Mathematical Modeling and Problem Solving
Mathematical Modeling and Problem Solving tests your ability to turn a real situation into mathematics, choose the right operations, carry out a multi-step calculation and judge whether the answer makes sense. Questions may involve budgeting, break-even, travel, recipes or event planning.
Core rules
- Identify what is given, what is asked and any assumptions.
- Break multi-step problems into smaller steps and label each answer.
- Use a formula or equation where possible; define any variable you introduce.
- Check units and reasonableness: a person's weekly wage is unlikely to be €5 or €5,000,000.
- For break-even, set income equal to costs: selling price × quantity = fixed cost + variable cost × quantity.
- Round up when the answer must be a whole number of items or people.
Worked example
A club pays €150 fixed costs plus €2.50 per item. Items sell for €6 each. (a) Find the break-even number. (b) Find profit if 100 items are sold. (a) Let n = number of items. 6n = 150 + 2.50n. Subtract 2.50n: 3.50n = 150. n = 150 ÷ 3.50 = 42.857..., so 43 items. (b) Income = 6 × 100 = €600. Costs = 150 + 2.50 × 100 = €400. Profit = €200.
Traps that cost marks
- Ignoring fixed costs when finding break-even.
- Rounding break-even down to 42, which would make a loss.
- Mixing income and profit.
- Not stating assumptions, such as all items being sold at full price.