GCSE Maths Practice: inverse-proportion

Understanding Inverse and Direct Proportion

This question tests whether you can recognise situations that do not show inverse proportion. At GCSE level, it is important to understand the difference between direct proportion and inverse proportion, as exam questions often ask you to compare the two.

What Is Inverse Proportion?

Inverse proportion occurs when one quantity increases while the other decreases, and the overall result stays the same. For example, if more workers are used to complete the same job, the time taken usually decreases.

The key idea is:

When one value goes up, the other goes down.

What Is Direct Proportion?

Direct proportion happens when two quantities increase or decrease together at a constant rate. If one value doubles, the other also doubles.

For example, if each apple costs the same amount, buying more apples increases the total cost in direct proportion.

How to Decide Which Type It Is

• If both quantities increase together → direct proportion.
• If one increases while the other decreases → inverse proportion.

This simple check can help you answer many GCSE questions quickly.

Worked Example (Direct Proportion)

Example: One notebook costs £2. How much do 5 notebooks cost?

• Number of notebooks increases
• Total cost increases at the same rate
• This is direct proportion

Worked Example (Inverse Proportion)

Example: 4 workers take 12 hours to complete a task. How long would 8 workers take?

• Number of workers increases
• Time taken decreases
• This is inverse proportion

Common Mistakes

• Thinking all word problems involve inverse proportion.
• Forgetting to check whether one quantity increases while the other decreases.
• Assuming speed and time are always direct proportion.
• Not reading the question carefully when it asks for examples that are not inverse proportion.

Real-Life Context

Direct proportion appears when shopping, budgeting, and measuring ingredients. Inverse proportion appears when sharing work, travelling faster or slower, or using more machines to complete a task.

Frequently Asked Questions

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

Do GCSE questions mix both types?
Yes. Many questions test whether you can correctly identify the relationship.

Study Tip

Always ask yourself: “If one value increases, what happens to the other?” This simple question helps you avoid confusion between direct and inverse proportion.