3 marks 371 point a3 0 2 lies on the line r 3i

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Unformatted text preview: umber of car accidents per month was 630. From October to December, the mean was 810 accidents per month. What was the mean number of car accidents per month for the whole year? Working: Answer: ………………………………………….. (Total 6 marks) 393. In an arithmetic sequence, the first term is –2, the fourth term is 16, and the nth term is 11 998. (a) Find the common difference d. (b) Find the value of n. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 267 394. Let f(x) = 2x, and g(x) = x , (x ≠ 2). x–2 Find (a) (g ° f) (3); (b) g–1 (5). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 268 395. The following diagram shows a circle of centre O, and radius 15 cm. The arc ACB subtends an angle of 2 radians at the centre O. C A B 15 cm Diagram not to scale 2 rad O AÔB = 2 radians OA = 15 cm Find (a) the length of the arc ACB; (b) the area of the shaded region. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 269 x 1 – 2 396. A vector equation of a line is = + t ,t∈ y 2 3 . Find the equation of this line in the form ax + by = c, where a, b, and c ∈ . Working: Answer: ………………………………………….. (Total 6 marks) 397. Two boats A and B start moving from the same point P. Boat A moves in a straight line at 20 km h–1 and boat B moves in a straight line at 32 km h–1. The angle between their paths is 70°. Find the distance between the boats after 2.5 hours. Working: Answer: ………………………………………….. (Total 6 marks) 270 9 1 398. Consider the expansion of 3x 2 – . x (a) How many terms are there in this expansion? (b) Find the constant term in this expansion. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 399. Let f(x) = sin 2x and g(x) = sin (0.5x). (a) Write down (i) the minimum value of the function f; (ii) the period of the function g. 271 (b) Consider the equation f(x) = g(x). Find the number of solutions to this equation, for 0 ≤ x ≤ 3π . 2 Working: Answers: (a) (i) …………………………………….. (ii) …………………………………….. (b) ................................................................. (Total 6 marks) 400. Solve the equation log27 x = 1 – log27 (x – 0.4). Working: Answer: ………………………………………….. (Total 6 marks) 272 401. The derivative of the function f is given by f′(x) = 1 – 0.5sinx, for x ≠ –1. 1+ x The graph of f passes through the point (0, 2). Find an expression for f(x). Working: Answer: ………………………………………….. (Total 6 mar...
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