C2 Paper

Paper Reference(s) 6664 Edexcel GCE Core Mathematics C2 Advanced Subsidiary Tuesday 10 January 2006 ? Evening Time: 1 hour 30 minutes Materials required for assessment Mathematical Formulae (Green) Items included with question papers Nil Candidates may utilize any adding machine EXCEPT those with the office for emblematic variable based math, separation or potentially joining. Accordingly applicants may NOT utilize adding machines, for example, the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G. Guidelines to Candidates In the crates on the appropriate response book, compose the name of the looking at body (Edexcel), your inside number, competitor number, the unit title (Core Mathematics C2), the paper reference (6664), your family name, other name and mark. At the point when a mini-computer is utilized, the appropriate response ought to be given to a suitable level of precision. Data for Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is given. Full stamps might be acquired for answers to ALL inquiries. The imprints for singular inquiries and the pieces of inquiries are appeared in round sections: e. g. (2). There are 9 inquiries on this paper. The complete imprint for this paper is 75. Guidance to Candidates You should guarantee that your responses to parts of inquiries are unmistakably marked. You should demonstrate adequate attempting to make your techniques understood to the Examiner. Answers without working may pick up no credit. N23552A This distribution may just be imitated as per Edexcel Limited copyright strategy.  ©2006 Edexcel Limited. 1. Given that f(1) = 0, (x) = 2ãâ€"3 + x2 †5x + c, where c is a consistent. (a) discover the estimation of c, (2) (b) factorize f(x) totally, (4) (c) discover the rest of f(x) is isolated by (2x †3). (2) 2. (a) Find the initial 3 terms, in rising forces of x, of the binomial extension of (1 + px)9, where p is a consistent. (2) The initial 3 terms are 1, 36x and qx2, where q is a consistent. (b) Find the estimation of p and the estimation of q. (4) N23552A 2 3. y B Figure 1 C P O A x In Figure 1, A(4, 0) and B(3, 5) are the end purposes of a distance across of the circle C. Discover (a) the specific length of AB, (2) (b) the directions of the midpoint P of AB, (2) (c) a condition for the circle C. (3) 4. The main term of a geometric arrangement is 120. The entirety to boundlessness of the arrangement is 480. (a) Show that the basic apportion, r, is 3 . 4 (3) (b) Find, to 2 decimal places, the contrast between the fifth and sixth terms. (2) (c) Calculate the whole of the initial 7 terms. (2) The whole of the principal n terms of the arrangement is more noteworthy than 300. (d) Calculate the littlest conceivable estimation of n. (4) N23552A 3 5. Figure 2 A 6m 5m B O In Figure 2 OAB is a segment of a circle, range 5 m. The harmony AB is 6 m long. 7 ? . (a) Show that cos AOB = 25 (2) ? (b) Hence discover the edge AOB in radians, offering your response to 3 decimal spots. (1) (c) Calculate the region of the area OAB. (2) (d) Hence figure the concealed region. (3) 6. The speed, v m sâ€1, of a train at time t seconds is given by v = ? (1. 2t †1), 0 ? t ? 30. The accompanying table shows the speed of the train at 5 second stretches. t v 0 5 1. 22 10 2. 28 15 20 6. 11 25 30 (a) Complete the table, giving the estimations of v to 2 decimal spots. 3) The separation, s meters, went by the train in 30 seconds is given by ? s = ? ? (1. 2 t ? 1) dt . ?0 (b) Use the trapezium rule, with all the qualities from your table, to assess the estimation of s. (3) 30 N23552A 4 7. The bend C has condition y = 2ãâ€"3 †5ãâ€"2 †4x + 2. (a) Find dy . dx (2) (b) Using the outcome from section (a), discover the directions of the defining moments of C. (4 ) d2 y (c) Find . dx (2) (d) Hence, or something else, decide the idea of the defining moments of C. (2) 8. (a) Find all the estimations of ? to 1 decimal spot, in the stretch 0? ? ? < 360? for which 5 sin (? + 30? ) = 3. (4) (b) Find all the estimations of ? , to 1 decimal spot, in the span 0? ? ? < 360? for which tan2 ? = 4. (5) N23552A 5 9. y Figure 3 2 A R B O x Figure 3 shows the concealed district R which is limited by the bend y = â€2ãâ€"2 + 4x and the 3 line y = . The focuses An and B are the purposes of crossing point of the line and the bend. 2 Find (a) the x-directions of the focuses An and B, (4) (b) the specific region of R. (6) TOTAL FOR PAPER: 75 MARKS END N23552A 6