All the possible values of lying in the interval 0 90

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Unformatted text preview: wer. B U C D A E V W F Graph G X Y Z Graph H (4) (c) Find an Eulerian trail for the graph G starting with vertex B. (3) (d) State a result which shows that the graph H has an Eulerian circuit. (2) (Total 12 marks) 447. The diagram below shows a weighted graph. 5 K 5 3 4 5 8 J 2 N M 3 2 7 L 3 1 2 P Q Use Prim’s algorithms to find a minimal spanning tree, starting at J. Draw the tree, and find its total weight. (Total 6 marks) 302 448. Let f(x) = x 3 . Find (a) f′ (x); (b) ∫ f ( x)dx. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 303 ˆ 449. In triangle ABC, AC = 5, BC = 7, A = 48°, as shown in the diagram. C 5 A 7 48° diagram not to scale B ˆ Find B, giving your answer correct to the nearest degree. Working: Answer: ………………………………………….. (Total 6 marks) 450. Consider the function f(x) = 2x2 – 8x + 5. (a) Express f(x) in the form a (x – p)2 + q, where a, p, q ∈ . 304 (b) Find the minimum value of f(x). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 451. Find the coefficient of x3 in the expansion of (2 – x)5. Working: Answer: ………………………………………….. (Total 6 marks) 305 452. Solve the equation ex = 5 – 2x, giving your answer correct to four significant figures. Working: Answer: ………………………………………….. (Total 6 marks) 453. Given that sin x = (a) cosx; (b) 1 , where x is an acute angle, find the exact value of 3 cos2x. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 306 454. For events A and B, the probabilities are P(A) = 3 4 , P(B) = . 11 11 Calculate the value of P (A ∩ B) if 6 ; 11 (a) P ( A ∪ B) = (b) events A and B are independent. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 455. The graph of y = x3 – 10x2 +12x + 23 has a maximum point between x = –1 and x = 3. Find the coordinates of this maximum point. Working: Answer: ………………………………………….. (Total 6 marks) 307 456. Three positive integers a, b, and c, where a < b < c, are such that their median is 11, their mean is 9 and their range is 10. Find the value of a. Working: Answer: ………………………………………….. (Total 6 marks) 457. Consider the functions f : x a 4 (x – 1) and g : x a (a) Find g–1. (b) 6–x . 2 Solve the equation (f ° g–1) (x) = 4. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 308 458. Calculate the acute angle between the lines with equations 4 4 r = + s and r...
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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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