Mathematical Modelling and Problem Solving Applied to Everyday Situations
What this domain tests
This domain asks you to choose and apply a model, validate the result, and communicate your reasoning. Rather than a separate topic, it is the reasoning cycle applied across the whole exam: translate a real situation into mathematics, solve it, then check whether the answer makes sense.
Core rules and concepts
- Choosing a model: decide whether the situation is linear (constant rate), proportional (passes through the origin), exponential (repeated percent change), or periodic. Identify the variables and their units before writing anything.
- Building the model: define the variables explicitly, write the relation, and state any constraints (for example, a length cannot be negative).
- Solving: apply the appropriate technique from arithmetic, algebra, geometry, statistics, or probability.
- Validating: substitute back into the original situation, check units, check the order of magnitude, and ask whether the answer is plausible in context.
- Communicating: show the model, the substitution, and the conclusion in sentences. Examiners award marks for visible reasoning, not only for a final number.
Worked example
A community garden is rectangular with a perimeter of 46 m. The length is 5 m more than twice the width. Find the dimensions.
Define $w$ as the width and $2w+5$ as the length. Perimeter: $2(w)+2(2w+5)=46$. Expand: $2w+4w+10=46$, so $6w=36$ and $w=6$. The length is $2(6)+5=17$.
Validate: perimeter $=2(6)+2(17)=12+34=46$ m, which matches. Check plausibility: both dimensions are positive and the length exceeds the width, as required. The garden measures 6 m by 17 m.
Traps that cost marks
- Skipping the variable definition, so the equation cannot be interpreted.
- Choosing a linear model for a situation with compounding percent change.
- Accepting a negative or absurd answer without checking constraints.
- Presenting only the final number when the question asks you to justify or explain.
- Ignoring the units in the final statement, or mixing them mid-calculation.