AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 15

1 mark · Easy difficulty · Reasoning

Determine whether Warren is correct about the perimeter of a rectangle with area 60 cm² and side length 10 cm, showing working to support the answer.

Practise this question

Question

Question 15 states that a rectangle has an area of 60 cm² and a side length of 10 cm. A speech statement from Warren reads: 'The perimeter of the rectangle is 32 cm because 60 ÷ 10 = 6'. Below this, the question asks 'Is Warren correct?', provides two tick boxes labelled 'Yes' and 'No', and instructs students to 'Show working to support your answer', worth 1 mark.

Mark scheme

Show the mark scheme Mark scheme table for question 15 showing B1 for 'Yes with valid working', with the example 'Yes and 6 + 10 + 6 + 10 (= 32)'. Additional guidance specifies that ticking Yes without valid reason awards B0, while accepted workings include '2 × (10 + 6) = 32', '20 + 12 = 32', and drawing a labelled rectangle with an explanation that sides are added to find the perimeter.

How to answer it

Reasoning with Area and Perimeter of a Rectangle

📌 What this question tests

This question tests your ability to connect area and perimeter, complete missing steps in mathematical reasoning, and provide a valid justification rather than just guessing "Yes" or "No".

Question 15 (1 Mark)

Evaluating a statement about the perimeter of a rectangle

💡 Key Knowledge

  • Area of a rectangle = length × width
  • If area = 60 cm² and one side = 10 cm, the other side is 60 ÷ 10 = 6 cm .
  • Perimeter = distance all the way around = 2 × (length + width) or side₁ + side₂ + side₃ + side₄ .
  • Warren's calculation ( 60 ÷ 10 = 6 ) finds the missing side length, not the perimeter itself. However, his final statement that the perimeter is 32 cm is indeed correct!

📐 Step-by-Step Calculation

  1. Find the other side:
    Width = 60 ÷ 10 = 6 cm
  2. Calculate the perimeter:
    Perimeter = 10 + 6 + 10 + 6 = 32 cm
    or 2 × (10 + 6) = 2 × 16 = 32 cm
    or 20 + 12 = 32 cm
  3. Conclude:
    Since the perimeter really is 32 cm, Warren is Yes (correct).

✅ Acceptable Full-Mark Responses [1 Mark]

Tick Yes AND show a complete perimeter calculation, such as:

  • Tick Yes and write: 6 + 10 + 6 + 10 = 32
  • Tick Yes and write: 2 × (10 + 6) = 32
  • Tick Yes and write: 20 + 12 = 32
  • Tick Yes and write: "2 lots of 10 and 2 lots of 6 make 32"
  • Tick Yes, draw a rectangle labelled with sides 10, 10, 6, 6 and state: "You add the sides to get the perimeter"
Mark Scheme Breakdown:
B1: Yes ticked with valid working shown.

❌ Common Errors (Score 0 Marks)

  • Ticking "Yes" without any working: A bare guess receives 0 marks.
  • Just repeating Warren's division: Writing only "60 ÷ 10 = 6" or "because 60 ÷ 10 is 6" does not explain where 32 came from!
  • Incomplete explanation: Writing "the sides are 10 and 6 so perimeter is 32" without showing the addition.
  • Arithmetic slips: Writing 6 + 10 + 6 + 10 but calculating the wrong total (e.g. 30).
  • Drawing sides without explanation: Drawing a rectangle with sides labelled 10 and 6 but not indicating that you add all four sides together.

🧠 Exam Technique & Examiner Insight

  • Explain the 'missing step': Warren skipped the step between finding the missing side (6 cm) and the final perimeter (32 cm). Your job in "Show working to support your answer" is to bridge that gap with clear arithmetic.
  • Always write the calculation: Even if a question is only 1 mark, whenever you see tick boxes paired with "Show working to support your answer", the mark is almost always conditional on the working!
  • No box ticked? The mark scheme allows the mark if neither box is ticked but your working explicitly concludes that it is 32 (e.g. 6 + 10 + 6 + 10 so it is 32 ), but don't take that risk—always tick the box!

Topics

Geometry and measures · 3.4.2 Mensuration and calculation

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.