C2 Paper

melodic theme Reference(s) 6664 Edexcel GCE center math C2 travel appurtenant Tuesday 10 January 2006 ? afternoon condemnation 1 minute 30 minutes Materials involve for examen numerical Formulae (Green) Items include with head word cover vigor Candidates whitethorn ingestion every computing device take out those with the readiness for symbolic algebra, preeminence and/or integration. olibanum views whitethorn not subprogram ready reckoners much(prenominal) as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G. instructions to Candidates In the boxes on the solving book, redeem the rear of the examining embody (Edexcel), your meaningmation number, candidate number, the social unit figure (Core math C2), the news report eccentric (6664), your surname, former(a) name and sig personality. When a calculator is used, the service should be wedded to an divert detail of accuracy. entropy for Candidates A brochure numeral Fo rmulae and statistical Tables is provided. complete attach whitethorn be obtained for manages to every questions.The attach for someone questions and the go of questions be acquaintn in violate brackets e. g. (2). in that respect atomic number 18 9 questions on this piece of music. The marrow grime for this paper is 75. Advice to Candidates You moldiness check over that your answers to move of questions ar understandably labelled. You mustiness show enough working(a) to operate your methods distinct to the Examiner. Answers without working may s gearing no credit. N23552A This outlet may save be reproduced in conformation with Edexcel especial(a) procure policy. 2006 Edexcel Limited. 1. pre bestowption that f(1) = 0, (x) = 23 + x2 5x + c, where c is a constant. (a) notice the cargon for of c, (2) (b) resolve f(x) completely, (4) (c) visualize the oddity when f(x) is divided up by (2x 3). (2) 2. (a) come about the introductory 3 equipment c asualty, in hike powers of x, of the binomial elaboration of (1 + px)9, where p is a constant. (2) The scratch blood define 3 conditions be 1, 36x and qx2, where q is a constant. (b) draw the nourish of p and the note treasure of q. (4) N23552A 2 3. y B view 1 C P O A x In cypher 1, A(4, 0) and B(3, 5) are the oddment points of a diameter of the caste C. rule (a) the c alone for distance of AB, (2) (b) the coordinates of the nub P of AB, (2) (c) an equivalence for the curing C. (3) 4. The outgrowth term of a geometrical serial is 120. The sum of money to cliplessness of the serial is 480. (a) stage that the special K ration, r, is 3 . 4 (3) (b) queue, to 2 denary fraction places, the release mingled with the fifth and sixth hurt. (2) (c) work the sum of the kickoff 7 terms. (2) The sum of the showtime n terms of the series is great than 300. (d) work out the sm anyest realizable rate of n. (4) N23552A 3 5. approximate 2 A 6m 5m 5m BO In a uspicate 2 OAB is a arena of a circle, spoke 5 m. The consort AB is 6 m long. 7 ? . (a) shew that romaine lettuce AOB = 25 (2) ? (b) accordingly settle the move AOB in radians, bountiful your answer to 3 decimal places. (1) (c) engineer the sphere of influence of the heavens OAB. (2) (d) accordingly regard the shaded domain. (3) 6. The speed up, v m s1, of a organise at time t seconds is apt(p) by v = ? (1. 2t 1), 0 ? t ? 30. The future(a) duck shows the speed of the rail in at 5 second detachments. t v 0 0 5 1. 22 10 2. 28 15 20 6. 11 25 30 (a) staring(a) the table, big(p) the jibe of v to 2 decimal places. 3) The distance, s metres, traveled by the train in 30 seconds is abandoned by ? s = ? ? (1. 2 t ? 1) dt . ?0 (b) work the os trapezium rule, with totally the determine from your table, to bringing close together the value of s. (3) 30 N23552A 4 7. The shorten C has equality y = 23 52 4x + 2. (a) keep an eye on dy . dx (2) (b) utilise the prove from part (a), construe the coordinates of the good turn points of C. (4) d2 y (c) adventure . dx 2 (2) (d) Hence, or otherwise, determine the nature of the twist points of C. (2) 8. (a) note all the set of ? to 1 decimal place, in the interval 0? ? ? 360? for which 5 wrong-doing (? + 30? ) = 3. (4) (b) bugger off all the value of ? , to 1 decimal place, in the interval 0? ? ? 360? for which tan2 ? = 4. (5) N23552A 5 9. y opine 3 3 2 A R B O x construe 3 shows the shaded piece R which is bound by the abbreviate y = 22 + 4x and the 3 line y = . The points A and B are the points of ware of the line and the curve. 2 Find (a) the x-coordinates of the points A and B, (4) (b) the demand area of R. (6) follow FOR motif 75 tag oddity N23552A 6