ACSI 2019 Y3 Core Mathematics Paper 2

FINAL EXAMINATION 2019 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY 7th October 2019 1 hour 30 minutes ADDITIONAL MATERIALS: Answer Paper (7 sheets) Graph Paper ( 1 sheet) 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. Answers in degrees are to be given to one decimal place. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. _____________________________________________________ This question paper consists of 4 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2019/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. Begin each question on a new page. 1 [Maximum mark: 7] (i) A triangle has the following lengths 4 3x+ meters, 2 3 9 x x − meters and 2 3x− meters, where 3x . Find the perimeter of the triangle, P , as a single fraction in its simplest form. [4] (ii) Given that the perimeter of the triangle is 2 meters, calculate the value of x . [3] 2 [Maximum mark: 11] (a) Factorize completely 2 2 26 9 16x xy y z− + − . [3] (b) (i) Given that 22()b y xy a −= , express x in terms of y , a and b . [3] (ii) Find the value(s) of x when 2a= , 3.125b=− and 17 3y= , leaving your answer correct to 4 significant figures. [2] (c) If the length of the base of a triangle is increased by 17% and the length of its perpendicular height is decreased by 17%, find the percentage change, if any, in its area. [3] 3 [Maximum mark: 8] The line 7xy+= intersects the curve 12xy= at P and Q . Find (a) the coordinates of P and Q , [4] (b) the equation of the perpendicular bisector of P and Q . [4]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2019/FinalExamination 3 4 [Maximum mark: 9] A, B, C and D are four points on a flat ground. D is due south of C and 55oABC= . 3.6AB= km, 1.8CD= km and 4.5AC = km. Calculate (a) CDA , [2] (b) the bearing of D from A, [2] (c) BCA , [2] (d) the shortest distan