IGCSE Additional Maths 0606 Command Words: Decode Exam Questions
IGCSE Additional Maths command words are the action verbs in exam questions (e.g., Calculate, Solve, Show that, Prove, Sketch, Factorize) that tell you exactly what the examiner expects you to do and how marks are awarded in the marking scheme.
They indicate the required level of working, reasoning, and mathematical notation, including when to present a formal proof versus a short method-based solution. Interpreting them correctly protects method marks, prevents avoidable losses from accuracy and significant figures, and improves time management across the paper.
Mastering these command words is a high-impact strategy because it aligns your answers directly with assessment objectives and examiner expectations.
- Decoding IGCSE Additional Maths Command Words for Better Marks
- Understanding the Difference Between Solve and Show That
- How to Interpret Instructions Like Sketch and Plot
- What Examiners Expect When They Use the Word “Hence”
- Precise Definitions of Calculate and Write Down
- Building a Command-Word System Using Marking Schemes and Assessment Objectives
- Grade Boundaries, Performance Strategy, and Subject Choice for Study Abroad Profiles
- Exam-Ready Training Plan for IGCSE Additional Maths Command Words
- Frequently Asked Questions
Decoding IGCSE Additional Maths Command Words for Better Marks
IGCSE Additional Maths command words are not “decorative” exam language. They are action verbs that tell you exactly what the examiner is assessing and how the marking scheme awards credit.
If you answer the mathematics correctly but ignore the command word, you can still lose marks because you failed the intended assessment objectives(method, reasoning, communication), not because your final number was wrong.
Based on our years of practical tutoring at Times Edu, students improve fastest when they treat command words as a checklist: What to write, how much work to show, which mathematical notation to use, and how to present accuracy (including rounding and significant figures). This is not “exam trickery.” It is how Cambridge-style assessments standardise marking across thousands of scripts.
Why command words matter more than students expect
A critical detail most students overlook in the 2026 exam cycle is that many high-difficulty questions are not “hard” because of algebra or calculus alone.
They are hard because they mix a technical step with a command word that requires a specific presentation standard—especially for Proof, Show that, and multi-part questions using Hence.
The examiner does not read your mind. The marking scheme rewards what is on the page: The correct method, correct structure, and correct notation. Command words are the easiest marks to protect because they are predictable.
Common misconceptions that cost marks
- Believing “I got the right answer, so my steps don’t matter” under Calculate, Show that, or Prove.
- Treating Sketch like Plot, then wasting time drawing a scale grid no one asked for.
- Misreading Hence as “repeat the previous answer” rather than “use the previous result to derive the new result efficiently.”
- Ignoring Accuracy requirements (rounding, units, significant figures) when the command word is Evaluate or Calculate.
>>> Read more: IGCSE Additional Maths Study Plan 2026: A Week-by-Week Schedule for Tough Topics
Understanding the Difference Between Solve and Show That
Students often treat “Solve” and “Show that” as interchangeable. They are not, and the marking scheme reflects that difference.
Solve: You must find unknown(s) and communicate the solution set
When a question says “Solve”, the examiner wants the value(s) of the variable that satisfies an equation or condition. You should present a clean final line such as “x=…x=…” Or “x∈{… }x∈{…}” Where appropriate.
What the marking scheme typically rewards for Solve
- Correct algebraic transformation steps.
- Correct handling of extraneous solutions (common with squaring or denominators).
- A final answer clearly stated, often in simplest exact form unless decimals are requested.
Solve checklist
- Start from the given equation/condition.
- Manipulate logically with valid operations.
- If you multiply by an expression, note domain restrictions when needed.
- Conclude with a clear solution statement using correct mathematical notation.
Show that: You must justify a given result with a structured chain of reasoning
“Show that” means the endpoint is already given. The examiner is assessing whether your method and reasoning could convincingly lead to the stated result. You are not trying to “discover” the answer; you are proving you can reach it correctly.
A strong Show that structure
- Start from the left-hand side (LHS) and transform to the right-hand side (RHS), or vice versa.
- Do not jump steps that hide key algebra.
- Use equality signs correctly in a continuous chain.
- Avoid writing the target statement first as if it is true without evidence.
A marking-scheme-reliable template
- LHS
== …
== …
== RHS
If you only write the final statement without the linking evidence, you typically earn minimal credit even if the endpoint matches.
