AHSEC 2nd Year Maths Syllabus 2024-25: Download Assam Board Class 12 Maths Syllabus FREE PDF

HS 2nd Year Maths Syllabus 2024 PDF Download: The Assam Higher Secondary Education Council (AHSEC) HS 2nd year Mathematics syllabus 2024–25 is available here for the new academic year. The students must go through the syllabus and complete their studies as per the curriculum. The school authorities must provide the updated syllabus to all the students to avoid any confusion. 

Here is the latest syllabus PDF provided for AHSEC Assam Board Class 12 Maths, along with the course structure. Check and download the complete mark distribution and period allocation in PDF format.

Assam HS 2nd Year Maths Course Structure 2024-25 PDF

Unit-wise Distribution of Marks and Periods:

Assam HS 2nd Year Maths Syllabus 2024-25 PDF

Unit-wise Distribution of Course contents :

Unit-I: 1. RELATIONS AND FUNCTIONS (Marks-04) (Periods-12)

Types of relations: Reflexive, symmetric, transitive and equivalence relations. Types of function, composition of functions and invertible function.

2. Inverse Trigonometric Functions: (Marks-04) (Periods-12)

Definition, range, domain, principal value branches. Graphsofinversetrigonometricfunctions. Elementary properties of inverse trigonometric functions.

Unit-II: ALGEBRA

1. Matrices : (Marks-06) (Periods 20)

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. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices, proof of uniqueness of inverse if it exist.

2. Determinants : (Marks-08) (Periods 20)

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 number of solutions of system of linear equations by example, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III : CALCULUS

1. Continuity and Differentiability :  (Marks-12) (Periods 20)

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigo- nometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivatives. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives.

2. Application of Derivatives : (Marks-10) (Periods 16)

Applications of derivatives : Rate of change, increasing/ decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals : (Marks-10) (Periods 20)

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of integrals of the type.

dx and problems based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals : (Marks-04) (Periods 10)

Applications in finding the area under simple curves, especially lines, arcs of circles/ parabolas/ ellipses (in standard form only),

5. Differential Equations : (Marks-08) (Periods 12)

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solution of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type :

dy / dx + Py = Q where P and Q are functions of x.

Unit-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

1. Vectors : (Marks-12) (Periods 20)

Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors(equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, 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.

2. Three-dimensional Geometry : (Marks 08) (Periods 14) 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.

Unit-V : LINEAR PROGRAMMING (Marks 06) (Periods 08)

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solution, optimal feasible solution.

Unit-VI : PROBABILITY (Marks 08) (Periods 16)

Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and it’s probability distribution.

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