What you'll learn
This domain tests quantitative reasoning in real contexts: ratios and proportions, percentages, unit rates, data interpretation, statistics, and probability. It's about applying math to situations, not abstract algebra.
Ratios and proportions
A ratio compares quantities. Set up a proportion and cross-multiply.
- Boys:girls = 3:5 in a class of 24 → 8 parts → each part 3 students → 15 girls.
- Scale: 1 inch = 25 miles → 4 inches = 100 miles.
Percentages
- X% of N = (X/100) × N.
- Percent change = (new − old) / old × 100. From $50 to $65 = 15/50 = 30% increase.
- Reverse percentages: "increased 20% to 60" → 1.2x = 60 → x = 50.
Rates
Speed = distance ÷ time; unit price = cost ÷ quantity. Keep units consistent.
Statistics
- Mean = sum ÷ count. Median = middle value. Mode = most frequent.
- The median resists outliers; the mean is pulled toward them.
- Range = max − min. Standard deviation measures spread.
- Adding a constant to every value shifts the mean but leaves the spread unchanged.
Probability
P(event) = favourable outcomes ÷ total outcomes. P(not event) = 1 − P(event). Read two-way tables carefully — the denominator depends on the group asked about.
Data interpretation
Many questions give a graph or table. Read the axis labels and units first, then find exactly what's asked. Watch for scale and for "per" units.
Exam strategy
- Underline the units and the exact quantity requested.
- Estimate to sanity-check (a 30% rise can't give an answer smaller than the original).
- Use the calculator, but set up the ratio/percentage correctly first.
Common mistakes
- Using the wrong base for a percentage change.
- Confusing mean and median.
- Misreading the denominator in a probability/two-way table.
This domain is very learnable — the same handful of setups recur, so steady practice pays off quickly.