PAss Functional Skills

Circle theorems

Circle theorems for GCSE Food Preparation Edexcel: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Food Preparation
  • Spec G4 · G9 · G6
  • 6 min read
  • 9 revision boxes

Introduction

2 boxes
2 min read

What is circle theorems?

Listen to this box

Transcript

A short spoken summary of circle theorems and where it is used.

A spoken walk-through of circle theorems before you read the notes.
The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ≈160\approx 160.
6 rows

The circle theorems reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ×10\times 10 moves every digit one column left.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
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
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 4

Learning

5 boxes
5 steps

How to work with circle theorems

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
  1. Read the question and write down what is being asked for.
  2. Set out the working for circle theorems 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: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Circle theorems

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ×10\times 10 moves every digit one column left.

  • Rule 1

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

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with circle theorems

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}.
  1. Read the question and write down what is being asked for.
  2. Set out the working for circle theorems 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: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: Circle theorems

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 circle theorems laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ×10\times 10 moves every digit one column left.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left
4 steps

How to work with circle theorems

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 circle theorems 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 circle theorems 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: ≈160\approx 160.
Answer: ≈160\approx 160

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Examples

2 boxes
3 marks · worked

Worked example: circle theorems

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: ≈160\approx 160.
2 marks · worked

Practice question 9: 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.
The layout below is the one the mark scheme expects.

Diagram showing circle theorems 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 circle theorems usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Food Preparation Edexcel paper?
Yes — it sits in the Sources and evidence strand.