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Four operations

Four operations for Access to HE Design and Technology: what it means, how to set the working out, and the questions it is asked in.
  • Access to HE
  • Design and Technology
  • Spec G11 · G17
  • 11 min read
  • 8 revision boxes

Introduction

2 boxes
3 min read

What is four operations?

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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.
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.
2 rows

The four operations reference table

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ≈160\approx 160.
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
Row 4 column 1
Row 4 column 2
a2+b2=c2a^2 + b^2 = c^2

Learning

4 boxes
3 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: 49=7\sqrt{49} = 7.
Answer: 49=7\sqrt{49} = 7
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.
    ×10\times 10 moves every digit one column left

  • Rule 2

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

  • Rule 3

    How four operations behaves in the 3rd of the cases the specification names.
    ≈160\approx 160
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.
  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: 49=7\sqrt{49} = 7.
Answer: ≈160\approx 160
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.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 3

    How four operations behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

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Examples

2 boxes
2 marks · worked

Worked example: four operations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
4 marks · worked

Practice question 8: ≈160\approx 160

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.
Worth knowing: ≈160\approx 160.

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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 Access to HE Design and Technology paper?
Yes — it sits in the Algebra strand.