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.
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.
