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Ratio and scale

Ratio and scale for Access to HE Statistics: what it means, how to set the working out, and the questions it is asked in.
  • Access to HE
  • Statistics
  • Spec P4 · P18 · P3
  • 7 min read
  • 10 revision boxes

Introduction

2 boxes
2 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.
Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
4 rows

The ratio and scale reference table

The specification wording is precise here, and the mark scheme follows that wording exactly.
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: ≈160\approx 160.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4

Learning

6 boxes
5 steps

How to work with ratio and scale

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 ratio and scale 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.
  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: ≈160\approx 160.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Ratio and scale

Check the answer against an estimate before you move on, so a place-value slip is caught here.

  • 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.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How ratio and scale 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 ratio and scale

Read the units in the question before you start; a converted unit is the most common slip.
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.
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
3 rules

Key facts: Ratio and scale

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • 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.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How ratio and scale behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
5 steps

How to work with ratio and scale

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 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: 49=7\sqrt{49} = 7.
Answer: ≈160\approx 160
2 rules

Key facts: Ratio and scale

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

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

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Examples

2 boxes
2 marks · worked

Worked example: ratio and scale

The specification wording is precise here, and the mark scheme follows that wording exactly.
3 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.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

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Topics
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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 Access to HE Statistics paper?
Yes — it sits in the Waves and light strand.