AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 8

4 marks · Easy difficulty · Short Answer

Convert between units of time (hours to minutes), mass (grams to kilograms), and distance (kilometres to miles using a given conversion rate).

Practise this question

Question

Question 8 consists of three parts: (a) asks to convert 3 and a half hours to minutes for 1 mark; (b) asks to convert 1400 grams to kilograms for 1 mark; (c) asks to convert 32 kilometres to miles using the conversion 8 kilometres = 5 miles for 2 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 8: 8(a) gives 210 with mark B1. 8(b) gives 1.4 with mark B1, noting to condone trailing zeros such as 1.40. 8(c) awards M1 for 32 divided by 8, or 4, or 32 times 5, or 160, or 5 divided by 8, or 8 divided by 5; and A1 for the final answer 20.

How to answer it

Converting Units of Time, Mass, and Distance

📌 What This Question Tests

This question assesses your ability to convert between different standard metric and imperial units across three everyday contexts:

  • Time: Converting mixed hours to minutes using the fact that 1 hour = 60 minutes.
  • Metric Mass: Converting grams to kilograms using the base prefix kilo = 1000.
  • Proportional Distance: Using a given ratio conversion (8 kilometres = 5 miles) to convert between metric and imperial distances.
Question 8 (a) • 1 Mark

Convert 3 ½ hours to minutes

Topic: Units of Time

📐 Step-by-Step Calculation

  1. Identify the conversion factor: 1 hour = 60 minutes
  2. Convert the whole hours: 3 × 60 = 180 minutes
  3. Convert the half hour: ½ × 60 = 30 minutes
  4. Add them together: 180 + 30 = 210 minutes

✅ Correct Answer

210 minutes

Mark Scheme: B1 for fully correct value of 210.

💡 Key Knowledge

  • Time does not use base 10 (decimals)! Always use 60 minutes = 1 hour .
  • Alternative method: Convert to an improper fraction or decimal first:
    3.5 × 60 = 210

❌ Common Errors

  • Treating time as base 100: Thinking 3 ½ hours means 350 minutes or writing 3.5 × 100.
  • Mixing up operations: Dividing by 60 instead of multiplying.
Question 8 (b) • 1 Mark

Convert 1400 grams to kilograms

Topic: Metric Mass

📐 Step-by-Step Calculation

  1. Recall the prefix kilo- means 1000: 1 kg = 1000 g
  2. Converting from a smaller unit (g) to a larger unit (kg) requires division:
  3. Calculate: 1400 ÷ 1000 = 1.4 kg

✅ Correct Answer

1.4 kg

Mark Scheme: B1 for 1.4 (Additional Guidance: condone trailing zeros such as 1.40).

🧠 Exam Technique

  • To divide by 1000, shift the digits 3 places to the right relative to the decimal point: 1400.0 → 1.4
  • Sense check: A kilogram is heavier than a gram, so the number of kilograms must be smaller than the number of grams.

❌ Common Errors

  • Multiplying instead of dividing: Giving an unreasonable answer like 1 400 000 kg.
  • Wrong power of 10: Dividing by 100 instead of 1000 to get 14 kg.
Question 8 (c) • 2 Marks

Convert 32 kilometres to miles (using 8 km = 5 miles)

Topic: Proportion & Unit Conversions

📐 Step-by-Step Calculation

  1. Find the scale factor: How many groups of 8 km fit into 32 km?
    32 ÷ 8 = 4
  2. Scale up the miles: Multiply the number of miles per 8 km by the scale factor:
    4 × 5 = 20 miles

✅ Correct Answer

20 miles

Mark Scheme:
• M1: For 32 ÷ 8 (or 4), OR 32 × 5 (or 160), OR 5 ÷ 8 (0.625), OR listing multiples 8, 16, 24, 32 .
• A1: Fully correct answer of 20 .

🧠 Alternative Method (Unitary Method)

  • Find 1 km in miles: 5 ÷ 8 = 0.625 miles
  • Multiply by 32 km: 32 × 0.625 = 20 miles
  • Top Tip: The scale factor method ( 32 ÷ 8 = 4 ) is usually much faster and avoids decimals!

❌ Common Errors

  • Flipping the ratio: Multiplying 32 by 8 and dividing by 5 ( 51.2 ) — remember miles are longer than kilometres, so the number of miles must be smaller than 32.
  • Stopping halfway: Writing 4 as the final answer after calculating 32 ÷ 8 , forgetting to multiply by 5.

Topics

Number · Ratio, proportion and rates of change · 3.1.3 Measures and accuracy · 3.3 Ratio, proportion and rates of change

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.