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Percentages and interest

Percentages and interest for GCSE Maths AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Maths
  • Higher
  • Spec G15 · G2
  • 14 min read
  • 7 revision boxes

Introduction

2 boxes
4 min read

What is percentages and interest?

Listen to this box

Transcript

A short spoken summary of percentages and interest and where it is used.

A spoken walk-through of percentages and interest 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 percentages and interest laid out step by step

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

The percentages and interest reference table

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 percentages and interest laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ≈160\approx 160.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 1 column 4
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 2 column 4

Learning

3 boxes
3 steps

How to work with percentages and interest

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.
  1. Read the question and write down what is being asked for.
  2. Set out the working for percentages and interest 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: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Percentages and interest

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.

  • Rule 1

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

  • Rule 2

    How percentages and interest behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7
4 steps

How to work with percentages and interest

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.
  1. Read the question and write down what is being asked for.
  2. Set out the working for percentages and interest 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: 34×25\frac{3}{4} \times \frac{2}{5}

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Examples

2 boxes
2 marks · worked

Worked example: percentages and interest

Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
2 marks · worked

Practice question 7: x2+5x+6=0x^2 + 5x + 6 = 0

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 percentages and interest 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.

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Common questions

How many marks is percentages and interest usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Maths AQA Higher paper?
Yes — it sits in the Probability strand.