• Question #1: What is sec(a)sin(a) + csc(a)cos(a) , if a = 45^o? (a) √2 (b) 2 (c) 1 (d) 1/√2 (e) 1/2
  • Answer: sec(a)sin(a) + csc(a)cos(a) = [1/cos(a)]sin(a) + [1/sin(a)]cos(a) = sin(a)/cos(a) + cos(a)/sin(a) = (√2/2)/(√2/2) + (√2/2)/(√2/2) = 1 + 1 = 2.

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• Question #2: In the standard (x,y) coordinate plane, 3 corners of a square are (4,–3), (–4,3), and (–4,-3). What are the coordinates of the square’s fourth corner?

  (a) (1/4, -1/3) (b) (4, 3) (c) (3, 4) (d) (3, -4) (e) (3, -4)

  • Answer: The easiest way to solve this problem is to sketch the 3 corners of the square. We notice that the fourth corner of the square is (4, 3).�

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• Question #3: Prizes totaling $60,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?

  (a) $5,000 (b) $10,000 (c) $15,000 (d) $25,000 (e) $65,000

  • Answer: The highest prize should be higher than one third of $60,000 and lower than $60,000. The only answer that satisfies this condition is $25,000.

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