PAss Functional Skills

Pythagoras theorem

Pythagoras theorem for A Level Engineering AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Engineering
  • Foundation
  • Spec A14
  • 12 min read
  • 10 revision boxes

Introduction

2 boxes
3 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.
Practise the routine version until it is automatic, then move to the multi-step questions.
6 rows

The pythagoras theorem reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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
34×25\frac{3}{4} \times \frac{2}{5}
Row 4 column 1
Row 4 column 2
49=7\sqrt{49} = 7

Learning

6 boxes
4 steps

How to work with 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.
  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: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Pythagoras theorem

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

  • 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.
    49=7\sqrt{49} = 7
5 steps

How to work with 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.
  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: 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.

  • 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
4 steps

How to work with pythagoras theorem

This idea appears again in the higher-mark questions, so it is worth over-learning.
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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Pythagoras theorem

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

  • 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.
    49=7\sqrt{49} = 7

20 minutes

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Examples

2 boxes
3 marks · worked

Worked example: pythagoras theorem

The specification wording is precise here, and the mark scheme follows that wording exactly.
4 marks · worked

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

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ≈160\approx 160.

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