GCSE Maths Practice: inverse-proportion

Question 9 of 10

This question checks whether you can recognise inverse proportion from pairs of values.

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\( \begin{array}{l} \text{Which of these value pairs follow inverse proportion?} \end{array} \)

Select all correct options:

Recognising Inverse Proportion from Value Pairs (Higher Tier)

This question tests your ability to identify inverse proportion using numerical value pairs. At Higher GCSE level, you are expected to recognise inverse proportion not only from formulas and word problems, but also directly from tables or sets of values.

The Key Rule

If two variables x and y are inversely proportional, their relationship can be written as:

y = \frac{k}{x}

This means that the product x × y is always equal to the same constant value k.

How to Test Value Pairs

  1. Multiply the x-value by the y-value for the first pair.
  2. Multiply the x-value by the y-value for the second pair.
  3. Compare the two products.
  4. If the products are equal, the values follow inverse proportion.

This method works regardless of whether the numbers are whole numbers, decimals, or fractions.

Worked Example (Not From the Options)

Example: Consider the pairs (x = 4, y = 15) and (x = 10, y = 6).

  • 4 × 15 = 60
  • 10 × 6 = 60

Because the products match, these values show inverse proportion.

Another Worked Example

Example: Consider the pairs (x = 6, y = 8) and (x = 12, y = 4).

  • 6 × 8 = 48
  • 12 × 4 = 48

Again, the constant product confirms inverse proportion.

What Does NOT Show Inverse Proportion?

If the products are different, the values do not follow inverse proportion.

Example: (x = 3, y = 7) and (x = 6, y = 5)

  • 3 × 7 = 21
  • 6 × 5 = 30

Since the products are not equal, this is not inverse proportion.

Common Higher-Tier Mistakes

  • Only checking whether x increases and y decreases.
  • Forgetting to multiply both pairs.
  • Making arithmetic errors with decimals.
  • Assuming a pattern without checking the product.

Why This Matters in Exams

GCSE Higher questions often ask you to identify inverse proportion from tables, graphs, or sets of values. Being confident with the constant-product test allows you to answer these questions quickly and accurately.

Study Tip

If you are unsure, always calculate x × y. A matching product is the clearest proof of inverse proportion.

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