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Paper Reference(s)

6665/01Edexcel GCECore Mathematics C3

Advanced

Friday 25 January 2013 Afternoon

Time: 1 hour 30 minutes

Materials required for examination Items included with question papers

Mathematical Formulae (Pink) Nil

Candidates may use any calculator allowed by the regulations of the JointCouncil for Qualifications. Calculators must not have the facility for symbolicalgebra manipulation or symbolic differentiation/integration, or haveretrievable mathematical formulae stored in them.

Paper Reference

6 6 6 5 0 1

This publication may be reproduced only in accordance with

Pearson Education Ltd copyright policy.2013 Pearson Education Ltd.

Printers Log. No.

P41486AW850/R6665/57570 5/5/5/5/6/

*P41486A0128*

Instructions to Candidates

In 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 Candidates

A 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 8 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 Candidates

You 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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1. The curve Chas equation

y x= ( )2 35

The pointPlies on Cand has coordinates (w, 32).

Find

(a) the value ofw,

(2)

(b) the equation of the tangent to Cat the pointPin the form y mx c= + , where m and

c are constants.

(5)

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Question 1 continued

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(Total 7 marks)

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2. g e( )x xx

= + 1 6

(a) Show that the equation g( )x = 0 can be written as

x x= +ln( )6 1, x < 6

(2)

The root of g( )x = 0 is .

The iterative formula

x xn n+ = +1 6 1ln( ) , x0 2=

is used to find an approximate value for .

(b) Calculate the values ofx1, x

2and x

3to 4 decimal places.

(3)

(c) By choosing a suitable interval, show that = 2.307 correct to 3 decimal places.

(3)

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(Total 8 marks)

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3. y

x

y = f (x)

Q(0,2)

P(3,0) O

Figure 1

Figure 1 shows part of the curve with equation y x= f ( ) ,x .

The curve passes through the points Q( , )0 2 and P( , )3 0 as shown.

(a) Find the value of ff ( )3 .

(2)

On separate diagrams, sketch the curve with equation

(b) y x= f 1( ) ,

(2)

(c) y x= f ( ) 2 ,

(2)

(d) y x= ( )2 12f .(3)

Indicate clearly on each sketch the coordinates of the points at which the curve crosses or

meets the axes.

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Q3

(Total 9 marks)

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4. (a) Express 6 cosR+8sinR in the formRcos(R), whereR > 0 and 02

c3 edexcel jan 2013

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