“Solve” vs “Show that”: Side-by-side comparison
| Command word | What the examiner is testing | What you must produce | Common mark loss |
|---|---|---|---|
| Solve | Finding correct unknown(s) and solution set | Values of variable(s), clearly stated | Missing solutions, extra solutions, unclear final line |
| Show that | Reasoning and method leading to a given result | A justified sequence of equalities or steps | Starting by assuming the result, skipping key steps |
From our direct experience with international school curricula, many students who are “good at maths” lose disproportionate marks because they write like problem-solvers, not like exam communicators. “Show that” is communication-heavy by design.
>>> Read more: IGCSE Maths Command Words 2026: What They Mean and How to Answer for Full Marks
How to Interpret Instructions Like Sketch and Plot
Graph-based command words are a frequent source of avoidable errors. The difference between Sketch and Plot is not artistic; it is procedural, and it affects time management.
Sketch: Key features matter, not perfect scale
A Sketch is a freehand representation showing the essential behaviour of the function. It usually does not require a precise scale unless explicitly stated.
What to include in a Sketch
- Intercepts (x- And y-intercepts) when they are accessible.
- Turning points (max/min) or stationary points if relevant.
- Asymptotes (vertical/horizontal/oblique) if they exist.
- End behaviour (how the graph behaves as x→±∞x→±∞).
- Correct general shape (e.g., cubic “S-shape,” reciprocal branches).
Sketch checklist (fast, exam-safe)
- Find intercepts quickly.
- Identify symmetry if present (odd/even).
- Find key points from prior parts of the question.
- Indicate asymptotes with dashed lines if appropriate.
- Label key coordinates clearly, even if not to scale.
Plot: Accuracy and scale are part of the assessment objectives
Plot usually implies you are given a table of values or asked to generate one, then place points accurately on axes with a scale and draw the curve/line accordingly.
What to include in a Plot
- A sensible, even scale on both axes.
- Correctly placed points with reasonable accuracy.
- A clear curve or straight line drawn through points.
- Labels for axes and units if relevant.
Sketch vs Plot comparison
| Command word | Scale required? | Data points required? | What earns marks |
|---|---|---|---|
| Sketch | Usually no | Not necessarily | Features, shape, intercepts, asymptotes, turning points |
| Plot | Yes, typically | Yes | Accurate points, correct scale, appropriate curve/line |
Based on our years of practical tutoring at Times Edu, students often waste time over-engineering sketches. A sketch is a communication tool: Show what matters and move on.
>>> Read more: IGCSE Maths Mock Improvement Plan 2026: A Practical Strategy to Raise Your Grade
What Examiners Expect When They Use the Word “Hence”
Hence is one of the most strategically important command words in IGCSE Additional Mathematics. It signals efficiency and logical dependence between parts of a question.
Hence: Use the previous result as a tool, not a decoration
When you see Hence, the examiner expects you to use a previously derived result to get to the new answer with minimal additional work. The marking scheme commonly allocates marks for:
- Correct use of the earlier result.
- A short chain of reasoning to reach the new result.
- Appropriate notation and clarity.
Typical hence pattern
- Part (a): Derive a relationship/result.
- Part (b): “Hence” use that relationship to find a value, prove a new statement, or simplify a new expression.
If you ignore the prior result and solve part (b) from scratch, you may still get marks, but you often lose efficiency and risk mistakes. In time-pressured papers, that trade-off is rarely worth it.
“Hence or otherwise”: You have permission to choose your method
Hence or otherwise means Cambridge expects the “hence” method to work neatly, but allows alternative approaches. This phrase matters for strategy:
- If the “hence” route is clear, it is usually the fastest.
- If you are stuck on part (a), you can still attempt part (b) using another method.
The pedagogical approach we recommend for high-achievers is to train both routes: The exam-efficient hence route, and a robust “otherwise” fallback in case earlier parts fail.
Common misconception with Hence
Students think Hence means “repeat the previous answer.” The correct interpretation is “use the previous answer as a lever.” You must still show at least a few steps linking the earlier result to the new one, aligned to the assessment objectives.
>>> Read more: IGCSE Maths Past Paper Strategy for 2026: How to Practice Smarter and Raise Your Grade
Precise Definitions of Calculate and Write Down
These command words look easy, but they are frequent sources of careless mark loss because they carry hidden expectations around working, rounding, and presentation.
Calculate: Method marks exist even if the final number is wrong
Calculate requires you to compute a numerical answer, typically showing sufficient working. If the marking scheme includes method marks, clear steps protect you when arithmetic slips.
