Mathematics

Mathematics — Class 12

CBSE (Indian Curriculum) · Ages 17-18

CBSE Class 12 Mathematics is a board examination subject and a prerequisite for engineering and most quantitative degrees. Calculus dominates the paper.

Content covers relations and functions, inverse trigonometric functions, matrices and determinants, continuity and differentiability, applications of derivatives, integrals and their applications, differential equations, vectors, three-dimensional geometry, linear programming and probability.

Integration alone carries the largest share of marks and is where preparation succeeds or fails. Students taking JEE alongside cover the same ground at greater depth, so board preparation and entrance preparation reinforce each other if planned together.

Key topics covered

• Relations & FunctionsTypes of relations, composition, invertibility and inverse trigonometry.
• Matrices & DeterminantsOperations, inverse, adjoint, and solving systems of linear equations.
• Continuity & DifferentiabilityContinuity, differentiability, chain rule, and implicit and logarithmic differentiation.
• Applications of DerivativesRate of change, tangents, normals, maxima, minima and optimisation.
• IntegralsIndefinite and definite integration, substitution, by parts and partial fractions.
• Differential EquationsOrder, degree, variable separable, homogeneous and linear equations.
• Vectors & 3D GeometryVector algebra, scalar and vector products, lines and planes in space.
• Linear Programming & ProbabilityGraphical LP, conditional probability, Bayes' theorem and distributions.