AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 3

✅ Correct Answer

The 5 missing combinations can be written in any order:

Full words (e.g. "White Ham") are also fully accepted.

🧠 Exam Technique: Be Systematic

• Fix one variable first: Pair White (W) bread with all fillings:
  WC , WH , WT
• Switch to the next variable: Pair Brown (B) bread with all fillings:
  BC , BH , BT
• Check total combinations: 2 bread options × 3 filling options = 6 total outcomes. Since the table has 6 rows, all spaces must be filled without repeats.

❌ Common Errors

• Writing duplicates: Writing WC again and missing another combination like BT .
• Invalid pairings: Pairing two fillings together (e.g. CH ) or two breads (e.g. WB ), ignoring the rule: "one type of bread and one filling".
• Using wrong letters: Inventing abbreviations that don't match the prompt.

💡 Mark Scheme Breakdown

• B2: All 5 missing combinations completed correctly with no incorrect additions or repeats.
• B1: 3 or 4 correct combinations provided (partial credit for a strong attempt).
• Note: The order in which you write the rows does not matter.

📐 Step-by-Step Solution

1. Count sandwiches containing Cheese (C):
   From the table, these are WC and BC .
   Number of cheese sandwiches = 2
2. Identify total possible sandwiches:
   Total outcomes = 6
3. Write as a fraction:
   Fraction = 2/6 (or simplified to 1/3)

✅ Acceptable Answers

• 2/6 or 1/3 (or any equivalent fraction like 4/12).
• Follow-Through (ft): If you made an error in part (a), the examiner will award the mark if your fraction correctly matches your list (e.g. if your table had 3 cheese sandwiches out of 6, 3/6 receives the follow-through mark).

❌ Common Traps

• Writing a ratio instead of a fraction: Writing 2 : 4 or 2 : 6 loses the mark because the question specifically asks for a fraction.
• Forgetting one of the breads: Thinking only of White Cheese ( 1/6 ) and overlooking Brown Cheese.
• Simplification blunders: If you write 2/6 and then simplify it incorrectly to 1/2 , you are safe here because the mark scheme explicitly states: "Ignore simplification attempts after correct answer". However, leaving it as 2/6 avoids unnecessary risk!

🧠 Tip: Do You Need to Simplify?

In GCSE Maths, unless the question explicitly asks for a fraction "in its simplest form", unsimplified fractions such as 2/6 receive full marks. Don't risk losing marks on unnecessary simplification!