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 $R/r$.