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Direct and inverse proportion

Direct and inverse proportion for ESOL Design and Technology: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Design and Technology
  • Spec N20
  • 4 min read
  • 8 revision boxes

Introduction

2 boxes
1 min read

What is direct and inverse proportion?

Listen to this box

Transcript

A short spoken summary of direct and inverse proportion and where it is used.

A spoken walk-through of direct and inverse proportion before you read the notes.
This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing direct and inverse proportion laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ≈160\approx 160.
6 rows

The direct and inverse proportion reference table

The examiner marks the working, so a correct answer with no method still drops marks.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left

Learning

4 boxes
5 steps

How to work with direct and inverse proportion

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing direct and inverse proportion laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for direct and inverse proportion in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Direct and inverse proportion

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

  • Rule 1

    How direct and inverse proportion behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How direct and inverse proportion behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
3 steps

How to work with direct and inverse proportion

This idea appears again in the higher-mark questions, so it is worth over-learning.
  1. Read the question and write down what is being asked for.
  2. Set out the working for direct and inverse proportion in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Direct and inverse proportion

The examiner marks the working, so a correct answer with no method still drops marks.

  • Rule 1

    How direct and inverse proportion behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How direct and inverse proportion behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

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Examples

2 boxes
4 marks · worked

Worked example: direct and inverse proportion

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing direct and inverse proportion laid out step by step

The same idea drawn out, so the method is visible.
4 marks · worked

Practice question 8: 34×25\frac{3}{4} \times \frac{2}{5}

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

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Common questions

How many marks is direct and inverse proportion usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the ESOL Design and Technology paper?
Yes — it sits in the Chemical change strand.