Additional Mathematics command words tell the student what kind of mathematical response is required. A student can know the topic and still lose marks by answering a different question from the one asked: calculating when the instruction asks for a proof, giving a decimal when an exact value is required, or ignoring an earlier result after the word “hence.”
For SEC G3 Additional Mathematics, this reading layer matters because questions often combine technique with reasoning and communication. The first step is therefore not always an equation. Sometimes it is recognising the instruction that defines what a complete answer must look like.
At eduKate Punggol, Mathematics tutorials are held at 83 Punggol Central, Singapore 828761, near Punggol MRT and Waterway Point, in small groups of up to three students. Command-word training is built into question reading so students learn to identify the required response before calculations begin.
“Solve”
Find all values satisfying the stated equation or condition, subject to any domain or interval restrictions. A solution is not complete if valid roots are missed or invalid roots are retained.
“Find”
Determine the requested quantity. Check whether the question specifies an exact value, a numerical approximation, coordinates, a gradient, a parameter or another form.
“Show that”
The target is already given. The student must produce a valid chain of reasoning from known information to that target. Simply rewriting the given result is not enough.
A strong solution makes the important transformations visible and avoids assuming the statement being proved.
“Hence”
Use a result established immediately before. The earlier result is usually intended to shorten or unlock the next part.
Do not unnecessarily restart the entire problem unless there is a clear reason.
“Deduce”
Infer a new result from something already known or established. The task is often shorter than a full derivation because the preceding mathematics has already done most of the work.
“Sketch”
Show the important qualitative features rather than creating a perfectly scaled drawing. Typical features may include intercepts, turning points, asymptotic behaviour, relative position or relevant labelled points, depending on the question.
“State”
Give the requested result concisely. Do not bury a simple required fact inside unnecessary working.
“Find the exact value”
Preserve fractions, surds, logarithmic expressions or exact trigonometric values where appropriate rather than replacing them prematurely with decimals.
“Hence or otherwise”
The previous result is likely useful, but another valid method may be acceptable if it remains mathematically sound and answers the question directly.
“Without solving”
Use structure rather than explicitly obtaining the roots or unknown values. Discriminants, coefficients, signs, graphs or relationships may provide the required conclusion.
Read restrictions as part of the command
Words such as “for x in the interval…”, “for all real x”, “positive”, “distinct”, “maximum”, “minimum” or “exact” change the mathematics. They are not decorative wording.
The five-second command-word scan
- Circle or mentally identify the command word.
- Underline the target quantity.
- Mark any interval, domain, exactness or diagram condition.
- Notice whether an earlier sub-part is likely to be used.
- Only then choose the method.
Common command-reading errors
- Solving when only a condition is required.
- Giving one trig root when all roots in an interval are needed.
- Ignoring “hence” and recreating a long derivation.
- Using a decimal when exact form is requested.
- Treating “show that” as permission to assume the conclusion.
- Sketching without key mathematical features.
How to practise command words
Use short questions where the main task is to identify what a complete response must contain before doing any calculation. This separates reading accuracy from algebraic difficulty.
Continue the Mathematics Improvements in Punggol lane
- Recognise the First Step in A-Math Questions.
- Exact Values, Approximation and Rounding.
- Productive Struggle in A-Math.
- A-Math Mathematical Communication and Sufficient Working.
Strong A-Math students do not merely read the topic; they read the instruction. Command words define the form of the answer, the amount of reasoning required and the conditions that must survive to the end.
Official reference: SEAB 2027 K341 G3 Additional Mathematics syllabus.
