Mathematics 30 June 1999 Grade 12 Diploma Exam

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<strong>30</strong>. Which of the following sums has the largest value? 100 A. ∑( k + 2) k = 1 100 ∑ B. 2k k = 1 100 k ∑ C. 2 D. k = 1 100 ⎛ ∑ k = 1 ⎜ 1 ⎞ ⎝ 2⎠ ⎟ k 31. A graduation committee is organizing the graduation banquet. The catering fee consists of a fixed cost and a cost per person. The total cost can be written as an arithmetic sequence, where n is the number of people attending the banquet. If the total cost for 100 people is c dollars and the total cost for 200 people is k dollars, then the common difference of the sequence is A. B. C. D. 200k − 100c 200 100k − 200c 200 k − c 200 k − c 100 20
32. If the sum of the first n terms of a sequence is S n = 3n 2 , n ∈ N, then the general term of the sequence is A. t n = 3n 2 – 3(n – 1) 2 , n ∈ N B. t n = 3(n + 1) 2 – 3(n) 2 , n ∈ N C. t n = 3(n – 1) 2 , n ∈ N D. t n = 3(n + 1) 2 , n ∈ N Numerical Response 6. If the general term of a sequence is t n = 2n + 3, where n ∈ N, then the sum of the first 20 terms, S 20 , is __________. (Record your answer in the numerical-response section on the answer sheet.) 33. A hockey arena has seating that is divided into sections lettered from A to Z inclusive and AA to XX inclusive. Each section consists of 20 rows with 16 seats in each row. At a sold-out hockey game, it is announced that a prize will be given to a person sitting in Section JJ. If you are sitting in section JJ, then what is the probability that you will win the prize? A. B. C. D. 1 50 1 320 1 16 000 1 16 640 21
Page 1 and 2: athematics 30 Mathematics 30 Mathem
Page 3 and 4: Multiple Choice • Decide which of
Page 5 and 6: 1. The function f (x) = x 3 - 6 is
Page 7 and 8: Use the following information to an
Page 9 and 10: Numerical Response 1. The polynomia
Page 11 and 12: 13. If (π, -6) satisfies the equat
Page 13 and 14: 14. Given that log b 64 = 3 , the v
Page 17 and 18: Numerical Response 4. An exponentia
Page 21 and 22: 25. The foci of a hyperbola are F 1
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Page 27 and 28: 37. In the expansion of (x + 2y) 8
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Page 41 and 42: Mathematics 30 Diploma Examination
Page 43 and 44: SAMPLE ANSWERS TO THE WRITTEN-RESPO
Page 45 and 46: • The store will lose money on th
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Page 49 and 50: A POSSIBLE SOLUTION Student A Stude

Mathematics 30 June 1999 Grade 12 Diploma Exam

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