IB Maths command terms tell you how much to write. "Write down" wants an answer with little or no working; "show that" wants every step to a result that is already printed; "hence" means you must use the part you have just done. Read the command term before anything else in the question, because the same mathematics can be worth different marks depending on what it asks you to do.
Your subject guide has the IB's own glossary of command terms. What follows is my plain-English version of the ones that matter most on Papers 1 and 2, with a single worked question that uses six of them.
The terms, from least to most writing
| Command term | What it asks you to write |
|---|---|
| Write down | The answer, with little or no working. It should be obvious from what you already have. |
| State | A name, value or short answer, without explanation. |
| Find / Calculate | The answer, with the working that gets you there. |
| Solve | All the values that satisfy the equation, by algebra on Paper 1 or by technology where allowed. |
| Sketch | The shape of a graph with its key features (intercepts, turning points, asymptotes) labelled. Not to scale. |
| Verify | A check that a given result is correct, usually by substituting it. |
| Show that | Every step from the information in the question to the given result. |
| Hence | The next step, using the result you have just found. |
| Hence or otherwise | The next step, using the previous result or any other valid method. |
| Deduce | A conclusion that follows from what you have already found, with little new working. |
| Justify | A valid reason or evidence for your answer. |
One question, six command terms
Here is a question I wrote to show how the terms change what you put on the page. It is in the style of an AA Paper 1 question.
Worked example · Paper 1 style
Let $p(x) = x^3 - 2x^2 - 5x + 6$.
(a) Write down the $y$-intercept of the graph of $y = p(x)$.
(b) Show that $(x - 1)$ is a factor of $p(x)$.
(c) Hence solve $p(x) = 0$.
(d) Sketch the graph of $y = p(x)$.
(e) Deduce the set of values of $x$ for which $p(x) < 0$.
(f) Justify why the equation $p(x) = 7$ has at least one solution with $x > 3$.
Solution
(a) Write down. $p(0) = 6$, so the $y$-intercept is $6$. That is all you need to write.
(b) Show that. By the factor theorem, $(x - 1)$ is a factor if $p(1) = 0$.
$$p(1) = 1 - 2 - 5 + 6 = 0$$
Since $p(1) = 0$, $(x - 1)$ is a factor of $p(x)$.
Notice the last sentence. The working on its own shows a number is zero; the sentence says what that means.
(c) Hence. Use the factor from (b). Dividing $p(x)$ by $(x - 1)$ gives
$$p(x) = (x - 1)(x^2 - x - 6) = (x - 1)(x - 3)(x + 2)$$
so $x = -2$, $x = 1$ or $x = 3$.
Solving the cubic another way, or reading the roots from a calculator, would not be using "hence".
(d) Sketch. A positive cubic shape crossing the $x$-axis at $-2$, $1$ and $3$, and the $y$-axis at $6$, with those points labelled. No scale is needed.
(e) Deduce. From the sketch, the curve is below the $x$-axis to the left of $-2$ and between $1$ and $3$:
$$x < -2 \quad \text{or} \quad 1 < x < 3$$
Very little new working is needed. That is the point of "deduce".
(f) Justify. $p(3) = 0$, which is less than $7$, and $p(4) = 64 - 32 - 20 + 6 = 18$, which is greater than $7$. $p$ is a polynomial, so its graph is continuous: it has no gaps or jumps. So the graph must cross the line $y = 7$ somewhere between $x = 3$ and $x = 4$, which means $p(x) = 7$ has a solution with $x > 3$.
The reasoning is the answer here. A number on its own would earn nothing.
"Show that" and "verify" are not the same
These two cause the most confusion, because both involve a result that is already printed.
Verify means check it. To verify that $x = 2$ is a solution of $2x^2 - 5x + 2 = 0$, substitute: $2(4) - 10 + 2 = 0$. Done.
Show that means derive it. Suppose a question says: "The equation $x^2 + kx + 4 = 0$, where $k > 0$, has equal roots. Show that $k = 4$." Substituting $k = 4$ and noticing that it works does not show that $k$ must be $4$. You start from the condition instead:
- Equal roots, so the discriminant is zero: $k^2 - 4(1)(4) = 0$.
- So $k^2 = 16$ and $k = \pm 4$.
- Since $k > 0$, $k = -4$ is rejected, so $k = 4$, as required.
The reason for rejecting $-4$ is part of the answer. Crossing it out silently is not.
"Hence" and "hence or otherwise"
"Hence" is a gift. It tells you which method the question was designed around. If you ignore it and start again from scratch, you can lose the marks even with the right answer, and you spend longer getting there.
"Hence or otherwise" leaves you free to choose. The previous result is nearly always still the fastest route, so look at it first.
How to use this in revision
When you practise, underline the command term before you start each part, and ask: how much should I write here? Then compare your answer with the markscheme. If you wrote three lines for a "write down" part, you lost time. If you wrote one number for a "justify" part, you lost marks.
Our maths command terms guide has every common term with a quick quiz. Command terms decide which marks are available, and how mark schemes work shows how those marks are split into method, accuracy and reasoning marks. To practise on real exam-style parts, open the AA SL questions or AA HL questions, or the AI SL questions if you take Applications and Interpretation.
A free account (no card) adds 5 more practice questions on every topic with instant feedback, full worked answers on free questions, and your streak and progress on any device. Create a free account and try one topic with the command terms underlined.
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FAQ
What is the difference between "show that" and "verify" in IB Maths?
"Show that" asks you to derive the given result from the information in the question, step by step. "Verify" asks you to check that a given result works, usually by substituting it. Substituting the answer is enough for "verify" but not for "show that".
What does "hence or otherwise" mean?
You may use the previous result (which is usually the quickest way) or any other valid method. "Hence" on its own means you must use the previous result.
Do I need working for "write down"?
No. "Write down" means the answer should be obvious with little or no working, so a short answer is fine. If it is taking several lines, check you have read the question correctly.
Plain-English definitions of the common maths command terms, the usual mistake with each, and a short drill.
See every command term, with a quick quiz →