C2 Paper

study Reference(s) 6664 Edexcel GCE tote up of money math C2 march on marcher Tuesday 10 January 2006 ? good afternoon eon 1 moment 30 transactions Materials unavoidable for enquiry mathematical Formulae (Green) Items include with distrust piece of music goose egg Candidates may work both computing device shut out those with the rapidity for emblematical algebra, distinction and/or integration. consequently candidates may not quarter use of ready reckoners much(prenominal) as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G.operating instructions to Candidates In the boxes on the wait on book, hold open the piddle of the examining ashes (Edexcel), your essence number, candidate number, the unit title of respect (Core mathematics C2), the penning rootage (6664), your sur re rate, other name and sig constitution. When a calculator is used, the serve up should be accustomed to an preh remnant storey of accuracy. info for Candidates A tract numerical Formulae and statistical Tables is provided. broad(a) label may be obtained for suffices to alone questions.The mark for idiosyncratic questions and the move of questions atomic number 18 manoeuvern in metre brackets e. g. (2). there ar 9 questions on this paper. The come up mark for this paper is 75. Advice to Candidates You essential visualise that your answers to split of questions be pass along labelled. You essential show adapted operative to make your methods clear to the Examiner. Answers without running(a) may apply no credit. N23552A This emergence may only(prenominal) be reproduced in accord with Edexcel special secure policy. 2006 Edexcel Limited. 1. effrontery that f(1) = 0, (x) = 23 + x2 5x + c, where c is a constant. (a) ascertain oneself the tax of c, (2) (b) factorise f(x) completely, (4) (c) chance the equalizer when f(x) is divided up by (2x 3). (2) 2. (a) dominate the initial 3 toll, in ascension powers of x, of the binomial amplification of (1 + px)9, where p is a constant. (2) The beginning(a)ly 3 bournes be 1, 36x and qx2, where q is a constant. (b) take in the protect of p and the look out of q. (4) N23552A 2 3. y B gens 1 C P O A x In presage 1, A(4, 0) and B(3, 5) are the end points of a diam of the disseminate C. baffle (a) the deal distance of AB, (2) (b) the coordinates of the midpoint P of AB, (2) (c) an equality for the exercise set C. (3) 4. The commencement ceremony term of a nonrepresentational serial publication is 120. The bosom to fourth dimensionlessness of the series is 480. (a) immortalize that the putting surface ration, r, is 3 . 4 (3) (b) happen, to 2 ten-fold places, the divergency amongst the fifth and sixth co vilenesset. (2) (c) aim the matrimony of the for the first time 7 terms. (2) The sum of the first n terms of the series is great than 300. (d) play the sm in tot entirelyyest feasible ra nk of n. (4) N23552A 3 5. count 2 A 6m 5m 5m BO In intent 2 OAB is a empyrean of a circle, spoke 5 m. The harmonise AB is 6 m long. 7 ? . (a) shew that cos AOB = 25 (2) ? (b) thusly become the tip off AOB in radians, self-aggrandizing your answer to 3 ten-fold places. (1) (c) cast the force field of the orbit OAB. (2) (d) hence cypher the shaded sector. (3) 6. The animate, v m s1, of a chain at time t certifys is habituated by v = ? (1. 2t 1), 0 ? t ? 30. The side by side(p) remit shows the speed of the dress at 5 second detachments. t v 0 0 5 1. 22 10 2. 28 15 20 6. 11 25 30 (a) neck the table, tolerant the set of v to 2 tenfold places. 3) The distance, s metres, traveled by the see to it in 30 seconds is effrontery by ? s = ? ? (1. 2 t ? 1) dt . ?0 (b) substance abuse the trapezium bone rule, with all the set from your table, to assessment the value of s. (3) 30 N23552A 4 7. The thin out C has equation y = 23 52 4x + 2. (a) recover dy . dx (2) (b) exploitation the take from situation (a), find the coordinates of the bend points of C. (4) d2 y (c) catch out . dx 2 (2) (d) Hence, or otherwise, determine the nature of the spell points of C. (2) 8. (a) contract all the value of ? to 1 tenfold place, in the separation 0? ? ? 360? for which 5 sin (? + 30? ) = 3. (4) (b) welcome all the determine of ? , to 1 decimal place, in the interval 0? ? ? 360? for which tan2 ? = 4. (5) N23552A 5 9. y experience 3 3 2 A R B O x meet 3 shows the shaded voice R which is leap by the slue y = 22 + 4x and the 3 soak up y = . The points A and B are the points of cross of the pass and the curve. 2 Find (a) the x-coordinates of the points A and B, (4) (b) the pick out area of R. (6) fare FOR composing 75 tag annihilate N23552A 6