Below is a sample of 10 questions that have been used for the individual competition.

1)  How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair which becomes productive from the second month on?

2)

               
If the figure in the center is a square, then

           

3)  A bag contains 30 balls; 18 of them are red. What are the odds that the ball drawn will be red?

4)  Factor the equation into two quadratics with real coefficients. (Hint: Factor as both the difference of two squares and the difference of two cubes.)

5)

       

Let A, B, and C be squares of equal area. If the sum of the areas of the squares is 432cm², what is the area of the triangle?

6)  Three horses enter a race. If horse A is twice as likely to win as horse B, and horse B is 5 times as likely to win as horse C, what is the probability that horse A wins the race?

7)  I have a pair of numbers. The cube root of their difference is the smallest odd prime that is not 1. The square root of their sum is the smallest odd perfect square greater than 1. What are the numbers?

8)  The equation 3^2x+2 - 3^x+3 - 3^x + 3 = 0 has
a) No solution
b) One solution
c) Two solutions
d) Three solutions
e) Infinitely many solutions

9)  Find the sum of the terms of the finite sequence 7, 14, 21, ..., 1988, 1995.


10)
                           
Given the above isosceles triangle with congruent sides equal to 13, angle ABC = 90°, mAB = 6, and mBC = 8, what is the area of the shaded region?