'C2 Paper\r'

'Paper Reference(s) 6664 Edexcel GCE amount of money Mathematics C2 Advanced Subsidiary Tuesday 10 January 2006 ? Afternoon Time: 1 instant 30 minutes Materials required for interrogative Mathematical Formulae (Green) Items included with question cover Nil Candidates may use whatever calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus panoramas may NOT use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G.\r\n instruction manual to Candidates In the boxes on the answer book, compile the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Core Mathematics C2), the piece reference (6664), your surname, other name and sig personality. When a calculator is used, the answer should be accustomed to an appropriate degree of accuracy. Information for Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. replete(p) insures may be obtained for answers to all in all questions.\r\nThe marks for individual questions and the break-dance of questions be give tongue ton in round brackets: e. g. (2). There are 9 questions on this paper. The total mark for this paper is 75. Advice to Candidates You must ensure that your answers to parts of questions are pass offly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit. N23552A This publication may only be reproduced in accordance with Edexcel Limited copyright policy. ©2006 Edexcel Limited. 1. Given that f(1) = 0, (x) = 2×3 + x2 †5x + c, where c is a constant. (a) find the assess of c, (2) (b) resolve f(x) completely, (4) (c) find the remainder when f(x) is divided by (2x †3). (2) 2. (a) invent the first 3 hurt, in asc differenceing powers of x, of the binomial expansion of (1 + px)9, where p is a constant. (2) The first 3 frontiers are 1, 36x and qx2, where q is a constant. (b) experience the value of p and the value of q. (4) N23552A 2 3. y B come in 1 C P O A x In Figure 1, A(4, 0) and B(3, 5) are the end points of a diameter of the circle C.\r\n convalesce (a) the exact length of AB, (2) (b) the coordinates of the midpoint P of AB, (2) (c) an equation for the circle C. (3) 4. The first term of a geometric series is 120. The integrality to infinity of the series is 480. (a) Show that the reciprocal ration, r, is 3 . 4 (3) (b) Find, to 2 denary places, the difference between the 5th and sixth price. (2) (c) seem the sum of the first 7 terms. (2) The sum of the first n terms of the series is greater than 300. (d) Calculate the smallest realizable value of n. (4) N23552A 3 5. Figure 2 A 6m 5m 5m B\r\nO In Figure 2 OAB is a orbit of a circle, radius 5 m. The reconcile AB is 6 m long. 7 ? . (a) Show that cos AOB = 25 (2) ? (b) and then find the angle AOB in radians, big(p) your answer to 3 decimal places . (1) (c) Calculate the area of the sector OAB. (2) (d) Hence depend the shaded area. (3) 6. The urge, v m sâ€1, of a train at time t routines is given by v = ? (1. 2t †1), 0 ? t ? 30. The following table shows the speed of the train at 5 second breakups. t v 0 0 5 1. 22 10 2. 28 15 20 6. 11 25 30 (a) Complete the table, giving the value of v to 2 decimal places. 3) The distance, s metres, travelled by the train in 30 seconds is given by ? s = ? ? (1. 2 t ? 1) dt . ?0 (b) white plague the trapezium rule, with all the set from your table, to adjudicate the value of s. (3) 30 N23552A 4 7. The bow C has equation y = 2×3 †5×2 †4x + 2. (a) Find dy . dx (2) (b) Using the result from part (a), find the coordinates of the turning points of C. (4) d2 y (c) Find . dx 2 (2) (d) Hence, or otherwise, determine the nature of the turning points of C. (2) 8. (a) Find all the values of ? to 1 decimal place, in the interval 0? ? ? < 360? for which 5 sin (? + 30? ) = 3. (4) (b) Find all the values of ? , to 1 decimal place, in the interval 0? ? ? < 360? for which tan2 ? = 4. (5) N23552A 5 9. y Figure 3 3 2 A R B O x Figure 3 shows the shaded region R which is jump by the curve y = â€2×2 + 4x and the 3 line y = . The points A and B are the points of crossbreeding of the line and the curve. 2 Find (a) the x-coordinates of the points A and B, (4) (b) the exact area of R. (6) TOTAL FOR radical: 75 MARKS END N23552A 6\r\n'