Calculate checklist
- Show the formula or transformation you used.
- Substitute correctly.
- Present the final value clearly.
- Apply the required Accuracy (rounding rules) and significant figures if specified.
If the question does not specify rounding, exact values (fractions, surds, ππ) are often preferred where appropriate. If you choose decimals, be consistent and avoid premature rounding.
Write down / State: Minimal working, but absolute precision
Write down or State means the examiner expects an answer directly from a known result, a graph, or information already established. No full derivation is required.
What can still go wrong
- Writing an ambiguous answer (e.g., missing “±±” or domain).
- Copying a value incorrectly from earlier work.
- Giving a decimal when an exact value is expected.
Calculate vs Write down comparison
| Command word | Working expected? | Typical risk | Best practice |
|---|---|---|---|
| Calculate | Yes, enough to award method marks | Losing method marks by skipping steps; rounding errors | Show substitutions and key steps; manage accuracy |
| Write down / State | No formal working | Precision errors; missing conditions | Give a clean, exact statement using correct notation |
From our direct experience with international school curricula, students who master this distinction gain “free marks” because they stop overspending time on Write down tasks and stop underwriting Calculate tasks.
>>> Read more: IGCSE Tutor 2026: How to Choose the Right One
Building a Command-Word System Using Marking Schemes and Assessment Objectives
If you want a dependable improvement, stop memorising definitions in isolation. Build a system that links IGCSE Additional Maths command words to the marking scheme logic and assessment objectives.
Practical mapping: Command word → examiner behaviour
| Command word | Examiner expects | Notation expectations | Typical pitfalls |
|---|---|---|---|
| Simplify | Equivalent expression in simplest form | Clear algebraic steps | Leaving factors that can cancel; messy final form |
| Expand | Multiply out brackets correctly | Correct distributive steps | Sign errors; missing terms |
| Factorise | Express as product of factors | Factor form, not expanded | Partial factorisation only |
| Evaluate | Numerical value for given input | Substitution, accurate arithmetic | Substituting incorrectly; rounding early |
| Prove | Formal logical argument | Structured proof, justified steps | Assuming what you must prove |
| Sketch | Key graph behaviour | Labels, key points | Plotting with scale; missing asymptotes |
| Differentiate / Integrate | Correct calculus operation | Proper derivative/integral notation + +C+C where required | Forgetting constant; rule misuse |
Accuracy and significant figures: The silent mark thief
Accuracy is often not a separate “math topic,” but it is an assessment objective linked to communication and correctness. If the paper specifies 3 significant figures and you give 2 d.p., you risk losing the final accuracy mark even with the correct method.
Accuracy discipline we teach
- Carry exact values through algebra whenever possible.
- Round only at the end unless instructed.
- If using decimals mid-way, keep extra digits and round at the final line.
- State the rounding explicitly when needed: “x=2.36x=2.36 (3 s.f.)”.
Grade Boundaries, Performance Strategy, and Subject Choice for Study Abroad Profiles
Grade boundaries vary by session, and you should not chase a single “magic score.” What matters is building a repeatable method to secure marks across the full paper, especially the command-word-driven marks that are easiest to control.
Where marks are commonly won and lost
Based on our years of practical tutoring at Times Edu, the majority of lost marks among capable students come from:
- Incomplete reasoning in Show that and Prove.
- Weak presentation for Solve (missing solutions, unclear set).
- Misinterpretation of Sketch, Plot, and Hence.
- Rounding and significant figures errors under Calculate and Evaluate.
This matters for grade outcomes because these errors scale across the paper. They are not “one-off mistakes,” but repeated leakage.
Academic pathway choices: How Additional Maths fits a strong application
For selective university pathways, Additional Maths is not only about content. It signals:
- Readiness for algebraic and calculus-based thinking,
- Comfort with mathematical notation and formal reasoning,
- Capacity to handle proof-style logic (useful for IB HL Maths, A-Level Maths/Further Maths, AP Calculus/Statistics depending on pathway).
From our direct experience with international school curricula, the students who benefit most are those targeting STEM-heavy programs or competitive schools where quantitative readiness is scrutinised. If your intended major is non-STEM, Additional Maths can still be valuable, but it must be balanced against overall GPA, language requirements, and extracurricular positioning.
The pedagogical approach we recommend for high-achievers is to align subject selection with a planned progression (IGCSE → IB/A-Level/AP), then build a portfolio narrative around academic rigor plus measurable outcomes.
