PAss Functional Skills

Ratio and scale

Ratio and scale for GCSE Statistics AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Statistics
  • Higher
  • Spec S17 · S12 · S11
  • 10 min read
  • 9 revision boxes

Introduction

2 boxes
1 min read

What is ratio and scale?

Listen to this box

Transcript

A short spoken summary of ratio and scale and where it is used.

A spoken walk-through of ratio and scale before you read the notes.
This idea appears again in the higher-mark questions, so it is worth over-learning.
3 rows

The ratio and scale reference table

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 ratio and scale 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}.
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
x2+5x+6=0x^2 + 5x + 6 = 0

Learning

5 boxes
5 steps

How to work with ratio and scale

Practise the routine version until it is automatic, then move to the multi-step questions.
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 ratio and scale 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: 49=7\sqrt{49} = 7
3 rules

Key facts: Ratio and scale

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

  • Rule 1

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

  • Rule 2

    How ratio and scale behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

    How ratio and scale behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
4 steps

How to work with ratio and scale

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 ratio and scale 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 ratio and scale 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: a2+b2=c2a^2 + b^2 = c^2.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Ratio and scale

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • Rule 1

    How ratio and scale behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How ratio and scale behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • Rule 3

    How ratio and scale behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
3 steps

How to work with ratio and scale

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

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: ratio and scale

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: ×10\times 10 moves every digit one column left.
2 marks · worked

Practice question 9: 49=7\sqrt{49} = 7

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

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
12,000+
Topics
10
Marking and solutions
Instant

Common questions

How many marks is ratio and scale usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Statistics AQA Higher paper?
Yes — it sits in the Waves and light strand.