Hello! In our last lesson, we focused on the crucial skill of presenting numerical answers with the correct accuracy, distinguishing between exact values and 3 s.f. approximations. This is a foundational part of communicating your work clearly in an IB exam.
Today, we take a step back to address an even more fundamental question: What is the examiner actually asking you to do? The answer lies in the command terms—the specific verbs like "calculate," "show that," or "write down" that begin almost every question. Misinterpreting these words is one of the most common reasons students lose marks, even when their underlying mathematics is sound.
For this lesson, our learning outcome is to translate common IB command terms into the form and depth of response required. We will explore how different terms demand different levels of working, from a simple answer to a formal proof. Mastering this will transform how you approach exam questions and is a vital step toward achieving your goal of a 7.
1. Why Command Terms Dictate Your Marks
Before we look at the terms themselves, it's essential to understand how IB examiners award marks. Your work is primarily assessed using three types of marks:
- M marks (Method): Awarded for attempting to use a correct method.
- A marks (Accuracy): Awarded for a correct answer, which usually depends on a preceding M mark.
- R marks (Reasoning): Awarded for clear explanations or justifications.
The command term in the question is your guide to which marks are available and how to earn them. A "write down" question might only have an A mark available, while a "justify" question will have R marks. A "calculate" question will have both M and A marks.
This article provides an excellent overview of these mark types. Please read the short section at the end of the article that explains this.
IB Math Command Terms Explained | Patricia Akao – IB Math Tutor Online
Scroll down to the heading "How marks are awarded: M, A and R marks". Read the table and the "Key insight" paragraph that follows it.
Focus on understanding the difference between M, A, and R marks. This will help you see why simply writing a final answer from your calculator is often not enough to secure all the marks.
2. The Official Glossary of Command Terms
The IB provides an official list of all command terms and their definitions for the Mathematics AA course. This is the ultimate source of truth for what each term means. Think of this as your reference dictionary.
Command terms for Mathematics: analysis and approaches
This document contains the official definitions for all the command terms you'll encounter.
Read through the full list of terms from "Calculate" to "Write down". You don't need to memorize every definition right now. The goal is to get a broad sense of the variety of instructions and the precision of the language used. We will break these down into practical groups next.
3. A Practical Guide: Grouping Command Terms
While the official list is comprehensive, it's more practical to group the terms by the type of response they require. This helps you quickly decide how to structure your answer in an exam. The resource you looked at earlier, from a professional IB Math tutor, does an excellent job of this.
We will now work through its categories, which provide clear, exam-focused advice.
IB Math Command Terms Explained | Patricia Akao – IB Math Tutor Online
This guide categorizes the command terms based on the type of work you need to show. This is an extremely useful way to think about them during an exam.
Please read the article from the beginning, starting with "One of the most overlooked reasons..." down to the end of Category 7 ("Algebraic operations"). Pay close attention to the "Exam tip" for each term.
Now, let's consolidate and highlight the most important distinctions you've just read about.
Group A: Answer Only
Terms: Write down, State, List, Identify
These require minimal or no working. The answer is usually something you can read from a graph, extract from information given in the question, or recall from memory. Writing extensive calculations for these questions wastes valuable exam time.
- Example: "The function is given. Write down the period of ."
- You are expected to know the formula Period = . Here, , so the period is . You should just write the answer. No M marks are available.
Group B: Show Your Method
Terms: Calculate, Find, Determine, Solve, Obtain
These are the most common terms and form the backbone of IB Math papers. You must show the steps of your method to earn M marks. A correct final answer with no supporting work may earn you no marks at all, especially on Paper 1. On Paper 2, you should still write down the setup (e.g., the equation you're solving) before using your TI-84.
- Example: "Solve the equation ."
- You need to show your algebraic steps:
- Then, you must check the domain of . Since , you reject .
- You need to show your algebraic steps:
Group C: Prove and Justify
Terms: Show that, Prove, Verify, Justify, Explain
These terms are about logical argument.
- Show that: The answer is given to you. Your task is to produce a clear, step-by-step argument that leads to this answer. Crucially, you cannot assume the result is true. Start with the given information and work forward.
- Prove: This requires a more formal, rigorous argument. This is often used for questions involving proof by induction or contradiction.
- Justify / Explain: These require you to give reasons for your answer, often in words. This is where you earn R marks. For instance, when classifying a stationary point, you can't just say it's a maximum. You must justify it by referring to a sign diagram or the value of the second derivative.
Group D: Follow the Path
Terms: Hence, Hence or otherwise, Deduce
These terms link different parts of a question together.
- Hence: You must use the result from the previous part. If you use another method, you will likely receive no marks, even if your answer is correct.
- Hence or otherwise: The "hence" route is suggested and is usually the most efficient. However, you are free to use any other valid method if you prefer.
- Deduce: Reach a conclusion from the information given. This implies a logical step rather than a long calculation.
Group E: Draw and Sketch
Terms: Draw, Sketch, Plot
These words have very specific meanings related to graphs. As you read in the article, they are not interchangeable.
Conclusion
Understanding command terms is not just about memorizing definitions; it's about developing an instinct for what the examiner wants to see. It’s the key to unlocking method and reasoning marks and using your time effectively.
Key Takeaways:
- Command terms are direct instructions on the form and depth of your answer.
- They tell you whether to show working, provide a proof, or give a written explanation.
- "Show that" means you must work forwards to the given answer, not assume it.
- "Hence" means you must use the preceding result.
- "Sketch" and "Draw" have different requirements for accuracy and scale.
- Aligning your response with the command term is essential for securing all available M, A, and R marks.
In our next lesson, we will build directly on this by looking at how to structure your answers. Now that you know what to do based on the command term, we will focus on how to present your multi-step solutions with clear notation, logical flow, and valid reasoning. This will bring together everything we've covered on algebra, accuracy, and communication.