PAss Functional Skills

Inequalities

Inequalities for GCSE Maths Edexcel Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Maths
  • Higher
  • Spec A9
  • 13 min read
  • 9 revision boxes

Introduction

2 boxes
4 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.
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.
3 rows

The inequalities reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
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
49=7\sqrt{49} = 7
Row 4 column 1
Row 4 column 2
x2+5x+6=0x^2 + 5x + 6 = 0

Learning

5 boxes
3 steps

How to work with inequalities

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ≈160\approx 160.
  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: ≈160\approx 160.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Inequalities

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 inequalities 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.

  • Rule 1

    How inequalities behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

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

  • Rule 3

    How inequalities behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
3 steps

How to work with inequalities

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
  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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: Inequalities

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 inequalities 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.

  • 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.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How inequalities behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with inequalities

The examiner marks the working, so a correct answer with no method still drops marks.
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 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: ≈160\approx 160.
Answer: ≈160\approx 160

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Examples

2 boxes
1 marks · worked

Worked example: inequalities

This idea appears again in the higher-mark questions, so it is worth over-learning.
4 marks · worked

Practice question 9: ≈160\approx 160

Read the units in the question before you start; a converted unit is the most common slip.
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: 49=7\sqrt{49} = 7.

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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 Maths Edexcel Higher paper?
Yes — it sits in the Cells and organisation strand.