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Unformatted text preview: ……….. ……………………………………………….. (Total 6 marks) 381 573. (a) The diagram shows part of the graph of the function f(x) = q . The curve passes x– p through the point A (3, 10). The line (CD) is an asymptote. y 15 C 10 A 5 –15 –10 –5 0 5 10 15 x –5 –10 –15 D Find the value of (i) p; (ii) q. 382 (b) The graph of f(x) is transformed as shown in the following diagram. The point A is transformed to A′ (3, –10). y 15 C 10 5 –15 –10 –5 0 5 10 15 x –5 –10 A –15 D Give a full geometric description of the transformation. Working: Answers: (a) (i) ……………………………………... (ii) ……………………………………... (b) .................................................................. (Total 6 marks) 383 574. (a) (b) 60 – 30 Find the scalar product of the vectors and 25 40 . Two markers are at the points P (60, 25) and Q (–30, 40). A surveyor stands at O (0, 0) and looks at marker P. Find the angle she turns through to look at marker Q. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 384 575. The mass m kg of a radio-active substance at time t hours is given by m = 4e–0.2t. (a) Write down the initial mass. (b) The mass is reduced to 1.5 kg. How long does this take? Working: Answer: ………………………………………….. (Total 6 marks) 576. It is given that dy = x3+2x – 1 and that y = 13 when x = 2. dx Find y in terms of x. Working: Answer: ………………………………………….. (Total 6 marks) 385 577. The function f is given by f(x) = x2 – 6x + 13, for x ≥ 3. (a) Write f(x) in the form (x – a)2 + b. (b) Find the inverse function f–1. (c) State the domain of f–1. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (c) .................................................................. (Total 6 marks) 386 578. (a) Factorize the expression 3 sin2 x – 11 sin x + 6. (b) Consider the equation 3sin2x – 11sin x + 6 = 0. (i) Find the two values of sin x which satisfy this equation, (ii) Solve the equation, for 0° ≤ x ≤ 180°. Working: Answers: (a) ........................................................... (b) (i) ……………………………………... (ii) ……………………………………... (Total 6 marks) 387 579. (a) (b) Find ∫(1 + 3 sin(x + 2))dx. The diagram shows part of the graph of the function f(x) = 1 + 3 sin(x + 2). The area of the shaded region is given by ∫ a 0 f ( x)dx . y 4 2 –4 –2 0 2 4 x –2 Find the value of a. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 388 580. The diagram shows the graph of y = f(x). y 0 x 389 On the grid below sketch the graph of y = f′ (x). y 0 x (Total 6 marks) 390 581. The diagram shows points...
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