Advanced Level Further Pure Mathematics F1 - Edexcel · Advanced Level Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 P44971RA0228 1. ... angle . clockwise

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 ReferenceThursday 14 May 2015 – Morning

Time: 1 hour 30 minutes

P44971RA©2015 Pearson Education Ltd.

5/1/1/1/1/1/1/

*P44971RA0128*Turn over

Pearson Edexcel InternationalAdvanced Level

Further Pure Mathematics F1Advanced/Advanced Subsidiary

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*P44971RA0228*

1. Given that

2z3 – 5z2 + 7z z z2 + az + b)

where a and b are real constants,

a b.(2)

z

2z3 – 5z2 + 7z – 6 = 0(3)

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Question 1 continued

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___________________________________________________________________________ Q1

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*P44971RA0428*

2. 1

n

rr

=∑ 2

1

n

rr

=∑ to show that

( ) ( )2 2

1

3 22

n

r

nr an bn c=

− = + +∑

where a, b and c(5)

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(Total 5 marks)

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3. It is given that and

2x2 – 7x + 4 = 0

2 2

(3)

αβ

and βα

ax2 + bx + c = 0, where a, b and c are integers.(3)

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4.

Q P

S xO

C

y

Figure 1

C y2 = 4ax, where a is a positive constant. The point S C and the point Q C.

The point P lies on C where y > 0 and the line segment QP is parallel to the x-axis.

PS

PQ.(1)

Given that the point P has x coordinate 9

a, (2)

PSQ.(3)

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5. In the interval 2 < x

6 – x2 cos x5

⎛⎝⎜

⎞⎠⎟

= 0, where x

has exactly one root .

width 0.25 which contains .(4)

. Give

(3)

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6. H

xy = 36

The three points P 6 6pp,

⎛⎝⎜

⎞⎠⎟

, Q 66qq,

⎛⎝⎜

⎞⎠⎟

and R 6 6rr,⎛

⎝⎜⎞⎠⎟

, where p, q and r are distinct,

H.

PQ is

pqy + x p + q)(4)

Given that PR QR,

H at the point R is parallel to the line PQ.(6)

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*P44971RA01628*

7. z = – 3k – 2ki, where k is a real, positive constant.

zk.

(3)

a + ib, where a and b k where necessary,

43z k+

z2

(5)

k A, B, C and D representing z, z*, 43z k+

and z2

respectively on a single Argand diagram.(3)

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(Total 11 marks)

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*P44971RA02028*

8. P =

−⎛⎝⎜

⎞⎠⎟

3 44 3a aa a

, where a is a constant and a > 0

P a.(3)

The matrix P U T onto the triangle T2.

The triangle T2 a, – 4a a, 8a a a).

T(3)

T2 a.(3)

V, represented by the 2 × 2 matrix Q

angle clockwise = 43

and 0 2π

Q, (2)

U V W. The matrix R W.

R.(2)

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*P44971RA02428*

9. n + ,

2

1

n

rr

=∑ r 1

6n n n2 + n

(6)

n + ,

7 123 5

6 1 123 1 6

−−

⎛⎝⎜

⎞⎠⎟

=+ −

−⎛⎝⎜

⎞⎠⎟

n n nn n

(6)

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TOTAL FOR PAPER: 75 MARKS

END

Q9

(Total 12 marks)

Documents

Advanced Level Further Pure Mathematics F1 - Edexcel · Advanced Level Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P44971RA0228* 1. ... angle . clockwise

Advanced Level Further Pure Mathematics F1 - Edexcel · Advanced Level Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 P44971RA0228 1. ... angle . clockwise