GCSE Maths Practice: direct-proportion

Understanding Direct Proportion in Real-Life Situations

Direct proportion describes a relationship between two quantities where an increase in one quantity causes a proportional increase in the other. This means that both quantities change at the same rate. Direct proportion is a key GCSE Maths concept and often appears in questions involving money, distance, time, and quantities.

The most important feature of direct proportion is that the unit rate remains constant. The unit rate is the amount per one unit, such as cost per item, distance per hour, or pay per hour. If the unit rate stays the same when quantities change, the relationship is directly proportional.

Using Unit Rate to Identify Direct Proportion

One reliable way to check for direct proportion is to calculate the unit rate in each situation and compare them.

Example: If 4 notebooks cost £8, the unit cost is £2 per notebook. If 10 notebooks cost £20, the unit cost is still £2 per notebook. Because the unit cost remains unchanged, this situation shows direct proportion.

Doubling and Scaling Checks

Another quick method is to check whether doubling one quantity doubles the other.

Example: If a car travels 40 miles in 1 hour, then at the same speed it should travel 80 miles in 2 hours. If the distance does not double when the time doubles, the relationship is not directly proportional.

Situations That Are Not Direct Proportion

Not all situations involving numbers show direct proportion. If the unit rate changes, then the relationship is not directly proportional.

• If hourly pay increases or decreases with more hours worked, it is not direct proportion.
• If a container does not scale evenly when filled or emptied, the relationship may not be proportional.
• Special offers or bonuses often break direct proportion.

Recognising these situations is just as important as identifying correct examples.

Why This Skill Matters

Understanding direct proportion helps in everyday decision-making. Shoppers compare unit prices, drivers estimate travel distances, and workers calculate expected pay. In exams, this skill helps students avoid traps where numbers look similar but the relationship is not proportional.

Frequently Asked Questions

Is doubling always required for direct proportion?
No. Any consistent scaling factor confirms direct proportion, not just doubling.

Do real-life situations always follow direct proportion exactly?
In GCSE exam questions, direct proportion is assumed to be exact unless stated otherwise.

Study Tip

For multiple-answer GCSE questions, check every option carefully. More than one situation may show direct proportion, and incorrect examples are often included to test understanding.