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Inequalities

Inequalities for GCSE Combined Science OCR Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • OCR
  • Combined Science
  • Foundation
  • Spec A17 · A6 · A9
  • 11 min read
  • 8 revision boxes

Introduction

2 boxes
2 min read

What is inequalities?

Listen to this box

Transcript

A short spoken summary of inequalities and where it is used.

A spoken walk-through of inequalities before you read the notes.
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 inequalities laid out step by step

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

The inequalities reference table

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: ≈160\approx 160.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4

Learning

4 boxes
5 steps

How to work with inequalities

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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 inequalities 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: ×10\times 10 moves every digit one column left
2 rules

Key facts: Inequalities

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 inequalities laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

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

  • Rule 2

    How inequalities behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
4 steps

How to work with inequalities

The specification wording is precise here, and the mark scheme follows that wording exactly.
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 inequalities 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: ×10\times 10 moves every digit one column left
3 rules

Key facts: Inequalities

Read the units in the question before you start; a converted unit is the most common slip.

  • Rule 1

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

  • Rule 2

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

  • Rule 3

    How inequalities 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
3 marks · worked

Worked example: inequalities

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 inequalities laid out step by step

The same idea drawn out, so the method is visible.
1 marks · worked

Practice question 8: ×10\times 10 moves every digit one column left

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

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Common questions

How many marks is inequalities usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Combined Science OCR Foundation paper?
Yes — it sits in the Cells and organisation strand.