AHSEC HS 2nd Year Mathematics Syllabus 2025: The Higher Secondary Final Year Mathematics course is structured to help students understand core mathematical concepts required for competitive exams, higher studies, and real-life applications. AHSEC has designed the syllabus with clear unit-wise marks and period distribution to ensure systematic learning.
Below is the updated and complete HS Class 12 Mathematics syllabus, including marks, periods, and detailed chapter-wise topics.
HS Mathematics: Marks & Period Distribution (Total: 100 Marks | 200 Periods)
| Unit No. | Title | Marks | Periods |
|---|---|---|---|
| Unit I | Relations & Functions | 08 | 24 |
| Unit II | Algebra | 14 | 40 |
| Unit III | Calculus | 44 | 78 |
| Unit IV | Vectors & 3D Geometry | 20 | 34 |
| Unit V | Linear Programming | 06 | 08 |
| Unit VI | Probability | 08 | 16 |
| Total | — | 100 | 200 |
Detailed HS 2nd Year Mathematics Syllabus 2025-26 (Chapter-Wise)
Unit I: Relations and Functions (Marks: 08 | Periods: 24)
1. Relations and Functions
- Types of Relations: Reflexive, Symmetric, Transitive, Equivalence
- Types of Functions
- Composition of Functions
- Invertible Functions
2. Inverse Trigonometric Functions
- Definitions, Domain & Range
- Principal Value Branches
- Graphs of Inverse Trigonometric Functions
- Basic Properties
Unit II: Algebra (Marks: 14 | Periods: 40)
1. Matrices
- Concept, Order, Types
- Zero, Symmetric & Skew-Symmetric Matrices
- Matrix Addition, Multiplication & Scalar Multiplication
- Non-commutative Property of Multiplication
- Existence of Non-zero Matrices with Zero Product
- Invertible Matrices & Uniqueness of Inverse
- Restriction: Square Matrices up to Order 2
2. Determinants
- Determinant (up to 3×3)
- Properties of Determinants
- Minors & Cofactors
- Area of a Triangle using Determinants
- Adjoint & Inverse of a Matrix
- Solving Linear Equations (2 or 3 variables) using Matrix Inverse
Unit III: Calculus (Marks: 44 | Periods: 78)
1. Continuity & Differentiability
- Basic Concepts
- Chain Rule
- Derivatives of Inverse Trigonometric & Implicit Functions
- Exponential & Logarithmic Functions
- Logarithmic Differentiation
- Parametric Differentiation
- Second Order Derivatives
2. Application of Derivatives
- Rate of Change
- Increasing & Decreasing Functions
- Maxima & Minima (First & Second Derivative Test)
- Simple Real-life Problems
3. Integrals
- Integration as Reverse of Differentiation
- Substitution, Partial Fractions, By Parts
- Standard Forms including:
- ∫ dx / (a² − x²)
- ∫ dx / (x² + a²)
- ∫ dx / (x² − a²)
- ∫ (px + q) / (ax² + bx + c) dx
- Definite Integrals & Fundamental Theorem (statement only)
4. Applications of Integrals
- Area under Curves
- Lines, Arcs of Circles, Parabolas & Ellipses (Standard Form)
5. Differential Equations
- Definition: Order, Degree
- General & Particular Solutions
- Separation of Variables
- Homogeneous Equations
- Linear Differential Equations: dy/dx + Py = Q
Unit IV: Vectors & 3D Geometry (Marks: 20 | Periods: 34)
1. Vectors
- Scalars & Vectors
- Magnitude & Direction
- Direction Cosines & Ratios
- Types of Vectors
- Position Vector
- Addition & Scalar Multiplication
- Vector Division in Ratio
- Dot Product & Projection
- Cross Product
2. Three-Dimensional Geometry
- Direction Ratios & Cosines
- Cartesian & Vector Equation of a Line
- Angle Between Lines
- Skew Lines & Shortest Distance
Unit V: Linear Programming (Marks: 06 | Periods: 08)
- Introduction to LPP
- Constraints, Objective Function
- Feasible & Infeasible Regions
- Graphical Method (Two Variables)
Unit VI: Probability (Marks: 08 | Periods: 16)
- Multiplication Theorem
- Conditional Probability
- Independent Events
- Total Probability Theorem
- Bayes’ Theorem
- Random Variable & Probability Distribution
Appendix
1. Proofs in Mathematics
- Direct Method
- Contrapositive
- Contradiction
- Counter-example
2. Mathematical Modelling
- Real-life Modelling using
- Matrices
- Calculus
- Linear Programming
Conclusion
This HS Final Year Mathematics syllabus provides a strong foundation for students preparing for board exams and competitive exams alike. With clear marks distribution and well-defined topics, following this syllabus ensures complete and structured preparation.
Important Links
| Class 12 Mathematics Syllabus PDF | Click Here |
| HS Class 12 Syllabus Home | Click Here |
| Official Website | Click Here |
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