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Paper Reference(s) 6667/01 Edexcel · PDF fileEdexcel GCE Further Pure Mathematics FP1 Advanced/Advanced Subsidiary Monday 10 June 2013 – Morning Time: 1 hour 30 minutes Materials

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    Paper Reference(s)

    6667/01Edexcel GCEFurther Pure Mathematics FP1Advanced/Advanced SubsidiaryMonday 10 June 2013 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 symbolic algebra manipulation or symbolic differentiation/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 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.

    Paper Reference

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    This publication may be reproduced only in accordance with Pearson Education Ltd copyright policy. 2013 Pearson Education Ltd.

    Printers Log. No.

    P41808AW850/R6667/57570 5/5/5/5/

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    1. M =

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    , where a is a constant.

    (a) Find det M in terms of a.(2)

    A triangle T is transformed to T by the matrix M.

    Given that the area of T is 0,

    (b) find the value of a.(3)

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    Question 1 continued

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    (Total 5 marks)

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    2. f (z) = z3 + 5z2 + 11z + 15

    Given that z = 2i 1 is a solution of the equation f(z) = 0, use algebra to solve f(z) = 0 completely.

    (5)

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