Ratio, Proportion and Rates of Change
What Ratio, Proportion and Rates of Change tests
This strand is about comparing quantities and describing how one quantity changes with another. Foundation questions cover simplifying and dividing in a ratio, direct and inverse proportion, unit rates, speed, density, percentage change, and simple and compound interest. Most marks come from setting up the correct relationship before calculating.
Core rules
- A ratio compares parts of the same whole. Simplify by dividing all parts by their HCF; keep the order.
- To divide a quantity in the ratio a:b, add the parts, find the value of one part, then multiply.
- Direct proportion: both quantities increase together, so the ratio stays constant. Inverse proportion: as one increases, the other decreases, so the product stays constant.
- Average speed = distance ÷ time. Density = mass ÷ volume.
- Percentage change = (change ÷ original) × 100%.
- Compound interest uses a multiplier each year: final amount = P(1 + r)^n.
Worked example
€500 is invested at 3% compound interest for 2 years. Find the final amount. Year 1 multiplier: 1.03. Year 2 multiplier: 1.03. Amount = 500 × 1.03² = 500 × 1.0609 = €530.45. The final amount is €530.45, so the interest is €30.45. Do not simply add 2 × 3% = 6% of €500; that would ignore interest on interest.
Traps that cost marks
- Writing a ratio in the wrong order, e.g. teachers:students instead of students:teachers.
- Using the new value as the denominator in percentage change.
- Mixing direct and inverse proportion.
- Forgetting to convert minutes to hours, or grams to kilograms, before using a rate formula.