PAss Functional Skills

Venn diagrams and sets

Venn diagrams and sets for A Level Statistics OCR Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Statistics
  • Foundation
  • Spec R5 · R16 · R4
  • 5 min read
  • 10 revision boxes

Introduction

2 boxes
4 min read

What is venn diagrams and sets?

Listen to this box

Transcript

A short spoken summary of venn diagrams and sets and where it is used.

A spoken walk-through of venn diagrams and sets before you read the notes.
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 venn diagrams and sets 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.
5 rows

The venn diagrams and sets reference table

The examiner marks the working, so a correct answer with no method still drops marks.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4
Row 2 column 5

Learning

6 boxes
5 steps

How to work with venn diagrams and sets

Practise the routine version until it is automatic, then move to the multi-step questions.
  1. Read the question and write down what is being asked for.
  2. Set out the working for venn diagrams and sets 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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: ≈160\approx 160
2 rules

Key facts: Venn diagrams and sets

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

  • Rule 1

    How venn diagrams and sets behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How venn diagrams and sets behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How venn diagrams and sets 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 venn diagrams and sets

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.
  1. Read the question and write down what is being asked for.
  2. Set out the working for venn diagrams and sets 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: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: Venn diagrams and sets

The examiner marks the working, so a correct answer with no method still drops marks.

  • Rule 1

    How venn diagrams and sets behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How venn diagrams and sets behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • Rule 3

    How venn diagrams and sets 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 venn diagrams and sets

Practise the routine version until it is automatic, then move to the multi-step questions.
  1. Read the question and write down what is being asked for.
  2. Set out the working for venn diagrams and sets 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
2 rules

Key facts: Venn diagrams and sets

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

  • Rule 1

    How venn diagrams and sets behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How venn diagrams and sets behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How venn diagrams and sets behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7

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Examples

2 boxes
4 marks · worked

Worked example: venn diagrams and sets

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 venn diagrams and sets 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.
2 marks · worked

Practice question 10: a2+b2=c2a^2 + b^2 = c^2

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 venn diagrams and sets laid out step by step

The same idea drawn out, so the method is visible.

Practice bank

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Topics
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Marking and solutions
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Common questions

How many marks is venn diagrams and sets usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Statistics OCR Foundation paper?
Yes — it sits in the Finance and accounts strand.