Would be drawn 2 total 8 marks 26 25 when the function

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Unformatted text preview: ………………………………….. (Total 4 marks) 28 29. Let z = x + yi. Find the values of x and y if (1 – i)z = 1 – 3i. Working: Answers: ………………………………………….. (Total 4 marks) 30. Find the value of a for which the following system of equations does not have a unique solution. 4x – y + 2z = 1 2x + 3y = –6 x – 2y + az = 7 2 Working: Answers: ………………………………………….. (Total 4 marks) 29 31. The diagram below shows the graph of y1 = f(x). The x-axis is a tangent to f(x) at x = m and f(x) crosses the x-axis at x = n. y 0 y1 = f(x) m n x On the same diagram sketch the graph of y2 = f(x – k), where 0 < k < n – m and indicate the coordinates of the points of intersection of y2 with the x-axis. Working: (Total 4 marks) 30 32. In a bilingual school there is a class of 21 pupils. In this class, 15 of the pupils speak Spanish as their first language and 12 of these 15 pupils are Argentine. The other 6 pupils in the class speak English as their first language and 3 of these 6 pupils are Argentine. A pupil is selected at random from the class and is found to be Argentine. Find the probability that the pupil speaks Spanish as his/her first language. Working: Answers: ………………………………………….. (Total 4 marks) 33. If 2x2 – 3y2 = 2, find the two values of dy when x = 5. dx Working: Answers: ………………………………………….. (Total 4 marks) 31 34. (a) Find a vector perpendicular to the two vectors: r r r OP = i – 3 j + 2 k rr r OQ = –2 i + j – k (b) If OP and OQ are position vectors for the points P and Q, use your answer to part (a), or otherwise, to find the area of the triangle OPQ. Working: Answers: (a) ………………………………………….. (b) …………………………………….......... (Total 4 marks) 32 35. Differentiate y = arccos (1 – 2x2) with respect to x, and simplify your answer. Working: Answers: ………………………………………….. (Total 4 marks) 36. Given f(x) = x2 + x(2 – k) + k2, find the range of values of k for which f(x) > 0 for all real values of x. Working: Answers: ………………………………………….. (Total 4 marks) 33 37. The area of the enclosed region shown in the diagram is defined by y ≥ x2 + 2, y ≤ ax + 2, where a > 0. y 2 0 a x This region is rotated 360° about the x-axis to form a solid of revolution. Find, in terms of a, the volume of this solid of revolution. Working: Answers: ………………………………………….. (Total 4 marks) 34 38. Using the substitution u = 1 x + 1, or otherwise, find the integral 2 ∫x 1 x + 1 dx . 2 Working: Answers: ………………………………………….. (Total 4 marks) 39. Given that (1 + x)5 (1 + ax)6 ≡ 1 + bx + 10x2 + ............... + a6 x11, find the values of a, b ∈ *. Working: Answers: ………………………………………….. (Total 4 marks) 35 40. A biased die...
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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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