PAss Functional Skills

Pythagoras theorem

Pythagoras theorem for ESOL Music: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Music
  • Spec N20
  • 4 min read
  • 7 revision boxes

Introduction

2 boxes
1 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.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
5 rows

The pythagoras theorem reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
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
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 4

Learning

3 boxes
3 steps

How to work with pythagoras theorem

Read the units in the question before you start; a converted unit is the most common slip.
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: 49=7\sqrt{49} = 7.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Pythagoras theorem

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: ≈160\approx 160.

  • 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

Work through the method one line at a time and write down what changes at each step.
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: 34×25\frac{3}{4} \times \frac{2}{5}

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
3 marks · worked

Worked example: 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.
3 marks · worked

Practice question 7: 34×25\frac{3}{4} \times \frac{2}{5}

Check the answer against an estimate before you move on, so a place-value slip is caught here.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
4,000+
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 ESOL Music paper?
Yes — it sits in the Reading and comprehension strand.