Integrated Problem Solving

Section 1What integrated problems are

Integrated problems combine skills from different parts of the syllabus. A question might use a graph, a percentage, a unit conversion, and an equation in the same situation. Watch out: the topic name is not printed above the exam question, so you must recognise the clues.

Section 2Read before calculating

Read the question twice before touching the calculator. Underline what is being asked, circle the useful numbers, and ignore extra information until you know whether it matters. This feels slow, but it saves time because it prevents solving the wrong problem beautifully.

Section 3Choose the model

The model is the mathematical tool that fits the situation. Constant rate suggests speed, distance, time, or gradient. A repeated percentage suggests compound interest or depreciation. A right triangle suggests Pythagoras or trigonometry.

Section 4Represent the information

Good problem solvers make the information visible. Use a table for data, a diagram for geometry, a number line for bounds, a Venn diagram for sets, and an equation when an unknown quantity is involved. In plain words, do not keep the whole problem in your head.

Section 5Work with units

Units are part of the mathematics. Convert before calculating if the units do not match, and write the unit on the final answer. Easy to mix up - 3 hours 30 minutes is 3.5 hours, not 3.30 hours.

Section 6Check reasonableness

A reasonable answer fits the question. A discount price should be less than the original price, a probability should be between 0 and 1, and a physical length should not be negative. Here's the trick: one quick estimate can expose a wrong calculator entry.

Section 7Communicate the answer

Integrated questions often reward clear working. Show the formula or method, substitute carefully, calculate, then state the answer in context. For example, do not stop at 14.2; say 14.2 metres, 14.2 dollars, or 14.2 minutes depending on the problem.