Western Australian

Junior Mathematics Olympiad 2009

Individual Questions 100 minutes

General instructions: Each solution in this part is a positive integer
less than 100. No working is needed for Questions 1 to 9. Calculators are not permitted. Write
your answers on the answer sheet provided.

1.
Evaluate

[1 mark]

2.
From each vertex of a cube, we remove a small cube
whose side length is one-quarter of the side length of the original cube. How
many edges does the resulting solid have?

[1 mark]

3.
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]

4.
What is the units digit of 2

^{2009}´ 3^{2009}´ 6^{2009}? [2 marks]
5.
At a pharmacy, you can get disinfectant at di_erent
concentrations of alcohol. For instance, a concentration of 60% alcohol means
it has 60% pure alcohol and 40% pure water. The pharmacist makes a mix with 3/5 litres of alcohol at
90% and 1/5 litres of alcohol at
50%.

How many percent is the concentration of that mix? [2 marks]

6.
If we arrange the 5 letters A, B, C, D and E in diferent
ways we can make 120 diferent “words". Suppose we list these words in alphabetical
order and number them from 1 to 120. So ABCDE gets number 1 and EDCBA gets
number 120.

What is the number for DECAB? [3 marks]

7.
Every station on the Metropolis railway sells
tickets to every other station. Each station has one set of tickets for each
other station. When it added some (more than one) new stations, 46 additional sets
of tickets had to be printed.

How many stations were there initially? [3 marks]

8.
At a shop, Alice
bought a hat for $32 and a certain number of hair clips at $4 each. The average
price of Alice 's
purchases (in dollars) is an integer.

What is the maximum number of hair clips that Alice could have bought? [3
marks]

9.
The interior angles of a convex polygon form an
arithmetic sequence:

143

^{0}, 145^{0}, 147^{0}, ….
How many sides does the polygon have? [4 marks]

10.

*For full marks, explain how you found your solution*.
A square ABCD has area 64 cm2. Let M be the midpoint
of BC, let d be the
perpendicular bisector of AM, and let d meet CD at F. How many cm2
is
the area of the triangle AMF?

[4 marks]

aduh boss...sy butuh translator dulu...sekian lama pl belajar berbahasa inggris.. tp sulitnya minta ampun.

ReplyDeletesalam kenal juga. Wah blognya bagus tuh. Aku jadi malu dengan tampilan blog aku yang culun.

ReplyDelete