Centre No. Candidate No.Paper Reference(s)

Surname Paper Reference

Initial(s)

6 6 6 66666/01

0 1

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Edexcel GCECore Mathematics C4AdvancedMonday 19 January 2009 Afternoon Time: 1 hour 30 minutes

Team Leaders use only

Question Leave Number Blank

1 2 3 4

Materials required for examination Mathematical Formulae (Green)

Items included with question papers Nil

5 6 7

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.

Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature. Check that you have the correct question paper. Answer ALL the questions. You must write your answer for each question in the space following the question. When a calculator is used, the answer should be given to an appropriate degree of accuracy.

Information for CandidatesA booklet Mathematical Formulae and Statistical Tables is provided. Full marks may be obtained for answers to ALL questions. The marks for individual questions and the parts of questions are shown in round brackets: e.g. (2). There are 7 questions in this question paper. The total mark for this paper is 75. There are 28 pages in this question paper. Any blank pages are indicated.

Advice to CandidatesYou must ensure that your answers to parts of questions are clearly labelled. You should show sufficient working to make your methods clear to the Examiner. Answers without working may not gain full credit.

TotalThis publication may be reproduced only in accordance with Edexcel Limited copyright policy. 2009 Edexcel Limited.

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N31013AW850/R6666/57570 3/3/3/3

Printers Log. No.

*N31013A0128*

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1.

A curve C has the equation y2 3y = x3 + 8. (a) Find dy in terms of x and y. dx

(4) (3)

(b) Hence find the gradient of C at the point where y = 3.

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*N31013A0228*

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Question 1 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ (Total 7 marks) Q1

*N31013A0328*

3

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2.

y 3

R O 2 Figure 1

x

3 . The region R is bounded by the curve, (1 + 4 x) the x-axis, and the lines x = 0 and x = 2, as shown shaded in Figure 1. Figure 1 shows part of the curve y = (a) Use integration to find the area of R. (4) The region R is rotated 360 about the x-axis. (b) Use integration to find the exact value of the volume of the solid formed. (5) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________4

*N31013A0428*

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*N31013A0528*

5

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*N31013A0628*

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Question 2 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ (Total 9 marks) Q2

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7

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3.

f ( x) =

27 x 2 + 32 x + 16 , (3 x + 2) 2 (1 x)

x