2009 Question 5

Let n be a positive integer.Let T be the set of points (x,y) in the plane where x and y are non-negative integers and x + y < n.
Each point of T is coloured red or blue.If a point (x,y) is red,then so are all points (x¹,y¹) of T with both x¹ and y¹ < y.Define an X-set to be a set of n blue points having distinct x-coordinates,and a Y-set to be a set of n blue points having distinct y-coordinates.Prove that the number of X-sets is equal to the number of Y-sets.

2009 Question 4

Find the smallest 7 digit number where
(i)the first digit is 8
(ii)all the digits are diferrent
(iii)the number is divisible by 3

2009 Question 3

1/2 x 2/3 x 3/4 x 4/5 x 5/6 x 6/7......x 2008/2009 + 2008/2009 =

2009 Question 2

The figure shows a rectangle 9cm long and 6 cm wide was divided into 4 triangles with areas S1,S2,S3 and S4 respectively.Given that S1=S2=S3+S4.Find S4

2009 Question 1

Find the value of (x²-x-2)(3x+2)

Easy Question

Find the value of 1222x12211221-1221x12221221