An unfamiliar question is unfamiliar in its wording, not in its mathematics. A short routine lets you choose a method from the wording and confirm it while you work.
This page belongs to the SPM Additional Mathematics guide. It pairs with handling a mixed-topic question without guessing formulas.
What does the student usually say?
“I know differentiation and I know quadratics, but when a question is not labelled, I do not know which one it wants.” Another version: “I start, run out of ideas halfway and have no idea what to try instead.”
The methods are not missing. The step that picks between them is.
What cues can I use?
| Wording in the question | Likely idea | Why |
|---|---|---|
| Maximum, minimum, greatest | Differentiation, or completing the square | A turning point gives the extreme value |
| Rate of change, how fast | Differentiation | Rates are derivatives |
| Area under a curve | Integration | Area is a definite integral |
| Sum of the first n terms | Progressions | The sum has its own formulas |
| Number of ways to arrange | Permutations | Order matters |
Worked example: two methods that agree
A rectangle has a perimeter of 40 cm. Find the greatest possible area.
Choose. “Greatest” is the cue for a turning point. Let one side be x, so the other side is 20 − x, and the area is A = x(20 − x) = 20x − x².
Method 1, differentiation. dA/dx = 20 − 2x. Set it to 0, so x = 10 and A = 10 × 10 = 100 cm².
Method 2, completing the square. A = −(x² − 20x) = −(x − 10)² + 100. The greatest value is 100 when x = 10.
Both methods give the same answer, 100 cm². The routine is to choose from the cue, then confirm.
What can I do myself?
- Underline the verb and the quantity in the question before writing anything.
- Write the topic you think it is, and the reason, in five words.
- Give the method three lines. If the working is not getting simpler, pick the next cue.
- After the answer, ask whether it is in the form the question wanted, such as a value, an interval or an expression.
Practise on the word-problem structure worksheet, and record each wrong choice in your mistake log.
When might one-to-one tuition help?
When you can pick a method correctly only after someone hints at it, you are missing the choosing step. A teacher can give you a fresh unlabelled question every few minutes and listen to your reasoning, so the choice becomes quick.
Bring two questions that stumped you to the one-hour trial class (from RM50). Read about online one-to-one Additional Mathematics tuition to see how a lesson is structured.