The Central Board of Secondary Education (CBSE) has officially released the revised Applied Mathematics syllabus for Class 12 for the academic session 2025-26. The syllabus, designed in accordance with the National Curriculum Framework (NCF) and the NEP 2025 guidelines, provides a thorough roadmap for students pursuing mathematics with a focus on real-world applications.
The syllabus is structured to support students aiming for careers in finance, economics, commerce, and social sciences. It details unit-wise marks distribution, course content, learning outcomes, and practical components. The syllabus PDF is freely accessible through the official CBSE website.
For an overall subject-wise breakdown, students can also check the CBSE Class 12 Syllabus 2025-26.
Direct link to download CBSE Class 12 Applied Mathematics Syllabus 2025-26 PDF
Click here to download CBSE 12th Applied Mathematics Syllabus 2026 PDF
CBSE Class 12 Applied Mathematics 2025-26: Key Highlights
| Particular | Details |
| Subject | Applied Mathematics |
| Class | 12th |
| Academic Session | 2025–26 |
| Theory Marks | 80 |
| Practical/Activity | 20 |
| Total | 100 |
| Exam Duration | 3 Hours |
CBSE Class 12 Applied Maths 2025-26: Marking Scheme
| Unit No. | Unit Name | Marks |
| I | Numbers, Quantification & Numerical Applications | 11 |
| II | Algebra | 10 |
| III | Calculus | 15 |
| IV | Probability Distributions | 10 |
| V | Inferential Statistics | 5 |
| VI | Time-Based Data | 6 |
| VII | Financial Mathematics | 15 |
| VIII | Linear Programming | 8 |
| Theory Total | 80 | |
| Internal Assessment | 20 |
CBSE 12th Applied Mathematics Syllabus 2026: Detailed Syllabus
| Unit | Topics Covered | Key Concepts and Subtopics |
| Unit I | Numbers, Quantification and Numerical Applications | - Modulo Arithmetic & Congruence: Definitions, modular operations, equivalence classes - Alligation and Mixture: Mean price, rule of alligation - Numerical Problems: Boats & streams, races, pipes & cisterns - Numerical Inequalities: Algebraic inequalities, comparison of numerical statements |
| Unit II | Algebra | - Matrices: Types, order, rows/columns, transpose, symmetric/skew-symmetric matrices - Matrix Algebra: Addition, subtraction, scalar & matrix multiplication - Determinants: Singular/non-singular, determinant calculation - Inverse of a Matrix: Cofactor method, inverse properties - Solving Equations: Cramer’s Rule, inverse matrix method |
| Unit III | Calculus | - Differentiation: First & second order, parametric, implicit - Applications: Rate of change, marginal cost/revenue, increasing/decreasing behavior, maxima & minima (first/second derivative tests) - Integration: Indefinite integrals (substitution, partial fractions, by parts), definite integrals, area under curves - Applications of Integration: Consumer/producer surplus, total cost/revenue, equilibrium price - Differential Equations: Formation, solving using variable separable method |
| Unit IV | Probability Distributions | - Random Variables: Discrete/continuous, distributions - Mathematical Expectation & Variance: Mean, variance, standard deviation - Binomial Distribution: Mean, variance, SD, Bernoulli trials - Poisson Distribution: Properties, formulas - Normal Distribution: Characteristics, Z-score, standard normal variate |
| Unit V | Inferential Statistics | - Population & Sampling: Random sampling (simple/systematic), representative vs non-representative - Parameters & Statistics: Conceptual understanding, Central Limit Theorem, limitations of sample-based inference - t-Test: Hypothesis testing, null & alternate hypotheses, degree of freedom, one-sample t-test |
| Unit VI | Time-Based Data | - Time Series: Definition, chronological data - Components: Trend, seasonal, cyclical, irregular - Analysis: Fitting straight-line trend, moving averages, method of least squares |
| Unit VII | Financial Mathematics | - Perpetuity & Sinking Funds: Concepts, real-life examples, differences from savings - Bond Valuation: Present value method, coupon rate, maturity, current price - EMI Calculation: Flat-rate & reducing-balance methods - CAGR: Compound annual growth, distinction from simple growth - Depreciation: Linear method, cost, residual value, useful life |
| Unit VIII | Linear Programming | - Introduction & Terminology: Decision variables, objective function, constraints, optimization concepts |
Practical Component (20 Marks)
Students will engage in activities and projects that involve using spreadsheets and data analysis. Suggested practical work includes:
- Plotting graphs of exponential, demand, and supply functions using Excel.
- Matrix operations including multiplication and finding the inverse.
- Dice roll simulations to study probability.
- Stock market data analysis.
- Interpreting data from sources like newspapers related to traffic, economics, sports.
- Analyzing real-world data trends (inflation, weather, pollution).
Course Objectives
- To equip students with the ability to apply mathematical and statistical tools in areas like business, economics, and the social sciences.
- To convert real-life scenarios into mathematical models using numerical, algebraic, or graphical forms.
- To interpret, organize, and analyze data meaningfully.
- To develop logical and analytical thinking.
- To enhance mathematical communication through conjectures and argument validation.
- To interlink mathematical concepts with other academic fields.
