CBSE Class 12 Mathematics Important Topics 2027
Every topic ranked by how often and how recently it was asked in 5 board + 2 official sample papers (2022–2026). Blue = board paper, green = sample paper.
Top 10 most important topics
| # | Topic | Chapter | Asked in | Importance |
|---|---|---|---|---|
| 1 | Maxima and minima (first and second derivative tests, absolute maximum/minimum) | Applications of Derivatives | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★★ |
| 2 | Graphical solution and optimal value at corner points (bounded and unbounded regions) | Linear Programming | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 3 | Scalar (dot) product and projection of a vector | Vectors | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 4 | Area under simple curves (lines, circles, parabolas and ellipses in standard form) | Applications of the Integrals | Board 2022Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 5 | Equation of a line in space (vector and Cartesian form) | Three-dimensional Geometry | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 6 | Types of relations: reflexive, symmetric, transitive and equivalence relations | Relations and Functions | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 7 | Total probability theorem and Bayes' theorem | Probability | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 8 | Rate of change of quantities | Applications of Derivatives | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 9 | Differentiability; derivatives of composite, implicit and inverse trigonometric functions | Continuity and Differentiability | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 10 | Conditional probability | Probability | Board 2022Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
Chapter-wise important topics
Relations and Functions · Relations and Functions
| Types of relations: reflexive, symmetric, transitive and equivalence relations asked 11× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| One-one (injective), onto (surjective) and bijective functions asked 5× | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| Equivalence classes and verifying relation properties asked 2× | Board 2025Sample 2025 | ★☆☆☆☆ |
Inverse Trigonometric Functions · Relations and Functions
| Definition, domain, range and principal value branch of inverse trigonometric functions asked 6× | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Finding principal values and simplifying inverse trigonometric expressions asked 6× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Graphs of inverse trigonometric functions asked 4× | Board 2024Board 2025Sample 2025Sample 2026 | ★☆☆☆☆ |
| Properties of inverse trigonometric functions asked 1× | Board 2026 | ★☆☆☆☆ |
Matrices · Algebra
| Addition, scalar multiplication and multiplication of matrices asked 6× | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★☆☆☆☆ |
| Transpose of a matrix; symmetric and skew-symmetric matrices asked 4× | Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| Types of matrices, order and equality of matrices asked 4× | Board 2024Board 2025Board 2026 | ★☆☆☆☆ |
| Invertible matrices and uniqueness of inverse asked 3× | Board 2023Board 2025 | ★☆☆☆☆ |
Determinants · Algebra
| Evaluation and properties of determinants asked 8× | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Solving a system of linear equations by matrix method / consistency asked 6× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Minors, cofactors and adjoint of a matrix asked 4× | Board 2023Board 2025Sample 2025Sample 2026 | ★☆☆☆☆ |
| Inverse of a matrix using adjoint asked 2× | Board 2023Sample 2026 | ★☆☆☆☆ |
| Area of a triangle using determinants asked 1× | Sample 2025 | ★☆☆☆☆ |
Continuity and Differentiability · Calculus
| Differentiability; derivatives of composite, implicit and inverse trigonometric functions asked 12× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Continuity of a function at a point and on an interval asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Derivatives of functions in parametric form and second-order derivatives asked 6× | Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Derivatives of exponential and logarithmic functions and logarithmic differentiation asked 4× | Board 2024Sample 2025Sample 2026 | ★☆☆☆☆ |
Applications of Derivatives · Calculus
| Maxima and minima (first and second derivative tests, absolute maximum/minimum) asked 18× | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★★ |
| Rate of change of quantities asked 13× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Increasing and decreasing functions asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
Integrals · Calculus
| Properties of definite integrals asked 9× | Board 2022Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Integration by substitution asked 8× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Integration by parts and special integrals asked 7× | Board 2022Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Definite integrals and the fundamental theorem of calculus asked 5× | Board 2023Board 2024Board 2025Sample 2026 | ★☆☆☆☆ |
| Integration using partial fractions asked 5× | Board 2022Board 2023Board 2024Board 2026Sample 2026 | ★☆☆☆☆ |
| Integration as the inverse of differentiation and standard integrals asked 1× | Board 2022 | ★☆☆☆☆ |
Applications of the Integrals · Calculus
| Area under simple curves (lines, circles, parabolas and ellipses in standard form) asked 14× | Board 2022Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
Differential Equations · Calculus
| Homogeneous differential equations asked 6× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Linear differential equations asked 6× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| Solution of variables-separable differential equations asked 4× | Board 2023Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| Order and degree; formation of a differential equation asked 4× | Board 2022Board 2023Board 2024Board 2026 | ★☆☆☆☆ |
Vectors · Vectors and Three-Dimensional Geometry
| Scalar (dot) product and projection of a vector asked 14× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Vector (cross) product of two vectors asked 8× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Vectors, types, position vector and direction cosines asked 6× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Addition of vectors, components and section formula asked 5× | Board 2023Board 2025Board 2026 | ★☆☆☆☆ |
Three-dimensional Geometry · Vectors and Three-Dimensional Geometry
| Equation of a line in space (vector and Cartesian form) asked 13× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Shortest distance between two skew lines asked 4× | Board 2022Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| Direction cosines and direction ratios of a line asked 4× | Board 2023Board 2024 | ★☆☆☆☆ |
| Angle between two lines asked 2× | Board 2023Board 2026 | ★☆☆☆☆ |
Linear Programming · Linear Programming
| Graphical solution and optimal value at corner points (bounded and unbounded regions) asked 15× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Formulation of a linear programming problem and feasible region asked 3× | Board 2024Board 2026Sample 2026 | ★☆☆☆☆ |
Probability · Probability
| Total probability theorem and Bayes' theorem asked 11× | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Conditional probability asked 13× | Board 2022Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Multiplication theorem and independent events asked 8× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
Importance = how often a topic was asked × how recent, with extra weight for the latest official sample paper.