MBSE Class 12th Mathematics Syllabus 2024-2025 PDF:- Download Online

Name of the Board

MBSE

Name of the Grade

12

Subjects

Mathematics

Year

2024-2025

Format

PDF/DOC

Provider

hsslive.co.in

Official Website

mbose.in

• Types of relations: Reflexive, symmetric, transitive, and equivalence relations.
• One to one and onto functions, composite functions inverse of a function binary operations.

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

• 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 (restricted to square matrices of order 2).
• Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

• Determinant of a square matrix (up to 3 x 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.
• Consistent inconsistency and number of solutions of a system of linear equations by examples, solving systems of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

• Continuity and differentiability, the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions.
• Derivatives of loge x and ex.
• Logarithmic differentiation.
• Derivative of functions expressed in parametric forms.
• Second-order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.

• Applications of derivatives: Rate of change, increasing/decreasing functions, tangents, and normals, approximation, 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).

• Integration as an 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. Definite integrals as a limit of 1a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

• Applications in finding the area under simple curves, especially lines, arcs of circles/ parabolas/ellipses (in standard form. only), area between the two above said curves (the region should be clearly identifiable).

• Definition, order, and degree, general and particular solutions of a differential equation. Formation of differential equations whose general solution is given.
• Solution of differential equations by the method of separation of variables; homogeneous differential equations of the first order and first degree.
• Solutions of linear differential equation of the type —

UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

• 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, the 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, scalar triple product.

• Direction cosines/ratios of a line joining two points.
• Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines.
• Cartesian and vector equation of a plane.
• The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

• Introduction, related terminology such as constraints, objective function, optimisation, different types of linear programming (L.P.) problems, mathematical formulation of LP.
• Problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

• Multiplications theorem on probability.
• Conditional probability, independent events, total probability
• Bayes-theorem Random variable, and its probability distribution, mean, and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution