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CBSE Class 12 · Mathematics (041)

CBSE Class 12 Maths revision, chapter by chapter

Revision notes, original board-style questions with the step marks shown, and a four-step Route to 95 for every chapter. In the 80-mark board paper, Calculus carries 35 marks and Vectors and Three-Dimensional Geometry 14, so those chapters repay revision first.

  • 13 of 13 chapters ready
  • 690 questions, each checked twice
  • Board paper: 80 marks, 3 hours, sections A to E

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Probability · Section C style · 3 marks

A fair coin is tossed twice and X is the number of tails. Find the probability distribution of X and its mean.

Worked answer

Answer: 14,12,14; mean 1

X takes the values 0,1,2 M1
P(X=0)=14, P(X=1)=12, P(X=2)=14 A1
Mean =0×14+1×12+2×14=1 A1

More Probability important questions →

The Route to 95 planSample papers 2026-27MCQ and case studies

Every Class 12 formula on one page: CBSE Class 12 Maths formula sheet (free PDF) · Three questions a day: CBSE Class 12 Maths Question of the Day

Class 12 formulas, one page each with the CBSE chapter, worked examples and the common mistakes: Derivative of sin x · Integration by parts · Power rule · Bayes' theorem · Magnitude of a vector · all formulas A–Z

Before the board exam: step marking: how to set out answers so no mark slips · CBSE board exam dates

Chapters

In NCERT order, the order most schools teach. Every chapter has notes, practice by step, four checkpoints and the places marks are usually lost. Each card counts its questions by marks (as in sections A to E of the paper) and by difficulty, from 1 (easy) to 4 (HOTS).

Chapter 1 · Relations and FunctionsRelations and Functions42 questions · 4 route steps · about 12 hoursCovers: Relations; Equivalence classes; Functions1 mark: 16 · 2 marks: 9 · 3 marks: 9 · 4 marks: 3 · 5 marks: 5Difficulty 1: 6 · 2: 17 · 3: 13 · 4: 6Chapter 2 · Relations and FunctionsInverse Trigonometric Functions47 questions · 4 route steps · about 10 hoursCovers: Principal value branches; Graphs; Compositions1 mark: 19 · 2 marks: 10 · 3 marks: 14 · 4 marks: 3 · 5 marks: 1Difficulty 1: 7 · 2: 20 · 3: 14 · 4: 6Chapter 3 · AlgebraMatrices63 questions · 4 route steps · about 7 hoursCovers: Order, construction and types; Operations; Transpose, symmetric and skew-symmetric matrices; Invertible matrices1 mark: 24 · 2 marks: 17 · 3 marks: 13 · 4 marks: 4 · 5 marks: 5Difficulty 1: 13 · 2: 28 · 3: 16 · 4: 6Chapter 4 · AlgebraDeterminants58 questions · 4 route steps · about 8 hoursCovers: Evaluating determinants; Area of a triangle and collinearity; Adjoint and inverse; Linear systems AX = B1 mark: 21 · 2 marks: 15 · 3 marks: 12 · 4 marks: 3 · 5 marks: 7Difficulty 1: 8 · 2: 29 · 3: 15 · 4: 6Chapter 5 · CalculusContinuity and Differentiability73 questions · 4 route steps · about 20 hoursCovers: Continuity; Differentiability; Rules; Inverse-trig simplification; Board tips1 mark: 23 · 2 marks: 20 · 3 marks: 20 · 4 marks: 4 · 5 marks: 6Difficulty 1: 13 · 2: 34 · 3: 20 · 4: 6Chapter 6 · CalculusApplication of Derivatives43 questions · 4 route steps · about 16 hoursCovers: Rate of change; Increasing and decreasing functions; Local maxima and minima; Absolute extrema on [a, b]; Optimisation strategy1 mark: 14 · 2 marks: 9 · 3 marks: 10 · 4 marks: 4 · 5 marks: 6Difficulty 1: 5 · 2: 19 · 3: 13 · 4: 6Chapter 7 · CalculusIntegrals67 questions · 4 route steps · about 28 hoursCovers: Standard integrals; Special forms; Techniques; Definite integrals; Board tips1 mark: 21 · 2 marks: 18 · 3 marks: 18 · 4 marks: 4 · 5 marks: 6Difficulty 1: 12 · 2: 32 · 3: 17 · 4: 6Chapter 8 · CalculusApplication of Integrals47 questions · 4 route steps · about 12 hoursCovers: What is in the syllabus; Key results; Method (write these steps in the exam)1 mark: 16 · 2 marks: 10 · 3 marks: 12 · 4 marks: 3 · 5 marks: 6Difficulty 1: 8 · 2: 17 · 3: 15 · 4: 7Chapter 9 · CalculusDifferential Equations50 questions · 4 route steps · about 16 hoursCovers: Order and degree; Solutions1 mark: 18 · 2 marks: 10 · 3 marks: 13 · 4 marks: 3 · 5 marks: 6Difficulty 1: 9 · 2: 19 · 3: 16 · 4: 6Chapter 10 · Vectors and Three-Dimensional GeometryVector Algebra49 questions · 4 route steps · about 7 hoursCovers: Basics; Section formula; Scalar (dot) product; Vector (cross) product1 mark: 19 · 2 marks: 13 · 3 marks: 10 · 4 marks: 3 · 5 marks: 4Difficulty 1: 10 · 2: 21 · 3: 12 · 4: 6Chapter 11 · Vectors and Three-Dimensional GeometryThree Dimensional Geometry46 questions · 4 route steps · about 7 hoursCovers: Direction cosines and ratios; Equation of a line; Angle between two lines; Shortest distance1 mark: 15 · 2 marks: 11 · 3 marks: 11 · 4 marks: 3 · 5 marks: 6Difficulty 1: 5 · 2: 16 · 3: 19 · 4: 6Chapter 12 · Linear ProgrammingLinear Programming49 questions · 4 route steps · about 4 hoursCovers: Terminology and formulation; Feasible region and corner points; Corner-point method1 mark: 17 · 2 marks: 10 · 3 marks: 14 · 4 marks: 3 · 5 marks: 5Difficulty 1: 9 · 2: 21 · 3: 13 · 4: 6Chapter 13 · ProbabilityProbability56 questions · 4 route steps · about 7 hoursCovers: Conditional probability and multiplication theorem; Independent events; Total probability and Bayes’ theorem; Random variable and its mean1 mark: 18 · 2 marks: 13 · 3 marks: 15 · 4 marks: 4 · 5 marks: 6Difficulty 1: 10 · 2: 21 · 3: 19 · 4: 6

