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Indices and standard form

Indices and standard form for GCSE Philosophy Edexcel Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Philosophy
  • Higher
  • Spec R17 · R2
  • 11 min read
  • 7 revision boxes

Introduction

2 boxes
3 min read

What is indices and standard form?

Listen to this box

Transcript

A short spoken summary of indices and standard form and where it is used.

A spoken walk-through of indices and standard form before you read the notes.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
4 rows

The indices and standard form reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 3 column 1
Row 3 column 2
a2+b2=c2a^2 + b^2 = c^2

Learning

3 boxes
5 steps

How to work with indices and standard form

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing indices and standard form laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for indices and standard form 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: ×10\times 10 moves every digit one column left
3 rules

Key facts: Indices and standard form

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 indices and standard form 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 indices and standard form behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How indices and standard form behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • Rule 3

    How indices and standard form behaves in the 3rd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
4 steps

How to work with indices and standard form

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 indices and standard form 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: 34×25\frac{3}{4} \times \frac{2}{5}

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Examples

2 boxes
1 marks · worked

Worked example: indices and standard form

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 indices and standard form laid out step by step

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

Practice question 7: a2+b2=c2a^2 + b^2 = c^2

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

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Common questions

How many marks is indices and standard form usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Philosophy Edexcel Higher paper?
Yes — it sits in the Statistics strand.