Command terms

Introduction

Every part of every exam question opens with a command term: a word or phrase such as "write down", "find", "show that" or "justify" that says what kind of answer is wanted. The terms have fixed meanings, used without explanation on the papers, and the markscheme is written to match them. A part that says "write down" gives a mark for the answer alone; a part that says "find" expects stages of working; a part that says "justify" gives nothing for a conclusion without a reason.

Reading the command term first, before the rest of the sentence, is the quickest way to know how much to write. The meanings that follow are given in plain words, grouped by the kind of answer they need, with a short demonstration of each. Most demonstrations use one hypothetical context so that the differences between the terms are easy to compare.

The context is a cup of coffee cooling in a room. Its temperature, $T$ °C, $t$ minutes after it is poured, is modelled by

The terms used most often

Some terms appear far more often than others. The table counts the command terms that open question parts on the papers for this course set from 2021 to 2022 and on the specimen papers, about 360 questions in all. The counts are approximate, because some parts open with a phrase rather than a single term.

Source: IB questionbank, Mathematics: applications and interpretation, papers from May 2021 to May 2022 and the specimen papers.

"Find" opens more parts than the next five terms in the table together. Prove, Investigate, Compare, Contrast, Distinguish, Construct and Label did not open any part in that period, although they remain part of the official list and can be used. Several phrases outside the list also appear often: "use … to …", "give a reason", "perform a hypothesis test", "complete the table", "give your answer to the nearest dollar".

Terms that need little or no working

Write down

"Write down" asks for an answer that can be read from the information given, with little or no calculation. Working does not need to be shown, and the part is usually worth 1 mark (sometimes 2 for two values). If a "write down" part seems to need a page of work, the question has probably been misread.

Because a GDC is available on every paper, "write down" is often used for a value found directly by the GDC from data already entered: "write down the value of $r$", "write down the p-value". The calculation happens in the calculator, and the answer is the only thing on the page.

State

"State" asks for a name, a value or a short answer, without explanation or calculation. It is used for hypotheses ("state the null hypothesis"), for conclusions ("state whether the result is significant") and for facts ("state the degrees of freedom"). Examiners' reports make the point that when the command term is "state", no further working is expected; a long explanation wastes time and may introduce an error.

List and identify

"List" asks for a sequence of short answers with no explanation, such as the outcomes in a sample space or the vertices of odd degree. "Identify" asks for an answer chosen from a set of possibilities, such as which of four graphs matches a function. Both are rare in this course.

Terms that need working

Calculate and find

"Calculate" asks for a numerical answer with the relevant stages of working shown. "Find" asks for an answer with relevant stages of working shown, and the answer may be a number, an expression, an equation or a set of values. In practice the two are marked the same way: an implied method mark for the set-up and an accuracy mark for the answer.

Determine

"Determine" asks for the only possible answer. It is used when there is exactly one correct value or one correct decision, and the working leading to it should be shown. It often appears in the form "determine whether …", which needs a calculation followed by a clear yes or no.

Solve, estimate, differentiate and integrate

"Solve" asks for the answer or answers to an equation or inequality by algebraic, numerical or graphical methods; a GDC method is acceptable in this course unless the question says otherwise. "Estimate" asks for an approximate value, such as a value read from a graph, a prediction from a regression line or an area found with the trapezoidal rule. "Differentiate" and "integrate" ask for a derivative or an integral of a given function.

Terms about a given result

Show that

"Show that" gives the answer and asks for the working that reaches it, without the formality of a proof. The marks are all for the working; the given answer earns nothing on its own. Two rules apply on every paper. The working must go forwards, from the information in the question to the result; substituting the given answer and checking that it fits is working backwards and earns no marks. When the result is rounded, a more accurate value must appear before the given one, so that the result is seen to be calculated.

"Show" (without "that") asks for the steps in a calculation or derivation. "Verify" asks for evidence that a result is correct, and here substituting a value is the right method: to verify that $t=11.89$ is a solution of $T(t)=40$, substitute it and show that the result is 40, to the accuracy given. "Prove" asks for a sequence of logical steps that reaches the result in a formal way; it is in the official list but did not open any part on the papers counted in the frequency table.

Hence and hence or otherwise

"Hence" means the previous result must be used to answer the part. A method that ignores it may score nothing, even if the answer is right, unless the markscheme allows another method. "Hence or otherwise" suggests using the previous result but gives credit for any correct method. In both cases the previous result is almost always the shortest route.

