GCSE Maths Practice: inverse-proportion

Question 10 of 10

This question tests your ability to recognise inverse proportionality in real-life situations.

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\( \begin{array}{l} \text{Which situations show inverse proportionality?} \end{array} \)

Select all correct options:

Recognising Inverse Proportion in Real-Life Situations (Higher Tier)

This question tests your ability to identify inverse proportionality in real-world contexts rather than through equations or calculations. At Higher GCSE level, students are expected to understand how inverse proportion appears across different subjects, including physics, engineering, and everyday problem solving.

What Does Inverse Proportion Mean?

Inverse proportion describes a relationship where:

  • One quantity increases
  • The other quantity decreases
  • Something important stays the same

This constant condition might be total work, distance, volume, or task difficulty.

Key Question to Ask

“If one value goes up, must the other go down for the same situation?”

If the answer is yes, the situation likely shows inverse proportion.

Worked Example (Not From the Options)

Example: A fixed job must be completed. If 5 workers take 20 hours, what happens if 10 workers are used?

  • Number of workers increases
  • Time taken decreases
  • Total work stays the same

This is inverse proportion.

Another Worked Example

Example: A car travels a fixed distance. If the speed is doubled, what happens to the travel time?

  • Speed increases
  • Time decreases
  • Distance stays the same

This is also inverse proportion.

What Is NOT Inverse Proportion?

Some situations involve both quantities increasing together. These are examples of direct proportion.

Example: If a car uses fuel at a constant rate, adding more petrol allows the car to travel further.

  • Petrol increases
  • Distance increases
  • Both change in the same direction

This is not inverse proportion.

Common Higher-Tier Mistakes

  • Assuming all word problems show inverse proportion.
  • Ignoring the condition that must stay constant.
  • Confusing inverse proportion with negative correlation.
  • Focusing only on the words “more” or “less” without analysing the relationship.

Why This Matters in Exams

GCSE Higher questions often ask you to identify proportional relationships without calculations. You may need to justify your answer using reasoning rather than numbers. Understanding the logic behind inverse proportion helps you answer these questions confidently.

Study Tip

Always identify what is staying the same. If one quantity increases and the other decreases while this condition remains fixed, the situation shows inverse proportion.

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