PAss Functional Skills

Quadratic expressions

Quadratic expressions for A Level Environmental Science Edexcel: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • Edexcel
  • Environmental Science
  • Spec P14 · P19 · P15
  • 14 min read
  • 7 revision boxes

Introduction

2 boxes
2 min read

What is quadratic expressions?

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Transcript

A short spoken summary of quadratic expressions and where it is used.

A spoken walk-through of quadratic expressions 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 quadratic expressions reference table

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 quadratic expressions 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}.
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
Row 3 column 1
Row 3 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 4

Learning

3 boxes
4 steps

How to work with quadratic expressions

The examiner marks the working, so a correct answer with no method still drops marks.
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 quadratic expressions 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: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Quadratic expressions

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

  • Rule 1

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

  • Rule 2

    How quadratic expressions behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7
5 steps

How to work with quadratic expressions

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 quadratic expressions 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

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Examples

2 boxes
4 marks · worked

Worked example: quadratic expressions

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 quadratic expressions laid out step by step

The same idea drawn out, so the method is visible.
2 marks · worked

Practice question 7: 49=7\sqrt{49} = 7

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 quadratic expressions laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.

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Common questions

How many marks is quadratic expressions usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Environmental Science Edexcel paper?
Yes — it sits in the Transformations strand.