Before you calculate anything in a modelling question, write down what each letter means, in which unit, and what you are assuming. Those three lines make the rest of the answer easy to check.
This lesson opens the modelling sequence in SPM Mathematics. The next step is choosing a simple model for a real situation.
What goes in the opening three lines?
Write the variables, the units, and the assumptions, in that order.
- Variables: one letter for each changing quantity.
- Units: the unit of each letter, such as RM, km or minutes.
- Assumptions: what you accept as fixed or ignore.
If the question supplies a letter, use it.
Worked example: hiring a van for a school trip
A school hires a van. The hire company charges RM120 for the day plus RM0.80 for each kilometre driven. The teacher wants the total cost for a trip.
Variables: let d be the distance driven in km, and C be the total cost in RM.
Assumptions: the charge per kilometre is the same for the whole trip, there are no tolls or parking fees, and the driver’s time is included in the RM120.
Model: C = 120 + 0.8d.
For d = 150 km, C = 120 + 0.8 × 150 = 120 + 120 = RM240.
Each part of the model matches one line above. The 120 is the fixed charge, the 0.8 is the rate, and the assumptions say when the answer can be trusted.
The mistake that costs marks
The common slip is starting with an equation and no definitions. The marker cannot tell whether the 0.8 is per km or per minute.
| Step | Wrong | Right |
|---|---|---|
| Opening | C = 120 + 0.8d | let C be the total cost in RM and d the distance in km |
| Assumptions | none written | constant rate, no tolls or parking |
| Answer | 240 | RM240 for a 150 km trip |
| Risk | a toll makes the answer wrong with no warning | the assumption shows where the model stops |
An unstated assumption can look like a correct answer until a toll appears.
Check yourself
A gardener charges RM35 per visit plus RM12 for each hour of work. Define the variables, state two assumptions, write the model, and find the cost of a 3-hour visit.
Answer
Let h be the hours worked and T be the total cost in RM.
Assumptions: the hourly rate is constant, and there are no extra charges for materials or travel.
Model: T = 35 + 12h.
For h = 3: T = 35 + 12 × 3 = 35 + 36 = RM71.
What to study next
Go on to choosing a simple model for a real situation, then explaining limitations and refining a model. The modelling practice set lets you test all of it.
The algebra step repair trainer helps if rearranging a model is where you slip. For a teacher to check your opening lines, see online one-to-one Mathematics tuition.