surname names
Number Number
■ ■
Mathematics
Advanced
PAPER 2: Pure Mathematics 2
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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
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.
Inexact answers should be given to three significant figures unless otherwise stated.
• There are 15 questions in this question paper. The total mark for this paper is 100. – use this
as a guide as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. y 4x3 7x 2 5x 10
(a) Find in simplest form
dy
(i)
dx
d2 y
(ii)
dx2
(3)
2
d y
(b) Hence find the exact value of x when =0
dx2
(2)
2
■■■■
,Question 1 continued
(Total for Question 1 is 5 marks)
3
Turn over
■■■■
, 2. Jamie takes out an interest‑free loan of £8100
Jamie makes a payment every month to pay back the loan.
Jamie repays £400 in month 1, £390 in month 2, £380 in month 3, and so on, so that the
amounts repaid each month form an arithmetic sequence.
(a) Show that Jamie repays £290 in month 12
(1)
After Jamie‟s Nth payment, the loan is completely paid back.
(b) Show that N 2 – 81N + 1620 = 0
(2)
(c) Hence find the value of N.
(2)
4
■■■■
Number Number
■ ■
Mathematics
Advanced
PAPER 2: Pure Mathematics 2
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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
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.
Inexact answers should be given to three significant figures unless otherwise stated.
• There are 15 questions in this question paper. The total mark for this paper is 100. – use this
as a guide as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. y 4x3 7x 2 5x 10
(a) Find in simplest form
dy
(i)
dx
d2 y
(ii)
dx2
(3)
2
d y
(b) Hence find the exact value of x when =0
dx2
(2)
2
■■■■
,Question 1 continued
(Total for Question 1 is 5 marks)
3
Turn over
■■■■
, 2. Jamie takes out an interest‑free loan of £8100
Jamie makes a payment every month to pay back the loan.
Jamie repays £400 in month 1, £390 in month 2, £380 in month 3, and so on, so that the
amounts repaid each month form an arithmetic sequence.
(a) Show that Jamie repays £290 in month 12
(1)
After Jamie‟s Nth payment, the loan is completely paid back.
(b) Show that N 2 – 81N + 1620 = 0
(2)
(c) Hence find the value of N.
(2)
4
■■■■
