CBSE Class 12 Applied Mathematics 2025-26
Your complete resource hub for CBSE Class 12 Applied Mathematics. Free study materials, comprehensive syllabus guide, sample papers, and premium products to help you score 90+.
What is Applied Mathematics?
Applied Mathematics is a specialized subject introduced by CBSE for students who want to use mathematical concepts in practical fields like commerce, economics, business, and social sciences. Unlike core mathematics which focuses heavily on theoretical concepts and advanced calculus, Applied Mathematics emphasizes real-world applications and problem-solving techniques that are directly useful in professional careers.
This subject is perfect for commerce students who need mathematics but don't plan to pursue higher studies in core mathematical sciences. It covers essential topics like financial mathematics, statistics, probability, linear programming, and data analysis – all skills that are highly valued in business, finance, data science, and management careers.
Applied Maths vs Core Maths: Key Differences
| Feature | Applied Mathematics | Core Mathematics |
|---|---|---|
| Focus | Practical applications in business & economics | Abstract theory and advanced calculus |
| Difficulty Level | Moderate, application-based | Higher, theory-heavy |
| Best For | Commerce, Business, Economics students | Science, Engineering aspirants |
| Topics | Financial Maths, Statistics, Probability, Linear Programming | Vectors, 3D Geometry, Trigonometry, Advanced Calculus |
| Career Paths | CA, CS, Business Analytics, Management | Engineering, Research, Teaching |
| Tools Used | Heavy use of Excel and practical tools | More manual calculations and proofs |
Who Should Choose Applied Mathematics?
Applied Mathematics is ideal if you:
- Are a commerce student needing mathematics for university admission
- Want to pursue CA, CS, BBA, BCom, Economics, or Business Analytics
- Prefer practical problem-solving over abstract theory
- Plan to work in business, finance, banking, or data analytics
- Want to develop Excel and data analysis skills
- Need Mathematics but find Core Maths too theoretical
Complete CBSE Class 12 Applied Maths Syllabus 2025-26
The Applied Mathematics syllabus is divided into two parts – Theory (80 marks) and Internal Assessment (20 marks).
Theory Syllabus (80 Marks)
| Unit | Topics | Marks |
|---|---|---|
| I. Numbers & Quantification | Modular Arithmetic, Congruence Modulo, Alligation & Mixture, Boats & Streams, Pipes & Cisterns, Races & Games, Numerical Inequalities | 11 |
| II. Algebra | Matrices, Determinants, Solving Linear Equations | 10 |
| III. Calculus | Differentiation & Its Applications, Integration & Its Applications, Differential Equations | 15 |
| IV. Probability Distributions | Probability Distribution Table, Binomial, Poisson, Normal Distribution | 10 |
| V. Inferential Statistics | Sampling, Hypothesis, One-Sample t-Test | 5 |
| VI. Time-based Data | Index Numbers, Time Series – Moving Averages & Least Squares | 6 |
| VII. Financial Mathematics | Perpetuity, Sinking Funds, EMI, CAGR, Depreciation, Bonds | 15 |
| VIII. Linear Programming | LPP Formulation, Corner Point Method | 8 |
Internal Assessment (20 Marks)
- Periodic Tests: 10 Marks
- Mathematics Activities/Practical Work: 5 Marks
- Portfolio: 5 Marks
Exam Pattern 2025-26
- Total Marks: 80 (Theory) + 20 (Internal)
- Time Duration: 3 Hours
- Section A: 20 MCQs (1 mark each) = 20 marks
- Section B: 5 questions (2 marks each) = 10 marks
- Section C: 6 questions (3 marks each) = 18 marks
- Section D: 4 questions (5 marks each) = 20 marks
- Section E: 3 Case Study questions (4 marks each) = 12 marks
Important Changes for 2025-26
- Deleted Topics:
- Algebra: Properties of Determinants,
- Calculus: Higher Order Derivatives (More than second order), Tangents and Normals, Properties of Definite Integrals
- Inferential Statistics: 2 Independent Groups t-test
- Financial Mathematics: Calculation of Returns, Nominal Rate of Return
- Linear Programming Problems: Transportation Problems
- Added Topics:
- Calculus: Area Under the Curve (Application of Integrals)
- Financial Mathematics: Valuation of Bonds
- Excel Practical: Now mandatory for all students in Internal Assessment
Important Dates 2025-26
- Board Exam Date: 09 March 2026
- Practical Exam: January 2026
Free Study Resources by Unit
Explore comprehensive free content for each unit. Get quality study materials, practice questions, and video tutorials at no cost.
