6667/01 Edexcel GCE - Pearson qualifications | Edexcel, · PDF file · 2018-04-20Paper Reference(s) 6667/01 Edexcel GCE Further Pure Mathematics FP1 Advanced/Advanced Subsidiary Monday

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6667/01Edexcel GCEFurther Pure Mathematics FP1Advanced/Advanced SubsidiaryMonday 30 January 2012 MorningTime: 1 hour 30 minutes

Materials required for examination Items included with question papersMathematical Formulae (Pink) Nil

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolicalgebra manipulation or symbolic differentiation/integration, or haveretrievable 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 to 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 9 questions in this question paper. The total mark for this paper is 75. There are 24 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.

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This publication may be reproduced only in accordance with Pearson Education Ltd copyright policy. 2012 Pearson Education Ltd.

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P40086AW850/R6667/57570 5/4/5

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1. Given that z1 1= i ,

(a) find arg( z1 ).(2)

Given also that z2 3 4= + i, find, in the form a b+ i , a b, ,

(b) z z1 2 ,(2)

(c) zz

2

1

.(3)

In part (b) and part (c) you must show all your working clearly.

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Question 1 continued

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2. (a) Show that f ( )x x x= + 4 1 has a real root in the interval [ . , . ]0 5 1 0 .(2)

(b) Starting with the interval [ . , . ],0 5 1 0 use interval bisection twice to find an interval of width 0.125 which contains .

(3)

(c) Taking 0.75 as a first approximation, apply the Newton Raphson process twice tof ( )x to obtain an approximate value of Give your answer to 3 decimal places.

(5)

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