APSMO Maths Olympiad practice

Each operation is undone by its opposite, in reverse order: dividing becomes multiplying, adding becomes subtracting, halving becomes doubling. The order matters as much as the operations. Undoing the steps in the original order gives the wrong answer, which is the most common slip we see.

The check forwards is not optional. It takes ten seconds and catches almost every mistake, and in a five-question contest a single caught mistake is a fifth of the marks.

Compare working backwards with guessing and checking on the first problem. A student guessing 10, then 12, then 14, then 15 needs four trials to land on the answer, and has no guarantee of stopping. Working backwards gets there in three steps, every time, and shows why the answer is right.

Guess and check still has its place, especially when steps cannot be reversed. Good problem solvers know several strategies and choose between them, which is what our classes practise, always on fresh problems.

If your child finds the problems hard

That is expected; the Olympiad is designed to stretch high achievers. Discussing solutions afterwards, as APSMO recommends, is where most learning happens.

Encourage drawing and writing, even when the answer seems obvious.

Other contests

Our AMC by year page covers the Australian Maths Trust's competition.

The Maths Challenge page covers a module with written solutions.