Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1...

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 Use black ink or ball-point pen. If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).

Coloured pencils and highlighter pens must not be used. Fill in the boxes at the top of this page with your name,

centre number and candidate number. Answer all questions and ensure that your answers to parts of questions are

clearly labelled. Answer the questions in the spaces provided

– there may be more space than you need. You should show sufficient working to make your methods clear. Answers

without working may not gain full credit. When a calculator is used, the answer should be given to an appropriate

degree of accuracy.

Information The total mark for this paper is 75. The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.

Advice Read each question carefully before you start to answer it. Try to answer every question. Check your answers if you have time at the end.

You must have:

Mathematical Formulae and Statistical Tables (Blue)

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

WFM01/01Paper ReferenceTuesday 27 January 2015 – Morning

Time: 1 hour 30 minutes

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Pearson Edexcel InternationalAdvanced Level

Further Pure Mathematics F1Advanced/Advanced Subsidiary

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1. f (x) = x 4 – x 3 – 9x 2 + 29x – 60

Given that x = 1 + 2i is a root of the equation f(xroots of the equation f(x) = 0

(7)

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Question 1 continued

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2. f (x) = x3 – 3x2 + 1

2 5x + 2, x 0

(a) Show that the equation f(x) = 0 has a root in the interval [2,3].(2)

x)

(5)

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3. Given that z = x + iy, where x y

(z – 2i)(z* – 2i) = 21 – 12i

where z z.(6)

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4. C y 2 = 12x

P (3p2, 6p) lies on C, where p 0

C P is

y + px = 6p + 3p3

(5)

C Q.

Given that p S

Q,(5)

PQS.(4)

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5.

4x 2 + 3x + 1 = 0

has roots .

+ .(2)

2 + 2).(2)

(4 – – )

px2 + qx + r = 0 where p, q r are integers to

(4)

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(Total 8 marks)

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6.

(i) A = 3 00 1

⎛⎝⎜

⎞⎠⎟

B = −

− −

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

32

12

12

32

A. (2)

B. (2)

A B isC.

C.(2)

(ii) M =+ −⎛

⎝⎜⎞⎠⎟

2 5 41

kk

, where k

M k.(4)

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(Total 10 marks)

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7. n,

(r a r b n n nr

n

+ + = + −=

∑ )( ) ( )( )1

16

2 11 1

where a b a b ,

a b.(8)

( )(r a r br

+ +=∑

9

20

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8.

u1= 5 u2 = 13

un+2 = 5un+1 – 6un n 1

n +,

un = 2n + 3n

(6)

n 2, where n ,

f (n) = 72n – 48n – 1

(6)

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TOTAL FOR PAPER: 75 MARKS

END

Q8

(Total 12 marks)

Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1...

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