A LEVEL EDEXCEL FURTHER MATHEMATICS CORE PURE MATHS QUESTION PAPER 1 2024

Please check the examination details below before entering your candidate information Candidate surname Other names Centre Number Candidate Number Pearson Edexcel Level 3 GCE Wednesday 22 May 2024 Afternoon (Time: 1 hour 30 minutes) 9FM0/01 Paper reference Total Marks Further Mathematics Advanced PAPER 1: Core Pure Mathematics 1 You must have: Mathematical Formulae and Statistical Tables (Green), calculator Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic 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). • 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. • Inexact answers should be given to three significant figures unless otherwise stated. Information • A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. • There are 8 questions in this question paper. 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. *P75682A0232* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2  1. f(z) = z z az bz 4 3 2   6   145 where a and b are real constants. Given that 2 + 5i is a root of the equation f(z) = 0 (a) determine the other roots of the equation f(z) = 0 (7) (b) Show all the roots of f(z) = 0 on a single Argand diagram. 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 9 marks) *P75682A0632* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 6  2. The roots of the equation 2 3 12 7 0 3 2 x x   x   are α, β and γ Without solving the equation, (a) write down the value of each of α + β + γ αβ + αγ + βγ αβγ (1) (b) Use the answers to part (a) to determine the value of (i) 2 2 2   α β γ (ii) (α – 1)(β – 1)(γ – 1) (iii) α 2 + β2 + γ 2 (7) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ __________________________________________________________