Edexcel A-Level Mathematics Practice Set 1 Pure Mathematics 1 (Paper 1)

Instructions to candidates • Use black ink or ball-point pen. • A pencil may be used for diagrams, sketches and graphs. • Write your name and other details in the spaces provided above. • Answer all questions in the spaces provided. • Show clearly how you worked out your answers. • Round answers to 3 significant figures unless otherwise stated. Information for candidates • There are 16 questions in this paper. • There are 100 marks available for this paper. • The marks available are given in brackets at the end of each question. • You may get marks for method, even if your answer is incorrect. Advice to candidates • Work steadily through the paper and try to answer every question. • Don’t spend too long on one question. • If you have time at the end, go back and check your answers. Exam Set MEP71 For examiner’s use Q Mark Q Mark 1 9 2 10 3 11 4 12 5 13 6 14 7 15 8 16 Total © CGP 2018 — copying more than 5% of this paper is not permitted 1 a) Answer ALL the questions. Write your answers in the spaces provided. Given that f(x) = x3 – 4x2 – 3x + 7, find f '(x). (2) Leave blank b) Hence find the values of x for which f(x) is a decreasing function, giving your answer in the form {x : x > a} « {x : x < b} where a and b are real numbers to be found. (3) 2 A helicopter flies between 3 locations, A, B and C, which are positioned such that AB = 9 km, AC = 5 km and angle ABC = 24°. Find the possible values of angle ACB to 1 decimal place. (3) A-level Edexcel Maths / Set 1 / Paper 1 2 © CGP 2018 — copying more than 5% of this paper is not permitted 3 a) b) Express _ 2 x 3 1 i 6 in the form axb where a and b are integers to be found. Hence find the x-coordinates of the points where the line y = 1 – 3x intersects the curve with equation _ 2 x 1 3 i 6 + 6x – 18 = y2 – y. (2) Leave blank (4) 4 For each of the following, prove that the statement is false. a) The exterior angles of a regular n-sided polygon are always acute. b) n For n Œ , n ≠ –1, ≥ 0. n + 1(1) (1) c) For n < 50, if n is an odd prime then one or both of n + 2 and n + 4 are prime.