III/2004/2 Continue reading
I/1999/2 – A point moves in the x,y plane so that the sum of the squares of its distances from the three fixed points is always .
Find the equation of the locus of the point and interpret it geometrically.
Explain why cannot be less than the sum of the squares of the distances of the three points from their centroid. Continue reading
I/2007/1 – A positive integer with 2n digits (the first of which must not be 0) is called a balanced number if the sum of the first n digits equals the sum of the last n digits. For example, 1634 is a 4-digit balanced number, but 123401 is not a balanced number. (i) Show that seventy 4-digit balanced numbers can be made using the digits 0, 1, 2, 3 and 4. (ii) Show that 4-digit balanced numbers can be made using the digits 0 to k. You may use the identity Continue reading