Each chapter on one page: Class 12 knowledge organisers (key facts, formulas, mistakes to avoid). Section E practice: Class 12 case study questions, chapter-wise. Exam technique: competency-based questions · theorems and proofs · the last 30 days. Where you stand: Class 12 baseline test · 12-day pre-board revision plan · 4-week pre-board plan.

Where the 80 marks come from

CBSE publishes marks by unit, not by chapter (curriculum 2025-26, unchanged for 2026-27). The other 20 marks are internal assessment.

UnitMarksChapters
Relations and Functions8Relations and Functions, Inverse Trigonometric Functions
Algebra10Matrices, Determinants
Calculus35Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations
Vectors and Three-Dimensional Geometry14Vector Algebra, Three Dimensional Geometry
Linear Programming5Linear Programming
Probability8Probability

Every topic in every chapter, to tick off as you go: CBSE Class 12 Maths syllabus 2026-27 checklist (printable).

Examiner Insights: common mistakes in CBSE Class 12 Maths, with fixes (our analysis of public sources) →

Exam season: 12-day pre-board revision plan · Final exam countdown · Results day: what next? · All exam-season plans

How each chapter works

Step 1

Secure the basics

The one-mark questions of Section A: multiple choice and assertion–reason.

Step 2

Board standard

The two- and three-mark questions of Sections B and C.

Step 3

Full marks on long answers

Five-mark answers and case studies (Sections D and E), written so no step mark slips.

Step 4

95+ stretch

The harder items that separate 95 from 90.

Each step ends in a 3 to 4 question checkpoint. Pass at 80% to move on; results are saved to your Route to 95 and to a linked parent's dashboard.

Also sitting JEE or CUET? See JEE and CUET maths for CBSE students: which chapters each exam uses, and practice in each exam's style.

Beyond the syllabus: the maths olympiad route (IOQM to IMO) with original IOQM-level practice sets, and competition-style problems for Class 12.

Parents: create a free account · Got a class code? Join your teacher's class

Sample papers on the 2026-27 pattern

When the chapters are secure, sit full papers against the clock: 80 marks, 38 questions, sections A to E, with a step-marking scheme. Original papers written to the CBSE pattern by us, not official CBSE papers.

Sample paper 1 · Board standardSample paper 2 · Board standardSample paper 3 · Above boardSample paper 4 · Above boardSample paper 5 · 95+ challengeAll sample papers

Before the exam: Class 12 exam strategy, on step marking, the last 30 days, competency-based questions and proofs.

Board exam 2027: Class 12 important questions, chapter-wise, ordered by the unit weightage so you revise the heaviest units first.

Section A practice: Class 12 assertion–reason questions, one for every chapter.

Done them all? Take a timed full mock, a new 80-mark paper in the board pattern each time, or a 30-mark timed test on one chapter (CBSE Pro or the free trial).

What's free

What is free for Class 12 without signing in?

The revision notes for every chapter, the important questions on each chapter page (half with their worked answers open), the MCQ and case-study sets, and our sample papers.

What does a free account add?

A free account (no card) adds 5 more practice questions on every chapter with instant feedback, full worked answers on free questions, and marking schemes for our sample papers. Every question in the chapter banks with its marking scheme is part of CBSE Pro.