F is defined by f xa ex 1 x i find the minimum value

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Unformatted text preview: ………………….. (Total 4 marks) 199 288. A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours? Working: Answers: ………………………………………….. (Total 4 marks) 289. Find (a) ∫ sin (3x + 7) dx; (b) ∫e –4 x dx . Working: Answers: ………………………………………….. (Total 4 marks) 200 290. Find the angle between the following vectors a and b, giving your answer to the nearest degree. a = –4i – 2j b = i – 7j Working: Answers: ………………………………………….. (Total 4 marks) 201 291. (a) On the following diagram, sketch the graphs of y = ex and y = cos x for –2 ≤ x ≤ 1. y 2 1 –2 –1 0 –1 1 x –2 (b) The equation ex = cos x has a solution between –2 and –1. Find this solution. Working: Answers: ………………………………………….. (Total 4 marks) 202 292. The function f is defined by f :xa 3 – 2x , 3 x≤ . 2 Evaluate f –1(5) . Working: Answers: ………………………………………….. (Total 4 marks) 293. (a) (b) Write the expression 3 sin2 x + 4 cos x in the form a cos2 x + b cos x + c. Hence or otherwise, solve the equation 3 sin2 x + 4 cos x – 4 = 0, 0° ≤ x ≤ 90°. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks) 203 294. The following diagram shows the graph of y = f (x). It has minimum and maximum points at (0, 0) and ( 1, 1 ). 2 y 3.5 3 2.5 2 1.5 1 0.5 –2 –1 0 1 2 3 x –0.5 –1 –1.5 –2 –2.5 3 . 2 (a) On the same diagram, draw the graph of y = f ( x – 1) + (b) What are the coordinates of the minimum and maximum points of 3 y = f ( x – 1) + ? 2 Working: Answers: ………………………………………….. 204 (Total 4 marks) 295. In the following diagram, O is the centre of the circle and (AT) is the tangent to the circle at T. T O A diagram not to scale If OA = 12 cm, and the circle has a radius of 6 cm, find the area of the shaded region. Working: Answers: ………………………………………….. (Total 4 marks) 205 296. Michele invested 1500 francs at an annual rate of interest of 5.25 percent, compounded annually. (a) Find the value of Michele’s investment after 3 years. Give your answer to the nearest franc. (3) (b) How many complete years will it take for Michele’s initial investment to double in value? (3) (c) What should the interest rate be if Michele’s initial investment were to double in value in 10 years? (4) (Total 10 marks) 297. The table below represents the weights, W, in grams, of 80 packets of roasted peanuts. Weight (W) Number of packets (a) 80 < W ≤ 85 85 < W ≤ 90 90 < W ≤ 95 95 < W ≤ 100 100 < W ≤ 105 5 10 15 26 13 105 < W ≤ 110 7 110 < W ≤ 115 4 Use the midpoint of each interval to find an estima...
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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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