| 1. The sequence a1, a2, a3, ... is defined by a1 = 8, a2 = 18, an+2 = an+1an. Find all terms which are perfect squares. |
|
| 2. A real number with absolute value less than 1 is written in each cell of an n x n array, so that the sum of the numbers in each 2 x 2 square is zero. Show that for n odd the sum of all the numbers is less than n. | |
| 3. Given a circle and its center O, a point A inside the circle and a distance h, construct a triangle BAC with ∠A = 90o, B and C on the circle and the altitude from A length h. | |
| 4. ABCD is a convex quadrilateral with ∠BAC = 30o, ∠CAD = 20o, ∠ABD = 50o, ∠DBC = 30o. If the diagonals intersect at P, show that PC = PD. |
|
| 5. Find a real-valued function f(x) on the non-negative reals such that f(0) = 0, and f(2x+1) = 3f(x) + 5 for all x. |
|
To avoid possible copyright problems, I have changed the wording, but not the substance, of the problems.
Brasil home
© John Scholes
jscholes@kalva.demon.co.uk
12 Oct 2003
Last corrected/updated 12 Oct 03