Course Overview

 MATHGYM is made up of six SETs, ranging from SET F (Years 6/7) through to SET A (Years 11/12). Each SET has ten pairs of problems. In the first of the pair, the "Training Problem", students are introduced to the strategies and skills needed to solve that particular type of problem. As this is the "teaching" problem, students are also provided with up to three hints and any necessary background theory. The second of the pair, the "Bonus Problem" is often a "parallel" problem. That is, the strategy introduced in the Training Problem is useful in the solution to the Bonus Problem. To encourage students to analyse and reflect on the Training Solution there are no hints given to the Bonus Problem.

 Each of the ten questions represents a different "topic" found regularly in Mathematics Competitions. Sometimes, a problem number will contain "various" topics. This is an attempt to expose students to less prevalent but interesting types of problems.

The Tutorial is designed to be developmental, where each new SET builds on the concepts and theory found in the previous one. The intention is that students will begin with SET F (if in years 6/7) and then progress to SET E the next year or when they feel that they are ready, and so on to SET A by Year 11/12. Of course a student is welcome to start on any SET - he/she can always register in multiple SETs.
Below is a broad description of the progression of the concepts and theory developed within each topic.

Problem NumberTopicTheory Progression SET F-> SET A
1Number TheoryPrime/composite, LCM/HCF,
Congruences
2PatternsSquares/cubes, Integer sums, Handshakes,
Arithmetic sequences, Infinite sums
3AlgebraTHOANS, Fractions,
Quadratics, Cubics
4AreasRectangles, Circles,
Composite shapes
5RatesSpeed/time,
Relative velocity
6LogicSums of squares, Venn diagrams,
Algebra patterns, Diophantine equations
7AveragesAverage, Proportion,
Averaging rates, Ratios, Growth rates
8Deductive GeometryParallels, Circles, Pythagoras,
Areas, Congruency/Similarity
9CountingPigeon-Hole principle, Combinations,
Permutations
10VariousNumber theory,
Probability

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