PAss Functional Skills

Pythagoras theorem

Pythagoras theorem for GCSE Combined Science AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Combined Science
  • Foundation
  • Spec P20 · P16 · P2
  • 4 min read
  • 8 revision boxes

Introduction

2 boxes
4 min read

What is pythagoras theorem?

Listen to this box

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 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}.
6 rows

The pythagoras theorem reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 3 column 1
Row 3 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left

Learning

4 boxes
3 steps

How to work with pythagoras theorem

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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 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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Pythagoras theorem

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.

  • Rule 1

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

  • Rule 2

    How pythagoras theorem behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
3 steps

How to work with pythagoras theorem

The examiner marks the working, so a correct answer with no method still drops marks.
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.
  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: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: Pythagoras theorem

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.

  • Rule 1

    How pythagoras theorem behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How pythagoras theorem behaves in the 2nd of the cases the specification names.
    ≈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
1 marks · worked

Worked example: pythagoras theorem

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.
4 marks · worked

Practice question 8: ×10\times 10 moves every digit one column left

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.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
6,000+
Topics
10
Marking and solutions
Instant

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 Combined Science AQA Foundation paper?
Yes — it sits in the Reading and comprehension strand.