Manipur State Board has published subject wise syllabus for this year Class 12 students in its official portal cohsem.nic.in Here we have published Class 12 COHSEM Syllabus 2024-25 for Maths subject. For more information regarding Council of Higher Secondary Education (COHSEM) Class 12 2024 Exam Date, Exam Pattern, Time, Date, How to prepare follow our website.
Board |
Council Of Higher Secondary Education (COHSEM) |
Topic |
Syllabus |
Subject |
Maths |
How to download Manipur Class 12 Syllabus 2024-25 – Maths?
- Step 1: Open your browser
- Step 2: Type cohsem.nic.in
- Step 3: Go to the Syllabus link active on the left panel of the home page of the website (Syllabus for Classes XI – XII).
- Step 4: Click on Class 12 Syllabus link 2024
Class 12 Maths
Units | Unitwise Weightage | Marks | Periods |
I | Relations and Functions [10 marks] | ||
(1) Relations and Functions | 5 | 9 | |
(2) Inverse Trigonometric Functions | 5 | 9 | |
II | Algebra [13 marks] | ||
(1) Matrices | 7 | 13 | |
(2) Determinants | 6 | 11 | |
III | Calculus [44 marks] | ||
(1) Continuity and Differentiability | 10 | 18 | |
(2) Applications of Derivatives | 8 | 14 | |
(3) Integrals | 14 | 26 | |
(4) Applications of Integrals | 4 | 7 | |
(5) Differential Equations | 8 | 14 | |
IV | Vectors and Three Dimensional Geometry [17 marks] | ||
(1) Vectors | 8 | 14 | |
(2) Three dimensional Geometry | 9 | 16 | |
V | Linear Programming [06 marks] | 6 | 11 |
VI | Probability [10 marks] | 10 | 18 |
Total: | 100 | 180 |
Unit-I: Relations and Functions
(1) Relations and Functions:
Relation in a set. Types of relations, reflexive, symmetric, transitive and equivalence relations. Types of functions, injective (one-one), subjective (onto), bijective functions. Inverse of a function.
(2) Inverse Trigonometric Functions :
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.
Unit-II: 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. Non-commutativity of multiplication of matrices and existence of nonzero matrices whose product is the zero matrix (restrict to square matrices of order 2)
Determinants:
Determinant of a square matrix (upto 3×3 matrices), 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 examples, 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:
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.
(2) Applications 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).
(3) Integrals:
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated.
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
(4) Applications of Integrals:
Application in finding the area under simple curves, especially lines, areas of circles, parabolas/ellipses (in standard form only), area under the curves y = sin x, y = cos x, etc. (the region should be clearly identifiable).
(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, homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type:
dy/dx + p(x)y = q(x), where p(x) and q(x) are functions of x and
dx/dy + p(y) = q(y), where p(y) and q(y) are functions of y
Unit-IV: Vectors and Three dimensional Geometry
(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.
(2) Three-dinensional Geometry:
Direction cosines, direction ratios. Cartesian and Vector equation of a line, Coplanar lines, Skew lines, Shortest distance between two lines. Cartesian and Vector equation of a plane. Angle between Two Lines. Conditions for perpendicularity and parallelism.
Unit-V: Linear Programming
(1) Linear Programming:
Introduction, definition of related terminology such as constraints, objective function, optimization.
Unit-VI: Probability
(1) Probability:
Multiplication theorem on probability, Conditional probability, independent events, total probability, Baye’s theorem.
Design of Question Paper
Here on this page we have uploaded Maths subject syllabus 2024. You can download the complete syllabus from the link mentioned below: