12th Syllabus of MP Board Maths

The syllabus for MP Board Class 12 Maths for the academic year 2025-2026 generally includes the following units:

Relations and Functions
- Types of relations: Reflexive, symmetric, transitive, and equivalence relations.
- One to one and onto functions, composite functions, and inverse of a function.
Inverse Trigonometric Functions
- Definition, range, domain, principal value branches.
- Graphs of inverse trigonometric functions.

Matrices
- Concept, notation, order, equality, types of matrices.
- Operations on matrices: Addition, multiplication, and scalar multiplication.
- Transpose of a matrix, symmetric and skew-symmetric matrices.
- Invertible matrices and proof of uniqueness of inverse.
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.
- Applications in solving a system of linear equations (in two or three variables) using inverse of a matrix.

Continuity and Differentiability
- Continuity and differentiability.
- Derivatives of composite functions, chain rule, derivatives of inverse trigonometric functions, implicit functions.
- Concept of exponential and logarithmic functions and their derivative.
- Logarithmic differentiation.
- Derivatives of functions expressed in parametric forms.
- Second order derivatives.
Applications of Derivatives
- 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).
Integrals
- Integration as inverse process of differentiation.
- Integration of a variety of functions by substitution, by partial fractions, and by parts.
- Evaluation of simple integrals.
- Fundamental theorem of calculus.
- Basic properties of definite integrals and evaluation of definite integrals.
Applications of Integrals
- Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only).
Differential Equations
- Definition, order and degree, general and particular solutions of a differential equation.
- Formation of differential equation whose general solution is given.
- Solution of differential equations by method of separation of variables.
- Homogeneous differential equations of first order and first degree.
- Solutions of linear differential equations.

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.
Three-dimensional Geometry
- Direction cosines/ratios of a line joining two points.
- Cartesian and vector equation of a line, coplanar and skew lines.
- Shortest distance between two lines.
- Cartesian and vector equation of a plane.
- Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.
- Distance of a point from a plane.

Linear Programming
- Introduction, related terminology such as constraints, objective function, optimization.
- Different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions.

Probability
- Conditional probability, multiplication theorem on probability.
- Independent events, total probability, Bayes’ theorem.
- Random variable and its probability distribution, mean and variance of a random variable.
- Repeated independent (Bernoulli) trials and Binomial distribution.