PAss Functional Skills

Pythagoras theorem

Pythagoras theorem for GCSE Sociology AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Sociology
  • Spec A10
  • 4 min read
  • 6 revision boxes

Introduction

2 boxes
3 min read

What is pythagoras theorem?

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Transcript

A short spoken summary of pythagoras theorem and where it is used.

A spoken walk-through of pythagoras theorem before you read the notes.
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 pythagoras theorem laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
5 rows

The pythagoras theorem reference table

Read the units in the question before you start; a converted unit is the most common slip.
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
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7

Learning

2 boxes
5 steps

How to work with pythagoras theorem

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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 pythagoras theorem 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: ≈160\approx 160
3 rules

Key facts: Pythagoras theorem

Work through the method one line at a time and write down what changes at each step.

  • Rule 1

    How pythagoras theorem behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

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

  • Rule 3

    How pythagoras theorem behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7

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Examples

2 boxes
1 marks · worked

Worked example: pythagoras theorem

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 pythagoras theorem laid out step by step

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

Practice question 6: ×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 pythagoras theorem laid out step by step

The same idea drawn out, so the method is visible.

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Common questions

How many marks is pythagoras theorem usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Sociology AQA paper?
Yes — it sits in the Reading and comprehension strand.