AQA GCSE Mathematics Paper 2 (Higher), June 2025: Question 4

3 marks · Medium difficulty · Multi-step Problem

Calculate the total percentage of discs removed from a box given the percentages of red and blue discs and the percentage removed of each color.

Practise this question

Question

Question 4 states: '70% of the discs in a box are red and the rest are blue. 40% of the red discs are removed. 50% of the blue discs are removed. In total, what percentage of the discs are removed from the box?' It provides lines for working and an answer space ending with a percent symbol, allocated 3 marks.

Mark scheme

Show the mark scheme Mark scheme table for question 4. M1 is awarded for finding 40% of 70% (e.g., 0.4 × 70 or 28). A second M1 is awarded for finding 50% of (100 - 70)% (e.g., 0.5 × 30 or 15). A1 is given for the final answer 43. Special case SC2 is given for 57 (percentage of discs not removed) and SC1 for 0.57.

How to answer it

Percentages: Finding a Percentage of a Percentage

📋 What this question tests

This question assesses your ability to combine multi-step percentage calculations within a real-world context:

  • Finding complementary percentages (total must equal 100%).
  • Calculating a percentage of an existing percentage or proportion.
  • Combining independent subgroups to find an overall total percentage.
  • Applying a concrete numerical model (e.g., choosing a total of 100 items) to simplify multi-step problems.

Question 4 (3 Marks)

Calculate the total percentage of discs removed from the box

📐 Step-by-Step Solution

Method 1: The "Assume 100 Discs" Strategy (Easiest & Most Reliable)

  1. Assume a total: Imagine there are 100 discs in the box altogether.
    • Red discs = 70% of 100 = 70 discs
    • Blue discs = 100% − 70% = 30% of 100 = 30 discs
  2. Calculate red discs removed:
    40% of 70 = 0.40 × 70 = 28 discs removed.
    [M1 awarded for a correct method to find 40% of 70%]
  3. Calculate blue discs removed:
    50% of 30 = 0.50 × 30 = 15 discs removed.
    [M1 awarded for a correct method to find 50% of (100 − 70)%]
  4. Find total removed:
    Total removed = 28 + 15 = 43 discs.
    Since our total was 100 discs, 43 out of 100 is 43%.
    [A1 awarded for the final answer of 43]

Method 2: Using Decimals / Multipliers

  • Red removed: 0.4 × 0.7 = 0.28 (M1)
  • Blue removed: 0.5 × 0.3 = 0.15 (M1)
  • Total removed: 0.28 + 0.15 = 0.43 = 43% (A1)

✅ Final Answer & Marks

Answer: 43%

Mark Breakdown:
• M1: Method for 40% of 70% (e.g. 0.4 × 70 or 28 or 0.28 )
• M1: Method for 50% of 30% (e.g. 0.5 × 30 or 15 or 0.15 )
• A1: Correct final value of 43

💡 Key Knowledge

  • Percentages sum to 100%: If 70% are red, the remaining 100% − 70% = 30% must be blue.
  • "Of" means multiply: Finding 40% of 70% mathematically means 0.40 × 0.70 .
  • Picking 100: When no starting number is given for a percentage problem, setting the total to 100 turns percentages directly into simple whole numbers.

🧠 Exam Technique & Examiner Insight

  • Show full working: The mark scheme explicitly notes: Do not accept 'of' for '×' without further method. Simply writing "40% of 70%" is not enough to secure the mark—you must write the multiplication calculation or show the result (28).
  • Double-check what is asked: Did the question ask for discs removed or discs remaining?
    • Removed = 43%
    • Remaining = 100 − 43 = 57%
    (Writing 57 gets a special case SC2, losing 1 mark for misreading).

❌ Common Errors to Avoid

  • Adding percentages directly: 40% + 50% = 90% . Total misconception! The percentages apply to different subgroups, not the total discs.
  • Averaging the percentages: Calculating (40% + 50%) ÷ 2 = 45% . This ignores that there are far more red discs (70%) than blue discs (30%).
  • Forgetting the blue discs: Only calculating 40% of 70% = 28% and forgetting to find the removed blue discs.
  • Leaving the answer as a decimal: Writing 0.43% instead of 43% (the % sign is already printed on the answer line).

Topics

Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 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.