PAss Functional Skills

Percentages and interest

Percentages and interest for A Level Maths AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Maths
  • Higher
  • Spec R12 · R3 · R20
  • 5 min read
  • 8 revision boxes

Introduction

2 boxes
3 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.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ≈160\approx 160.
3 rows

The percentages and interest reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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: 49=7\sqrt{49} = 7.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 3 column 4
Row 3 column 5

Learning

4 boxes
4 steps

How to work with percentages and interest

Read the units in the question before you start; a converted unit is the most common slip.
  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: ≈160\approx 160.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Percentages and interest

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • Rule 1

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

  • 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

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.
  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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Percentages and interest

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

  • Rule 1

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

  • Rule 2

    How percentages and interest behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

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Examples

2 boxes
2 marks · worked

Worked example: percentages and interest

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

Practice question 8: 34×25\frac{3}{4} \times \frac{2}{5}

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

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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 A Level Maths AQA Higher paper?
Yes — it sits in the Probability strand.