Mm a on the graph mark clearly in the same way and

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Unformatted text preview: marks) 400 593. Consider the equation 2(p + iq) = q – ip – 2 (1 – i), where p and q are both real numbers. Find p and q. Working: Answers: ………………………………………….. (Total 6 marks) 401 594. The diagram shows the graph of f(x). (a) On the same diagram, sketch the graph of 1 , indicating clearly any asymptotes. f ( x) y 2 1 –2 –1 0 1 x 2 –1 –2 (b) On the diagram write down the coordinates of the local maximum point, the local 1 minimum point, the x-intercepts and the y-intercept of . f ( x) Working: (Total 6 marks) 402 595. Find the angle between the plane 3x – 2y + 4z = 12 and the z-axis. Give your answer to the nearest degree. Working: Answer: ………………………………………….. (Total 6 marks) 596. Consider the function f(t) = 3 sec2t + 5t. (a) Find f′(t). (b) Find the exact values of (i) f(π); (ii) f′ (π); Working: Answers: (a) ........................................................... (b) (i) ……………………………………... (ii) ……………………………………... (Total 6 marks) 403 597. The first four terms of an arithmetic sequence are 2, a – b, 2a +b + 7, and a – 3b, where a and b are constants. Find a and b. Working: Answers: ………………………………………….. (Total 6 marks) 598. Solve log16 3 100 – x 2 = 1 2 . Working: Answers: ………………………………………….. (Total 6 marks) 404 599. Calculate the area enclosed by the curves y = lnx and y = ex – e, x > 0. Working: Answer: ………………………………………….. (Total 6 marks) 600. On a television channel the news is shown at the same time each day. The probability that Alice watches the news on a given day is 0.4. Calculate the probability that on five consecutive days, she watches the news on at most three days. Working: Answer: ………………………………………….. (Total 6 marks) 405 601. Consider the equation (1 + 2k)x2 – 10x + k – 2 = 0, k ∈ which the equation has real roots. . Find the set of values of k for Working: Answer: ………………………………………….. (Total 6 marks) x 3 602. Let f(x) = sin arcsin – arccos , for –4 ≤ x ≤ 4. 4 5 (a) On the grid below, sketch the graph of f(x). y 2 1 –5 –4 –3 –2 –1 1 0 2 3 4 5 x –1 –2 406 (b) On the sketch, clearly indicate the coordinates of the x-intercept, the y-intercept, the minimum point and the endpoints of the curve of f(x). (c) Solve f(x) = – 1 . 2 Working: Answer: (c) ………………………………………….. (Total 6 marks) 407 603. Consider the equation 2xy2 = x2y + 3. (a) Find y when x = 1 and y < 0. (b) Find dy when x = 1 and y < 0. dx Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 408 604. Let y = e3x sin(πx). dy . dx (a) Find (b) Find the smallest positive value of x for which dy = 0. dx Working: Answers: (a) ……...
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