Paper Reference(s) 6663/01 Edexcel GCE

1 This publication may only be reproduced in accordance with London Qualifications Limited copyright policy. 2005 London Qualifications s Log. 7/7/5/5/3/ Paper Reference(s) 6663/01 Edexcel GCECore Mathematics C1 Advanced SubsidiaryMonday 10 January 2005 AfternoonTime: 1 hour 30 minutes Materials required for examinationItems included with question papersMathematical Formulae (Green)NilCalculators may NOT be used in this to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initial(s) must write your answer for each question in the space following the you need more space to complete your answer to any question, use additional answer for CandidatesA booklet Mathematical Formulae and Statistical Tables is marks may be obtained for answers to ALL Paper has ten questions.

2 Pages 2 and 20 are total mark for this Paper is to CandidatesYou must ensure that your answers to parts of questions are clearly must show sufficient working to make your methods clear to the Examiner. Answers withoutworking may gain no credit.*N23490A*Turn overExaminer s use only Team Leader s use onlyQuestion (s)SignaturePaper Reference666301 PMT2 BLANK PAGEN23490 APMTL eaveblank31.(a) Write down the value of .(1)(b) Find the value of .(2)_____3216 1216 Turn overN23490AQ1(Total 3 marks)PMTL eaveblank42.(i) Given that y= 5x3+ 7x+ 3, find(a)(3)(b)(1)(ii) Find (4) + ,dyxN23490 APMTL eaveblank5 Question 2 continued_____Turn overN23490AQ2(Total 8 marks) that the equation kx2+ 12x+ k= 0, where kis a positive constant, has equal roots,find the value of k.

3 (4)_____N23490AQ3(Total 4 marks)PMTL eaveblank7 Turn the simultaneous equationsx+ y= 2x2+ 2y= 12.(6)_____(Total 6 marks) rth term of an arithmetic series is (2r 5).(a) Write down the first three terms of this series.(2)(b) State the value of the common difference.(1)(c) Show that (3)_____1(25)(4).nrrnn= = N23490 APMTL eaveblank9 Question 5 continued_____Turn overN23490AQ5(Total 6 marks) 1 Figure 1 shows a sketch of the curve with equation y= f(x). The curve crosses the x-axisat the points (2, 0) and (4, 0). The minimum point on the curve is P(3, 2).

4 In separate diagrams sketch the curve with equation(a)y= f(x),(3)(b)y= f(2x).(3)On each diagram, give the coordinates of the points at which the curve crosses the x-axis,and the coordinates of the image of Punder the given 4 xP(3, 2)PMTL eaveblank11 Question 6 continuedTurn overN23490AQ6(Total 6 marks) curve Chas equation The point Pon Chas x-coordinate 1.(a) Show that the value of at Pis 3.(5)(b) Find an equation of the tangent to Cat P.(3)This tangent meets the x-axis at the point (k, 0).(c) Find the value of k.

5 (2)_____ddyx254, =+ N23490 APMTL eaveblank13 Question 7 continued_____Turn overN23490AQ7(Total 10 marks) 2 The points A(1, 7), B(20, 7) and C(p, q) form the vertices of a triangle ABC, as shown inFigure 2. The point D(8, 2) is the mid-point of AC.(a) Find the value of pand the value of q.(2)The line l, which passes through Dand is perpendicular to AC, intersects ABat E.(b) Find an equation for l, in the form ax+ by+ c= 0, where a, band care integers.(5)(c) Find the exact x-coordinate of E.(2)_____N23490 AyA(1, 7)B(20, 7)C(p, q)D( 8, 2)xOPMTL eaveblank15 Question 8 continued_____Turn overN23490AQ8(Total 9 marks) gradient of the curve Cis given byThe point P(1, 4) lies on C.

6 (a) Find an equation of the normal to Cat P.(4)(b) Find an equation for the curve Cin the form y= f(x).(5)(c) Using show that there is no point on Cat which the tangent is parallel to the line y= 1 2x.(2)_____2d(31) ,dyxx= 2d(31) .dyxx= N23490 APMTL eaveblank17 Question 9 continued_____Turn overN23490AQ9(Total 11 marks) thatf(x) = x2 6x+ 18, ,(a) express f(x) in the form (x a)2+ b, where aand bare integers.(3)The curve Cwith equation y= f(x), , meets the y-axis at Pand has a minimum pointat Q.(b) In the space provided on page 19, sketch the graph of C, showing the coordinates ofPand Q.

7 (4)The line y= 41 meets Cat the point R.(c) Find the x-coordinate of R, giving your answer in the form p+ q 2, where pand qare integers.(5)_____N23490 APMTL eaveblank19 Question 10 continued_____TOTAL FOR Paper : 75 MARKSENDN23490AQ10(Total 12 marks)PMT20 BLANK PAGEN23490 APMT