Mathematics Applications: Working with Data, Percentages and Financial Modelling
Core concepts you must command
Mathematics Applications rewards steady numerical discipline more than clever tricks. Across the syllabus you need fluency in data display and summary statistics (mean, median, mode, range, standard deviation, box plots, histograms, cumulative frequency), percentage change and the unitary method, ratio and proportion, and financial mathematics including simple and compound interest, appreciation and depreciation, and reducing-balance loans. You should also be confident converting between fractions, decimals and percentages, and reading tables and graphs critically.
Traps that cost marks
- Percentage change direction: a 20% rise followed by a 20% fall does not return to the original value; multiply by 1.2 then 0.8 to see why.
- Simple versus compound interest: compound interest applies to the accumulated balance, not the original principal, each period.
- Depreciation wording: "reduces by 15% per year" means multiply by 0.85 each year, not subtract 15% of the original repeatedly.
- Standard deviation: it measures spread about the mean; adding a constant to every score leaves it unchanged.
- Rounding too early: carry full calculator precision and round only the final answer.
Worked example
A car worth $24,000 depreciates at 12% per annum, compounding annually. Find its value after 3 years.
Each year the value is multiplied by 0.88, so value = 24000 × 0.88³ = 24000 × 0.681472 ≈ $16,355.33.
Rule of thumb
For repeated percentage change, write the multiplier first (1 + r for growth, 1 − r for decay), raise it to the number of periods, then multiply by the starting amount. This single habit prevents most financial errors.