Volume 26
, Issue 2

1990 Everyone knows why they entered the actuarial field. The allure of what success as an actuary can bring - money, status, power - is a powerful attraction in anyone's book.

Given a circle $x^2 + y^2 = p$, centre $(0,0)$ radius $\sqrt{p}$, does the circle always pass through points whose co-ordinates are rational numbers?

Mathematics is generally regarded as one of the few disciplines (some would say the only discipline) which is built on rock-solid foundations.

Senior Division

First Prize: $\$150$and a Certificate Le Strange, Elizabeth Teresa Sydney Church of England Girls Grammar School The new teacher's age is an odd number which leaves the remainder 1 when divided by 3, and the remainder 9 when divided by 11. How old is the teacher? Q.805 Solve for$x$and$y$: $$\sqrt{x+y} + \sqrt{x-y} = 5\sqrt{x^2 - y^2}$$ $$\frac{2}{\sqrt{x+y}} - \frac{1}{\sqrt{x-y}} = 1$$ Q.793 The vertices of a regular tetrahedron lie on a sphere of radius$R$, and its faces are tangential to a sphere of radius,$r$. Calculate$R/r\$.