JEE Math Formulas - Free Download

📐 Algebra Formulas

Essential algebraic formulas for JEE

1 Quadratic Equations

Standard Form

ax² + bx + c = 0

Solution

x = (-b ± √(b² - 4ac)) / 2a

Discriminant

D = b² - 4ac

D > 0: Real & distinct | D = 0: Equal | D < 0: Complex

Roots Relationship

Sum: α + β = -b/a

Product: αβ = c/a

2 Binomial Theorem

Expansion

(a + b)ⁿ = Σ ⁿCᵣ · aⁿ⁻ʳ · bʳ

General Term

Tᵣ₊₁ = ⁿCᵣ · aⁿ⁻ʳ · bʳ

Middle Term (n even)

T₍ₙ/₂₊₁₎

Middle Terms (n odd)

T₍ₙ₊₁₎/₂ and T₍ₙ₊₃₎/₂

3 Sequences & Series

Arithmetic Progression (AP)

nth term: aₙ = a + (n-1)d

Sum of n terms: Sₙ = n/2[2a + (n-1)d]

Also: Sₙ = n/2(a + l) where l = last term

Geometric Progression (GP)

nth term: aₙ = arⁿ⁻¹

Sum of n terms: Sₙ = a(rⁿ - 1)/(r - 1)

Sum to infinity (|r| < 1): S∞ = a/(1 - r)

📊 Calculus Formulas

Differentiation and Integration formulas

1 Differentiation Rules

d/dx(xⁿ) = nxⁿ⁻¹

d/dx(eˣ) = eˣ

d/dx(ln x) = 1/x

d/dx(aˣ) = aˣ ln a

d/dx(sin x) = cos x

d/dx(cos x) = -sin x

d/dx(tan x) = sec²x

d/dx(cot x) = -cosec²x

Product Rule

d/dx(uv) = u(dv/dx) + v(du/dx)

Quotient Rule

d/dx(u/v) = [v(du/dx) - u(dv/dx)]/v²

Chain Rule

d/dx[f(g(x))] = f'(g(x)) · g'(x)

2 Integration Formulas

∫ xⁿ dx = xⁿ⁺¹/(n+1) + C

∫ eˣ dx = eˣ + C

∫ 1/x dx = ln|x| + C

∫ aˣ dx = aˣ/ln a + C

∫ sin x dx = -cos x + C

∫ cos x dx = sin x + C

∫ sec²x dx = tan x + C

∫ cosec²x dx = -cot x + C

3 Definite Integration Properties

∫ₐᵇ f(x)dx = F(b) - F(a)

∫ₐᵇ f(x)dx = -∫ᵇₐ f(x)dx

King's Property

∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx

📍 Coordinate Geometry

Lines, circles, and conic sections

1 Straight Lines

Slope

m = (y₂-y₁)/(x₂-x₁)

Distance

d = √[(x₂-x₁)² + (y₂-y₁)²]

Section Formula (Internal)

x = (mx₂+nx₁)/(m+n)

y = (my₂+ny₁)/(m+n)

Slope-Intercept Form

y = mx + c

Point-Slope Form

y - y₁ = m(x - x₁)

2 Circle

Standard Form

(x-h)² + (y-k)² = r²

Center: (h,k), Radius: r

General Form

x² + y² + 2gx + 2fy + c = 0

Center: (-g,-f), r = √(g²+f²-c)

3 Parabola

y² = 4ax

Vertex: (0,0), Focus: (a,0), Directrix: x = -a

x² = 4ay

Vertex: (0,0), Focus: (0,a), Directrix: y = -a

📐 Trigonometry

All trigonometric identities and formulas

1 Fundamental Identities

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = cosec²θ

2 Compound Angle Formulas

sin(A±B) = sinA·cosB ± cosA·sinB

cos(A±B) = cosA·cosB ∓ sinA·sinB

tan(A±B) = (tanA ± tanB)/(1 ∓ tanA·tanB)

3 Double & Triple Angle Formulas

Double Angle

sin2θ = 2sinθ·cosθ

Double Angle

cos2θ = cos²θ - sin²θ

tan2θ = 2tanθ/(1 - tan²θ)

➡️ Vectors & 3D Geometry

Vector operations and 3D formulas

1 Vector Operations

Magnitude

|a| = √(x² + y² + z²)

Dot Product

a·b = |a||b|cosθ

Cross Product

a×b = |a||b|sinθ n̂

Complete JEE Math Formulas