Ratio, Proportion & Rates of Change – AQA GCSE Maths (8300)

Key Concepts

• Understanding and simplifying ratios
• Direct and inverse proportion
• Percentages: increase, decrease, and change
• Compound measures (speed, density, pressure)
• Exchange rates and best buys
• Proportional reasoning and scaling

Definitions & Examples

• Ratio: A comparison of two quantities, e.g., 3:4.
• Direct Proportion: Two quantities increase/decrease at the same rate, e.g., y = 2x.
• Inverse Proportion: One quantity increases as the other decreases, e.g., y = 12/x.
• Percentage Change: ((new - original)/original) × 100%
• Compound Measure: Combination of two measures, e.g., speed = distance ÷ time.

Methods

• Simplify ratios by dividing both parts by their greatest common factor
• Use direct proportion equations (y = kx) and inverse proportion equations (y = k/x)
• Calculate percentage increase/decrease using the formula
• Apply scaling to recipes, maps, models
• Convert units in compound measures
• Use proportional reasoning to solve word problems

Advantages & Disadvantages

• Advantages: Useful for real-life applications, supports reasoning skills, widely applied in science, finance, and everyday problem-solving.
• Disadvantages: Can be confusing when multiple steps are required, errors easily occur if units are inconsistent, negative or fractional scaling may be tricky.

Practice Questions

• Simplify the ratio 18:24
• y is directly proportional to x. When x = 5, y = 15. Find y when x = 12.
• y is inversely proportional to x. When x = 4, y = 6. Find y when x = 12.
• A price of £80 is reduced by 25%. Calculate the new price.
• A car travels 150 km in 3 hours. Calculate its average speed.
• A model is 1:50 scale. A wall is 2m high in real life. What is the height of the model wall?