ACSI 2015 Y3 Core Mathematics Paper 2

Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2015 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 Wednesday 7 October 2015 1 hour 30 minutes INSTRUCTIONS TO STUDENTS Do not open this examination paper until instructed to do so. A calculator is required for this paper. Answer all the questions on the answer sheets provided. At the end of the examination, fasten the answer sheets together. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. The maximum mark for this paper is 80. ______________________________________________________________ This question paper consists of 6 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2015/FinalExamination 2 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for correct method, provided this is shown by written working. You are therefore advised to show all working. Answer all the questions on the answer sheets provided. Please start each question on a new page. 1 [Maximum mark : 8] (a) The curve     22 4 1y p x x p     has a minimum point and cuts the x- axis at two points. Find the range of values of p. [5 marks] (b) Show that 24 8 11xx is positive for all real values of x . [3 marks] 2 [Maximum mark : 8] (a) Solve 2 135 253 xx  , giving your answer correct to 2 decimal places. [4 marks] (b) Find the range of values of x which satisfy 8145 3 xxx     . [4 marks] 3 [Maximum mark :7] The figure shows a circular cylinder inscribed in a sphere with centre O and radius of 10 cm. The height of the cylinder is AB and AC = r cm is the base radius. (a) Given that AOC radians, express r in terms of . [1 mark] (b) Express OA in terms of r only. [1 mark] (c) Show that the height of the cylinder, 220 1 sin cmAB [3 marks] (d) Hence, express the volume of the cylinder in terms of . [2 marks] 10 cm r cm O B A C

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2015/FinalExamination 3 4 [Maximum mark : 9] Solutions to this question by accurate drawing will not be accepted. In the diagram above, the points A(2, 7), B(9, 5) and C(5, 3) are the midpoints of the straight lines LM, MN and LN respectively. Given al