AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 6

Mark scheme

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Q Answer Mark Comments

6 × 10–3 condone extra zeros which do not affect

the value eg 6.0 × 10–3

B1 correct value not in standard form

(allow value written as a × 10n )

eg 0.006 or 0.6 × 10–2

or

B2 given calculation with 0.6 written as

6 × 10–1 eg 6 × 10–1 ÷ 100

6(a)

or

value whose only non-zero digit is 6

correctly converted to standard form

answer

eg 0.0006 = 6 × 10–4

Additional Guidance

6 × 10–1 ÷ 102 B1

1.2 × 108 condone extra zeros which do not affect

the value eg 1.20 × 108

B1 120000000 or 120 million

or 12 × 107 or 120 × 106

or 1.2 × 10a × 10b where a + b = 8

6(b) B2

or

value whose only non-zero digits are 12

correctly converted to standard form

answer

eg 12 000 000 = 1.2 × 107

How to answer it

Calculating and Converting with Standard Form

📌 What this question tests

This question assesses your ability to perform non-calculator arithmetic with decimals and powers of 10, and correctly express the final values in standard form ( A × 10ⁿ where 1 ≤ A < 10 and n is an integer).

Question 6 (a)

Work out 0.6 ÷ 100. Give your answer in standard form. [2 marks]

📐 Step-by-Step Calculation

Method 1: Decimal Division first

Divide by 100: Move digits 2 places to the right.
0.6 ÷ 100 = 0.006
Convert to standard form: Place the decimal point after the first non-zero digit ( 6 ).
0.006 = 6 × 10⁻³

Method 2: Convert to index form first

Write 0.6 as 6 × 10⁻¹ and 100 as 10² .
Subtract indices: (6 × 10⁻¹) ÷ 10² = 6 × 10⁻¹⁻² = 6 × 10⁻³

✅ Final Answer & Mark Breakdown

6 × 10⁻³

B2: Complete correct answer 6 × 10⁻³ (also accepts 6.0 × 10⁻³ ).
B1 (Partial mark):

Correct value not in standard form, e.g. 0.006 or 0.6 × 10⁻²
Setting up calculation correctly: 6 × 10⁻¹ ÷ 100 or 6 × 10⁻¹ ÷ 10²
A place value slip correctly converted to standard form (e.g. 0.0006 = 6 × 10⁻⁴ ).

💡 Key Knowledge

Standard form rule: The front number A must strictly satisfy 1 ≤ A < 10.
Numbers smaller than 1 always have a negative power of 10.
Counting places: In 0.006 , the digit 6 is in the 3rd decimal place (thousandths), so the power is -3 .

❌ Common Traps

Leaving answer as 0.6 × 10⁻²: Although numerically correct, 0.6 is less than 1, so it is not in standard form (loses 1 mark).
Wrong power sign: Writing 6 × 10³ instead of 6 × 10⁻³ . Remember that 6 × 10³ = 6000 .
Counting zeros instead of decimal places: Thinking two zeros after the decimal point means the index is -2 instead of -3 .

Question 6 (b)

Work out 40 × 30 × 10⁵. Give your answer in standard form. [2 marks]

📐 Step-by-Step Calculation

Multiply the non-power numbers first:
40 × 30 = 1200
Combine with the existing power of 10:
1200 × 10⁵
Adjust to standard form:
Rewrite 1200 as 1.2 × 10³ .
(1.2 × 10³) × 10⁵ = 1.2 × 10³⁺⁵ = 1.2 × 10⁸

✅ Final Answer & Mark Breakdown

1.2 × 10⁸

B2: Complete correct answer 1.2 × 10⁸ (condones extra trailing zeros like 1.20 × 10⁸ ).
B1 (Partial mark):

Correct value as ordinary number: 120 000 000 or 120 million
Correct value partially converted: 12 × 10⁷ or 120 × 10⁶
Split indices: 1.2 × 10ᵃ × 10ᵇ where a + b = 8
Incorrect number of zeros correctly converted: e.g. 12 000 000 = 1.2 × 10⁷ .

🧠 Exam Technique: Adjusting the Power

When you have a number like 1200 × 10⁵ :

To make 1200 become 1.2 , you divide by 1000 (move the decimal point 3 places left).
To keep the total value identical, you must multiply the power term by 10³ (add 3 to the power):
5 + 3 = 8 → 1.2 × 10⁸ .

❌ Common Traps

Stopping at 12 × 10⁷ or 1200 × 10⁵: Neither is in standard form because the lead number is not between 1 and 10.
Subtracting powers instead of adding: Students often mistakenly decrease the power when moving the decimal left, giving 1.2 × 10² .
Miscounting zeros: Calculating 40 × 30 = 120 instead of 1200 .

Topics

Number · 3.1.1 Structure and calculation