Mathematics (College) quiz

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Sample questions

• Define a binary operation on Z, the set of integers, by the equation m • n = m + n + mn. Which of the following statements is (are) true about the binary structure (Z, • )? I. This structure is not a group since the operation is not associative. II. This structure is not a group since there is no identity element. III. This structure is not a group since not all elements have an inverse. IV. This structure is a group.
• What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
• Consider the system of linear equations w + 3x + 2y + 2z = 0 w + 4x + y = 0 3w + 5x + 10 y + 14z = 0 2w + 5x + 5y + 6z = 0 with solutions of the form (w, x, y, z), where w x, y, and z are real. Which of the following statements is FALSE?

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