AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 9

4 marks · Easy difficulty · Multi-step Problem

Calculate the simplified ratio of the total values of discs in two boxes, and find the probability of randomly picking a disc greater than 6 from Box A.

Practise this question

Question

Question 9 shows two rectangular boxes containing numbered circular discs. Box A contains 5 discs with values: 2, 2, 3, 4, and 9. Box B contains 8 discs with values: 1, 1, 1, 2, 3, 4, 4, and 9. Part (a) asks to work out the ratio of the total value of numbers in Box A to Box B in simplest form, worth 3 marks. Part (b) states one disc is picked at random from Box A and asks for the probability that the number on the disc is greater than 6, worth 1 mark.

Mark scheme

Show the mark scheme Mark scheme for Question 9. Part (a): M1 for adding values in either box (2 + 2 + 3 + 4 + 9 = 20 or 1 + 1 + 1 + 2 + 3 + 4 + 4 + 9 = 25); A1 for the unsimplified ratio 20 : 25; A1ft for 4 : 5 (or equivalent unitary ratios 0.8 : 1 or 1 : 1.25), with Special Case SC2 for 5 : 4. Part (b): B1 for 1/5 or equivalent fraction, decimal, or percentage.

How to answer it

Ratio of Totals & Basic Probability

📋 What this question tests

This question assesses fundamental number and probability skills:

  • Summing data: Accurately finding the total value of items displayed in visual sets.
  • Simplifying ratios: Writing an unsimplified ratio in the form a : b and cancelling it down using common factors to its simplest whole number form.
  • Basic theoretical probability: Calculating single-event probability using Number of successful outcomes / Total number of possible outcomes .
  • Acceptable mathematical notation: Expressing probabilities correctly as fractions, decimals, or percentages rather than ratios or odds.

Part (a) Ratio of Values in Box A and Box B

3 Marks

📐 Step-by-Step Calculation

  1. Find the total for Box A:
    2 + 2 + 3 + 4 + 9 = 20
  2. Find the total for Box B:
    1 + 1 + 1 + 2 + 3 + 4 + 4 + 9 = 25
  3. Write the initial ratio (Box A : Box B):
    20 : 25
  4. Simplify to lowest terms:
    Divide both parts by their highest common factor (5):
    20 ÷ 5 = 4 and 25 ÷ 5 = 5
    Final ratio = 4 : 5

✅ Mark Scheme Breakdown

  • M1 (Method): Correct sum of either box seen (e.g., 20 or 25 , or written addition).
  • A1 (Accuracy): Unsimplified ratio 20 : 25 (or equivalent).
  • A1ft (Final): 4 : 5 (or unitary forms 0.8 : 1 or 1 : 1.25 ).
Special Case: Writing 5 : 4 (reversing the ratio) scores SC2 (2 out of 3 marks).

💡 Key Knowledge

  • Order Matters: The question asks for Box A : Box B. Always write values in the exact order requested.
  • Simplest Form: A ratio a : b is in simplest form when a and b are integers that share no common factors other than 1.
  • Unitary Ratio: Writing a ratio in the form 1 : n or n : 1 is also accepted by examiners.

❌ Common Errors to Avoid

  • Counting discs instead of values: Box A has 5 discs and Box B has 8 discs. Writing 5 : 8 is incorrect because the question asks for the total value.
  • Missed digits when adding: Box B has three 1s and two 4s. Crossing discs off as you sum them prevents miscounting.
  • Reversing order: Giving 5 : 4 instead of 4 : 5 loses the final accuracy mark.
  • Leaving unsimplified: Stopping at 20 : 25 leaves 1 mark on the table.

Part (b) Probability of Picking a Disc Greater Than 6

1 Mark

✅ Correct Answer

1/5 (or 0.2 , 20% )

B1: Awarded for correct fraction, decimal, or percentage.

🧠 Exam Technique

  1. Identify the pool: The question states "picked at random from Box A" (ignore Box B completely).
  2. Count total outcomes: Box A contains discs {2, 2, 3, 4, 9} → Total = 5.
  3. Count successful outcomes: Which values are greater than 6? Only 9 is greater than 6 → exactly 1 disc.
  4. Write as a fraction: 1/5 .

❌ Common Misconceptions & Traps

  • Using ratio notation for probability: Writing 1 : 5 or saying "1 in 5" scores 0 marks (B0). Probability must be written as a fraction, decimal, or percentage.
  • Looking at Box B: Using all discs from both boxes (total 13) instead of just Box A.
  • Misreading "greater than 6": Discs with value 2, 2, 3, 4 do not qualify; only 9 is strictly greater than 6.

Topics

Ratio, proportion and rates of change · Probability · Number · 3.3 Ratio, proportion and rates of change · 3.5 Probability · 3.1.1 Structure and calculation

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.