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Curved graphs

Curved graphs for GCSE Music AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Music
  • Foundation
  • Spec N19 · N7 · N12
  • 12 min read
  • 9 revision boxes

Introduction

2 boxes
3 min read

What is curved graphs?

Listen to this box

Transcript

A short spoken summary of curved graphs and where it is used.

A spoken walk-through of curved graphs before you read the notes.
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.
5 rows

The curved graphs reference table

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 1 column 4
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4

Learning

5 boxes
5 steps

How to work with curved graphs

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 curved graphs 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: ×10\times 10 moves every digit one column left
3 rules

Key facts: Curved graphs

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 curved graphs 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 curved graphs behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How curved graphs behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 3

    How curved graphs behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
4 steps

How to work with curved graphs

Read the units in the question before you start; a converted unit is the most common slip.
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 curved graphs 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: a2+b2=c2a^2 + b^2 = c^2.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Curved graphs

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How curved graphs behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How curved graphs behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 3

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

How to work with curved graphs

Work through the method one line at a time and write down what changes at each step.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for curved graphs 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: 49=7\sqrt{49} = 7.
Answer: 49=7\sqrt{49} = 7

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Examples

2 boxes
2 marks · worked

Worked example: curved graphs

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 curved graphs 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.
3 marks · worked

Practice question 9: ×10\times 10 moves every digit one column left

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 curved graphs laid out step by step

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

Practice bank

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Topics
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Common questions

How many marks is curved graphs usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Music AQA Foundation paper?
Yes — it sits in the Forces and motion strand.