Two aircraft are flying at the same height show that

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Unformatted text preview: t. Working: Answers: ....…………………………………….......... (Total 3 marks) 140 200. Given that events A and B are independent with P(A ∩ B) = 0.3 and P(A ∩ B′) = 0.3, find P(A ∪ B). Working: Answers: ....…………………………………….......... (Total 3 marks) 201. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, .... Working: Answers: ....…………………………………….......... (Total 3 marks) 141 202. For the function f : x a 1 sin 2x + cos x, find the possible values of sin x for which f′(x) = 0. 2 Working: Answers: ....…………………………………….......... (Total 3 marks) 203. Find the real number k for which 1 + ki, (i = − 1 ), is a zero of the polynomial z2 + kz + 5. Working: Answers: ....…………………………………….......... (Total 3 marks) 204. Let a be the angle between the vectors a and b, where a = (cos θ)i + (sin θ)j, b = (sin θ)i + (cos θ)j and 0 < θ < π . 4 142 Express α in terms of θ. Working: Answers: ....…………………………………….......... (Total 3 marks) 7 205. The coefficient of x in the expansion of x + 1 2 is 7 . Find the possible values of a. 3 ax Working: Answers: ....…………………………………….......... (Total 3 marks) 143 206. For what values of m is the line y = mx + 5 a tangent to the parabola y = 4 – x2? Working: Answers: ....…………………………………….......... (Total 3 marks) 207. The tangent to the curve y2 – x3 at the point P(1, 1) meets the x-axis at Q and the y-axis at R. Find the ratio PQ : QR. Working: Answers: ....…………………………………….......... (Total 3 marks) 144 208. The sum of an infinite geometric sequence is 13 1 , and the sum of the first three terms is 13. 2 Find the first term. Working: Answers: ....…………………………………….......... (Total 3 marks) ˆ 209. In a triangle ABC, A B C = 30°, AB = 6cm and AC = 3 2 cm. Find the possible lengths of [BC]. Working: Answers: ....…………………………………….......... (Total 3 marks) 145 210. Solve the differential equation xy dy = 1 + y2, given that y = 0 when x = 2. dx Working: Answers: ....…………………………………….......... (Total 3 marks) 211. If z is a complex number and |z + 16| = 4 |z + l|, find the value of | z|. Working: Answers: ....…………………………………….......... (Total 3 marks) 146 212. In how many ways can six different coins be divided between two students so that each student receives at least one coin? Working: Answers: ....…………………………………….......... (Total 3 marks) 213. The following graph is that part of the graph of y = f(x) for which f(x) ≥ 0. y 4 3 2 1 –2 –1 0 1 2 x 147 Sketch, on the axes provided below, the graph of y2 = f(x) for –2 ≤ x ≤ 2. y 4 3 2 1 –2 –1 0 1 2 x –1 –2 –3 –4 (Total 3 marks) 214. (a) Sketch and label the curves y – x2 for –2 ≤ x ≤ 2, and y = – 1 ln x for 0 < x ≤ 2. 2 (2) (b)...
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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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