OT2: Mathematical problem solving: Construct extended arguments to solve problems presented in an unstructured form, including problems in context.

The idea

This outcome requires you to tackle problems that are not broken into steps and may be set in real-world contexts. You must decide what is being asked, identify relevant mathematics, and build a coherent chain of reasoning. For example, a problem might describe a company's profit model and ask for the break-even point without telling you to form equations. You would define variables, translate conditions into equations or inequalities, solve them, and justify each stage. Extended arguments mean linking multiple concepts, such as algebra and calculus, and checking that the solution makes sense in the original situation. You need to plan, execute, and review your approach, communicating each step clearly so that a reader can follow your logic.

What earns the marks

• Translating unstructured information into a mathematical model by defining variables and forming equations, inequalities or functions.
• Selecting and applying appropriate mathematical techniques, such as differentiation, integration or algebraic manipulation, without being prompted.
• Maintaining logical flow across multiple steps, ensuring each conclusion follows from previous work and is clearly justified.
• Interpreting results in the original context, including checking units, scale and reasonableness of answers.
• Using correct mathematical notation and terminology throughout the argument.

Common mistakes and how to put them right

• Starting calculations without identifying what the problem is asking.

  Put it right: Read the whole problem, underline key information, and state the goal before beginning.

• Ignoring context when forming equations, such as mixing units or misinterpreting rates.

  Put it right: Convert all quantities to consistent units and define variables with their units.

• Presenting disconnected calculations without explanation.

  Put it right: Write connecting sentences that explain why each step follows and how it contributes to the solution.

Exam tips

• Spend time planning: jot down knowns, unknowns and a route to the answer before writing formal solutions.
• Show all stages of your reasoning, including how you formed equations, because method marks are available for correct processes even if arithmetic slips occur.
• After solving, re-read the original problem to ensure your answer addresses the actual question and is realistic in context.