Numbers & Quantification
11 Marks
• Alligation & Mixture • Boats & Streams • Pipes & Cisterns • Races & Games
- 15 Free MCQs
- 15 Solved Examples
- 2 Case Studies
- Formula Sheet
Algebra
10 Marks
- 20 Solved Examples
- 15 Free MCQs
- 3 Video Tutorials
- Matrix Operations Guide
Calculus
15 Marks
- 25 Solved Examples
- 15 Free MCQs
- 4 Video Tutorials
- Formulas & Shortcuts
Probability Distributions
10 Marks
- 20 Solved Examples
- 15 Free MCQs
- 3 Video Tutorials
- Distribution Tables
Inferential Statistics
5 Marks
- 12 Solved Examples
- 15 Free MCQs
- 2 Video Tutorials
- t-Test Step Guide
Time-based Data
6 Marks
- 15 Solved Examples
- 15 Free MCQs
- 2 Video Tutorials
- Excel Templates
Financial Mathematics
15 Marks
- 25 Solved Examples
- 15 Free MCQs
- 4 Video Tutorials
- Financial Formulas
Linear Programming
8 Marks
- 15 Solved Examples
- 20 Free MCQs
- 3 Video Tutorials
- Graphing Techniques
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CBSE Official Sample Papers (Latest Pattern)
Official sample papers released by CBSE - these define the exact exam pattern and question types for your board exams
CBSE Board Question Papers (Actual Board Exams)
Real questions that appeared in CBSE board examinations - practice with these to understand actual exam difficulty and patterns
School Question Papers for Additional Practice
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Unit Test / Monday Test Papers (UT-1 / MT-1)
First assessment papers covering Units 1-2 (Numbers, Algebra)
Second Unit Test / Monday Test Papers (UT-2 / MT-2)
Second assessment papers covering Units 3-4 (Calculus, Probability)
Half Yearly / Term-1 Examination Papers
Comprehensive papers covering first half of syllabus (Units 1-4)
Pre-Board Examination Papers
Full syllabus papers (all 8 units) in board exam format - best for final preparation
💡 Pro Tip for Board Exam Success
Solve all CBSE sample papers at least 3 times and previous year board papers at least 2 times under timed conditions (3 hours). This is the most effective way to score 85+ marks.
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✓ 50+ Case Study Questions with Solutions
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- Chapter-wise concept explanations
- Solved NCERT and sample paper questions
- Exam strategies and tips
- Common mistakes to avoid
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Proven strategies and tips from toppers
High Priority Topics (Practice More)
Financial Mathematics – 15 marks
Focus heavily on EMI calculations, sinking funds, bonds valuation, and depreciation. This unit alone contributes 15 marks and is highly scoring if you practice regularly.
Calculus – 15 marks
Master differentiation applications (maxima-minima, marginal cost) and integration applications (area under curve, consumer surplus). Practice mixed problems.
Algebra – 10 marks
Matrices and determinants are straightforward if you practice regularly. Focus on matrix operations, inverse, and solving equations using both methods.
Probability – 10 marks
Learn distribution formulas thoroughly. Practice identifying which distribution to use in a given problem. Normal distribution questions are very scoring.
Scoring Topics (Don't Miss These Easy Marks)
- Time Based Data (6 marks): Easiest unit! Moving averages and least squares are formula-based and straightforward.
- Linear Programming (8 marks): Graph-based questions are scoring if you practice the graphical method properly.
- Inferential Statistics (5 marks): t-Test questions follow a fixed format. Practice the steps thoroughly.
Smart Study Techniques
1. Formula Mastery
Create formula flashcards and revise daily. Don't just memorize - understand when to apply each formula.
2. Step-wise Writing
Always show complete working in exams. Even if your final answer is wrong, you get marks for correct method.
3. Time Management
Allocate 25-30 minutes daily for each high-weightage unit (>10 marks). Consistency beats cramming.
4. Previous Year Analysis
Identify repeated question patterns from past 5 years. Some question types appear almost every year.
5. Mock Tests
Solve at least 15-20 sample papers in exam conditions (3 hours, no breaks). This builds exam temperament.
6. Excel Practice
Don't ignore Excel practical - it's 5 easy marks in internal assessment. Practice all financial and statistical functions.
❌ Common Mistakes to Avoid
- Skipping steps in calculus solutions - you lose method marks
- Memorizing formulas without understanding applications
- Not attempting all questions (there's NO negative marking!)
- Skipping sub-parts of questions
- Poor time management - spending too long on difficult questions
- Not using formula sheet for quick revision before exam
- Ignoring case study questions practice
- Not practicing MCQs seriously
Exam Day Time Management Strategy
- First 20 minutes: Attempt all MCQs (Section A) - don't overthink
- Next 40 minutes: Complete 2-mark and 3-mark questions (Sections B & C)
- Next 25 minutes: Solve Case Studies (Section E) - these are scoring
- Next 50 minutes: Attempt 5-mark questions (Section D) - show all steps
- Last 15 minutes: Review answers, check calculations, attempt any skipped questions
Frequently Asked Questions
Common questions about Applied Mathematics answered
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