Deduce and predict

"Deduce" asks for a conclusion reached from information already given, usually earlier results, with little new calculation. "Predict" asks for an expected result, typically from a model: "predict the temperature after 30 minutes" is answered by substituting into $T(t)$ and giving 23.0 °C, with units.

Terms about diagrams

The five diagram terms ask for different levels of precision, and markschemes reward exactly what each one asks for.

A sketch does not need to be to scale, unlike a graph that a question asks you to draw, but it must be the right shape in the right place, with the key features labelled by their coordinates or values. For the coffee model, a sketch over $0\le t\le 30$ needs the starting point $(0,90)$, a curve that decreases more and more slowly, and the horizontal asymptote $T=20$, which the curve approaches but never reaches.

The cooling graph shows the features a markscheme would look for. The curve starts at the labelled point $(0,90)$, falls steeply at first and then more slowly, ends at the labelled point at $t=30$, and stays above the dashed asymptote $T=20$. A sketch that crosses the asymptote, or that ends at the edge of the domain without a value, loses marks even when the general shape is right.

Terms that need words

Justify and explain

"Justify" asks for valid reasons or evidence that support an answer or a conclusion. "Explain" asks for a detailed account that includes reasons or causes. Both are usually marked with a reasoning mark (R1) for the reason and an answer mark (A1) for the conclusion, and markschemes routinely add "do not award R0A1": a correct conclusion with no valid reason scores zero.

The reason must be specific to the question. Markschemes regularly list vague answers that are not accepted, such as "the sample is too small" without any link to the question, or "the shape of the graph" without saying which feature.

Interpret and comment

"Interpret" asks you to use your knowledge and understanding to recognise trends and draw conclusions from given information. "Comment" asks for a judgement based on a given statement or the result of a calculation. Both need the context: the answer should name the real quantities and say what the result means for them.

Describe, suggest, and the comparison terms

"Describe" asks for a detailed account, for example of a pattern in a scatter diagram (direction, strength, form, outliers). "Suggest" asks you to propose a possible answer, such as a reason for an outlier or an improvement to a model; any sensible, specific suggestion earns the mark. "Compare" asks for similarities, "contrast" for differences and "compare and contrast" for both, each referring to all the items throughout. "Distinguish" asks you to make the differences clear. "Demonstrate" asks you to make something clear by reasoning or evidence, with examples or practical application, and "investigate" asks for a systematic examination to establish facts. These last terms are rare on the papers but appear in the language of the exploration.

Reading command terms quickly

Most lost marks connected with command terms come from answering a different question from the one asked: giving a description when an explanation is wanted, a number when an expression is wanted, a fresh method when "hence" was written. A short routine on every part prevents most of them.

1. Underline the command term.

2. Check the marks. One mark means one line; two marks usually means a method and an answer; more means stages.

3. Read the rest of the sentence for the form of the answer ("in terms of $k$", "in the form $y=mx+c$", "to the nearest whole number", "in context").

4. After answering, reread the command term and check that the answer does what it asks.

The full meaning of each term matters most when two terms seem close. "Write down" and "state" both need only an answer; "calculate" and "find" both need working; "explain" and "justify" both need reasons. Terms in the same group call for answers of the same size, so knowing which group a term belongs to is enough to decide how much to write.

Summary

• Each command term has a fixed meaning that sets the kind of answer and the amount of working.

• Write down, state, list and identify need an answer only; write one line with units.

• Calculate, find, determine and solve need stages of working; the set-up line earns the method mark.

• Show that needs forward working to the given result, with a more accurate value before a rounded one; verify allows substitution.

• Hence means use the previous result; hence or otherwise allows any method.

• Sketch needs shape and labelled key features; draw needs accuracy and scale; plot needs points in the right place.

• Justify and explain need a valid reason as well as a conclusion: do not expect any credit for a conclusion alone.

• Interpret and comment need the context: name the real quantities and say what the result means.

• Find is by far the most common term, followed by write down, hence, state and calculate.

Self-check

• To do:

  I can say how much working each common command term needs.

• To do:

  I can answer a "write down" or "state" part in a single line.

• To do:

  I can write the method line for a "find" or "calculate" part that uses the GDC.

• To do:

  I can set out a "show that" part working forwards, with an unrounded value before the given one.

• To do:

  I can tell when substitution is allowed (verify) and when it is not (show that).

• To do:

  I can use a previous result when a part says "hence".

• To do:

  I can sketch a graph with every key feature labelled.

• To do:

  I can give a reason and a conclusion for a "justify" or "explain" part.

• To do:

  I can interpret a parameter of a model in the words of its context.

• To do:

  I can write a comparison that refers to both items.