2010 Sun Life Financial Canadian Open Mathematics Challenge – PART A
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Muhammad Yusuf
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1. Determine the integer equal to
2. Determine all values of x for which x - (8 - x) = 8 - (x - 8).
3. In the diagram, each of the
three circles has centre O. Diameter CD of the largest circle passes through points B, A and O. The lengths of the radii of the circles are OA = 2, OB = 4, and OC = 6. What is the area of the shaded region?
4. Determine the number of digits
of the integer equal to
5. What point on the line with
equation y = x is
closest to the point P(-3, 9)?
6. On a calculus exam, the
average of those who studied was 90% and the average of those who did not study
was 40%. If the average of the entire class was 85%, what percentage of the
class did not study?
7. In the diagram, rectangle ABCD has AB = 20 and BC = 10. Points W and K are outside of the rectangle
with WA = KC = 12
and WB = KD = 16. Determine
the length of WK and express your answer in the
form WK = m√n, where m and n are positive integers with m > 1.
8. Determine all values of x for which (x2+3x+2)(x2-2x-1)(x2-7x+12)+24 = 0.
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