JEE Mathematics Formula Sheet 2026

x = (−b ± √(b²−4ac)) / 2a

D = b² − 4ac

D>0: real roots, D=0: equal, D<0: complex

α + β = −b/a

αβ = c/a

aₙ = a + (n−1)d

Sₙ = n/2[2a + (n−1)d] = n/2(a + l)

aₙ = arⁿ⁻¹

Sₙ = a(rⁿ−1)/(r−1)

S∞ = a/(1−r)

|r| < 1

AM ≥ GM: (a+b)/2 ≥ √(ab)

e^(iθ) = cosθ + i sinθ

|z| = √(x² + y²)

arg(z) = tan⁻¹(y/x)

||z₁| − |z₂|| ≤ |z₁ + z₂| ≤ |z₁| + |z₂|

A⁻¹ = (1/det A)[d, −b; −c, a]

Expand along any row/column

ⁿPᵣ = n!/(n−r)!

ⁿCᵣ = n!/[r!(n−r)!]

(a+b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ

T(r+1) = ⁿCᵣ · aⁿ⁻ʳ · bʳ

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

sin(A±B) = sinA cosB ± cosA sinB

cos(A±B) = cosA cosB ∓ sinA sinB

sin2A = 2sinA cosA; cos2A = cos²A − sin²A

sin²(A/2) = (1−cosA)/2; cos²(A/2) = (1+cosA)/2

a/sinA = b/sinB = c/sinC = 2R

c² = a² + b² − 2ab cosC

Δ = ½ab sinC = √(s(s−a)(s−b)(s−c))

sin⁻¹x + cos⁻¹x = π/2; tan⁻¹x + cot⁻¹x = π/2

d = √((x₂−x₁)² + (y₂−y₁)²)

(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)

y = mx + c

tanθ = |(m₁−m₂)/(1+m₁m₂)|

d = |ax₁ + by₁ + c| / √(a² + b²)

x² + y² + 2gx + 2fy + c = 0; center(−g,−f), r=√(g²+f²−c)

y² = 4ax; focus(a,0), directrix x = −a

x²/a² + y²/b² = 1; e = √(1−b²/a²)

x²/a² − y²/b² = 1; e = √(1+b²/a²)

y = mx + a/m

y = mx ± √(a²m²+b²)

LR = 2b²/a

a⃗ · b⃗ = |a||b|cosθ = a₁b₁ + a₂b₂ + a₃b₃

|a⃗ × b⃗| = |a||b|sinθ

[a⃗ b⃗ c⃗] = a⃗ · (b⃗ × c⃗)

Volume of parallelepiped

proj = (a⃗ · b⃗)/|b⃗|

ax + by + cz = d; normal = (a, b, c)

d = |ax₁ + by₁ + cz₁ − d| / √(a²+b²+c²)

(x−x₁)/a = (y−y₁)/b = (z−z₁)/c

lim f(x)/g(x) = lim f'(x)/g'(x)

For 0/0 or ∞/∞

lim (sinx/x) = 1; lim ((1+1/n)^n) = e

d/dx(xⁿ) = nxⁿ⁻¹

(uv)' = u'v + uv'

(u/v)' = (u'v − uv')/v²

dy/dx = dy/du · du/dx

d/dx(ln x) = 1/x; d/dx(eˣ) = eˣ

d/dx(sinx) = cosx; d/dx(cosx) = −sinx; d/dx(tanx) = sec²x

f'(x) = 0 and f''(x) > 0 → minima; f''(x) < 0 → maxima

∫u·v dx = u∫v dx − ∫(u'∫v dx)dx

ILATE rule

∫f(g(x))g'(x)dx = ∫f(t)dt

∫ₐᵇ f(x)dx = F(b) − F(a)

A = ∫ₐᵇ |f(x)| dx

A = ∫ₐᵇ |f(x) − g(x)| dx

∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx

dy/dx + P(x)y = Q(x); IF = e^(∫P dx)

f(y)dy = g(x)dx

P(A∪B) = P(A) + P(B) − P(A∩B)

P(A|B) = P(A∩B)/P(B)

P(A|B) = P(B|A)P(A)/P(B)

P(X=r) = ⁿCᵣ pʳ qⁿ⁻ʳ

q = 1−p

μ = np; σ² = npq

x̄ = Σxᵢ/n

σ² = Σ(xᵢ − x̄)²/n = Σxᵢ²/n − x̄²

σ = √(variance)