Maths command terms explained
The first word of a maths question tells you what the examiner or teacher wants. "State" wants just the answer; "show that" wants every step; "justify" wants a reason. Here is what each common command term asks for, the mistake students most often make with it, and a quick drill.
IB Math Revision is an independent site, not affiliated with, endorsed by or connected to the International Baccalaureate (IB) or any exam board. These definitions are our own plain-English summaries. For the official list and wording for your course, see your subject guide (for MYP maths, start with the IB's MYP mathematics subject brief (PDF) and ask your teacher for the guide).
Quick quiz: which command term is it?
Six questions. Pick the command term that matches the description.
The command terms
Roughly from "least to write" to "most to write".
State
What it asks for: Give the answer only. No working or reasons are needed.
Common mistakeWriting a long explanation and running out of time on later questions.
Quick drill
State the gradient of y = 4x − 7.
Show the answer
4
Identify
What it asks for: Pick out the right answer from a set of possibilities, such as a graph, a list or a diagram.
Common mistakeDescribing everything you can see instead of naming the one thing asked for.
Quick drill
Identify which of 9, 15, 23, 27 is prime.
Show the answer
23
Calculate
What it asks for: Work out a numerical answer, showing the working that gets you there.
Common mistakeGiving only the final number, so a slip loses every mark.
Quick drill
Calculate 15% of 240, showing your working.
Show the answer
0.15 × 240 = 36
Determine
What it asks for: Reach the only possible answer, using the information you are given.
Common mistakeGuessing or checking one value instead of showing that the answer must be this one.
Quick drill
Determine x if 3x + 5 = 20.
Show the answer
3x = 15, so x = 5
Solve
What it asks for: Find the value or values that make an equation or inequality true, by algebra or by using technology where allowed.
Common mistakeStopping at one solution when there are two (for example a quadratic).
Quick drill
Solve x² = 49.
Show the answer
x = 7 or x = −7
Estimate
What it asks for: Find an approximate value, usually by rounding first, and say it is approximate.
Common mistakeWorking out the exact answer on a calculator instead of rounding sensibly.
Quick drill
Estimate 48.7 × 9.8.
Show the answer
About 50 × 10 = 500
Describe
What it asks for: Say what you see or what happens, in words, with enough detail for someone else to picture it.
Common mistakeExplaining why instead of saying what, or giving one vague word.
Quick drill
Describe the pattern 3, 7, 11, 15, …
Show the answer
It starts at 3 and goes up by 4 each time.
Explain
What it asks for: Give the reasons or causes: say why or how something happens.
Common mistakeDescribing what happens without saying why.
Quick drill
Explain why an odd number squared is always odd.
Show the answer
An odd number is 2k + 1; (2k + 1)² = 4k² + 4k + 1 = 2(2k² + 2k) + 1, which is odd.
Justify
What it asks for: Give valid reasons or evidence that support your answer or conclusion.
Common mistakeRepeating the answer more firmly instead of giving a reason for it.
Quick drill
Is 91 prime? Justify your answer.
Show the answer
No: 91 = 7 × 13, so it has factors other than 1 and itself.
Verify
What it asks for: Show that a given result is correct, usually by substituting or checking it.
Common mistakeAssuming it is true and not showing the check.
Quick drill
Verify that x = 3 solves 2x² − 5x − 3 = 0.
Show the answer
2(9) − 15 − 3 = 18 − 18 = 0 ✓
Show that
What it asks for: Write out every step that leads to the given answer. The answer is already given, so the working is what earns the marks.
Common mistakeJumping to the given answer or working backwards from it.
Quick drill
Show that (x + 3)² = x² + 6x + 9.
Show the answer
(x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9
Prove
What it asks for: Use a logical argument, step by step from known facts, to show something is always true.
Common mistakeChecking a few examples, which shows it works sometimes, not always.
Quick drill
Prove that the sum of two even numbers is even.
Show the answer
2a + 2b = 2(a + b), which is a multiple of 2, so it is even.
Sketch
What it asks for: Draw a quick graph or diagram showing the general shape and the key features (intercepts, turning points, asymptotes), labelled. Not to scale.
Common mistakePlotting points carefully but leaving out or not labelling the key features.
Quick drill
What must a sketch of y = x² − 4 show?
Show the answer
A U-shaped curve, the y-intercept (0, −4) and the x-intercepts (−2, 0) and (2, 0), labelled.
Plot
What it asks for: Mark points accurately on a grid, using the given scales.
Common mistakeJoining points with straight lines when the graph should be a smooth curve, or the other way round.
Quick drill
Plotting y = 2x + 1 for x = 0, 1, 2: which points?
Show the answer
(0, 1), (1, 3), (2, 5)
Three habits that save marks
- Underline the command term before you start. It tells you how much to write.
- Match the effort to the term. Don't write an essay for "state", and don't give a bare number for "show that" or "justify".
- "Show that" means the answer is given. The marks are for the steps, so never skip from the question to the answer.
Next steps
See how marks are given for each step, and how MYP criteria and grades work.
How mark schemes work How MYP maths grades work