lOMoARcPSD|43750544
Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Tuesday 13 June 2023
Paper
Afternoon (Time: 2 hours)
reference 9MA0/02
Mathematics
Advanced
PAPER 2: Pure Mathematics 2
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation
and integration, or have retrievable mathematical formulae stored in them.
Instructions
•• IfUsepencil
black ink or ball-point pen.
is used for diagrams/sketches/graphs it must be dark (HB or B).
• centre number
Fill in the boxes at the top of this page with your name,
and candidate number.
• clearly labelled. and ensure that your answers to parts of questions are
Answer all questions
• 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.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 15 questions in this question paper. The total mark for this paper is 100.
• –Theusemarks for each question are shown in brackets
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. Turn over
P72805A
©2023 Pearson Education Ltd.
N:1/1/1/
*P72805A0148*
Downloaded by Ved ()
, lOMoARcPSD|43750544
1.
f (x) = x3 + 2x2 – 8x + 5
DO NOT WRITE IN THIS AREA
(a) Find f ′′(x)
(2)
(b) (i) Solve f ′′(x) = 0
(ii) Hence find the range of values of x for which f (x) is concave.
(2)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P72805A0248*
Downloaded by Ved ()
, lOMoARcPSD|43750544
Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 4 marks)
3
*P72805A0348*
Downloaded by Ved ()
Turn over
, lOMoARcPSD|43750544
2. A sequence u1, u2, u3 ... is defined by
u1 = 35
DO NOT WRITE IN THIS AREA
nπ
un +1 = un + 7 cos − 5(−1) n
2
(a) (i) Show that u2 = 40
(ii) Find the value of u3 and the value of u4
(3)
Given that the sequence is periodic with order 4
(b) (i) write down the value of u5
25
(ii) find the value of
u
r 1
r
(3)
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
___________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P72805A0448*
Downloaded by Ved ()
Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Tuesday 13 June 2023
Paper
Afternoon (Time: 2 hours)
reference 9MA0/02
Mathematics
Advanced
PAPER 2: Pure Mathematics 2
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation
and integration, or have retrievable mathematical formulae stored in them.
Instructions
•• IfUsepencil
black ink or ball-point pen.
is used for diagrams/sketches/graphs it must be dark (HB or B).
• centre number
Fill in the boxes at the top of this page with your name,
and candidate number.
• clearly labelled. and ensure that your answers to parts of questions are
Answer all questions
• 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.
• Inexact answers should be given to three significant figures unless
otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 15 questions in this question paper. The total mark for this paper is 100.
• –Theusemarks for each question are shown in brackets
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. Turn over
P72805A
©2023 Pearson Education Ltd.
N:1/1/1/
*P72805A0148*
Downloaded by Ved ()
, lOMoARcPSD|43750544
1.
f (x) = x3 + 2x2 – 8x + 5
DO NOT WRITE IN THIS AREA
(a) Find f ′′(x)
(2)
(b) (i) Solve f ′′(x) = 0
(ii) Hence find the range of values of x for which f (x) is concave.
(2)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P72805A0248*
Downloaded by Ved ()
, lOMoARcPSD|43750544
Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 4 marks)
3
*P72805A0348*
Downloaded by Ved ()
Turn over
, lOMoARcPSD|43750544
2. A sequence u1, u2, u3 ... is defined by
u1 = 35
DO NOT WRITE IN THIS AREA
nπ
un +1 = un + 7 cos − 5(−1) n
2
(a) (i) Show that u2 = 40
(ii) Find the value of u3 and the value of u4
(3)
Given that the sequence is periodic with order 4
(b) (i) write down the value of u5
25
(ii) find the value of
u
r 1
r
(3)
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
___________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P72805A0448*
Downloaded by Ved ()
