PAss Functional Skills

Indices and standard form

Indices and standard form for ESOL Business Studies: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Business Studies
  • Spec P9
  • 14 min read
  • 10 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.
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 indices and standard form laid out step by step

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

The indices and standard form reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
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
49=7\sqrt{49} = 7
Row 2 column 4
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 3 column 4

Learning

6 boxes
3 steps

How to work with indices and standard form

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  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: ≈160\approx 160.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Indices and standard form

Practise the routine version until it is automatic, then move to the multi-step questions.

  • Rule 1

    How indices and standard form behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How indices and standard form behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
5 steps

How to work with indices and standard form

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 indices and standard form 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 indices and standard form 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: ≈160\approx 160.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Indices and standard form

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 indices and standard form laid out step by step

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

  • Rule 1

    How indices and standard form behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How indices and standard form behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
4 steps

How to work with indices and standard form

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
  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.
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: ≈160\approx 160
3 rules

Key facts: Indices and standard form

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: 49=7\sqrt{49} = 7.

  • Rule 1

    How indices and standard form behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How indices and standard form behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
3 marks · worked

Worked example: indices and standard form

The examiner marks the working, so a correct answer with no method still drops marks.
2 marks · worked

Practice question 10: x2+5x+6=0x^2 + 5x + 6 = 0

This idea appears again in the higher-mark questions, so it is worth over-learning.

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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 ESOL Business Studies paper?
Yes — it sits in the Probability strand.