AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 18

2 marks · Easy difficulty · Short Answer

Calculate the mass of a metal solid with a volume of 11 cm³ and a density of 8.5 g/cm³.

Practise this question

Question

Question 18 reads: 'A metal solid has volume 11 cm³. The density of the metal is 8.5 g/cm³. Work out the mass of the solid.' Below are several answer lines ending with 'Answer [blank] g' and a mark allocation of 2 marks.

Mark scheme

Show the mark scheme Mark scheme table for question 18: Method mark M1 for '11 × 8.5' (or equivalent). Accuracy mark A1 for '93.5' (or equivalent, accept 93 or 94 with 93.5 seen, Special Case 1 mark for digits 935).

How to answer it

Calculating Mass from Density and Volume

📋 What this question tests

This question assesses your ability to recall and apply the compound measure formula relating density, mass, and volume, perform standard multiplication with a decimal, and state the final answer with correct place value.

Question 18

A metal solid has volume 11 cm³. The density of the metal is 8.5 g/cm³. Work out the mass of the solid. [2 marks]

💡 Key Knowledge

  • Density formula: Density = Mass ÷ Volume
  • Rearranged for mass: Mass = Density × Volume
  • Units as a clue: The unit g/cm³ shows that grams (mass) are divided by cubic centimetres (volume).
  • Both values given have matching volume units ( cm³ ), so no unit conversion is required.

📐 Step-by-Step Calculation

Step 1: Identify given values:
• Volume ( V ) = 11 cm³
• Density ( d ) = 8.5 g/cm³
Step 2: State the rearranged relationship:
Mass = Density × Volume
Step 3: Substitute the values:
Mass = 8.5 × 11
Step 4: Calculate:
8.5 × 10 = 85
8.5 × 1 = 8.5
85 + 8.5 = 93.5 g

✅ Correct Answer & Marks

Answer: 93.5 g

Mark Breakdown:
  • M1: Method mark for showing multiplication 11 × 8.5 (or equivalent).
  • A1: Accuracy mark for 93.5 (also accepts 93 or 94 if 93.5 is seen in the working).
  • Special Case (SC1): Awarded for finding the correct digits 935 if a decimal point error was made without working (e.g. answering 935 or 9.35).

🧠 Exam Technique

  • Formula Triangle: Remember M on top, with D and V on the bottom. Cover M to see D × V .
  • Always write the calculation: Even if you miscalculate the arithmetic, writing 11 × 8.5 guarantees the method mark ( M1 ).
  • Estimate to check: 11 is roughly 10. 10 × 8.5 = 85. Since 11 > 10, the answer must be slightly more than 85. 93.5 makes complete sense.

❌ Common Errors to Avoid

  • Dividing instead of multiplying: A very common misconception is calculating 11 ÷ 8.5 = 1.29 or 8.5 ÷ 11 = 0.77 . Always check the triangle before deciding the operation.
  • Decimal point slip: Working out 85 × 11 = 935 and forgetting to restore the decimal place, leaving an answer of 935 g.
  • Rounding prematurely: Rounding to 94 or 93 without first showing 93.5 could risk losing the final accuracy mark if the method is not clearly visible.

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 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.