AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 4

3 marks · Easy difficulty · Multi-step Problem

Use a conversion graph of yellow paint to red paint to determine the amount of red paint for 5 litres of yellow paint, and calculate the total orange paint made using 10 litres of yellow paint.

Practise this question

Question

A line graph showing the relationship between red paint and yellow paint used to make orange paint. The horizontal axis is labelled 'Red paint (litres)' from 0 to 8 with gridlines, and the vertical axis is labelled 'Yellow paint (litres)' from 0 to 10 with gridlines. A straight line starts at (0, 0) and passes through (4, 5) and (8, 10). Part (a) asks for the amount of red paint Ola uses if she uses 5 litres of yellow paint. Part (b) asks for the total amount of orange paint Pip makes if he uses 10 litres of yellow paint.

Mark scheme

Show the mark scheme Mark scheme table for question 4. For 4(a), the accepted answer is in the range [3.9, 4.1] for 1 B mark. For 4(b), Alternative method 1 gives B2 for [17.9, 18.1], with a partial mark B1 for finding red paint [7.9, 8.1] or calculating their reading + 10. Alternative method 2 awards M1 for doubling their part (a) or (their (a) + 5) * 2, and A1ft for [17.9, 18.1] or ft 2 * their (a) + 10.

How to answer it

Mixing Paint: Reading Conversion Graphs & Total Quantities

📋 What this question tests

This question assesses your ability to interpret a linear conversion graph in context, accurately read scales on both axes, scale up values using direct proportion, and solve a contextual word problem requiring you to find the total mixture (orange paint = red paint + yellow paint).

Question 4 (a)

Reading a value directly from the conversion graph [1 Mark]

✅ Correct Answer

4 litres

Acceptable range: [3.9, 4.1] for 1 Mark (B1)

💡 Key Knowledge

  • Vertical axis: Yellow paint (litres). Notice that 10 small squares = 2 litres, meaning 1 small square = 0.2 litres (or 5 small squares = 1 litre).
  • Horizontal axis: Red paint (litres). The scale is identical: 1 small square = 0.2 litres.
  • 5 litres on the vertical axis lies halfway between 4 and 6 (5 small squares above 4).

🧠 Exam Technique: Step-by-Step Read-Off

  1. Find 5 on the vertical axis (Yellow paint).
  2. Use a ruler to track horizontally across to the straight line.
  3. From the intersection point on the line, look directly down to the horizontal axis (Red paint).
  4. The line meets exactly at 4 on the horizontal axis.

❌ Common Errors

  • Mixing up the axes: Starting at 5 on the red paint axis (horizontal) and reading off 6.25 on the yellow axis. Always check which axis represents which colour!
  • Miscounting grid squares: Assuming each small square represents 0.1 instead of 0.2.

Question 4 (b)

Finding the total amount of orange paint made [2 Marks]

✅ Correct Answer

18 litres

Acceptable range: [17.9, 18.1] for 2 Marks (B2 or M1 A1ft)

📐 Step-by-Step Calculations

Method 1: Direct Read-off + Total

  1. Find 10 litres of yellow paint on the vertical axis.
  2. Read across to the line and down: Red paint = 8 litres.
  3. Orange paint is made by mixing red and yellow:
    Total = Red + Yellow = 8 + 10 = 18 litres

Method 2: Proportion (Doubling part a)

  1. 5 litres yellow needed 4 litres red (from part a).
  2. 10 litres yellow is double 5 litres: 4 × 2 = 8 litres red.
  3. Total orange: (4 + 5) × 2 = 9 × 2 = 18 litres .

🧠 How Marks Are Awarded

  • B1: Finding that 10 litres of yellow paint requires 8 litres (accept 7.9 to 8.1) of red paint, OR calculating their reading + 10 .
  • M1: Using proportional reasoning: 2 × their (a) or (their (a) + 5) × 2 .
  • Full Marks (B2 or A1ft): Providing the final total of 18 litres (or follow-through from an incorrect reading in part a: 2 × their (a) + 10 ).

❌ The Biggest Calculation Trap

  • Giving 8 as the final answer: The most frequent mistake is reading 8 litres from the graph and stopping there. The question asks for the amount of orange paint, not red! Remember:
    Orange = Red + Yellow.
  • Forgetting units or context: Always re-read the final sentence to ensure you are answering the specific question asked.

Topics

Algebra · Ratio, proportion and rates of change · 3.2.2 Graphs · 3.3 Ratio, proportion and rates of change

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.