JEE Mains weightage (typical):
  Algebra:         30% (Complex numbers, Matrices, Sequences)
  Calculus:        25% (Limits, Derivatives, Integrals)
  Coordinate Geometry: 20% (Lines, Circles, Conics)
  Vectors & 3D:   10%
  Trigonometry:   10%
  Probability:     5%

Complex Numbers:
  z = a + bi, |z| = √(a²+b²)
  Euler: e^(iθ) = cos θ + i sin θ
  De Moivre: (cos θ + i sin θ)^n = cos nθ + i sin nθ
  Cube roots of unity: 1, ω, ω² where ω = e^(2πi/3)

Sequences & Series:
  AP: nth term = a + (n-1)d, Sum = n/2[2a + (n-1)d]
  GP: nth term = ar^(n-1), Sum = a(1-r^n)/(1-r), r≠1
  Sum of infinite GP: a/(1-r), |r| < 1
  1+2+...+n = n(n+1)/2
  1²+2²+...+n² = n(n+1)(2n+1)/6

Binomial Theorem:
  (a+b)^n = Σ C(n,r) a^(n-r) b^r
  General term: T(r+1) = C(n,r) a^(n-r) b^r

Trigonometry:
  sin²θ + cos²θ = 1
  sin(A±B) = sinA cosB ± cosA sinB
  cos(A±B) = cosA cosB ∓ sinA sinB
  tan(A+B) = (tanA + tanB)/(1 - tanA tanB)
  sin 2θ = 2 sinθ cosθ
  cos 2θ = cos²θ - sin²θ = 1 - 2sin²θ = 2cos²θ - 1

Limits:
  lim(x→0) sin x/x = 1
  lim(x→0) (1+x)^(1/x) = e
  lim(x→∞) (1 + 1/x)^x = e
  L'Hôpital's rule for 0/0 or ∞/∞ forms

Differentiation:
  d/dx(x^n) = nx^(n-1)
  d/dx(e^x) = e^x
  d/dx(ln x) = 1/x
  d/dx(sin x) = cos x
  Chain rule: d/dx f(g(x)) = f'(g(x))·g'(x)

Integration:
  ∫x^n dx = x^(n+1)/(n+1) + C
  ∫e^x dx = e^x + C
  ∫sin x dx = -cos x + C
  ∫cos x dx = sin x + C
  Integration by parts: ∫u dv = uv - ∫v du