H29992AThis publication may only be reproduced in accordance with Edexcel Limitedcopyright policy.©2008EdexcelLimited.Paper Reference(s)6663/01Edexcel GCECore Mathematics C1Advanced SubsidiaryMonday 2June2008–MorningTime: 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 this question 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 notgain fullcredit.www.mymathscloud.com
H29992A21.Find .(3)2.Factorise completelyx3–9x.(3)3.Figure 1Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through thepoint (0, 7) and has a minimum point at (7, 0).On separate diagrams, sketch the curve with equation(a) y = f(x) + 3,(3)(b) y = f(2x).(2)On each diagram, show clearly the coordinates of the minimum point and the coordinatesof the point at which the curve crosses the y-axis.4.f(x)= 3x + x3, x > 0.(a) Differentiate to find f ¢(x).(2)Given that f ¢(x) = 15,(b) find the value of x.(3)ôõó+xxd)52(2www.mymathscloud.com
H29992A35.A sequence, , , ... is defined by= 1,xn + 1= axn–3, n ³1,where a is a constant.(a) Find an expression for in terms of a.(1)(b) Show that = a2–3a –3.(2)Given that = 7,(c) find the possible values ofa.(3)6.The curve C has equationy= and the line l has equation y = 2x + 5.(a) Sketch the graphs of C and l, indicating clearly the coordinates ofany intersections with the axes.(3)(b) Find the coordinates of the pointsof intersection of C and l.(6)7.Sue is training for a marathon. Her training includes a run every Saturday starting with arun of 5km on the first Saturday. Each Saturday she increases the length of her run fromthe previous Saturday by 2 km.(a) Show that on the 4th Saturday of training she runs 11 km.(1)(b) Find an expression, in terms of n, for the length of her training run on the nthSaturday.(2)(c) Show that the total distance she runs on Saturdays in n weeks of training is n(n + 4) km.(3)On the nth Saturday Sue runs 43 km.(d) Find the value of n.(2)(e) Find the total distance, in km, Sue runs on Saturdays in n weeks of training.(2)1x2x3x1x2x3x3xx3www.mymathscloud.com
H29992A48.Given that the equation 2qx2+ qx –1 = 0, where q is a constant, has no real roots,(a) show that q2 + 8q < 0.(2)(b) Hence find the set of possible values of q.(3)9.The curve C has equation y = kx3–x2+ x –5, where k is a constant.(a) Find.(2)The point A with x-coordinate –lies onC. The tangent to C at A is parallel to the linewith equation 2y –7x + 1 = 0.Find(b) the value of k,(4)(c) the value of the y-coordinate of A.(2)xydd21www.mymathscloud.com
H29992A510.Figure 2The points Q (1, 3) and R (7, 0) lie on the line, as shown in Figure 2.The length of QR is a√5.(a) Find the value of a.(3)The lineis perpendicular to, passes through Q and crosses the y-axis at the point P, asshown in Figure 2.Find(b) an equation for ,(5)(c) the coordinates of P,(1)(d) the area of ΔPQR.(4)11.The gradient of a curve C is given by= , x¹0.(a) Show that = x2+ 6 + 9x–2.(2)The point (3, 20) lies on C.(b) Find an equation for the curve C in the form y = f(x).(6)TOTAL FOR PAPER: 75 MARKSEND1l2l1l2lxydd222)3(xx+xyddwww.mymathscloud.com
