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NIOS Class 12 Mathematics — Formula Sheet

NIOS Class 12 Mathematics formula sheet, chapter by chapter — 43 formulas across 8 chapters. Follows the NIOS syllabus.

How to Use the Formula Sheet

  1. Write, don't just read — writing each formula out helps it stick.
  2. Understand the derivation — you can rebuild a formula you half-remember.
  3. Group related formulas — link the ones that build on each other.
  4. Test yourself — cover the sheet and write the formulas from memory.

Chapter-Wise Formulas — 8 Chapters

2

Relations and Functions - I

2 entries
Order matters: A × B ≠ B × A (unless A = B or one is empty)
For y = 1/f(x), domain excludes where f(x) = 0
The full Relations and Functions - I formula sheet
3

Trigonometric Functions - I

9 entries
For any point P(x, y) on the unit circle corresponding to angle θ, we define: sin θ = y, cos θ = x.
tan θ = y/x (defined when x ≠ 0), cot θ = x/y (defined when y ≠ 0).
Memory trick for sin values: sin 0 = √(0/4), sin π/6 = √(1/4), sin π/4 = √(2/4), sin π/3 = √(3/4), sin π/2 = √(4/4). Simplify to get 0, 1/2, 1/√2, √3/2, 1.
Cosine values are the reverse: cos 0 = 1, cos π/6 = √3/2, cos π/4 = 1/√2, cos π/3 = 1/2, cos π/2 = 0.
Graph of y = sin θ: starts at 0, rises to maximum 1 at π/2, returns to 0 at π, falls to minimum -1 at 3π/2, returns to 0 at 2π. It is continuous and wave-shaped.
The full Trigonometric Functions - I formula sheet
4

Trigonometric Functions - II

7 entries
Product-to-Sum: 2sinAcosB = sin(A+B) + sin(A−B)
Product-to-Sum: 2cosAsinB = sin(A+B) − sin(A−B)
sin2A = 2sinAcosA = 2tanA/(1+tan²A)
cos2A = cos²A − sin²A = 2cos²A − 1 = 1 − 2sin²A = (1−tan²A)/(1+tan²A)
tan2A = 2tanA/(1−tan²A)
The full Trigonometric Functions - II formula sheet

5 more chapters below

Formula sheets for all 8 chapters with formulas.

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Frequently Asked Questions

Where can I find NIOS Class 12 Mathematics Formula Sheet?

This page has formula sheet for 8 chapters of NIOS Class 12 Mathematics for the board exams 2027. Each chapter links to its own page with the full set.

Go through the syllabus first, then work chapter by chapter: learn the ideas, practise questions, and revise with notes and flashcards. Leave time at the end to revise every chapter once more under timed conditions.

Learn the formulas you use most first, and understand what each symbol means so you can apply them. Knowing where a formula comes from helps you rebuild it if you forget it in the exam.

Browse Formula Sheet by Chapter

8 chapters

2

Relations and Functions - I

3

Trigonometric Functions - I

4

Trigonometric Functions - II

5

Relations Between Sides and Angles of a Triangle

6

Sequences and Series

7

Some Special Sequences

8

Complex Numbers

9

Quadratic Equations and Linear Inequalities

More Mathematics Resources

NIOS Class 12

Practice Quiz

Test yourself with quick quizzes

Important Questions

Exam-style questions with answers

Revision Notes

Key concepts and quick revision points

Chapter Summary

Understand each chapter at a glance

Concept Maps

Diagrams showing how topics connect

Flashcards

Quick-fire cards for active recall practice

Syllabus

Chapter list and the topics in each

Other NIOS Class 12 Subjects

PhysicsChemistry