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Direct and inverse proportion

Direct and inverse proportion for GCSE Art and Design Edexcel Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Art and Design
  • Foundation
  • Spec S12 · S17
  • 14 min read
  • 7 revision boxes

Introduction

2 boxes
2 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.
The specification wording is precise here, and the mark scheme follows that wording exactly.
3 rows

The direct and inverse proportion reference table

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: 49=7\sqrt{49} = 7.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 4
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7
Row 3 column 4

Learning

3 boxes
4 steps

How to work with direct and inverse proportion

Check the answer against an estimate before you move on, so a place-value slip is caught here.
  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: ×10\times 10 moves every digit one column left.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Direct and inverse proportion

Work through the method one line at a time and write down what changes at each step.
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: x2+5x+6=0x^2 + 5x + 6 = 0.

  • Rule 1

    How direct and inverse proportion behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How direct and inverse proportion behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
3 steps

How to work with direct and inverse proportion

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}.
  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: a2+b2=c2a^2 + b^2 = c^2.
Answer: ≈160\approx 160

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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.
1 marks · worked

Practice question 7: 49=7\sqrt{49} = 7

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

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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 GCSE Art and Design Edexcel Foundation paper?
Yes — it sits in the Chemical change strand.