Exam-Ready Training Plan for IGCSE Additional Maths Command Words
To make IGCSE Additional Maths command words automatic, you need deliberate practice, not passive reading.
Step-by-step training protocol (Times Edu method)
- Step 1: Build a command-word glossary. Create a one-page sheet with definitions and “what to write” expectations for each command word.
- Step 2: Convert marking schemes into patterns. For each command word, collect 5–10 examples and note what earned the method marks.
- Step 3: Drill with timed micro-sets. Do 10-minute sets focused on one command word category: Proof/justification, algebra solving, graph interpretation, accuracy.
- Step 4: Error log using examiner language. Classify errors as “command-word error,” “notation error,” “accuracy error,” or “concept error.”
- Step 5: Weekly mixed-paper simulation. Mix topics and command words, because the exam does not isolate skills.
A critical detail most students overlook in the 2026 exam cycle is that command words are a repeatable advantage. Once trained, they stop being a risk and become a scoring framework.
Frequently Asked Questions
What are the most common command words in IGCSE Add Maths?
The most frequent IGCSE Additional Maths command words tend to be Calculate, Solve, Show that, Prove, Simplify, Expand, Factorise, Sketch, Evaluate, and calculus instructions such as Differentiate and Integrate.These are the action verbs that appear repeatedly because they map cleanly to assessment objectives and marking-scheme structures.
From our direct experience with international school curricula, the most time-efficient preparation is to master the top 10 command words first, then add less common verbs like Compare and Describe once your core execution is consistent.
Does "show that" require a step-by-step proof?
Show that requires a structured justification, but it is not always a full formal proof in the same style as Prove. You must present a clear chain of steps that leads to the given result, using correct mathematical notation and without assuming what you are trying to establish.Based on our years of practical tutoring at Times Edu, the safest approach is to write enough steps that the marking scheme can award method marks even if a minor algebra slip occurs later.
What does "hence or otherwise" mean in an exam?
Hence or otherwise means you may use the previous part’s result (hence) or choose an alternative method (otherwise). It is designed to keep the paper fair: Students who struggled earlier are not completely blocked from later marks.The pedagogical approach we recommend for high-achievers is to practice both the hence pathway and a backup method, so your score is not overly dependent on one earlier step.
How many marks are lost for ignoring command words?
The mark loss depends on how the marking scheme allocates method and reasoning marks, but ignoring command words can cost anything from a single communication mark to most of the questions. A correct final answer may still earn limited credit if the command word demanded a method, a proof, or a particular representation.Based on our years of practical tutoring at Times Edu, the highest losses occur when students answer Prove as if it were Solve, or treat Show that as a one-line conclusion.
Do I need a scale drawing when the word "sketch" is used?
Usually, no. Sketch typically requires the key features and correct shape without a precise scale, unless the question explicitly requests a scale or a plotted graph. You should prioritise intercepts, turning points, asymptotes, and overall behaviour.From our direct experience with international school curricula, over-plotting sketches is one of the most common time-management errors among strong students.
What is the difference between simplify and factorise?
Simplify means rewriting an expression in a simpler equivalent form, often by cancelling, combining like terms, or reducing complexity. Factorise means express an expression as a product of factors, such as extracting a common factor or writing a quadratic as (x−a)(x−b)(x−a)(x−b) where possible.A marking-scheme-reliable rule is: If the final form is a product, you are factorising; if the final form is reduced but not necessarily a product, you are simplifying.
Where can I find the official list of IGCSE command verbs?
The official command-word guidance is typically found in the syllabus and assessment documentation for your specific exam board and syllabus code. Schools also often provide examiner command-word glossaries aligned to their chosen specification.Based on our years of practical tutoring at Times Edu, we advise students to cross-check the wording used in their actual past papers and marking schemes, because that is where the practical interpretation is most consistent.
Conclusion
If you are aiming for top grades, treat IGCSE Additional Maths command words as a scoring system, not vocabulary. The fastest gains come from aligning your working, proof structure, notation, and accuracy to what the marking scheme consistently rewards.
Based on our years of practical tutoring at Times Edu, we can diagnose your current script style in one session, then build a personalized roadmap that links command-word execution to your broader pathway (IB, A-Level, AP) and your study abroad profile. If you want a targeted plan for your current level, your school timeline, and your university goals, contact Times Edu for a 1:1 academic consultation and a personalized preparation track.
