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Four operations

Four operations for A Level Design and Technology OCR: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Design and Technology
  • Spec N12 · N4
  • 12 min read
  • 9 revision boxes

Introduction

2 boxes
2 min read

What is four operations?

Listen to this box

Transcript

A short spoken summary of four operations and where it is used.

A spoken walk-through of four operations before you read the notes.
Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
4 rows

The four operations reference table

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 four operations laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

5 boxes
5 steps

How to work with four operations

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  1. Read the question and write down what is being asked for.
  2. Set out the working for four operations 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: a2+b2=c2a^2 + b^2 = c^2.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Four operations

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

  • Rule 1

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

  • Rule 2

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

How to work with four operations

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 four operations 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: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Four operations

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 four operations laid out step by step

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

  • Rule 1

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

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
3 steps

How to work with four operations

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 four operations 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 four operations 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: a2+b2=c2a^2 + b^2 = c^2

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Examples

2 boxes
3 marks · worked

Worked example: four operations

Work through the method one line at a time and write down what changes at each step.
Worth knowing: ≈160\approx 160.
4 marks · worked

Practice question 9: a2+b2=c2a^2 + b^2 = c^2

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: ×10\times 10 moves every digit one column left.

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Common questions

How many marks is four operations usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Design and Technology OCR paper?
Yes — it sits in the Number strand.