Maths › Command words
Command words
Command words indicate the type of response required. For example, show that requires enough working to establish the given result, hence asks you to use an earlier result, and prove requires a general argument. Read the whole question and consult your awarding organisation’s published guidance because requirements depend on context.
Recall: just state it
- State / Write down
- Give the fact or the answer with no working and no justification. If a question says write down, it is telling you that no method is expected, so do not invent one. “Write down the period of y = tan x.” Answer: π radians.
- Define
- Give the precise meaning, in the terms the specification uses. A worked example is not a definition.
Establish it: the proof verbs
- Prove
- Give a complete, general argument with every step justified. Checking cases is not a proof unless the cases are exhaustive, and a diagram is not an argument. “Prove that the sum of the first n odd numbers is n².” Answer: induction or a direct algebraic argument, not three examples.
- Show that
- Reach a result you have already been given. Because the target is printed, every line has to be visible or there is nothing to credit.
- Verify
- Substitute the given value or values and confirm the statement holds. Unlike show that, you are not expected to derive anything. “Verify that x = 2 is a root.” Answer: substitute and get zero.
- Disprove
- Produce a single counterexample and state plainly which claim it defeats. One well-chosen case is a complete answer.
- Deduce / Hence
- Use the result you have just established. Hence means the previous part is meant to do the work, so a fresh start from first principles risks no marks even when the answer is right. “Hence or otherwise” relaxes that: the intended route is easiest, but any sound method scores.
Work it out: numbers and algebra
- Solve
- Find every value satisfying the equation, over the interval given. Losing the second root, or the trigonometric solutions outside the first quadrant, is the standard way to drop marks here.
- Find / Calculate / Determine / Evaluate
- Work out the value, showing enough method to be followed. Give exact form when the question asks for it, and otherwise round sensibly and say what you rounded to.
- Express / Write in the form
- Rearrange into exactly the shape specified, and state the constants asked for. Marks are for the named constants, so finish by writing them out. “Express 3sin x + 4cos x in the form Rsin(x + α).” Answer: give R and α, not just the working.
- Estimate
- Give a value of the right size from sensible assumptions or from a graph, and say what you assumed.
Explain it: in words
- Explain / Give a reason
- Say why, not what. The mark is for the cause or the property that forces the result, not for restating the result in different words.
- Interpret
- Say what the number means in the context of the question, in the units of that context. A gradient is a rate of something per something, and naming both is the answer. “Interpret the gradient.” Answer: the cost rises by £4 per extra unit produced.
- Comment on
- Give a short judgement with a reason attached, usually about whether a model or a conclusion is reasonable.
- Criticise
- Weigh the limitations against the strengths and reach a supported conclusion. For a model, that usually means naming an assumption and saying what it ignores.
Draw it
- Sketch
- The right shape, with intercepts, asymptotes and turning points marked and the axes labelled. Accuracy of scale is not required; correctness of features is.
- Plot
- Mark the given points accurately on the axes provided, then draw the line or curve through them.
- Draw
- Produce an accurate diagram to scale, with instruments where the question implies them.
See also the key ideas for each topic and the revision checklist.