Assam Board AHSEC Class 12 Mathematics Syllabus, Important Topics and Marking Scheme

S.No

Title

No. of Periods

1

Relations and Functions

24

2

Algebra

40

3

Calculus

78

4

Vectors and Three-Dimensional Geometry

34

5

Linear Programming

08

6

Probability

16

Total

200

Chapters

Unit- 1 Relations And Functions

Chapter 1 

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

Chapter 2- Inverse Trigonometric Functions 

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

Unit- 2 Algebra

Chapter- 1 Matrices

Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skewsymmetric 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

Chapter-2 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 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- 3 Calculas

Chapter- 1 Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric 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

Chapter- 2 Application of Derivatives

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).

Chapter- 3 Integrals

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

Chapter- 4 Applications of the Integrals 

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

Chapter- 5 Differential Equations

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:

Unit- 4 Vectors And Three-Dimensional Geometry

Chapter- 1 Vectors

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.

Chapter- 2 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

Unit- 5 Linear Programming

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- 6 Probability

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

Title

Marks

Relations and Functions

08

Algebra

14

Calculus

44

Vectors and Three-Dimensional Geometry

20

Linear Programming

06

Probability

08

Total

200

Exam

Assam Higher Secondary Education Council Examination (AHSECE), also called as Assam AHSEC

Exam Conducting Body

Assam Higher Secondary Education Council (AHSEC)

Total Marks

100

Duration

3 hours

No. of Sections

3

No. of Questions 

29

Section- A (Very Short Answer Type Questions)

1 mark each x 10 questions = 10 marks

Section- B (Short Answer Type Questions)

4 mark each x 12 questions = 48 marks

Section – C (Long Answer Type Questions)

6 mark each x 7 questions = 42 marks