example:

Problem 1

A library has 6 floors. There are 10 000 more books on the second floor than the first. The number of books on the third floor is the same as the number on the second. There are 10 000 fewer books on the fourth floor than the third and twice as many books on the fifth floor as there are on the fourth. On the sixth floor there are 4 000 fewer books than on the fifth. Coincidentally the number of books on the sixth floor is the same as the number on the first. Altogether, how many thousands of books are there in the library? [1 mark]

Let there be x thousand books on the first floor.
On the second floor there are x + 10 thousand books.
On the third floor there are x + 10 thousand books.
On the fourth floor there are x thousand books.
On the fifth floor there are 2x thousand books.
On the sixth floor there are 2x − 4 thousand books.
Thus we have 2x − 4 = x and so x = 4. The total number of
books, in thousands, is therefore
x + x + 10 + x + 10 + x + 2x + x = 7x + 20= 7 × 4 + 20 = 48.

UWA, with the Australian Mathematical Olympiads Committee, is hosting the 2010 WA Junior Mathematics Olympiad for all bright Year 9 and exceptional Year 8 students.

The Olympiad is a WA high school competition with teams of four students (Year 9 or below) representing their schools.

The aim of the competition is to identify the most gifted students in Mathematics.

contoh soal :

1. A certain 2-digit number x has the property that if we put a 2 before it and a 9 afterwards we get a 4-digit number equal to 59 times x. What is x? [2 marks]
2. Four friends go shing and catch a total of 11 sh. Each person caught at least one sh. The following ve statements each have a label from 1 to 16. What is the sum of the labels of all the statements which must be true?

1: One person caught exactly 2 sh.
2: One person caught exactly 3 sh.
4: At least one person caught fewer than 3 sh.
8: At least one person caught more than 3 sh.
16: Two people each caught more than 1 sh. [2 marks]

soal olimpiade matematika smp (australia) dan pembahasannya yang bisa di unduh: