Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1...
Transcript of Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1...
![Page 1: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/1.jpg)
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
P45876RA©2015 Pearson Education Ltd.
5/5/5/5/
*P45876RA0128*Turn over
Pearson Edexcel InternationalAdvanced Level
Further Pure Mathematics F1Advanced/Advanced Subsidiary
![Page 2: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/2.jpg)
Leave blank
2
*P45876RA0228*
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)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 3: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/3.jpg)
Leave blank
3
*P45876RA0328* Turn over
Question 1 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q1
(Total 7 marks)
![Page 4: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/4.jpg)
Leave blank
4
*P45876RA0428*
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)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 5: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/5.jpg)
Leave blank
5
*P45876RA0528* Turn over
Question 2 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q2
(Total 7 marks)
![Page 6: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/6.jpg)
Leave blank
6
*P45876RA0628*
3. Given that z = x + iy, where x y
(z – 2i)(z* – 2i) = 21 – 12i
where z z.(6)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 7: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/7.jpg)
Leave blank
7
*P45876RA0728* Turn over
Question 3 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q3
(Total 6 marks)
![Page 8: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/8.jpg)
Leave blank
8
*P45876RA0828*
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)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 9: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/9.jpg)
Leave blank
9
*P45876RA0928* Turn over
Question 4 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 10: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/10.jpg)
Leave blank
10
*P45876RA01028*
Question 4 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 11: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/11.jpg)
Leave blank
11
*P45876RA01128* Turn over
Question 4 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q4
(Total 14 marks)
![Page 12: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/12.jpg)
Leave blank
12
*P45876RA01228*
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)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 13: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/13.jpg)
Leave blank
13
*P45876RA01328* Turn over
Question 5 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 14: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/14.jpg)
Leave blank
14
*P45876RA01428*
Question 5 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 15: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/15.jpg)
Leave blank
15
*P45876RA01528* Turn over
Question 5 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q5
(Total 8 marks)
![Page 16: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/16.jpg)
Leave blank
16
*P45876RA01628*
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)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 17: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/17.jpg)
Leave blank
17
*P45876RA01728* Turn over
Question 6 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 18: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/18.jpg)
Leave blank
18
*P45876RA01828*
Question 6 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 19: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/19.jpg)
Leave blank
19
*P45876RA01928* Turn over
Question 6 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q6
(Total 10 marks)
![Page 20: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/20.jpg)
Leave blank
20
*P45876RA02028*
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
)
(3)___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 21: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/21.jpg)
Leave blank
21
*P45876RA02128* Turn over
Question 7 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 22: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/22.jpg)
Leave blank
22
*P45876RA02228*
Question 7 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 23: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/23.jpg)
Leave blank
23
*P45876RA02328* Turn over
Question 7 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q7
(Total 11 marks)
![Page 24: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/24.jpg)
Leave blank
24
*P45876RA02428*
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)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 25: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/25.jpg)
Leave blank
25
*P45876RA02528* Turn over
Question 8 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 26: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/26.jpg)
Leave blank
26
*P45876RA02628*
Question 8 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 27: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/27.jpg)
Leave blank
27
*P45876RA02728* Turn over
Question 8 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
![Page 28: Advanced Level Further Pure Mathematics F1 - Squarespace · Further Pure Mathematics F1 Advanced/Advanced Subsidiary. Leave blank 2 *P45876RA0228* 1. f(x) = x4 – x3 – 9x2 + 29x](https://reader035.fdocuments.us/reader035/viewer/2022062413/5af2451b7f8b9ac2469076a4/html5/thumbnails/28.jpg)
Leave blank
28
*P45876RA02828*
Question 8 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
TOTAL FOR PAPER: 75 MARKS
END
Q8
(Total 12 marks)