GCSE Maths Practice: inverse-proportion

Solving Inverse Proportion Problems Using a Constant (Higher Tier)

This question focuses on a key Higher GCSE Maths skill: using algebra to solve inverse proportion problems. You must recognise the relationship, calculate the constant of proportionality, and then use it to find an unknown value.

The Inverse Proportion Relationship

If y is inversely proportional to x, this is written as:

y ∝ \frac{1}{x}

which leads to the equation:

y = \frac{k}{x}

Here, k is the constant of proportionality. This constant links all valid pairs of x and y values.

Why the Constant Is Important

In inverse proportion, x and y change, but their product remains constant:

x × y = k

Once you have found k, you can calculate y for any value of x.

Step-by-Step Method

1. Write down the inverse proportion formula.
2. Substitute the given values of x and y.
3. Solve to find the constant k.
4. Substitute the new value of x.
5. Calculate the corresponding value of y.

This structured method is exactly what examiners expect to see in Higher-tier answers.

Worked Example (Different Values)

Example: y is inversely proportional to x. When x = 6, y = 20. Find y when x = 10.

• y = k / x
• 20 = k / 6 → k = 120
• y = 120 / 10
• y = 12

The product x × y stays constant at 120.

Another Worked Example

Example: y is inversely proportional to x. When x = 9, y = 8. Find y when x = 3.

• y = k / x
• 8 = k / 9 → k = 72
• y = 72 / 3
• y = 24

Common Higher-Tier Mistakes

• Using y = kx instead of y = k / x.
• Forgetting to calculate the constant first.
• Dividing by the wrong value of x.
• Not checking whether the answer is sensible.

Why This Skill Matters

Inverse proportion often appears in GCSE Higher exams combined with algebra, rearranging formulas, or multi-step reasoning. Confidence with constants allows you to solve these questions quickly and accurately.

Study Tip

Always find the constant k first. Once you have it, the rest of the problem becomes straightforward.