AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 3

2 marks · Easy difficulty · Short Answer

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

Practise this question

Question

Question 3 states: 'A metal solid has volume 11 cm³. The density of the metal is 8.5 g/cm³. Work out the mass of the solid.' Worth 2 marks, with blank working space and an answer line ending with the unit 'g'.
Question text

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]

Answer g

Mark scheme

Show the mark scheme Mark scheme table for Question 3 showing: Method mark M1 for '11 × 8.5' (oe), and Accuracy mark A1 for '93.5' (oe, accept 93 or 94 with 93.5 seen, Special Case SC1 for digits 935).

Q Answer Mark Comments

11 × 8.5 M1 oe

3 93.5 oe accept 93 or 94 with 93.5 seen

A1

SC1 digits 935

How to answer it

Calculating Mass from Density and Volume

📋 What this question tests

This question assesses your ability to recall and rearrange the compound measure relationship between density, mass, and volume, and carry out a direct decimal multiplication accurately.

Question 3 (2 Marks)

Topic: Compound Measures (Density, Mass, and Volume)

💡 Key Knowledge

  • Density formula:
    Density = Mass ÷ Volume
  • Rearranged for Mass:
    Mass = Density × Volume
  • Units check:
    Volume is in cm³ , density is in g/cm³ , so mass will automatically be in grams ( g ). No unit conversions are needed!

📐 Step-by-Step Calculation

  1. Identify given values:
    Volume = 11 cm³
    Density = 8.5 g/cm³
  2. Set up the calculation:
    Mass = 11 × 8.5
  3. Compute the final value:
    11 × 8 = 88
    11 × 0.5 = 5.5
    88 + 5.5 = 93.5

✅ Correct Answer & Mark Breakdown

Answer: 93.5 g

Mark Scheme Breakdown:
  • M1: For writing down or attempting 11 × 8.5 (or equivalent method).
  • A1: For the accurate final value of 93.5 . (Rounding to 93 or 94 is only accepted if 93.5 is clearly shown in your working).

❌ Common Errors & Traps

  • Wrong operation (Dividing instead of multiplying): Calculating 11 ÷ 8.5 or 8.5 ÷ 11 . Remember the formula triangle: Mass is at the top!
  • Place value slip: Getting the digits right but misplacing the decimal point (e.g. answering 935 without working scores only a special case mark of SC1 ).
  • Unnecessary rounding: Writing just 94 without showing 93.5 in the working line will lose the accuracy mark.

🧠 Exam Technique & Examiner Insight

  • Use the Formula Triangle: Draw a triangle with M on top, and D and V at the bottom. Cover M with your finger to instantly see D × V .
  • Look at the units for clues: The density unit g/cm³ literally means "grams per cm³" (grams divided by cm³). To get just grams, you must multiply by cm³: (g/cm³) × cm³ = g .
  • Always show your working: Even if you make an arithmetic error in multiplication, writing 11 × 8.5 guarantees you the M1 method mark.

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