PAss Functional Skills

Quadratic expressions

Quadratic expressions 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 G8
  • 12 min read
  • 7 revision boxes

Introduction

2 boxes
1 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.
Work through the method one line at a time and write down what changes at each step.
5 rows

The quadratic expressions 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 quadratic expressions laid out step by step

The same idea drawn out, so the method is visible.
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
×10\times 10 moves every digit one column left
Row 4 column 1
Row 4 column 2
x2+5x+6=0x^2 + 5x + 6 = 0

Learning

3 boxes
5 steps

How to work with quadratic expressions

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 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: ×10\times 10 moves every digit one column left.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Quadratic expressions

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: ×10\times 10 moves every digit one column left.

  • Rule 1

    How quadratic expressions behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How quadratic expressions behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with quadratic expressions

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.
  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: x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
3 marks · worked

Worked example: quadratic expressions

Read the units in the question before you start; a converted unit is the most common slip.
3 marks · worked

Practice question 7: ≈160\approx 160

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 quadratic expressions laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ≈160\approx 160.

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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 Maths AQA Higher paper?
Yes — it sits in the Transformations strand.