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Multiplication
Small numbers, reference 10
7 × 8 without tables
Multiplying by 11
Add the neighbour
Multiplying by factors
× 5, × 25, × 15
Just below 100
96 × 97 in one line
Just above 100
106 × 104
One above, one below
98 × 134
Reference multiples of ten
42 × 48 with reference 40
Three digits near 1000
994 × 1013
4-digit multiplication, reference 10 000
9 985 × 10 021
General 4-digit multiplication
3 826 × 47 by splitting
No close reference number
23 × 79 with two references
Squares
Addition & subtraction
Division
Fractions
Percentages
Checking answers
Finance
Rule of 72
doubling time in one division
Present and future value
discounting a single cash flow
Perpetuity and Gordon growth
CF / (r − g)
Annuity factors
a fixed stream for n years
NPV of a short cash-flow strip
three years and an outlay
Payback and its reciprocal
years to get the money back
Cost of equity (CAPM)
rf + β × ERP
WACC
blended cost of capital
Unlevering and relevering beta
Hamada in one division
Terminal value
the tail of a DCF
Multiples and the equity bridge
EV/EBITDA to equity value
Implied growth from a multiple
reverse the Gordon formula
Free cash flow build
EBIT(1−t) + D&A − capex − ΔNWC
DuPont and ROIC
margin × turnover × leverage
Cash conversion cycle
DSO + DIO − DPO
Duration and DV01
price move for a yield move
Forward rates from spots
2 × s₂ − s₁, then exact
Option payoffs and parity
breakeven, intrinsic, parity
LBO quick math
equity in, equity out, MoM
Accretion / dilution
compare the earnings yields
Breakeven and operating leverage
fixed / contribution
Statistics for finance
Weighted mean (portfolio return)
60/40 at 9% and 3%
Variance the fast way
E[x²] − (E[x])²
Sharpe ratio & coefficient of variation
(r − rf) / σ
z-scores
(x − μ) / σ
68 / 95 / 99.7
sigma ladder and tails
Correlation from covariance
ρ = cov / σxσy
Two-asset portfolio risk
σp with a correlation term
Beta two ways
cov/var, or ρ·σᵢ/σm
Regression slope and R²
b = ρ·σy/σx, R² = ρ²
Standard error and the √n rule
SE = σ / √n
Confidence intervals
mean ± 2 SE
t-statistics and significance
t = estimate / SE
And, or, neither
independence in three moves
Bayes on a 2×2 table
base rates beat intuition
Expected value of a payoff
Σ p × payoff
Annualising volatility
σ_daily × √252
Binomial mean and spread
np and √(npq)
Log vs simple returns
ln(1 + r) and when it matters