Of a and of b given that a b working answer

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Unformatted text preview: (c) (f ° g)(x). Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (c) ………………………………………….. (Total 6 marks) 691. The displacement s metres of a car, t seconds after leaving a fixed point A, is given by s = 10t – 0.5t2. (a) Calculate the velocity when t = 0. (b) Calculate the value of t when the velocity is zero. 463 (c) Calculate the displacement of the car from A when the velocity is zero. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (c) ………………………………………….. (Total 6 marks) 692. Let f(x) = 2 + cos (2x) – 2sin (0.5x) for 0 ≤ x ≤ 3, where x is in radians. (a) On the grid below, sketch the curve of y = f(x), indicating clearly the point P on the curve where the derivative is zero. y 4 3 2 1 0 0.5 1 1.5 2 2.5 3x –1 –2 –3 –4 464 (b) Write down the solutions of f(x) = 0. Working: Answer: (b) ………………………………………….. (Total 6 marks) 693. The population p of bacteria at time t is given by p = 100e0.05t. Calculate (a) the value of p when t = 0; (b) the rate of increase of the population when t = 10. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 465 694. The derivative of the function f is given by f′(x) = e–2x + 1 , x < 1. 1− x The graph of y = f(x) passes through the point (0, 4). Find an expression for f(x). Working: Answer: …………………………………………........ (Total 6 marks) 695. Let f be a function such that (a) ∫ 3 0 f ( x ) dx = 8 . Deduce the value of 3 (i) ∫ (ii) ∫ ( f ( x ) + 2 ) dx . 0 2 f ( x) dx ; 3 0 466 (b) ∫ d c f ( x − 2)dx = 8 , write down the value of c and of d. Working: Answers: (a) (i) …………………………………… (ii) …………………………………... (b) c = ......................., d = ....................... (Total 6 marks) 696. The diagram below shows a circle of radius 5 cm with centre O. Points A and B are on the ˆ circle, and AOB is 0.8 radians. The point N is on [OB] such that [AN] is perpendicular to [OB]. A 5 cm O 0.8 N B 467 Find the area of the shaded region. Working: Answer: …………………………………………........ (Total 6 marks) 697. Part of the graph of the periodic function f is shown below. The domain of f is 0 ≤ x ≤ 15 and the period is 3. f(x) 4 3 2 1 0 0 (a) 1 2 3 4 5 6 7 8 9 10 x Find (i) f(2); (ii) f′(6.5); (iii) f′(14). 468 (b) How many solutions are there to the equation f(x) = 1 over the given domain? Working: Answers: (a) (i) ……………………………………… (ii) ……………………………………… (iii) ……………………………………… (b) ……………………………………… (Total 6 marks) 698. The function f(x) is defined as f(x) = –(x – h)2 + k. The diagram be...
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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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