Hong Kong Maths Olympiad Heat Individual (94-95)

1.Find the square root of 1234567654321.

2.Given that f(1/x)=x/(1-x²), find the value of f(2).

3.Solve 3^2x=9=(3^x).

4.A three-digit number is selected at random. Find the probability that the numbere selected is a perfect square,

5.Given that sinx+cosx=1/5 and 0¡Øx<£k,find tanx.

6.How many pairs of positive integeres x, y are there satisfying xy-3x-2y+10?

7.x, y are positive integeers and 3x+5y=123. Find the least value of |x-y|.

8.Find the remainder when 1997⁹¹³ is divided by 10.

9.In figure 1, if BC=3DE,find the value of r where r=Area of £G ADE/Area of £GBDC.

Figure1

10.A, B, C, D are points on the sides of the right-angled triangle PQR as shown in figure 2. If ABCD is a square, QA=8 and BR=18, find AB.

Figure2