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Unformatted text preview: FINITE MATHEMATICS FOR THE SOCIAL AND MANAGEMENT SCIENCES Math 51-14 Fall 2002 MID-TERM EXAM There are 10 questions in all; together they are worth 110%. You may choose to do any, or all, of these questions. The value of each question, as a percentage, is denoted. Write your solutions in the blue books provided (not on this handout). If you are asked to provide an explanation, be as clear and precise as you can. If no explanation is requested, do not provide any, but clearly display all the steps of your working ... I am looking for the correct application of a technique, the answer is largely irrelevant. 1. Without doing any calculation determine the number of points of intersection of each of the following systems of two lines. Give brief geometric reasons for your answers. ( a ) 2 x +6 y = 0- 3 x- 9 y = 0 ( b ) 2 x +6 y = 0- 3 x- 9 y = 6 ( c ) 2 x +6 y =- 4- 3 x- 9 y = 6 Note that your reasons must be geometric. 9% 2. Without doing any calculation determine the number of points of intersection of each of the following systems of three planes. Give brief geometric reasons for your answers....
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- Fall '07