GCSE Maths Practice: inverse-proportion

Question 10 of 10

This question checks whether you can recognise inverse proportion in real-life situations.

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\( \begin{array}{l}\text{Which situations represent inverse proportion?}\end{array} \)

Select all correct options:

Recognising Inverse Proportion in Everyday Situations

This question checks your understanding of inverse proportion using real-life situations rather than calculations. At GCSE level, being able to recognise inverse proportion is just as important as being able to solve numerical problems.

What Does Inverse Proportion Mean?

Inverse proportion describes a relationship where:

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

For example, the total amount of work, distance, or quantity does not change — only how it is shared or completed.

Key Question to Ask Yourself

“If one value goes up, does 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 distance is travelled. If the speed doubles, what happens to the time?

  • Speed increases
  • Time decreases
  • The distance stays the same

This is a clear example of inverse proportion.

Another Worked Example

Example: A job requires a fixed amount of effort. If the number of workers increases, what happens to the time needed?

  • Number of workers increases
  • Time taken decreases
  • The job itself stays the same

This again shows inverse proportion.

What Is NOT Inverse Proportion?

Some situations involve values increasing together. These are examples of direct proportion, not inverse proportion.

Example: If each notebook costs the same amount, buying more notebooks increases the total cost.

  • Quantity increases
  • Total cost increases
  • Both values move in the same direction

Common Mistakes

  • Assuming all word problems show inverse proportion.
  • Forgetting to check whether something stays constant.
  • Mixing up direct and inverse proportion.
  • Only focusing on words like “more” or “less” without thinking about the relationship.

Real-Life Uses

Inverse proportion appears in many everyday contexts, such as sharing food, travelling faster or slower, filling or emptying containers, and working in teams. Recognising these relationships helps you understand problems quickly in exams.

Frequently Asked Questions

Is inverse proportion always about time?
No. It can involve portions, speed, workers, machines, or rates.

Can a situation be neither direct nor inverse?
Yes. If the relationship is irregular or changing, it may be neither.

Study Tip

Always check whether one quantity increases while the other decreases for the same total situation. This quick test can help you choose the correct answers confidently.

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