2nd Vietnam 1963


1. A conference has 47 people attending. One woman knows 16 of the men who are attending, another knows 17, and so on up to the last woman who knows all the men who are attending. Find the number of men and women attending the conference.
2. For what values of m does the equation x² + (2m + 6)x + 4m + 12 = 0 has two real roots, both of them greater than -2.
3. Solve the equation sin³x cos 3x + cos³x sin 3x = 3/8.
4. The tetrahedron SABC has the faces SBC and ABC perpendicular. The three angles at S are all 60^o and SB = SC = 1. Find its volume.
5. The triangle ABC has perimeter p. Find the side length AB and the area S in terms of ∠A, ∠B and p. In particular, find S if p = 23.6, A = 52.7 deg, B = 46 4/15 deg.

To avoid possible copyright problems, I have changed the wording, but not the substance, of the problems.