AQA GCSE Mathematics Paper 3 (Higher), June 2025: Question 1

Unit Conversions: Imperial to Metric Mass

What this question tests

This question assesses your ability to convert between units using a given conversion rate ( 2.2 pounds = 1 kg ). Specifically, it checks whether you can correctly identify the direction of the operation (multiplying vs dividing) and handle decimal values accurately.

Question 1 • 2 Marks

Convert 8.25 pounds into kilograms

Given conversion: 2.2 pounds = 1 kilogram

📐 Step-by-Step Calculation

Step 1: Identify the relationship
Every 1 kg contains 2.2 pounds:

1 kg = 2.2 pounds

Step 2: Choose the correct operation
To convert from pounds to kilograms, you divide by the conversion factor:

8.25 ÷ 2.2

Step 3: Evaluate accurately

8.25 ÷ 2.2 = 3.75

Final result: 3.75 kg

✅ Mark Scheme Breakdown

[M1] Method Mark:
Awarded for showing 8.25 ÷ 2.2 (or an equivalent method such as 8.25 / 2.2 ).
[A1] Accuracy Mark:
Awarded for 3.75 (oe).
Note: The examiner will accept 3.8 only if 3.75 is explicitly shown in your working.

Total: 2 marks available.

💡 Key Knowledge

Direction rule: Going from a smaller unit to a larger unit requires division. Since 1 pound is less than 1 kilogram (1 lb ≈ 0.45 kg), there will be fewer kilograms than pounds.
Sense check: Because 2.2 lb = 1 kg:
• 2.2 lb = 1 kg
• 4.4 lb = 2 kg
• 6.6 lb = 3 kg
• 8.8 lb = 4 kg
8.25 lb is just under 8.8 lb, so the answer must be slightly under 4 kg. 3.75 kg makes complete sense!

🧠 Exam Technique

Always write down your method: Even if you make an arithmetic error on your calculator or paper, writing 8.25 ÷ 2.2 guarantees the M1 mark.
Do not round prematurely: Always write the exact value ( 3.75 ) first before choosing whether to round.
Check the provided unit: The answer line already says kg . Do not convert further!

❌ Common Traps & Mistakes (from Examiner Reports)

Multiplying instead of dividing: Calculating 8.25 × 2.2 = 18.15 . A quick sense check avoids this: 8.25 lb cannot be 18 kg when 1 kg is over 2 pounds!
Unnecessary further conversions (M1A0): Finding 3.75 and then multiplying by 1000 to write 3750 g on the answer line. The mark scheme specifies "Do not ignore further working". Writing 3750 next to the printed unit "kg" forfeits the accuracy mark!
Embedded answers without a clear statement (M1A0): Writing only 2.2 × 3.75 = 8.25 without clearly stating 3.75 on the answer line.