PAss Functional Skills

Inequalities

Inequalities for GCSE Engineering OCR Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • OCR
  • Engineering
  • Higher
  • Spec G1
  • 6 min read
  • 8 revision boxes

Introduction

2 boxes
2 min read

What is inequalities?

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Transcript

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

A spoken walk-through of inequalities before you read the notes.
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: x2+5x+6=0x^2 + 5x + 6 = 0.
5 rows

The inequalities reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2

Learning

4 boxes
5 steps

How to work with inequalities

This idea appears again in the higher-mark questions, so it is worth over-learning.
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: a2+b2=c2a^2 + b^2 = c^2.
Answer: ≈160\approx 160
2 rules

Key facts: 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.

  • 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.
    ×10\times 10 moves every digit one column left

  • Rule 3

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

How to work with inequalities

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.
  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: 49=7\sqrt{49} = 7.
Answer: ≈160\approx 160
3 rules

Key facts: Inequalities

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

  • Rule 1

    How inequalities behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • 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.
    49=7\sqrt{49} = 7

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Examples

2 boxes
3 marks · worked

Worked example: inequalities

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 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.
2 marks · worked

Practice question 8: x2+5x+6=0x^2 + 5x + 6 = 0

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ×10\times 10 moves every digit one column left.

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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 Engineering OCR Higher paper?
Yes — it sits in the Cells and organisation strand.