Every key formula and result from the Class 10 Maths NCERT syllabus, organised by chapter, in one place. This page grows as we publish Solutions for each chapter — currently covers Chapters 1–3, with more added as they’re completed.
Class 10 Maths Formulas Handbook
Chapter 1: Real Numbers
- Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b
- HCF × LCM = Product of the two numbers (for exactly two numbers)
- Fundamental Theorem of Arithmetic: every composite number has a unique prime factorisation (order aside)
- Proof-of-irrationality method: assume rational (p/q, coprime, q≠0) → derive a common factor in p and q → contradiction
More chapters (Polynomials, Pair of Linear Equations, Quadratic Equations, and the rest of the syllabus) will be added here as their Solutions posts go live — see our full Class 10 coverage.
How to Use This Handbook
Formulas alone won’t get you full marks — CBSE examiners award marks for showing correct working, not just stating a result. Use this page as a quick lookup while solving problems in our Chapter 1 Solutions and Extra Questions, not as a replacement for practicing the full method.
Frequently Asked Questions
Is this handbook complete for the full Class 10 Maths syllabus?
Not yet — it currently covers Chapter 1 (Real Numbers) and will expand chapter by chapter as we publish Solutions for the rest of the book, so check back as more chapters go live.
Can I download this as a PDF?
Not currently — this page is kept live and editable so formulas stay accurate as chapters are added; you’re welcome to bookmark this page or print it directly from your browser.
Chapter 3: Pair of Linear Equations in Two Variables
- General form: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
- Intersecting (unique solution): a₁/a₂ ≠ b₁/b₂
- Parallel (no solution, inconsistent): a₁/a₂ = b₁/b₂ ≠ c₁/c₂
- Coincident (infinite solutions): a₁/a₂ = b₁/b₂ = c₁/c₂
- Methods: substitution, elimination; reciprocal substitution (u = 1/(x−y), v = 1/(x+y)) for speed/time word problems
Chapter 4: Quadratic Equations
- Standard form: ax²+bx+c = 0 (a≠0)
- Quadratic formula: x = [−b±√(b²−4ac)]/2a
- Discriminant D = b²−4ac: D>0 distinct real roots, D=0 equal real roots, D<0 no real roots
- Sum of roots = −b/a, Product of roots = c/a
- Factorisation: split the middle term bx into two terms whose product = a×c×x² and sum = bx
Chapter 5: Arithmetic Progressions
- nth term: aₙ = a + (n−1)d
- Sum (a,d known): Sₙ = (n/2)[2a+(n−1)d] | Sum (a,l known): Sₙ = (n/2)(a+l)
- See full Chapter 5 Solutions
