0606 Command Words Decoded: Show, Find, Solve, Determine, Prove

Cambridge chooses its question verbs deliberately. Each command word in a 0606 paper is an instruction about how much working the mark scheme expects, and students who can read them stop losing marks to misunderstood questions. Here is the working decode, from least to most demanding.

”Write down” / “State”

No working expected, no method marks available. The answer is one step from what’s in front of you, the period of a graph, the value of $c$ in a completed square. If you find yourself calculating, you’ve misread either the question or your earlier work.

”Find” / “Calculate” / “Solve”

The standard commands: working is expected and carries most of the marks (M marks). “Solve” specifically means all solutions, for trig equations that means every value in the stated range (the missing-solutions trap), and for quadratics it can mean rejecting an invalid root with a stated reason (”$x = -2$ rejected since length cannot be negative”, the rejection sentence is often a mark).

”Express in the form…”

A destination format is specified: $a(x + p)^2 + q$, $R\sin(\theta + \alpha)$, partial form of a circle equation. The accuracy marks attach to that exact form, finishing with an equivalent but differently-shaped answer drops them. Identify the target form’s parameters and present them explicitly.

”Show that” ★ the big one

The answer is printed on the paper; you are being marked entirely on the route. Every algebraic step must be visible, the step you consider “obvious” is routinely the step carrying the mark. Two rules: never work backwards from the given result as your main argument, and never skip the line where the given form first appears. “Show that” questions are also a gift: the printed result lets you verify your part (i) before it feeds part (ii)…

”Hence” ★ the most-ignored

“Hence” means use the previous part. The parts of a 0606 question are a designed staircase: (i) show that the derivative is such-and-such, (ii) hence find the stationary points. Solving (ii) from scratch with a different method typically scores poorly even if correct, because the mark scheme is written for the intended route. “Hence or otherwise” loosens this, another method may score fully, but the “hence” route is nearly always shorter. When stuck on a “hence”, re-read the previous part: the question is telling you the key unlocks this door.

”Determine”

Reach a conclusion and justify it. “Determine whether the line meets the curve” wants the discriminant computed and a stated verdict: ”$b^2 - 4ac = -8 < 0$, so the line does not meet the curve.” The conclusion sentence carries its own mark more often than not.

”Prove”

Most common with trig identities: transform one side into the other through visible, justified steps, never moving terms across the identity as if it were an equation. Complete logical chain, no gaps.

”Sketch”

Shape and key features, not plotted precision: intercepts, turning points, asymptotes labelled. For modulus graphs and trig graphs, the B marks attach to specific labelled features, axis crossings, amplitude, period.

Train the read, not just the maths

In timed practice, underline the command word before starting each part, and after marking ask: did I lose anything to the command rather than the content? Most students find two or three marks per paper hiding there, a free grade nudge with no new mathematics. For the full marking system behind this, read how to show working for full marks.

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