AQA GCSE Mathematics Paper 2 (Higher), June 2025: Question 9

1 mark · Medium difficulty · Reasoning

Evaluate whether doubling follower count from 35 000 to 70 000 represents an increase of 200%, giving a reason.

Practise this question

Question

Question 9 states that an influencer's followers increase from 35 000 to 70 000. The influencer claims their followers increased by 200% because 70 000 is 35 000 times 2. Checkboxes are provided for 'Yes' and 'No', followed by the prompt: 'Give a reason for your answer.' Worth 1 mark.

Mark scheme

Show the mark scheme Mark scheme for question 9: B1 mark awarded for 'No' with a correct reason, such as 'it's gone up by 100%' or 'going up by 200% would be 105 000'. Additional guidance provides examples of accepted statements like (70000 - 35000)/35000 = 100% and rejected statements such as incomplete calculations or incorrect percentages.

How to answer it

Understanding Percentage Increase: The "Doubling" Trap

📌 What this question tests

This question evaluates your conceptual understanding of percentage increase versus percentage of an amount, specifically:

  • Understanding that doubling a value (multiplying by 2) represents a 100% increase, not a 200% increase.
  • Applying the percentage change formula: (Change ÷ Original) × 100% .
  • Constructing a valid written justification with accurate supporting mathematical facts.

Question 9 Breakdown

1 Mark • Target Skill: Mathematical Reasoning & Percentages

✅ Correct Answer

Box to tick: No

Acceptable reasons (any one of the following):

  • It has increased by 100%.
  • A 200% increase would give 105 000 followers (since 35 000 + 70 000 = 105 000).
  • Adding 100% gives 70 000.
  • (70 000 − 35 000) ÷ 35 000 = 100%

💡 Key Knowledge

  • The Original is 100%: The starting value always represents 100%.
  • "Percentage of" vs "Increase of":
    • 70 000 is 200% of 35 000.
    • However, the increase is only the extra amount: 70 000 − 35 000 = 35 000 (which is 100%).
  • Multiplier Rule:
    A 100% increase = multiply by 2.0 (1 + 1.00)
    A 200% increase = multiply by 3.0 (1 + 2.00)

📐 Step-by-Step Proofs

Proof Method 1: Calculate Actual % Increase
  1. Find the absolute increase:
    70 000 − 35 000 = 35 000
  2. Divide by the original amount:
    35 000 ÷ 35 000 = 1
  3. Convert to a percentage:
    1 × 100% = 100% (not 200%)
Proof Method 2: Calculate a True 200% Increase
  1. Find 200% of the original:
    2 × 35 000 = 70 000
  2. Add this increase onto original total:
    35 000 + 70 000 = 105 000
  3. Conclusion:
    A 200% increase results in 105 000, not 70 000.

🧠 Exam Technique & Examiner Commentary

  • Mark Scheme Requirement: This is a B1 mark. You must tick No and provide a valid reason to secure the mark.
  • Keep it simple: Writing "No, it's gone up by 100%" is completely sufficient and avoids making arithmetic slips elsewhere.
  • Avoid "Choice" deductions: If you write two contradictory statements (e.g. one correct and one mathematically incorrect), examiners call this a "choice" and award 0 marks.
  • Non-contradictory extra comments (such as "influencers don't get that many followers") are ignored as long as your mathematical reason is correct.

❌ Common Errors to Avoid

  • Incomplete Calculation: Writing just (70 000 − 35 000) ÷ 35 000 without showing that it equals 100% scores 0 marks.
  • Incorrect Arithmetic in Reason: Writing "No, because a 200% increase would be 140 000" scores 0 marks because 140 000 is incorrect (it would be 105 000).
  • Stating Value Without Percentage: Writing "No, it only went up by 35 000" scores 0 marks because it fails to explain why 200% is incorrect.
  • The 50% Confusion: Saying "It went up by 50%" (incorrectly dividing the increase by the new total rather than the original).
Mark Scheme Reference: [1 mark total] Award B1 for "No" selected along with an accurate reason confirming either that the increase is 100%, or that an increase of 200% leads to 105 000.

Topics

Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change

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