PAss Functional Skills

Circle theorems

Circle theorems for A Level Combined Science Edexcel Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • Edexcel
  • Combined Science
  • Foundation
  • Spec R11 · R18 · R17
  • 12 min read
  • 10 revision boxes

Introduction

2 boxes
4 min read

What is circle theorems?

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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.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
5 rows

The circle theorems reference table

Work through the method one line at a time and write down what changes at each step.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4

Learning

6 boxes
4 steps

How to work with circle theorems

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 circle theorems 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}.
  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: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Circle theorems

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How circle theorems behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
4 steps

How to work with circle theorems

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.
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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: Circle theorems

Work through the method one line at a time and write down what changes at each step.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7
4 steps

How to work with circle theorems

The specification wording is precise here, and the mark scheme follows that wording exactly.
  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: ×10\times 10 moves every digit one column left.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Circle theorems

Read the units in the question before you start; a converted unit is the most common slip.

  • 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.
    ≈160\approx 160

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Examples

2 boxes
4 marks · worked

Worked example: circle theorems

Work through the method one line at a time and write down what changes at each step.
1 marks · worked

Practice question 10: ≈160\approx 160

The examiner marks the working, so a correct answer with no method still drops marks.
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 A Level Combined Science Edexcel Foundation paper?
Yes — it sits in the Sources and evidence strand.