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Inequalities

Inequalities for A Level Engineering AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Engineering
  • Higher
  • Spec R10 · R12
  • 5 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.
Read the units in the question before you start; a converted unit is the most common slip.
5 rows

The inequalities reference table

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.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 4 column 1
Row 4 column 2
a2+b2=c2a^2 + b^2 = c^2

Learning

5 boxes
3 steps

How to work with 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: 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.
  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: ≈160\approx 160
2 rules

Key facts: Inequalities

Check the answer against an estimate before you move on, so a place-value slip is caught here.

  • Rule 1

    How inequalities behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • 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
5 steps

How to work with inequalities

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

Key facts: Inequalities

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.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • Rule 1

    How inequalities behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

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

  • Rule 3

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

How to work with inequalities

Work through the method one line at a time and write down what changes at each step.
  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: x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
1 marks · worked

Worked example: inequalities

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.
3 marks · worked

Practice question 9: ≈160\approx 160

Practise the routine version until it is automatic, then move to the multi-step questions.

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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 A Level Engineering AQA Higher paper?
Yes — it sits in the Cells and organisation strand.