Class 12 Maths Syllabus: CBSE Units, Marks and Chapter Topics

Unit-wise marks in the latest syllabus

These unit marks have stayed the same across recent sessions. Your school awards the 20 internal marks for periodic tests and maths activities. Applied Mathematics (241) is a separate subject with its own syllabus, so check which one your school has registered you for.

Class 12 maths syllabus chapter by chapter

Unit I: Relations and Functions

• Relations and functions: reflexive, symmetric and transitive relations, equivalence relations; one-one and onto functions
• Inverse trigonometric functions: definition, domain, range, principal value branch and graphs

Unit II: Algebra

• Matrices: order, types, equality, transpose, symmetric and skew symmetric matrices, addition and multiplication, invertible matrices (mainly of order 2 and 3)
• Determinants: up to order 3, minors and cofactors, adjoint and inverse, area of a triangle, solving linear equations with the matrix method and testing consistency

Unit III: Calculus

• Continuity and differentiability: chain rule, derivatives of inverse trigonometric, implicit, exponential and logarithmic functions, logarithmic differentiation, parametric forms, second order derivatives
• Applications of derivatives: rate of change, where a function rises or falls, and finding maximum and minimum values with the first and second derivative tests
• Integrals: substitution, partial fractions, integration by parts, standard forms, definite integrals and their properties, the fundamental theorem of calculus
• Applications of integrals: area under simple curves such as lines, circles, parabolas and ellipses in standard form
• Differential equations: order and degree, general and particular solutions, variables separable, homogeneous equations, linear equations of the form dy/dx + Py = Q

Unit IV: Vectors and Three Dimensional Geometry

• Vectors: magnitude and direction, direction cosines and ratios, types of vectors, section formula, scalar (dot) and vector (cross) products, projection
• Three dimensional geometry: direction cosines of a line, vector and Cartesian equations of a line, angle between two lines, skew lines and the shortest distance between them

Unit V: Linear Programming

• Formulating problems, graphical method in two variables, feasible and infeasible regions, optimal solutions

Unit VI: Probability

• Conditional probability, multiplication theorem, independent events, total probability, Bayes' theorem, a random variable with its distribution, mean of a random variable

How the board paper is designed

CBSE frames the paper around skills as well as chapters. The latest design asks for about 55% of marks on remembering and understanding, 25% on applying, and 20% on analysing, evaluating and creating.

What to focus on first

• Integrals and their applications are the single largest scoring block. Practise every standard form until you can recognise it in seconds.
• Matrices and determinants are short and predictable; they reward neat working more than cleverness.
• Probability questions, especially Bayes' theorem, often appear as long or case-study questions. Draw a tree diagram every time.
• Linear programming is only 5 marks but nearly risk free if you draw the graph carefully and check every corner point.
• Three dimensional geometry long answers usually test shortest distance or angle between lines; learn the vector forms.

Twelve weeks to the board exam: a maths routine

1. Weeks 1 to 4: calculus only, chapter by chapter in NCERT order, finishing every exercise and the miscellaneous exercise.
2. Weeks 5 and 6: matrices, determinants, relations and inverse trigonometry.
3. Weeks 7 and 8: vectors, 3D geometry and linear programming.
4. Week 9: probability, with extra Bayes' theorem problems.
5. Weeks 10 to 12: one full sample paper every two days, timed at three hours, then rework every mark you lost.

Books and practice

The NCERT textbook (Parts I and II) and its exemplar problems are the base for the board exam; most board questions are close to NCERT exercises in style. Add the official sample papers and CBSE class 12 previous papers for timing. Students aiming for engineering entrance alongside boards will find that the JEE Main syllabus builds on the same chapters with harder problems.