A-Level Mathematics Exam Board: Edexcel PRACTISE PAPERS

Answer ALL the questions. Write your answers in the spaces provided. 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) 1 a) Given that f(x) = x 3 – 4x 2 – 3x + 7, find f '(x). (2) 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) 3 © CGP 2018 — copying more than 5% of this paper is not permitted Leave blank A-level Edexcel Maths / Set 1 / Paper 1 3 a) Express 2x3 1 6 _ i in the form ax b where a and b are integers to be found. (2) b) Hence find the x-coordinates of the points where the line y = 1 – 3x intersects the curve with equation 2x3 1 6 _ i + 6x – 18 = y 2 – y. (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. (1) b) For nŒ, n ≠ –1, n n +1 ≥ 0. (1) c) For n 50, if n is an odd prime then one or both of n + 2 and n + 4 are prime. (1) 4 © CGP 2018 — copying more than 5% of this paper is not permitted Leave blank A-level Edexcel Maths / Set 1 / Paper 1 6 The circle C has equation x 2 – 8 + y 2 + 4y – 29 = 0. The centre of C is at the point X. a) Find: i) the coordinates of the point X. (2) ii) the radius of the circle C. (1) 5 The elastic energy stored in a large industrial spring, E, in joules, is directly proportional to the square of how far it is extended, x, in metres. When the spring is extended by ( 2 – 1) m, it has (7 2 – 9) joules of elastic energy. Find the exact amount of elastic energy in the spring when it is extended by 2 m, giving your answer in joules in the form 2, where a + b a and b are integers. (5) 5 © CGP 2018 — copying more than 5% of this paper is not permitted Leave blank A-level Edexcel Maths / Set 1 / Paper 1 7 a) Express x x x 4 9 4 8 3 2 2 - + + as a single fraction in its simplest form. (2) b) Hence, or otherwise, solve the equation: log3 (4x 2 + 8x + 3) – log 3 (4x 2 – 9) = 2, x 1.5