N25561AThis publication may only be reproduced in accordance with Edexcel Limitedcopyright policy.©2008EdexcelLimited.Paper Reference(s)6663/01Edexcel GCECore Mathematics C1Advanced SubsidiaryWednesday 9January2008-AfternoonTime: 1 hour 30 minutesMaterials required for examinationItems included with question papersMathematical Formulae (Green)NilCalculators may NOT be used in this examination.Instructions to CandidatesWrite the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Core Mathematics C1), the paper reference (6663), your surname, initials and signature.Information for CandidatesA booklet ‘Mathematical Formulae and Statistical Tables’ is provided.Full marks may be obtained for answers to ALL questions.There are 11questions in thisquestion paper. The total mark for this paper is 75.Advice to CandidatesYou must ensure that your answers to parts of questions are clearly labelled.You must show sufficient working to make your methods clear to the Examiner. Answerswithout working may gain no credit.www.mymathscloud.com
N25561A21.Find . (4)2.(a)Write down the value of . (1)(b)Simplify .(2)3.Simplify, giving your answer in the form a+ bÖ3, where aand bare integers.(4)4.The point A(–6, 4)and the pointB(8, –3) lie on the line L. (a)Find an equation for Lin the form ax+ by+ c= 0, where a, band care integers.(4)(b)Find the distance AB, giving your answer in the form kÖ5,where kis an integer.(3)5.(a)Write in the form 2xp+ 3xq, where pand qare constants.(2)Given that y= 5x–7 +, x> 0,(b)find , simplifying the coefficient of each term. (4)ôõó-+xxxd)743(52411643)16(12x3235Ö+Ö-xx32+Öxx32+Öxyddwww.mymathscloud.com
N25561A3Turn over6.Figure 1Figure 1 shows a sketch of the curve with equation y= f(x). The curve crosses the x-axis at the points(1, 0) and (4, 0). The maximum point on the curve is (2, 5).In separate diagrams, sketch the curves with the following equations. On each diagram show clearly the coordinates of the maximum point and of each point at which the curve crosses the x-axis.(a)y= 2f(x),(3)(b)y= f(–x).(3)The maximum point on the curve with equation y= f(x+ a) is on the y-axis.(c)Write down the value of the constant a.(1)1(2, 5)4xywww.mymathscloud.com
N25561A47.A sequence is given by = 1,xn+ 1= xn(p+ xn),where pis a constant (p≠ 0).(a)Find x2in terms of p.(1)(b)Show that x3= 1 + 3p+ 2p2.(2)Given that = 1,(c)find the value of p,(3)(d)write down the value of .(2)8.Theequationx2+ kx+ 8 = khas no real solutions for x.(a)Show that ksatisfies k2+ 4k–32 < 0.(3)(b)Hence find the set of possible values of k.(4)9.The curve Chas equation y= f(x), x> 0, and f¢(x) = 4x–6Öx+ .Given that the point P(4, 1) lieson C,(a)find f(x) and simplify your answer.(6)(b)Find an equation of the normal to Cat the point P(4, 1).(4)1x3x2008x28xwww.mymathscloud.com
N25561A510.The curve Chas equationy= (x+ 3)(x–1)2.(a)Sketch C, showing clearly the coordinates of the points where the curve meets thecoordinate axes.(4)(b)Show that the equation of Ccan be written in the formy= x3+ x2–5x+ k,where kis a positive integer, and state the value of k.(2)There are two points on Cwhere the gradient of the tangent to Cis equal to 3.(c)Find the x-coordinates of these two points.(6)11.The first termof an arithmetic sequence is 30 and the common difference is –1.5.(a)Find the value of the 25th term.(2)The rthterm of the sequence is 0.(b)Find the value of r.(2)Thesum of the first nterms of the sequence is Sn.(c)Find the largest positive value of Sn. (3)TOTAL FOR PAPER: 75 MARKSENDwww.mymathscloud.com
