Density

The mark-scheme form is $\rho = m/V$ -- mass divided by volume. The zero-scoring versions are $\rho = V/m$ (inverted) and $\rho = m \times V$ (multiplied). Keep the rearrangements consistent too: $m = \rho V$ and $V = m/\rho$. Turning the formula upside down is the most repeated density error in the reports.

A definition must say mass per unit volume -- "how heavy something is" or "how compact it is" earns nothing, because neither mentions volume. Two objects of equal mass can have very different densities. Every numerical density also needs its unit, $\text{g/cm}^3$ or $\text{kg/m}^3$: a correct number written bare loses the final mark.

The volume of an irregular solid is the rise in the liquid level, $V =$ (final reading) $-$ (initial reading) -- not the final reading on its own, which also counts the water that was already in the cylinder. Read the scale at eye level at the bottom of the meniscus, otherwise a parallax error shifts both readings.

Powers of ten sink density answers. $1\ \text{cm}^3 = 1 \times 10^{-6}\ \text{m}^3$ and $1\ \text{g} = 1 \times 10^{-3}\ \text{kg}$. Keep the pair matched before dividing: grams with $\text{cm}^3$ gives $\text{g/cm}^3$, kilograms with $\text{m}^3$ gives $\text{kg/m}^3$. Mixing them -- grams over $\text{m}^3$ -- is wrong by a factor of a thousand or a million.

"It is heavy, so it sinks" and "it is big, so it floats" both ignore volume. A steel ship floats because its average density -- hull plus the air inside it -- is below that of water, while a tiny steel pin sinks because steel is about $7.9\ \text{g/cm}^3$. When a question supplies density data, compare the two numbers and say which is larger.

Displacement measures the volume only of a solid that is fully submerged. A solid that floats pushes aside less liquid than its own volume, so $V$ comes out too small and $\rho = m/V$ therefore comes out too large. Hold it under with a thread or a sinker, and keep it clear of the cylinder walls so that no liquid splashes out.

Mass ($m$, in g or kg) is how much matter an object contains; density ($\rho$) is the mass packed into each unit of volume. A balance reads mass -- not weight, and not density -- so you still have to divide by the volume. Two objects of equal mass have very different densities if their volumes differ.