SACE Stage 2 Essential Mathematics cheat sheet

Simple interest: I = P × r × t, where r is the annual decimal rate and t is time in years; total amount A = P(1 + rt).

Compound interest: A = P(1 + r/n)^(nt) for n compounding periods per year; continuous growth uses A = Pe^(rt).

Depreciation: straight-line value = P − (P × r × t); reducing-balance value = P(1 − r)^t.

Percentage change = (new − old) / old × 100%; percentage of a quantity = rate × quantity, with rate expressed as a decimal.

Unit conversion chains multiply by fractions equal to 1 (e.g. 1000 m / 1 km) so unwanted units cancel.

Rate problems use the relationship quantity = rate × time; rearrange to isolate the unknown before substituting.

Scale drawings: actual length = drawing length × scale factor; areas scale by the square of the linear factor.

Rounding rule: carry full precision through intermediate steps and round only the final answer to the stated accuracy.

Mean = sum of values / number of values; median is the middle value of ordered data; mode is the most frequent value.

Range = maximum − minimum; interquartile range IQR = Q3 − Q1 and captures the middle 50% of ordered data.

Standard deviation measures spread about the mean; a larger value indicates greater dispersion of data.

Perimeter sums edge lengths; area formulas: rectangle l×w, triangle ½bh, circle πr²; volume of prism = base area × height.

Pythagoras: a² + b² = c², with c the hypotenuse; used for right-triangle distances and diagonal lengths.

Loan repayment total = regular payment × number of payments; interest paid = total repayments − principal borrowed.

Budget balance: income − fixed expenses − variable expenses = surplus (positive) or deficit (negative).

Probability of an event = favourable outcomes / total equally likely outcomes; all probabilities lie between 0 and 1.