That the degree of each face is the length of the

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Unformatted text preview: arks) 9 2 243. Determine the constant term in the expansion of x – 2 . x Working: Answers: ………………………………………….. (Total 4 marks) 166 244. (a) Sketch, on the given axes, the graphs of y = x2 and y – sin x for –1 ≤ x ≤ 2. y –1 –0.5 0 0.5 1 1.5 2 x 167 (b) Find the positive solution of the equation x2 = sin x, giving your answer correct to 6 significant figures. Working: Answers: (b) ………………………………………….. (Total 4 marks) 245. The following diagram represents the lengths, in cm, of 80 plants grown in a laboratory. 20 15 frequency 10 5 0 (a) 0 10 20 30 40 50 60 length (cm) 70 80 90 100 How many plants have lengths in cm between (i) 50 and 60? (ii) 70 and 90? (2) 168 (b) Calculate estimates for the mean and the standard deviation of the lengths of the plants. (4) (c) Explain what feature of the diagram suggests that the median is different from the mean. (1) (d) The following is an extract from the cumulative frequency table. length in cm cumulative less than frequency . . 50 22 60 32 70 48 80 62 . . Use the information in the table to estimate the median. Give your answer to two significant figures. (3) (Total 10 marks) 246. Note: Radians are used throughout this question. (a) Draw the graph of y = π + x cos x, 0 ≤ x ≤ 5, on millimetre square graph paper, using a scale of 2 cm per unit. Make clear (i) the integer values of x and y on each axis; (ii) the approximate positions of the x-intercepts and the turning points. (5) (b) Without the use of a calculator, show that π is a solution of the equation π + x cos x = 0. (3) 169 (c) Find another solution of the equation π + x cos x = 0 for 0 ≤ x ≤ 5, giving your answer to six significant figures. (2) (d) Let R be the region enclosed by the graph and the axes for 0 ≤ x ≤ π. Shade R on your diagram, and write down an integral which represents the area of R . (2) (e) Evaluate the integral in part (d) to an accuracy of six significant figures. (If you consider d it necessary, you can make use of the result ( x sin x + cos x ) = x cos x .) dx (3) (Total 15 marks) 1 247. In this question the vector km represents a displacement due east, and the vector 0 represents a displacement due north. 0 km 1 The diagram shows the path of the oil-tanker Aristides relative to the port of Orto, which is situated at the point (0, 0). y 40 Not to scale 30 Path of Aristides 0 1 20 1 0 10 10 20 30 40 50 x Orto 170 The position of the Aristides is given by the vector equation x 0 6 = +t y 28 – 8 at a time t hours after 12:00. (a) Find the position of the Aristides at 13:00. (2) (b) Find (i) the velocity vector; (ii) the speed of the Aristides. (4) (c) Find a cartesian equation for the path of the Aristides in the form ax + by = g . (4) 18 Another ship, the cargo-vessel Boadicea, is stationary, with position vector km. 4 (d) Show that the two ships will collide, and find the time of collision. (4) 5 To avoid collision, the Boadicea starts to mo...
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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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