AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 5

2 marks · Easy difficulty · Reasoning

Show that the total distance walked (400 metres, 250 metres, and 380 metres) is greater than 1 kilometre.

Practise this question

Question

Question 5 states: 'Jenny walks 400 metres to the shop, 250 metres to the park, 380 metres home. Show that Jenny walks more than 1 kilometre.' The question is worth 2 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 5: M1 is awarded for adding the distances (400 + 250 + 380 or 1030) or converting one or more distances to kilometres or showing 1000. A1 is awarded for showing 1030 and 1000, 1.03, or stating 30 metres more.

How to answer it

Metric Distance Conversions & Comparison

📋 What this question tests

This question tests your ability to add several distances together in metres (m), recall and apply the metric conversion factor between metres and kilometres ( 1 km = 1000 m ), and present a clear numerical comparison to satisfy a "Show that..." instruction.

Question 5 (2 Marks)

Full Solution & Examiner Guidance

📐 Step-by-Step Method

You can solve this using either of two simple approaches:

Method A (Compare in metres):

  1. Sum the distances walked:
    400 m + 250 m + 380 m = 1030 m
  2. State the comparison value:
    1 km = 1000 m
  3. Conclude:
    1030 m > 1000 m (or note she walks 30 m more).

Method B (Compare in kilometres):

  1. Sum total distance: 1030 m
  2. Convert to km: 1030 ÷ 1000 = 1.03 km
  3. Conclude: 1.03 km > 1 km

✅ Mark Scheme Breakdown

  • Method Mark [M1]:
    For showing the addition 400 + 250 + 380 (or getting 1030 ), OR showing any individual conversion (e.g. 0.4 , 0.25 , 0.38 ), OR stating 1000 .
  • Accuracy Mark [A1]:
    For clearly showing both values: 1030 and 1000 , OR calculating 1.03 (km), OR stating it is 30 (metres) extra.
Special Case: Writing 10.3 gains SC1 if conversion arithmetic slipped by a factor of 10.

💡 Key Knowledge

  • The prefix kilo- always means 1000.
  • 1 km = 1000 m
  • To convert from metres to kilometres, divide by 1000 ( m ÷ 1000 = km ).
  • To convert from kilometres to metres, multiply by 1000 ( km × 1000 = m ).
  • When comparing two quantities, always convert them into the same unit before comparing.

🧠 Exam Technique: "Show that..."

  • Never just write words: A "Show that" question requires numerical proof. Writing "Yes, she walked more than 1 km" scores 0 marks without numbers.
  • Show the threshold: Explicitly state 1000 m or convert to 1.03 km to make the direct comparison obvious to the examiner.
  • Don't panic about notation: The examiner ignores inequality signs, so whether you write 1030 > 1000 or just show both numbers side by side, full marks are awarded.

❌ Common Traps & Misconceptions

  • Wrong metric conversion: Thinking that 1 km = 100 m (confusing kilometres with centimetres).
  • Decimal point errors: Writing 1030 m = 10.3 km or 1.3 km instead of 1.03 km .
  • Double-counting routes: Adding an extra leg, e.g., working out 1030 and then adding another 380 on top (this loses the A mark: M1A0).
  • Stopping halfway: Finding 1030 m but never mentioning 1000 m or converting to km.

Topics

Number · Ratio, proportion and rates of change · 3.1.1 Structure and calculation · 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.