Problem Solving and Mathematical Modelling
Problem Solving and Mathematical Modelling tests the transfer of mathematics to unfamiliar, real-life situations. You must read carefully, identify the variables and constraints, choose a model, carry out the mathematics, and interpret the result in context. Contexts include money, rates, travel, scale drawings and comparison of offers.
Core rules and concepts
- Read the question twice: underline what is given and circle what is asked.
- Define variables in words, including units, before forming an equation.
- Look for a fixed charge plus a variable rate; this usually gives a linear model of the form total = fixed + rate × quantity.
- Unitary method: find the value of one unit, then multiply.
- Scale drawings: scale = drawing length ÷ real length; convert units before calculating.
- Financial formulae: simple interest I = PRT/100; profit = selling price − cost price; percentage profit is based on cost price.
- Check whether the answer is sensible: units, size of number, and whether it answers the question asked.
Worked example
Taxi A charges P15 fixed plus P8 per kilometre. Taxi B charges P5 fixed plus P10 per kilometre. For what distance do they charge the same? Let d be the distance in kilometres. Taxi A: 15 + 8d. Taxi B: 5 + 10d. Set equal: 15 + 8d = 5 + 10d. Subtract 8d: 15 = 5 + 2d. Subtract 5: 10 = 2d. So d = 5 km. Check: A charges 15 + 40 = P55; B charges 5 + 50 = P55.
Traps that cost marks
Forming an expression for the wrong quantity; mixing cents and pula; forgetting the fixed charge; giving a numerical answer without units; and stopping before relating the result back to the original context.