JEE Maths Formula Sheet 2025 – Complete List for Main & Advanced

Mathematics is a crucial subject for JEE Main and Advanced. Having all important formulas at your fingertips can save valuable time during the exam. This comprehensive formula sheet covers all topics from Class 11 and 12 that are essential for JEE.

Algebra Formulas

Quadratic Equations

Standard form: ax² + bx + c = 0
Roots: x = (-b ± √(b² – 4ac)) / 2a
Sum of roots (α + β) = -b/a
Product of roots (αβ) = c/a
Discriminant (D) = b² – 4ac
If D > 0: Two distinct real roots
If D = 0: Two equal real roots
If D < 0: Two complex conjugate roots

Arithmetic Progression (AP)

nth term: aₙ = a + (n-1)d
Sum of n terms: Sₙ = n/2 [2a + (n-1)d] = n/2 (a + l)
Common difference: d = aₙ – aₙ₋₁

Geometric Progression (GP)

nth term: aₙ = arⁿ⁻¹
Sum of n terms: Sₙ = a(rⁿ – 1)/(r – 1) when r ≠ 1
Sum of infinite GP (|r| < 1): S∞ = a/(1 – r)

Binomial Theorem

(a + b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ (r = 0 to n)
General term: Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ
ⁿCᵣ = n! / (r!(n-r)!)
Middle term: T₍ₙ₊₂₎/₂ when n is even

Permutation & Combination

ⁿPᵣ = n!/(n-r)!
ⁿCᵣ = n!/(r!(n-r)!)
ⁿCᵣ = ⁿCₙ₋ᵣ
ⁿC₀ + ⁿC₁ + ⁿC₂ + … + ⁿCₙ = 2ⁿ

Trigonometry Formulas

Basic Identities

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
sin(-θ) = -sinθ, cos(-θ) = cosθ

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)

Double Angle Formulas

sin2A = 2sinA cosA
cos2A = cos²A – sin²A = 2cos²A – 1 = 1 – 2sin²A
tan2A = 2tanA/(1 – tan²A)

Half Angle Formulas

sin(A/2) = ±√((1 – cosA)/2)
cos(A/2) = ±√((1 + cosA)/2)
tan(A/2) = (1 – cosA)/sinA = sinA/(1 + cosA)

Product to Sum Formulas

2sinA cosB = sin(A+B) + sin(A-B)
2cosA sinB = sin(A+B) – sin(A-B)
2cosA cosB = cos(A+B) + cos(A-B)
2sinA sinB = cos(A-B) – cos(A+B)

Calculus Formulas

Limits

lim(x→0) sinx/x = 1
lim(x→0) tanx/x = 1
lim(x→0) (eˣ – 1)/x = 1
lim(x→0) (aˣ – 1)/x = ln(a)
lim(x→0) (1 + x)^(1/x) = e
lim(x→∞) (1 + 1/x)ˣ = e

Differentiation

d/dx (xⁿ) = nxⁿ⁻¹
d/dx (eˣ) = eˣ
d/dx (aˣ) = aˣ ln(a)
d/dx (ln x) = 1/x
d/dx (sin x) = cos x
d/dx (cos x) = -sin x
d/dx (tan x) = sec²x
d/dx (cot x) = -cosec²x
d/dx (sec x) = sec x tan x
d/dx (cosec x) = -cosec x cot x

Integration

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1)
∫1/x dx = ln|x| + C
∫eˣ dx = eˣ + 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
∫sec x tan x dx = sec x + C
∫cosec x cot x dx = -cosec x + C

Integration by Parts

∫u dv = uv – ∫v du
Priority order (ILATE): Inverse, Logarithmic, Algebraic, Trigonometric, Exponential

Coordinate Geometry Formulas

Straight Lines

Distance between two points: √((x₂-x₁)² + (y₂-y₁)²)
Section formula (internal): ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
Slope: m = (y₂-y₁)/(x₂-x₁) = tanθ
Slope-intercept form: y = mx + c
Point-slope form: y – y₁ = m(x – x₁)
Two-point form: (y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁)
Intercept form: x/a + y/b = 1
General form: ax + by + c = 0
Distance from point to line: |ax₁ + by₁ + c|/√(a² + b²)
Angle between lines: tanθ = |(m₁-m₂)/(1+m₁m₂)|

Circle

Standard form: (x-h)² + (y-k)² = r²
General form: x² + y² + 2gx + 2fy + c = 0
Center: (-g, -f), Radius: √(g² + f² – c)
Length of tangent from (x₁,y₁): √(x₁² + y₁² + 2gx₁ + 2fy₁ + c)

Parabola

Standard form: y² = 4ax (opens right)
Vertex: (0, 0), Focus: (a, 0)
Directrix: x = -a
Length of latus rectum: 4a

Ellipse

Standard form: x²/a² + y²/b² = 1 (a > b)
Eccentricity: e = √(1 – b²/a²)
Foci: (±ae, 0)
Length of latus rectum: 2b²/a

Hyperbola

Standard form: x²/a² – y²/b² = 1
Eccentricity: e = √(1 + b²/a²)
Foci: (±ae, 0)
Asymptotes: y = ±(b/a)x

Vectors & 3D Geometry

Vector Operations

Magnitude: |a⃗| = √(a₁² + a₂² + a₃²)
Unit vector: â = a⃗/|a⃗|
Dot product: a⃗ · b⃗ = |a⃗||b⃗|cosθ = a₁b₁ + a₂b₂ + a₃b₃
Cross product: |a⃗ × b⃗| = |a⃗||b⃗|sinθ
Scalar triple product: [a⃗ b⃗ c⃗] = a⃗ · (b⃗ × c⃗)

3D Geometry

Distance formula: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)
Direction ratios: (a, b, c)
Direction cosines: l = a/r, m = b/r, n = c/r where r = √(a²+b²+c²)
l² + m² + n² = 1
Equation of plane: ax + by + cz + d = 0
Distance from point to plane: |ax₁ + by₁ + cz₁ + d|/√(a² + b² + c²)

Probability & Statistics

Probability

P(A) = n(A)/n(S)
P(A∪B) = P(A) + P(B) – P(A∩B)
P(A∩B) = P(A) × P(B|A)
P(A’) = 1 – P(A)
Bayes’ theorem: P(A|B) = P(B|A)P(A)/P(B)

Statistics

Mean: x̄ = Σxᵢ/n
Variance: σ² = Σ(xᵢ – x̄)²/n
Standard deviation: σ = √(variance)
Coefficient of variation: CV = (σ/x̄) × 100

Matrices & Determinants

Matrix Operations

(AB)ᵀ = BᵀAᵀ
(AB)⁻¹ = B⁻¹A⁻¹
A⁻¹ = adj(A)/|A|
|adj(A)| = |A|ⁿ⁻¹
|kA| = kⁿ|A| (for n×n matrix)

Determinant Properties

|AB| = |A||B|
|Aᵀ| = |A|
|A⁻¹| = 1/|A|
If any row/column is zero, |A| = 0
Interchanging rows/columns changes sign

Tips for Using This Formula Sheet

Regular Revision: Go through these formulas daily during your preparation
Practice Application: Don’t just memorize – solve problems using each formula
Create Flashcards: Make formula flashcards for quick revision
Understand Derivations: Know how formulas are derived for better retention
Group Similar Formulas: Learn related formulas together

Recommended Books for JEE Maths

RD Sharma for basics
Cengage Mathematics series
Arihant’s Skills in Mathematics
Previous Year JEE Papers

Note: This formula sheet covers the most important formulas for JEE. Always refer to the official JEE syllabus and practice extensively with previous year papers.