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Unformatted text preview: .......................... (Total 6 marks) 812. The following diagram shows a circle of centre O, and radius r. The shaded sector OACB has an area of 27 cm2. Angle AOB = θ = 1.5 radians. A C B r O 553 (a) Find the radius. (b) Calculate the length of the minor arc ACB. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 554 813. Two unbiased 6-sided dice are rolled, a red one and a black one. Let E and F be the events E : the same number appears on both dice; F : the sum of the numbers is 10. Find (a) P(E); (b) P(F); (c) P(E ∪ F). Working: Answers: (a) ………………………………………….. (b) .................................................................. (c) …………………………………….......... (Total 6 marks) 555 814. Let f(x) = (3x + 4)5. Find (a) f′(x); (b) ∫f(x)dx. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 815. Find the exact solution of the equation 92x = 27(1–x). Working: Answer: ....…………………………………….......... (Total 6 marks) 556 816. The curve y = f(x) passes through the point (2, 6). Given that dy = 3x2 – 5, find y in terms of x. dx Working: Answer: ....…………………………………….......... (Total 6 marks) 817. (a) Given that log3x – log3(x – 5) = log3A, express A in terms of x. (b) Hence or otherwise, solve the equation log3x – log3(x – 5) = 1. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 557 3 − 2 818. Find the cosine of the angle between the two vectors and . 4 1 Working: Answer: ....…………………………………….......... (Total 6 marks) 819. The 45 students in a class each recorded the number of whole minutes, x, spent doing experiments on Monday. The results are ∑x = 2230. (a) Find the mean number of minutes the students spent doing experiments on Monday. 558 Two new students joined the class and reported that they spent 37 minutes and 30 minutes respectively. (b) Calculate the new mean including these two students. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 820. The function f is given by f(x) = e(x–11) –8. (a) Find f–1(x). (b) Write down the domain of f–l(x). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 559 821. The graph of y = f(x) is shown in the diagram. y 2 1 –2 –1 0 1 2 3 4 5 6 7 8 x –1 –2 (a) On each of the following diagrams draw the required graph, (i) y = 2f(x); y 2 1 –2 –1 0 1 2 3 4 5 6 7 8 x 1 2 3 4 5 6 7 8 x –1 –2 (ii) y = f(x – 3). y 2 1 –2 –1 0 –1 –2 560 (b) The point A (3, –1) is on the graph of f. The point A′ is the corresponding point on the graph of y = –f(x) + 1. Find the coordinates of A′. Work...
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