Maths formula sheet

49 formulas you'll actually use, chapter by chapter. Search for any of them.

Updated 28 October 2026Free · no sign-up

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Quadratics and sequences

Roots: x = (−b ± √(b² − 4ac)) / 2a
Sum and product of roots: α + β = −b/a, αβ = c/a
AP sum: Sₙ = n/2 [2a + (n − 1)d]
GP sum: Sₙ = a(rⁿ − 1)/(r − 1)
Infinite GP (|r| < 1): S = a/(1 − r)
Σn, Σn²: n(n+1)/2, n(n+1)(2n+1)/6

Permutations and binomial

Permutations: ⁿPᵣ = n! / (n − r)!
Combinations: ⁿCᵣ = n! / (r!(n − r)!)
General term: Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ
Sum of coefficients: 2ⁿ

Trigonometry

Pythagorean identity: sin²x + cos²x = 1
sin(A ± B): sin A cos B ± cos A sin B
cos(A ± B): cos A cos B ∓ sin A sin B
tan(A + B): (tan A + tan B)/(1 − tan A tan B)
Double angle: sin 2x = 2 sin x cos x, cos 2x = 1 − 2sin²x
Sine rule: a/sin A = b/sin B = c/sin C = 2R
Cosine rule: c² = a² + b² − 2ab cos C

Coordinate geometry

Distance: √((x₂ − x₁)² + (y₂ − y₁)²)
Section formula: ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
Point to line distance: |ax₁ + by₁ + c| / √(a² + b²)
Circle centre and radius: x² + y² + 2gx + 2fy + c = 0 → (−g, −f), √(g² + f² − c)
Parabola y² = 4ax: focus (a, 0), directrix x = −a
Ellipse eccentricity: e = √(1 − b²/a²)
Hyperbola eccentricity: e = √(1 + b²/a²)

Limits and derivatives

Standard limit: lim x→0 (sin x)/x = 1
e as a limit: lim x→0 (1 + x)^(1/x) = e
Power rule: d/dx xⁿ = nxⁿ⁻¹
Trig derivatives: d/dx sin x = cos x, d/dx tan x = sec²x
Exp and log: d/dx eˣ = eˣ, d/dx ln x = 1/x
Product rule: (uv)′ = u′v + uv′
Quotient rule: (u/v)′ = (u′v − uv′)/v²

Integrals

Power: ∫xⁿ dx = xⁿ⁺¹/(n + 1) + C
Reciprocal: ∫1/x dx = ln|x| + C
Inverse tan: ∫1/(1 + x²) dx = tan⁻¹x + C
By parts: ∫u v dx = u∫v dx − ∫(u′∫v dx) dx
King's property: ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a − x) dx

Vectors and 3D

Dot product: a · b = |a||b| cos θ
Cross product size: |a × b| = |a||b| sin θ
Scalar triple product: [a b c] = a · (b × c)
Point to plane distance: |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c²)

Probability and matrices

Addition rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Conditional: P(A|B) = P(A ∩ B) / P(B)
Binomial distribution: P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ
Binomial mean, variance: np, npq
Inverse of a matrix: A⁻¹ = adj A / |A|
Determinant of product: |AB| = |A||B|

Complex numbers

Modulus: |a + ib| = √(a² + b²)
De Moivre: (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ
Cube roots of unity: 1 + ω + ω² = 0, ω³ = 1

How to use this sheet

This is the core list for JEE Main Maths: 49 formulas across 9 chapters, written the way you'd use them in a problem. Revise one chapter a day in the last month, and test yourself in Formula Sprint; recalling a formula in two seconds is very different from recognising it.

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Questions students ask

Which maths formulas are most important for JEE Main?

The ones used across chapters: kinematics, energy conservation and Ohm's law in Physics; mole concept and equilibrium in Chemistry; quadratics, trigonometry and integration in Maths.

Is this formula sheet enough for revision?

It covers the formulas most often used in JEE Main and NEET. Use your NCERT and coaching notes for derivations and special cases.