• Question #1: You have large, medium, and small books in the ratio of 7:6:3 and you have a total of 32 books. How many small books do you have?

  (a) 3 (b) 4 (c) 5 (d) 6 (e) 7

  • Solution: If the number of large books is x, the number of medium books is y and the number of small books is z, x/y = 7/6 x/z = 7/3 x + y + z = 32(6/7)x + (3/7)x + x = 32 x = 14 and z = 6

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• Question #2: In the standard coordinate plane (x, y), what are the coordinates x₁ and y₁ of A, if A is the point in the first quadrant of the plane that is determined by the intersection of the y = 2x line and the x² + y² = 1 circle?

  (a) x₁ = 1/√5 and y₁ = 2/√5 (b) x₁ = 1/√3 and y₁ = 2/√3 (c) x₁ = 1/ and y₁ = 1 (d) x₁ = √5 and y₁ = 2√5 (e) x₁ = 2 and y₁ = 2

  • Answer: We solve the system of equations: x² + y² = 1. x² + (2x)² = 1. 5�x² = 1. Since x and y are positive, x₁ = 1/√5 and y₁ = 2/√5

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• Question #3: What is the length of side b in the triangle below? Figure not drawn to scale ?

  (a) 2 (b) 3 (c) 4 (d) 5 (e) 6

  • Answer: sin(30^o) = b/c. 1/2 = b/c. b = 3.�

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