PAss Functional Skills

Circle theorems

Circle theorems for Access to HE Combined Science: what it means, how to set the working out, and the questions it is asked in.
  • Access to HE
  • Combined Science
  • Spec G14
  • 7 min read
  • 7 revision boxes

Introduction

2 boxes
2 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.
The specification wording is precise here, and the mark scheme follows that wording exactly.
3 rows

The circle theorems reference table

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 3 column 1
Row 3 column 2
≈160\approx 160

Learning

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

Key facts: 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.

  • 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.
    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

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.
  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: ≈160\approx 160

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Examples

2 boxes
4 marks · worked

Worked example: circle theorems

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 circle theorems laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
1 marks · worked

Practice question 7: x2+5x+6=0x^2 + 5x + 6 = 0

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

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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 Access to HE Combined Science paper?
Yes — it sits in the Sources and evidence strand.