Assam HS 2nd Year Maths Syllabus 2026-27 PDF Download - Check AHSEC 2nd Year Mathematics Pattern

Unit Number

Units

Marks

I

Relations and Functions

8

II

Algebra

10

III

Calculus

35

IV

Vector and Three-Dimensional Geometry

16

V

Linear Programming

5

VI

Probability

6

Appendix

Proofs in Mathematics

-

Mathematical Modelling

-

Project Work

-

20

Total

-

100

Units

Chapters

Relations and Functions

• Types of relations

• 
  

  • Reflexive, Symmetric, Transitive, Equivalence relations.

  • Types of functions, composition of functions and invertible functions

• Inverse Trigonometric Functions

• 
  

  • Definition, range, domain, principal value branches.

  • Graphs of inverse trigonometric functions.

  • Elementary properties of inverse trigonometric functions

Algebra

• Matrices

• 
  

  • Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices.

  • Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication.

  • Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2).

  • Invertible matrices, proof of the uniqueness of the inverse if it exists.

• Determinants

• 
  

  • Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle.

  • Adjoint and inverse of a square matrix.

  • Consistency, inconsistency and the number of solutions of a system of linear equations by example.

Calculus

• Continuity and Differentiability

• 
  

  • Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, and derivative of implicit function.

  • Concept of exponential and logarithmic functions and their derivatives.

  • Logarithmic differentiation. Derivatives of functions expressed in parametric forms.

  • Second-order derivatives.

• Application of Derivatives

• 
  

  • Rate of change, increasing/decreasing functions, maxima and minima.

  • Simple problems.

• Integrals

• Application of Integrals

• Differentials Equations

• 
  

  • Definition, order and degree, general and particular solutions of a differential equation.

  • Solution of differential equations by the method of separation of variables.

  • Solution of homogeneous differential equations of first order and first degree.

Vectors and Three-Dimensional Geometry

• Vectors

• 
  

  • Vectors and scalars, the magnitude and direction of a vector.

  • Direction cosines/ ratios of vectors.

  • Types of vectors, position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, and position vector of a point dividing a line segment in a given ratio.

  • Scalar (dot) product of vectors, projection of a vector on a line.

  • Vector (cross) product of vectors.

• Three-Dimensional Geometry

• 
  

  • Direction cosines and direction ratios of a line joining two points.

  • Cartesian and vector equation of a line.

  • Angle between two lines, skew lines, shortest distance between two lines.

Linear Programming

• Introduction

• Related terminology

Probability

• Multiplication theorem on probability.

• Conditional probability, independent events, total probability

• Baye’s theorem

• Random variable and its probability distribution.