight units, their sub-topics, and the marks distribution are stated in full with no rationalisation footnote and no separate "deleted content" annexure.

What has shifted is the assessment philosophy. The CBSE curriculum document (page 13) states that the board is "progressively allowing more space to learning-outcome based assessment in place of textbook driven assessment." In practice, this means students should expect more questions framed around real-life situations

— case-study style problems on EMI, bond valuation, dice roll probability, time-series data on weather or inflation, and LPP scenarios drawn from diet or manufacturing contexts. The core competencies tested will still come from the prescribed syllabus, but the question style is designed to eliminate rote learning and predictability.

If a deletion is notified mid-session through a CBSE circular, this page will be updated the same day to reflect it. Until then, treat the eight-unit structure above as the complete and final syllabus.

Applied Mathematics vs Core Mathematics (041 vs 241)

The CBSE Scheme of Studies (page 9 of the curriculum document) is explicit: Mathematics (Code 041) and Applied Mathematics (Code 241) cannot be taken together. A student who opts for one cannot register for the other as a separate elective. This is a hard registration rule, and it prevents a common subject-selection mistake made by Commerce and Humanities students.

CBSE’s stated rationale (page 1 of the curriculum document) is that the senior secondary Mathematics syllabus originally designed for Science subjects "may not be appropriate for the students who wish to pursue Commerce or Social Science-based subjects in university education." Applied Mathematics therefore covers the same broad areas — calculus, algebra, probability — but tilts every topic toward

real commercial, economic, and social-science applications (marginal cost, EMI, bond valuation, time-series data, LPP for manufacturing problems). If your target degree is in B.Com, Economics, BBA, Statistics, or Social Sciences, Applied Mathematics (241) is the appropriate choice; if you are aiming for B.Sc. Physics, Chemistry, Engineering, or Computer Science, choose Core Mathematics (041) instead.

Chapter-wise Study Material

Chapter-wise study material for every unit above:

Additional chapter-level resources for the rest of your subjects are organised on the CBSE notes portal, which you can browse by class and subject.

Frequently Asked Questions

Can I take both Mathematics (041) and Applied Mathematics (241) in Class 12?

No. The CBSE Scheme of Studies (curriculum document, page 9) explicitly states that Mathematics (Code 041) and Applied Mathematics (Code 241) cannot be taken together. You must choose one — Applied Mathematics if your target is Commerce, Economics, or Social Sciences; Core Mathematics if your target is Physical Sciences or Engineering.

What are the maximum marks for the Class 12 Applied Maths theory exam?

The theory paper carries 80 marks, with a duration of 3 hours. Internal assessment adds 20 marks, bringing the total to 100 marks. The theory weightage is split across eight units, with Calculus and Financial Mathematics each carrying 15 marks — the joint highest.

Are there any deletions in the class 12 applied maths syllabus 2026-27?

Verified against the official CBSE curriculum document on 2026-07-13: no deletions are noted in the official PDF for this session. All eight units and their listed sub-topics stand as published. The change to be aware of is the shift toward competency-based, real-life-situation questions in the Board exam, not any reduction in content.

What type of spreadsheet practicals are required for the internal assessment?

The official curriculum lists six spreadsheet practicals, including dice roll simulation for probability, matrix multiplication and inverse of a matrix for algebra, stock market data sheets for financial mathematics, plotting function graphs to find maxima/minima, and analysing weather, inflation, or pollution data for time-series work.

These, along with a project from the suggested list of 25 topics, together account for the 20 marks of internal assessment.

Reference: CBSE Class 12 Applied Mathematics curriculum document, session 2026-27 as stated on cbseacademic.nic.in.