PAss Functional Skills

Circle theorems

Circle theorems for ESOL Sociology: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Sociology
  • Spec A7 · A6
  • 7 min read
  • 7 revision boxes

Introduction

2 boxes
4 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.
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: x2+5x+6=0x^2 + 5x + 6 = 0.
3 rows

The circle theorems 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
×10\times 10 moves every digit one column left
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

3 boxes
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.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
  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: ×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

Practise the routine version until it is automatic, then move to the multi-step questions.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • Rule 3

    How circle theorems behaves in the 3rd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
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: x2+5x+6=0x^2 + 5x + 6 = 0.
  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: 49=7\sqrt{49} = 7

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
2 marks · worked

Worked example: circle theorems

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

Practice question 7: 49=7\sqrt{49} = 7

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: 49=7\sqrt{49} = 7.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
12,000+
Topics
10
Marking and solutions
Instant

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 ESOL Sociology paper?
Yes — it sits in the Sources and evidence strand.