Class 12 Maths Notes

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Class 12 Maths Notes

One place for all your Class 12 Maths revision, arranged in the official NCERT order. Part 1 (Chapters 1–6) covers relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, and application of derivatives. Part 2 (Chapters 7–13) covers integrals, application of integrals, differential equations, vector algebra, three dimensional geometry, linear programming and probability. Each chapter has key formulas, exam pointers and solved examples alongside the full syllabus overview — written for CBSE boards and JEE Main.

Class:12Subject:MathematicsCovers:CBSE · JEE

9 Key Formulas

DWritten byDeep Narayan

UpdatedSeptember 2026

Key Concept Summary

What is covered in Class 12 Maths?

Class 12 Maths has 13 chapters in two NCERT books. Part 1 covers relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, and application of derivatives. Part 2 covers integrals, application of integrals, differential equations, vector algebra, three dimensional geometry, linear programming and probability.

About the Class 12 Maths Notes

These chapter-wise notes condense the complete Class 12 mathematics syllabus into quick-revision sheets. Each chapter page gives you the essential concepts, the key formulas together, exam pointers for the exam hall, and a quick FAQ answering the most-asked questions.

How to use these notes

Use each chapter page for last-minute revision: read the quick answer, scan the key formulas, then test yourself with the exam pointers. Calculus carries the largest share of board marks, so master continuity, differentiation and integration first.

Follows the NCERT chapter order

The CBSE syllabus is split into two books: Mathematics Part 1 (Chapters 1–6) and Part 2 (Chapters 7–13). This note lists every chapter in that order, so the sequence matches the NCERT book you study from — Relations and Functions through Linear Programming and Probability.

Algebra — Relations, Functions and Matrices (Chapters 1–4)

Relations and Functions — types of relations, one-one and onto functions, composition and invertible functions.
Inverse Trigonometric Functions — principal values and the standard inverse identities.
Matrices — operations, transpose, symmetric and skew-symmetric matrices, invertibility.
Determinants — properties, adjoint and inverse, and solving systems of linear equations.

Dedicated chapter pages

All 13 NCERT chapters now have dedicated pages — jump to any of them from the related links below.

Differential Calculus (Chapters 5–6)

Continuity and Differentiability — the limit definition, the chain, product and quotient rules, logarithmic and implicit differentiation.
Application of Derivatives — rate of change, increasing and decreasing functions, tangents and normals, maxima and minima.

Product and quotient rules

\frac{d}{d x} (uv) = u^{'} v + u v^{'}, \frac{d}{d x} (\frac{u}{v}) = \frac{u ^{'} v - u v ^{'}}{v ^{2}}

Differentiability implies continuity

A differentiable function is always continuous, but a continuous function need not be differentiable — |x| is the classic example. This fact appears directly in board and JEE MCQs.

Integral Calculus (Chapters 7–9)

Integrals — indefinite and definite integrals, substitution, integration by parts and the fundamental theorem of calculus.
Application of Integrals — area under a curve and between two curves.
Differential Equations — order and degree, variable-separable form, and first-order linear equations.

Integration by parts and a symmetric-limit property

\int u d v = uv - \int v d u, \int_{0}^{a} f (x) d x = \int_{0}^{a} f (a - x) d x

Vectors and 3D Geometry (Chapters 10–11)

Vector Algebra — dot and cross products, projection of vectors, and their geometric meaning.
Three Dimensional Geometry — direction cosines, equations of lines and planes, and distance and angle between them.

Dot and cross products

a \cdot b = ∣ a ∣∣ b ∣ cos θ, ∣ a \times b ∣ = ∣ a ∣∣ b ∣ sin θ

Probability and Linear Programming (Chapters 12–13)

Probability — conditional probability, multiplication theorem, Bayes' theorem, random variables and their distributions.
Linear Programming — formulating constraints, the feasible region, and maximising or minimising the objective function.

Bayes' theorem and binomial mean/variance

P (A ∣ B) = \frac{P ( B ∣ A ) P ( A )}{P ( B )}, μ = n p, σ^{2} = n pq

Quick Revision

Key formulas at a glance

Memorise these equations — direct application numericals and derivations in CBSE & JEE frequently hinge on these.

Inverse of a matrix

A^{- 1} = \frac{adj ( A )}{∣ A ∣}

Product of determinants

∣ A B ∣ = ∣ A ∣∣ B ∣

Product rule

(uv)^{'} = u^{'} v + u v^{'}

Quotient rule

(\frac{u}{v})^{'} = \frac{u ^{'} v - u v ^{'}}{v ^{2}}

Second derivative test

f^{''} (a) < 0 \Rightarrow max, f^{''} (a) > 0 \Rightarrow min

Integration by parts

\int u d v = uv - \int v d u

Symmetric-limit property

\int_{0}^{a} f (x) d x = \int_{0}^{a} f (a - x) d x

Bayes' theorem

P (A ∣ B) = \frac{P ( B ∣ A ) P ( A )}{P ( B )}

Binomial mean/variance

μ = n p, σ^{2} = n pq

Exam Strategy

How this chapter is asked

High-yield question patterns observed across CBSE boards, JEE Main & Advanced, and NEET.

A function is invertible iff it is bijective.
A⁻¹ exists iff |A| ≠ 0.
Differentiability implies continuity, but not vice versa.
Second derivative test: f'' < 0 → max, f'' > 0 → min.
Use ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx for symmetric limits.
In linear programming, the optimum lies at a corner point of the feasible region.

FAQ

Frequently asked questions

How many chapters are there in Class 12 Maths?

Exactly 13, split into two NCERT books. Part 1 has 6 chapters — relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, and application of derivatives. Part 2 has 7 — integrals, application of integrals, differential equations, vector algebra, three dimensional geometry, linear programming and probability. This hub links each chapter's dedicated revision notes.

Which Class 12 maths topics are most important for JEE?

Calculus — continuity and differentiability, applications of derivatives and integrals — carries the largest weight, followed by matrices and determinants, vectors and probability. Calculus is the first thing to master for both boards and JEE Main.

What is the hardest topic in Class 12 maths?

Many students find differential equations and the applications of derivatives the most demanding. Break them into small steps, practise the standard forms, and use the key-formulas sections as a quick revision sheet before the exam.

How should I revise Class 12 maths?

Practise the core formulas (inverse of a matrix, product and quotient rules, integration by parts, Bayes' theorem), then solve past board and JEE-style problems using the key-formulas and exam pointers in each chapter page.

Next Chapters

Continue learning

All Class 11 & 12 Notes Class 12 Maths NCERT Solutions Relations and Functions Notes Inverse Trigonometric Functions Notes Matrices Notes Determinants Notes Continuity and Differentiability Notes Application of Derivatives Notes Integrals Notes Application of Integrals Notes Differential Equations Notes Vector Algebra Notes Three Dimensional Geometry Notes Linear Programming Notes Probability Notes Maths Tutor in Mohali

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