Equation log2 5x2 x 2 2 2 log2 x working answers

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Unformatted text preview: ) Show that f has an inverse function. Find this inverse and verify your result. (5) (Total 12 marks) 193 278. Consider the following sets: kπ kπ }; B = z k = cos + i sin k ∈ {0, 1, 2, 3 } and i = – 1 2 2 A = {3n(mod l0) | n ∈ (a) Show that B is a group under normal multiplication. (4) (b) Write down the multiplication table for A(mod 10). (2) (c) Find the order of each element of A. (3) (d) Hence, or otherwise, show that the two groups are isomorphic. Find this isomorphism. (2) (Total 11 marks) 279. Find two integers x and y such that the greatest common divisor of (242,165) = 242x + 165y. (Total 5 marks) 280. The diagram shows a weighted graph. B 4 C 10 6 4 A 5 2 4 L 4 3 I 3 2J 5 D K 6 12 2 G 6 5 H M 2 E 8 3 F 20 194 Use Kruskal’s algorithm to find a minimum spanning tree as follows: (a) state the major steps in the algorithm; (2) (b) execute the algorithm showing the steps in your work; (4) (c) sketch the minimum spanning tree found, and write down its weight. (2) (Total 8 marks) 281. Test whether the following is a convergent series: ∞ ∑ (– 1) n =1 n +1 1 . n! If it is, then find an approximation for the sum to two decimal places; if it is not, explain why this is so. (Total 5 marks) 195 282. Given the following frequency distribution, find (a) the median; (b) the mean. Number (x) 1 2 3 4 5 6 Frequency (f) 5 9 16 18 20 7 Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 283. The diagram shows part of the graph with equation y = x2 + px + q. The graph cuts the x-axis at –2 and 3. y 6 4 2 –3 –2 –1 0 1 2 3 4 x –2 –4 –6 196 Find the value of (a) p; (b) q. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 284. Each year for the past five years the population of a certain country has increased at a steady rate of 2.7% per annum. The present population is 15.2 million. (a) What was the population one year ago? (b) What was the population five years ago? Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 197 285. The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. 5 7 diagram not to scale 8 Find (a) the size of the smallest angle, in degrees; (b) the area of the triangle. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 198 286. The point P ( 1 , 0 ) lies on the graph of the curve of y = sin(2x –1) . 2 Find the gradient of the tangent to the curve at P. Working: Answers: ………………………………………….. (Total 4 marks) 287. Use the binomial theorem to complete this expansion. (3x +2y)4 = 81x4 + 216x3 y +... 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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