Whether you are approaching your final exams, or you’re at the stage of mid-course exams, you’re probably beginning to put in some practice of past paper questions. Sometimes it isn’t the maths which is hard, but understanding the language of the question; and each question will contain certain keywords which tell you how you should be tackling the question, and what you should be writing down. I can’t emphasise enough how important it is to understand what, in the context of exam questions, these keywords – technically known as “command terms” – mean. There are over 30 of them, and my list below covers the more common ones.

**Write down: **You can obtain the answer with very little, if any, calculation; this may follow on from a previous answer. There will be no marks for showing working.

**Hence: **You* must* use what you have just done to obtain the answer. For example: “Differentiate the function f(*x*) = 2*x*^{2} – 8x + 1 and hence find the vertex of the graph *y* = 2*x*^{2} – 8x + 1.” You could find the vertex in other ways, but the question here is asking you to find the *x* value which makes the derivative zero. Sometimes a question will use **hence or otherwise**; usually, the “hence” method will be simplest, but you are free to use any other method to find the answer.

**Show that: **You are being asked to show that a particular statement is true. So, to take a trivial example, “Show that the equation 2*x* – 6 = 10 has a solution *x* = 8.” Rather than solving the equation, you could simply substitute

*x* = 8, and then 16 – 6 = 10, thus showing that *x* = 8 is the solution. Be careful though: *all* the marks are for the working, so make sure you have shown enough, and that you aren’t simply stating what the question has asked you to show.

**Plot** and **Sketch: **“Plot” means that you must mark relevant points on a graph; “sketch” means that you should show a graph with roughly the correct shape, marking key points such as axis intercepts. Scales are not necessary on a sketch, although you must give an *indication* of scale, and also label the axes.

**Estimate: **Obtain an approximate value.

**Calculate, evaluate: **Obtain a numerical answer, showing working as necessary.

**Find: **Obtain an answer, probably algebraic, showing working as necessary.

**State: **A brief answer requiring no working.

**Prove: **Write out a formal proof. Most likely in HL; for example, “Prove by mathematical induction ….”

**Simplify: **Usually requires the simplification of an algebraic expression. For example: “Expand (*x* – 2)^{3} and simplify the answer.” The correct solution is

*x*^{3} – 6*x*^{2} + 12*x* – 8. Anything more complicated will not score full marks.

**Exact: **If a question asks you to find a result in an exact form, the answer will be an irrational number which you must not write as a rounded decimal. Most likely it will involve π or a square root. For example, find the hypotenuse of the right-angled triangle with shorter sides 4cm and 6cm, giving your answer in an exact form. The answer is √52, but you will get no marks for 7.211…

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