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Pythagoras theorem

Pythagoras theorem for A Level Maths AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Maths
  • Foundation
  • Spec G20 · G15
  • 13 min read
  • 6 revision boxes

Introduction

2 boxes
4 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.
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 pythagoras theorem 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}.
4 rows

The pythagoras theorem reference table

The examiner marks the working, so a correct answer with no method still drops marks.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7
Row 3 column 4
Row 3 column 5
Row 4 column 1
Row 4 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 4 column 4
Row 4 column 5

Learning

2 boxes
5 steps

How to work with pythagoras theorem

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.
  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.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Pythagoras theorem

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 pythagoras theorem laid out step by step

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

  • Rule 1

    How pythagoras theorem behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How pythagoras theorem 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
2 marks · worked

Worked example: pythagoras theorem

Work through the method one line at a time and write down what changes at each step.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
2 marks · worked

Practice question 6: ≈160\approx 160

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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 A Level Maths AQA Foundation paper?
Yes — it sits in the Reading and comprehension strand.