Pearson Edexcel Level 3 GCE Mathematics Advanced Level Paper 1: Pure Mathematics QUESTION PAPER

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Pearson Edexcel Level 3 GCE Mathematics Advanced Level Paper 1: Pure Mathematics QUESTION PAPER  Pearson Edexcel Level 3 GCE Mathematics Advanced Level Paper 1 : Pure Mathematics Paper A Ti... me: 2 hours Paper Reference(s) 9MA0/01 You must have: Mathematical Formulae and Statistical Tables, 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). • 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 13 questions in this paper. The total mark is 100. • 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. • If you change your mind about an answer, cross it out and put your new answer and any working underneath. Answer ALL questions. 1. Use proof by contradiction to prove the statement: ‘The product of two odd numbers is odd.’ (5 marks) 2. (a) Prove that the sum of the first n terms of an arithmetic series is S =n  2a +  n - 1 d  . (3 marks) (b) Hence, or otherwise, find the sum of the first 200 odd numbers. (2 marks) 3. A curve has the equation y =ln 3x - e- 2 x . Show that the equation of the tangent at the point with an x-coordinate of 1 is  e2 + 2   e2 + 3  y =∣ e2 ∣ x - ∣ e2 ∣ + ln 3  ?  ? . (6 marks) - ? „ t „ ? 4. The curve C has parametric equations x =7sin t - 4 , y =7 cos t + 3 , 2 3 . 2 2 (a) Show that the cartesian equation of C can be written as , where a, b and c are integers which should be stated. (3 marks) (b) Sketch the curve C on the given domain, clearly stating the endpoints of the curve. (3 marks) (c) Find the length of C. Leave your answer in terms of π. (2 marks) [Show More]

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