Mathematical Modeling · Form 5
Mathematical Modeling: Paper 2 Answering Guide
How Mathematical Modeling appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
Modelling questions are the most open in the paper: a real scenario you must translate into maths yourself. They reward students who can connect chapters, spotting that a worded problem is really a quadratic, or a rate, or a variation, and who interpret their answer rather than stopping at a number.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
Worked Paper-2 example: a food-stall profit model
A food stall has a fixed daily cost of RM120. Each packet of nasi lemak costs RM2 to make and is sold for RM5.
Let n be the number of packets sold in a day. (a) Form a model for the daily profit, P, in RM.
(b) Find the profit when 80 packets are sold. (c) Find the number of packets that must be sold to break even, and comment on what happens below that number.
- (a) State the relationship: Profit = Revenue − Total cost.
- Substitute: P = 5n − (120 + 2n).
- Simplify to the model: P = 5n − 120 − 2n = 3n − 120.
- (b) Substitute n = 80 into the model: P = 3(80) − 120.
- Simplify: P = 240 − 120 = RM120.
- (c) Break even means P = 0: 3n − 120 = 0.
- Solve: 3n = 120, so n = 40 packets.
- Interpret: exactly 40 packets covers all costs; selling fewer than 40 makes P negative, that is, the stall runs at a loss.
How to check this answer before you hand it in
Test the model at an easy value you can reason about. If the stall sells 0 packets, the model gives P = 3(0) − 120 = −RM120, exactly the fixed cost lost with no sales, which is correct, so the model is trustworthy.
Then verify the break-even the other way round: 40 packets earn 40 × RM5 = RM200 in revenue against a cost of 120 + 40 × RM2 = RM200, so the profit is indeed RM0. Two quick checks like these catch a wrong sign or a dropped term before it costs you the marks.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How are the marks usually split in an open modelling question?
Roughly into four: forming a correct model, showing the substitution, reaching the right answer with units, and interpreting what it means. The middle-arithmetic mark is the one most students secure; the model and interpretation marks are the ones most often dropped, so guard those two deliberately.
What if I define my variables differently from the marking scheme?
That is fine, as long as you define them clearly and use them consistently throughout. Markers follow your own definitions, not a fixed letter.
Problems only start when you switch meaning halfway, say, letting n mean packets in part (a) but minutes in part (b). Pick your symbols, state them once, and keep them.
Do units really matter in the final answer of a modelling question?
Yes. In a real-context question the unit is part of the answer, and dropping it commonly costs the accuracy mark 'RM120' scores, '120' may not.
Units also catch errors: if your working produces litres where the question wanted minutes, the mismatch tells you a step went wrong before you hand it in.