PAss Functional Skills

Curved graphs

Curved graphs for A Level Environmental Science AQA: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Environmental Science
  • Spec S6
  • 4 min read
  • 8 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.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
4 rows

The curved graphs reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 3 column 1
Row 3 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 4 column 1
Row 4 column 2
49=7\sqrt{49} = 7

Learning

4 boxes
4 steps

How to work with curved graphs

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.
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.
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: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: Curved graphs

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

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

  • Rule 3

    How curved graphs behaves in the 3rd of the cases the specification names.
    ≈160\approx 160
5 steps

How to work with curved graphs

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

Key facts: Curved graphs

Practise the routine version until it is automatic, then move to the multi-step questions.
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.
    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.
    34×25\frac{3}{4} \times \frac{2}{5}

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Examples

2 boxes
2 marks · worked

Worked example: curved graphs

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: ×10\times 10 moves every digit one column left.
2 marks · worked

Practice question 8: a2+b2=c2a^2 + b^2 = c^2

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

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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 A Level Environmental Science AQA paper?
Yes — it sits in the Forces and motion strand.