Pressure

The accepted definition is force per unit area -- force divided by area. "The force on an area", "the amount of push on a surface" and "force times area" all score zero. Pair the words with the symbol equation $p = F/A$ and the unit pascal (Pa, or $\text{N/m}^2$): the definition and the unit are separate marks, and the unit is the one routinely dropped.

Errors here are rearrangements, not arithmetic. To find pressure divide force by area; $A/F$ gives a meaningless tiny number. To find a force, multiply: $F = pA$. Examiners flag candidates who divide pressure by weight -- the weight is the force $F$, so it belongs on top. Check: for an area under $1\ \text{m}^2$, the pressure must be a bigger number than the force.

Area is a length squared, so the conversion factor is squared too: $1\ \text{cm}^2 = 1 \times 10^{-4}\ \text{m}^2$ (divide by $10\,000$, not by $100$) and $1\ \text{mm}^2 = 1 \times 10^{-6}\ \text{m}^2$. Leaving the area in $\text{cm}^2$ and labelling the answer "Pa" makes it wrong by a factor of $10\,000$; dividing by $100$ leaves it out by $100$.

An equation must be built from quantity symbols. Writing "$\text{N/m}^2$" when asked to state the equation for pressure earns nothing -- the answer wanted is $p = F/A$. The same fault appears as word/symbol/unit mixtures such as "pressure = N ÷ area". Quote the symbol equation first, then give the unit separately on the numerical answer.

The $F$ in $p = F/A$ is a force in newtons, not a mass in kilograms. A car of mass $1200\ \text{kg}$ does not press with 1200 units of force -- convert first: $W = mg = 1200 \times 10 = 12\,000\ \text{N}$. Substituting the mass straight in makes the pressure ten times too small and leaves the working in the wrong unit.

The $A$ in $p = F/A$ is the area actually in contact with the surface, not the object's whole surface area -- on a diagram, shade the contact face only. The force must also be drawn normal (at right angles) to that surface; a force sketched along the surface, or at an angle, is not the force this equation uses.

A force (N) and a pressure (Pa) are different quantities, and the area decides which is large. The same weight gives a huge pressure on a drawing-pin point and a tiny pressure under a snowshoe. Never argue that one object presses harder simply because it is heavier -- compare $F/A$, not $F$.