AQA A-LEVEL FURTHER MATHEMATICS Paper 3 7367/3M MECHANICS||QUESTIONS & MARKING SCHEME MERGED| GRADED A+||

A-level FURTHER MATHEMATICS Paper 3 Mechanics Time allowed: 2 hours Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. l You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Discrete or Statistics). You will have 2 hours to complete both papers. Instructions l Use black ink or black ball‑point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l You must answer each question in the space provided for that question. If you require extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). l Do not write outside the box around each page or on blank pages. l Show all necessary working; otherwise marks for method may be lost. l Do all rough work in this book. Cross through any work that you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 50. Advice l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not necessarily need to use all the space provided. Please write clearly in block capitals. Centre number Candidate number Surname ________________________________________________________________________ Forename(s) ________________________________________________________________________ Candidate signature ________________________________________________________________________ For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 TOTAL I declare this is my own work. 2 Answer all questions in the spaces provided. 1 State the dimensions of power. Circle your answer. [1 mark] ML2T 3 ML3T 3 ML3T 2 ML2T 2 2 The force (3i þ 4j) N acts at the point with coordinates (0, 2) The unit vectors i and j are directed along the x-axis and the y-axis respectively. Calculate the magnitude of the moment of this force about the origin. Circle your answer. [1 mark] 6Nm 8Nm 10 N m 14 N m Jun23/7367/3M Do not write outside the box (02) 3 3 A uniform disc has mass 6 kg and diameter 8 cm A uniform rectangular lamina, ABCD, has mass 4 kg, width 8 cm and length 20 cm The disc is fixed to the lamina to form a composite body as shown in the diagram below. A B D 20 cm 8cm C The sides AB, AD and CD are tangents to the disc. Calculate the distance of the centre of mass of the composite body from AD Circle your answer. [1 mark] 4 cm 5.6 cm 6.4 cm 8.8 cm 4 A car of mass 1400 kg drives around a horizontal circular bend of radius 60 metres. The car has a constant speed of 12 m s1 on the bend. Calculate the magnitude of the resultant force acting on the car. [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box Jun23/7367/3M Turn over s (03) 4 5 A region bounded by the curve with equation y ¼ 4 x2 , the x-axis and the y-axis is shown below. O x y The region is rotated through 360 around the x-axis to create a uniform solid. 5 (a) Show that the distance of the centre of mass of the solid from the circular face is 5 8 [5