Physics 0625 · syllabus 1.4
Cambridge IGCSE Physics 0625 — Density topical past papers
Density as mass per unit volume, how to measure it for liquids and for regular and irregular solids, and using density to predict what floats and what sinks.
- Questions
- 1,202
- Years
- 2009–2026
- With mark scheme
- 99%
- Questions 2022–2026
- 344
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
What Density covers
Density tells you how much mass is packed into each cubic metre, or each cubic centimetre, of a material: ρ = m/V, in kg/m³ or g/cm³. It belongs to the material rather than to a particular object, so a steel paper clip and a steel girder have the same density. Water's density is about 1.0 g/cm³, which is 1000 kg/m³, a useful check on any answer.
Measuring a density always means finding a mass with a balance and a volume by some other route. For a rectangular block, measure its sides with a ruler and multiply them; for a liquid, read its volume in a measuring cylinder and find its mass from the balance readings with and without the liquid in the cylinder; for an irregular object that sinks, lower it into water and take the rise in level of a measuring cylinder, or the water a displacement can pushes out into a cylinder, as its volume.
An object floats in a liquid that is denser than it is and sinks in one that is less dense. Extended candidates apply the same comparison to two liquids that do not mix: the less dense one floats on top, so several such liquids settle in layers in order of density. Density is examined on all four written papers and measured in Papers 5 and 6, and it comes back in the pressure under a liquid and in convection, where a warmed fluid becomes less dense and rises.
In the syllabus
The headings this topic has in the Cambridge International 2026–2028 syllabus, as the board prints them.
- 1.4 Density
What you should be able to do
- Use ρ = m/V in both g/cm³ and kg/m³, and convert between the two
- Plan density measurements for a liquid, a rectangular block and an irregular stone, naming the apparatus for each
- Find a volume by displacement, with a measuring cylinder or a displacement can
- Decide from densities whether an object floats or sinks in a liquid
- Decide which of two liquids that do not mix will float on the other (Extended)
Key ideas
- Density ρ = m/V, in kg/m³ or g/cm³; 1 g/cm³ = 1000 kg/m³
- Volume of a rectangular block = length × width × height; volume of a cylinder = πr²h
- Volume of an irregular solid = rise in the liquid level, or the volume of liquid displaced
- An object floats if its density is less than the liquid's, and sinks if it is greater
How Density has been examined
From 2022 to 2026, Density was on Paper 3 · Theory (Core) in 14 of 14 exam series, worth about 14% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Multiple Choice (Core) | 143 | 11% | 14 of 14 |
| Paper 2 · Multiple Choice (Extended) | 109 | 9% | 14 of 14 |
| Paper 3 · Theory (Core) | 45 | 14% | 14 of 14 |
| Paper 4 · Theory (Extended) | 26 | 8% | 12 of 14 |
| Paper 6 · Alternative to Practical | 21 | 18% | 12 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 1. The bank files this topic together with neighbouring ones, so these figures count every question in its chapters, including some on those topics.
Filed in Momentum under: Measurements and Units, Forces and Pressure.
A worked example
A stone of mass 135 g is lowered into a measuring cylinder holding 60.0 cm³ of water, and the level rises to 110.0 cm³. Find the stone's density in g/cm³ and in kg/m³, and decide whether it would float in mercury, which has a density of 13.6 g/cm³.
- Volume of the stone = rise in level = 110.0 − 60.0 = 50.0 cm³
- Density = m/V = 135 / 50.0 = 2.70 g/cm³
- In kg/m³: 2.70 × 1000 = 2700 kg/m³
- 2.70 g/cm³ is less than 13.6 g/cm³, so the stone floats in mercury, although it sinks in water
Answer: 2.70 g/cm³, or 2700 kg/m³; it would float in mercury
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Converting g/cm³ to kg/m³ with the wrong factor — the factor is 1000, so 2.7 g/cm³ is 2700 kg/m³, not 27 or 0.0027 kg/m³
- Taking the final reading of the measuring cylinder as the object's volume — the volume is the rise, the final reading minus the starting reading
- Leaving the container's mass in — the liquid's mass is the reading with the liquid minus the reading for the empty container
- Deciding whether something floats from its mass or its size — the comparison of densities decides it, which is why a large log floats and a small pebble sinks
- Letting water splash out, or air bubbles cling to the object, when measuring by displacement — either makes the measured volume wrong, so lower the object gently on a thread and tap any bubbles free
Exam technique
- In a method, name the balance and the measuring cylinder or ruler, say what you measure with each, and finish with ρ = m/V
- Keep units matched: grams with cm³ gives g/cm³, and kilograms with m³ gives kg/m³
- When asked whether something floats, quote both densities and say which is larger
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.