Formula sheet

Bookmark formulas to build your personal reference sheet.

Mathematics

Power Rule

d/dx[xⁿ]=n·xⁿ⁻¹

Chain Rule

d/dx[f(g(x))]=f'(g(x))·g'(x)

Product Rule

d/dx[u·v]=u'v+uv'

Log Derivative

d/dx[ln(u)]=u' / u

L'Hôpital

lim f/g=lim f'/g' (when 0/0 or ∞/∞)

Power Integral

∫ xⁿ dx=xⁿ⁺¹ / (n+1)+C (n≠−1)

2nd Derivative Test

f''(x)<0→local maxf''(x)>0→local min

Quadratic Formula

x=(−b±√(b²−4ac)) / 2a

Discriminant

Δ>0→2 real rootsΔ=0→1 rootΔ<0→no real roots

Absolute Inequality

|ax+b|≤c⟺−c≤ax+b≤c

Infinite Geometric Series

S∞=a / (1−r) (|r|<1)

Logarithm Laws

ln(AB)=ln A+ln Bln(A/B)=ln A−ln Bln(Aⁿ)=n·ln Aln(eˣ)=x

Inclusion-Exclusion

|A∪B|=|A|+|B|−|A∩B|

Addition Rule

P(A∪B)=P(A)+P(B)−P(A∩B)

Independent Events

P(A∩B)=P(A)·P(B) (if independent)

Bayes' Theorem

P(A|B)=P(B|A)·P(A) / P(B)

Permutations

P(n,k)=n! / (n−k)! (order matters)

Combinations

C(n,k)=n! / (k!·(n−k)!) (order doesn't)

Normal Symmetry

P(−a<Z<a)=1−2·P(Z>a)

Logic & Reasoning

Contrapositive

P→Q≡¬Q→¬P(Always valid)

Converse Fallacy

P→Q⟹Q→P ✗(NOT valid — common trap)

De Morgan's Laws

¬(P ∧ Q)≡¬P ∨ ¬Q¬(P ∨ Q)≡¬P ∧ ¬Q

Disjunctive Syllogism

P ∨ Q and ¬P→Q must be TRUE

Necessary vs Sufficient

'A is necessary for B'≡B→A'A is sufficient for B'≡A→B

Inclusion-Exclusion (Venn)

|A∪B|=|A|+|B|−|A∩B|Both=|A|+|B|−|those with at least one|

Data Analysis & Numerical Reasoning

Percentage Change

% Change=(New−Old) / Old×100

Gross Profit Margin

GPM=(Revenue−COGS) / Revenue×100

Operating Margin

Op. Margin=(Revenue−COGS−OpEx) / Revenue×100

Compound Growth

Value=P×(1+r₁)×(1+r₂)×…×(1+rₙ)Do NOT add rates — multiply the factors.

Weighted Average

x̄_w=Σ(wᵢ·xᵢ) / Σwᵢ

EBITDA

EBITDA=EBIT+Depreciation+Amortisation