6 marks 357 534 find all the values of in the interval

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Unformatted text preview: find integers x and y such that 17x + 31y = 1. (3) (b) Given that 17p + 31q = 1, where p, q ∈ show that p ≥ 11 and q ≥ 6. (2) (Total 5 marks) 374 564. Consider the following matrix M. A B C D E (a) A 0 1 1 1 1 B 1 0 0 2 1 C 1 0 0 2 1 D 1 2 2 0 1 E 1 1 1 1 0 Draw a planar graph G with 5 vertices A, B, C, D, E such that M is its adjacency matrix. (7) (b) Give a reason why G has a Eulerian circuit. (3) (c) Find a Eulerian circuit for G. (3) (d) Find a spanning tree for G. (2) (Total 15 marks) 375 565. For positive integers k and n let uk = 1 + 2(–1) k and S2n = k +1 n (a) Show that S2n = 2n ∑u k. k =1 4k – 1 ∑ 2k (2k + 1) . k =1 (3) ∞ (b) Hence or otherwise, determine whether the series ∑u k is convergent or not, justifying k =1 your answer. (4) (Total 7 marks) 566. A student measured the diameters of 80 snail shells. His results are shown in the following cumulative frequency graph. The lower quartile (LQ) is 14 mm and is marked clearly on the graph. 90 Cumulative frequency 80 70 60 50 40 30 20 10 0 5 0 10 15 LQ = 14 20 25 30 35 40 45 Diameter (mm) (a) On the graph, mark clearly in the same way and write down the value of (i) the median; (ii) the upper quartile. 376 (b) Write down the interquartile range. Working: Answer: (b) ………………………………………….. (Total 6 marks) 567. The graph of the function f(x) = 3x – 4 intersects the x-axis at A and the y-axis at B. (a) Find the coordinates of (i) A; (ii) B. 377 (b) Let O denote the origin. Find the area of triangle OAB. Working: Answers: (a) (i) ……………………………………... (ii) ……………………………………... (b) .................................................................. (Total 6 marks) 568. The equation kx2 + 3x +1 = 0 has exactly one solution. Find the value of k. Working: Answer: ……………………………………….. (Total 6 marks) 378 569. A painter has 12 tins of paint. Seven tins are red and five tins are yellow. Two tins are chosen at random. Calculate the probability that both tins are the same colour. Working: Answer: ………………………………………….. (Total 6 marks) 570. Complete the following expansion. (2 + ax)4 = 16 + 32ax + … Working: Answer: ………………………………………….. (Total 6 marks) 379 571. Arturo goes swimming every week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year (52 weeks). (a) How far does Arturo swim in the final week? (b) How far does he swim altogether? Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 380 4 572. A vector equation for the line L is r = + t 4 3 . 1 Which of the following are also vector equations for the same line L? A. 4 r = + t 4 2 . 1 B. 4 r = + t 4 6 . 2 C. 0 r = + t 1 1 . 3 D. 7 r = + t 5 3 . 1 Working: Answers: ………………………………………...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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