Class 12 Maths
Calculus is 35 of the 80 marks
Derivatives
- d/dx (xⁿ)
- n·xⁿ⁻¹
- d/dx (sin x)
- cos x
- d/dx (cos x)
- −sin x
- d/dx (tan x)
- sec² x
- d/dx (eˣ)
- eˣ
- d/dx (ln x)
- 1/x
- d/dx (sin⁻¹x)
- 1/√(1−x²)
- d/dx (tan⁻¹x)
- 1/(1+x²)
- Product rule
- (uv)′ = u′v + uv′
- Quotient rule
- (u/v)′ = (u′v − uv′)/v²
Integrals
- ∫ xⁿ dx
- xⁿ⁺¹/(n+1) + C, n ≠ −1
- ∫ 1/x dx
- ln|x| + C
- ∫ eˣ dx
- eˣ + C
- ∫ sin x dx
- −cos x + C
- ∫ sec²x dx
- tan x + C
- ∫ 1/(x²+a²) dx
- (1/a)·tan⁻¹(x/a) + C
- ∫ 1/√(a²−x²) dx
- sin⁻¹(x/a) + C
- ∫ 1/(x²−a²) dx
- (1/2a)·ln|(x−a)/(x+a)| + C
- ∫ √(a²−x²) dx
- (x/2)√(a²−x²) + (a²/2)sin⁻¹(x/a) + C
- By parts
- ∫u·v dx = u∫v dx − ∫(u′∫v dx) dx
Definite integral properties
- ∫₀ᵃ f(x) dx
- ∫₀ᵃ f(a−x) dx
- ∫₋ₐᵃ f(x) dx
- 2∫₀ᵃ f(x) dx if even · 0 if odd
- ∫ₐᵇ f(x) dx
- −∫_bᵃ f(x) dx
Vectors & 3D
- Dot product
- a·b = |a||b|cosθ
- Cross product
- |a×b| = |a||b|sinθ
- Projection of a on b
- (a·b)/|b|
- Line, vector form
- r = a + λb
- Shortest distance (skew)
- |(a₂−a₁)·(b₁×b₂)| / |b₁×b₂|
- Plane
- r·n̂ = d
Matrices & probability
- Inverse
- A⁻¹ = adj(A)/|A|, |A| ≠ 0
- System AX = B
- X = A⁻¹B
- Conditional probability
- P(A|B) = P(A∩B)/P(B)
- Bayes' theorem
- P(Eᵢ|A) = P(Eᵢ)P(A|Eᵢ) / Σ P(Eⱼ)P(A|Eⱼ)
Standard CBSE Class 12 Mathematics formulae. Check anything you are unsure of against NCERT before you rely on it.