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Compound measures

Compound measures for A Level Maths AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Maths
  • Higher
  • Spec P17 · P11
  • 5 min read
  • 10 revision boxes

Introduction

2 boxes
1 min read

What is compound measures?

Listen to this box

Transcript

A short spoken summary of compound measures and where it is used.

A spoken walk-through of compound measures 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 compound measures laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
5 rows

The compound measures reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 3 column 4
Row 4 column 1
Row 4 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 4 column 4

Learning

6 boxes
3 steps

How to work with compound measures

This idea appears again in the higher-mark questions, so it is worth over-learning.
  1. Read the question and write down what is being asked for.
  2. Set out the working for compound measures 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: Compound measures

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 49=7\sqrt{49} = 7.

  • Rule 1

    How compound measures behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How compound measures behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How compound measures behaves in the 3rd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
5 steps

How to work with compound measures

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  1. Read the question and write down what is being asked for.
  2. Set out the working for compound measures 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
2 rules

Key facts: Compound measures

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ×10\times 10 moves every digit one column left.

  • Rule 1

    How compound measures behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How compound measures behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How compound measures behaves in the 3rd of the cases the specification names.
    ≈160\approx 160
3 steps

How to work with compound measures

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  1. Read the question and write down what is being asked for.
  2. Set out the working for compound measures 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: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Compound measures

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

  • Rule 1

    How compound measures behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How compound measures behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

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Examples

2 boxes
1 marks · worked

Worked example: compound measures

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 compound measures laid out step by step

The same idea drawn out, so the method is visible.
4 marks · worked

Practice question 10: ×10\times 10 moves every digit one column left

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 compound measures 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.

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Common questions

How many marks is compound measures usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Maths AQA Higher paper?
Yes — it sits in the Ecosystems strand.