GCSE Maths Practice: direct-proportion

Question 8 of 10

This question checks your ability to recognise direct proportion from different cost calculations.

‹ ›

\( \begin{array}{l}\text{Which of the following calculations show direct proportion?}\end{array} \)

Select all correct options:

Direct proportion means the unit cost stays constant when quantities change.

Recognising Direct Proportion Using Unit Cost

Direct proportion describes a relationship where two quantities increase or decrease together at a constant rate. In GCSE Maths, this idea is often tested using cost and quantity examples. The key feature of direct proportion in these problems is that the cost per item remains the same, even when the number of items changes.

When identifying whether a situation shows direct proportion, you are not required to calculate the final price in detail. Instead, you should focus on whether the relationship between quantity and cost is consistent.

The Role of Unit Cost

The most reliable way to check for direct proportion is to find the unit cost. The unit cost is the cost of one item. If the unit cost stays the same before and after the change in quantity, then the relationship is directly proportional.

Example: If 6 oranges cost £3.00, the unit cost is £3.00 ÷ 6 = £0.50 per orange. If 10 oranges cost £5.00, the unit cost is still £0.50 per orange. Because the unit cost remains constant, this situation shows direct proportion.

Scaling Quantities Up or Down

Direct proportion can also be identified by scaling. If the quantity is multiplied or divided by a number, the cost should be multiplied or divided by the same number.

Example: If the number of items doubles, the total cost should also double. If the number of items halves, the total cost should also halve. This consistent scaling confirms a direct proportional relationship.

Common Mistakes to Avoid

  • Assuming all price changes show direct proportion.
  • Forgetting to check the unit cost.
  • Confusing direct proportion with inverse proportion.
  • Thinking discounts or offers still follow direct proportion.

For example, special offers such as “buy one get one free” do not follow direct proportion because the unit cost changes.

Why This Skill Matters

Being able to recognise direct proportion is important not only for exams but also for everyday decision-making. Unit pricing helps shoppers compare value, businesses calculate costs accurately, and recipes are scaled correctly. Understanding this concept allows you to spot when prices are fair and when they are not.

Frequently Asked Questions

Do I always need to calculate the final cost?
No. Often, checking whether the unit cost stays the same is enough.

How can I tell if something is not direct proportion?
If the unit cost changes, or if the relationship does not scale evenly, it is not direct proportion.

Study Tip

In GCSE Maths multiple-answer questions, check every option carefully. Even if one example is correct, others may also show direct proportion. Never assume only one answer unless the question says so.

Related Quizzes