Mathematics 30 June 1999 Grade 12 Diploma Exam

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Use the following information to answer the next question. Owners of vehicles in North America are required to purchase licence plates. In Alberta, standard licence plates consist of 3 letters followed by 3 digits. Written Response—10% 2. • Determine the maximum number of different standard licence plates available. State any assumption(s) that you make. A POSSIBLE SOLUTION 26 26 26 10 10 10 = 17 576 000 L L L D D D All letters and digits can be used and can be repeated. 26 C 3 × 10 C 3 × 3! × 3! = 1 <strong>12</strong>3 200 All letters and digits can be used but no letter or digit can be repeated. • Using the same assumptions that you stated above, determine the probability that you would receive MRF 456 if you were randomly issued a standard licence plate. A POSSIBLE SOLUTION probability = 1 17 576 000 probability = 1 1<strong>12</strong>3 200 6
• Assume that it becomes necessary to increase the number of available licence plates. Provide two alternative proposals in which a maximum of 6 characters, consisting of letters and/or digits, can be used, then provide 2 alternate proposals to increase the number of licence plates. In your explanation, include any assumptions you make and determine the number of licence plates for each proposal. A POSSIBLE SOLUTION Two Alternate Proposals: 26 6 Using 6 letters where the letters can be repeated. OR 26 C 3 × 10 C 3 × 6! Using 3 letters and 3 digits which can repeat in any position. Two Alternate Proposals: 26 C 3 × 10 C 3 × 6! = 224 640 000 No letter or digit can be repeated. The letters and digits can go in any place. OR (36) 6 use either letters or digits (can choose from 36) with repetitions. 7
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Page 5 and 6: 1. The function f (x) = x 3 - 6 is
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Page 9 and 10: Numerical Response 1. The polynomia
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Page 13 and 14: 14. Given that log b 64 = 3 , the v
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Page 21 and 22: 25. The foci of a hyperbola are F 1
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Mathematics 30 June 1999 Grade 12 Diploma Exam

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