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 max f''(x) > 0 → local min
Quadratic Formula
x = (−b ± √(b² − 4ac)) / 2a
Discriminant
Δ > 0 → 2 real roots Δ = 0 → 1 root Δ < 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 B ln(A/B) = ln A − ln B ln(Aⁿ) = n·ln A ln(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