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Karnataka Board Class 10 Mathematics — Formula Sheet

Karnataka Board Class 10 Mathematics formula sheet, chapter by chapter — 36 formulas across 8 chapters. Follows the KSEEB / PUE 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

1

Real Numbers

5 entries
√2, √3, √5, and √p (where p is prime) are all irrational
Example: For 72 = 2³ × 3² and 48 = 2⁴ × 3, HCF = 2³ × 3¹ = 24.
Example: For 72 = 2³ × 3² and 48 = 2⁴ × 3, LCM = 2⁴ × 3² = 144.
For any two positive integers a and b: HCF(a,b) × LCM(a,b) = a × b.
Example: For 72 and 48, HCF = 24, LCM = 144, and 24 × 144 = 72 × 48 = 3456.
The full Real Numbers formula sheet
2

Introduction to Trigonometry

4 entries
Reciprocal relationships: cosec A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A
sin² A + cos² A = 1 (most important and frequently used)
1 + tan² A = sec² A (valid for A ≠ 90°)
Three fundamental identities: (1) sin²A + cos²A = 1 (Pythagorean identity), (2) 1 + tan²A = sec²A, (3) cot²A + 1 = cosec²A.
The full Introduction to Trigonometry formula sheet
3

Polynomials

8 entries
Expressions like 1/x + 1, √x + 2 are NOT polynomials because they contain negative or fractional powers
For quadratic ax² + bx + c with zeros α, β: Sum = -b/a, Product = c/a
A real number k is a zero of polynomial p(x) if p(k) = 0.
For example, if p(x) = x² - 3x - 4, then p(4) = 16 - 12 - 4 = 0, so 4 is a zero.
For quadratic polynomial ax² + bx + c with zeroes α and β: Sum of zeroes: α + β = -b/a.
The full Polynomials 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 Karnataka Board Class 10 Mathematics Formula Sheet?

This page has formula sheet for 8 chapters of Karnataka Board Class 10 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

1

Real Numbers

2

Introduction to Trigonometry

3

Polynomials

5

Pair of Linear Equations in Two Variables

7

Quadratic Equations

9

Arithmetic Progressions

12

Statistics

14

Probability

More Mathematics Resources

Karnataka Board Class 10

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

Flashcards

Quick-fire cards for active recall practice

Syllabus

Chapter list and the topics in each

Other Karnataka Board Class 10 Subjects

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