surname names
Number Number
Further Mathematics
� �
Advanced Subsidiary
PAPER 1: Core Pure Mathematics
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 11 questions in this question paper. The total mark for this paper is 80.
– 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. z = 3 – 3i
(a) Write z in the form r (cos θ + i sin θ) where –π < θ π
(2)
(b) Show and label on a single Argand diagram
(i) the point P representing z
(ii) the point Q representing iz
(2)
(c) Describe the geometrical transformation that maps P onto Q
(2)
2
■■■■
,Question 1 continued
(Total for Question 1 is 6 marks)
3
■■■■ Turn over
, 2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
f (z) = 4z3 – 12z2 – 95z + 325
Given that f (–5) = 0
(a) determine f (z) in the form (z + a)(bz2 + cz + d) where a, b, c and d are integers.
(3)
(b) 8i
Hence show that the complex roots of f (z) = 0 are
2 (2)
(c) Determine the values of z such that f (2z – 1) = 0
(2)
4
■■■■
Number Number
Further Mathematics
� �
Advanced Subsidiary
PAPER 1: Core Pure Mathematics
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 11 questions in this question paper. The total mark for this paper is 80.
– 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. z = 3 – 3i
(a) Write z in the form r (cos θ + i sin θ) where –π < θ π
(2)
(b) Show and label on a single Argand diagram
(i) the point P representing z
(ii) the point Q representing iz
(2)
(c) Describe the geometrical transformation that maps P onto Q
(2)
2
■■■■
,Question 1 continued
(Total for Question 1 is 6 marks)
3
■■■■ Turn over
, 2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
f (z) = 4z3 – 12z2 – 95z + 325
Given that f (–5) = 0
(a) determine f (z) in the form (z + a)(bz2 + cz + d) where a, b, c and d are integers.
(3)
(b) 8i
Hence show that the complex roots of f (z) = 0 are
2 (2)
(c) Determine the values of z such that f (2z – 1) = 0
(2)
4
■■■■
