PAss Functional Skills

Direct and inverse proportion

Direct and inverse proportion for GCSE Maths Edexcel Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Maths
  • Foundation
  • Spec G19
  • 5 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.
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.
Worth knowing: ×10\times 10 moves every digit one column left.
4 rows

The direct and inverse proportion reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 4
Row 2 column 5

Learning

3 boxes
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.
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.
  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.
  4. Check the answer against an estimate before writing it down.
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: 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.
    ≈160\approx 160

  • 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}

  • Rule 3

    How direct and inverse proportion behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
3 steps

How to work with direct and inverse proportion

Practise the routine version until it is automatic, then move to the multi-step questions.
  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: a2+b2=c2a^2 + b^2 = c^2

20 minutes

Get your predicted grade

Twenty questions gives you a predicted grade, your target, and the gap between them — plus the topics that close it fastest.
Get my predicted grade

Examples

2 boxes
4 marks · worked

Worked example: 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.
2 marks · worked

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

Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
5,000+
Topics
10
Marking and solutions
Instant

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 Maths Edexcel Foundation paper?
Yes — it sits in the Chemical change strand.