GCE Core Mathematics C1 MAY 2006

8/9/2019 GCE Core Mathematics C1 MAY 2006

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6663101Edexcel GCECore Mathematics ClAdvanced SubsidiaryMonday 22 }l4ay 2006 - MorningTime: t hour 30 minutesMaterials required for examination Items included with question papersMathematical Formulae (Green)

Calculators may NOT be used in this examination.

Instructions to Candidates

Examiner's use only

Team Leader's use only

In the boxes above, write your centre number, candidate number, your surname, initial(s) andslgnature.Check that you have the correct question paper.You must write your answer for each question in the space following the question.Information for CandidatesA booklet 'Mathematical Formulae and Statistical Tables' is provided.Full marks may be obtained for answers to ALL questtons.The marks for individual questions and the parts of questions are shown in round brackets: e.g. Q).There are 11 questions in this questionpaper. The total mark for this paper is 75.There are 24 pages in this question paper. Any blank pages are indicated.Advice to Candidates

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You must ensure'that your answers to partsYou must show sufftcient working to makeworking may gain no credit.ofquestions are clearly labelled.your methods clear to the examiner. Answers without

This publication may be reproduced only in accordoce withEdexcel Limited copyright policy.O2006 Edexcel Limited.

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1. rrna J(or' +2+ x)dx, giving each tenn in its simplest form. (4)Leaveblank

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Find the set of values of x for whichf -lx - 18 > o. (4)

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tt-Lear eblank3. On separate diagrams, sketch the graphs of

(a) y: lx + 3)2,(b) y: (x f 3)2 + k, where fr is a positive constant.Show on each sketch the coordinates of each point at which the graph meets the axes.

(3)

(2)

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A sequence ar, az, a3, "' is defined bYar:3,an+r:3an- 5, n) l'

(a) Find the value of a2 andthe value of a3'5(b) Calculate the vaiue of la,'

(2)

(3)

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(4)

5. Differentiate with respect to 'r(a) xo + 6!x, (3)

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6. (a)(b)

Expand and simplif1 (4 + '/:X+ - {:).Exoress -29- in the form a + btb,where a and b are integers.' 4+ r/3

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7. An athlete prepares for a race by completing a practice mn on each of 11 consecutivedays. On each day after the first day, he runs further than he ran on the previous day. Thelengths of his 11 practice runs form an arithmetic sequence with first term a km andcofllmon difference dkm.He runs 9 km on the 1lth day, and he runs a total of 77 km over the 11 day period.Find the value of a and the value of d (7)

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Leaveblank8. The equation f + 2px + (3p + 4): 0, wherep is a positive constant, has equal roots.(a) Find the value ofp.(b) For this value ofp, solve the equation f + 2px + (3p + 4) : 0.

(4)

(2)

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Leaveblankg. Given that f(:r) : (f - 6x)(x - 2) + 3x,(a) express f(x) in the form x(af + bx * c), where a, b and c are constants. (3)(b) Hence factorise f(x) completely' e)(c) Sketch the graph of y:f(x), showing the coordinates of each point at which the graph

meets the axes. (3)

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10. The curve c with equation y : f(x), x * 0, passes through the point (3,7 +).Given that f'(-rr) : 2*+\,x(a) frnd f(x). (s)(b) Verifv that f(2): 5. (1)(c) Find an equation for the tangent to C at the point (2, 5), giving your answer in the

form ax + by + c: O, where a, b and c are integers. (4)

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11. The line /1 passes through the points P(-1,2) and QOl, 8).(a) Find an equation for /1 in the form y: mx * c, where m and c are constants.

(4)

The line /2 passes through the point R(l0, 0) and is perpendicular to /1. The lines /1 and 12intersect at the point S.(b) Calculate the coordinates of S. (s)(c) Show that the length of RS is 3^/5.

(2)(d) Hence, or otherwise, find the exact area of triangle PQR.

(4)

GCE Core Mathematics C1 MAY 2006

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