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Direct and inverse proportion

Direct and inverse proportion for ESOL Philosophy: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Philosophy
  • Spec A12 · A2 · A16
  • 5 min read
  • 10 revision boxes

Introduction

2 boxes
4 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 examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ×10\times 10 moves every digit one column left.
5 rows

The direct and inverse proportion reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7

Learning

6 boxes
5 steps

How to work with 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.
Worth knowing: 49=7\sqrt{49} = 7.
  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: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Direct and inverse proportion

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • 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.
    a2+b2=c2a^2 + b^2 = c^2
3 steps

How to work with direct and inverse proportion

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 49=7\sqrt{49} = 7.
  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: ≈160\approx 160.
Answer: ×10\times 10 moves every digit one column left
3 rules

Key facts: Direct and inverse proportion

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • 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.
    a2+b2=c2a^2 + b^2 = c^2
4 steps

How to work with direct and inverse proportion

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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: 49=7\sqrt{49} = 7.
Answer: ≈160\approx 160
2 rules

Key facts: Direct and inverse proportion

Practise the routine version until it is automatic, then move to the multi-step questions.

  • Rule 1

    How direct and inverse proportion behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

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

  • Rule 3

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

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Examples

2 boxes
4 marks · worked

Worked example: direct and inverse proportion

Read the units in the question before you start; a converted unit is the most common slip.
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: 34×25\frac{3}{4} \times \frac{2}{5}.
2 marks · worked

Practice question 10: ≈160\approx 160

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.

Practice bank

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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 Philosophy paper?
Yes — it sits in the Chemical change strand.