CLASS 10: FOUNDATION BUFFS
Quadratic Equations
Roots: x = [-b ± √(b² - 4ac)] / 2a
Discriminant: D = b² - 4ac
Trig Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Arithmetic Progression
aₙ = a + (n-1)d
Sₙ = n/2 [2a + (n-1)d]
CLASS 11: INTERMEDIATE RAID
Complex Numbers
z = a + ib
|z| = √(a² + b²)
Argument: θ = tan⁻¹(b/a)
Conic Sections
Parabola: y² = 4ax
Ellipse: x²/a² + y²/b² = 1
Hyperbola: x²/a² - y²/b² = 1
Limits & Derivatives
d/dx(xⁿ) = nxⁿ⁻¹
d/dx(sin x) = cos x
d/dx(cos x) = -sin x
CLASS 12: ELITE CALCULUS
Integration Hub
∫ xⁿ dx = xⁿ⁺¹/(n+1) + C
∫ 1/x dx = log|x| + C
∫ eˣ dx = eˣ + C
Matrices & Det
A⁻¹ = (1/|A|) * adj(A)
|A| = a₁₁(a₂₂a₃₃ - a₃₂a₂₃)...
Vector & 3D
a·b = |a||b|cosθ
a×b = |a||b|sinθ n̂
Dist: |ax₁+by₁+cz₁+d|/√(a²+b²+c²)