ACSI 2018 Y3 Core Mathematics Paper 2

FINAL EXAMINATION 2018 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY 8th October 2018 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/Y3IPCoreMathPaper2/2018/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: 6] (i) Express 22 2 2 3( ) yx x xy y x y − +− − + as a single fraction in its simplest form. [3] (ii) Hence or otherwise, find the value of x when w = 1.25 and y = 0.03 if 22 2 2 3( ) yx wx xy y x y − +=− − + . [3] 2 [Maximum mark: 10] (a) Expand and simplify 3( ) 4[2 2(3 4 )]y x x y x y− + − − − . [3] (b) Solve the equation 211 45 4xx+= . [3] (c) The solution of 5 3 48xx =+ is 15ab+ . Find the values of the integers a and b. [4] 3 [Maximum mark: 9] (a) AB and CD are straight lines intersecting at the point E. The angles between the lines are shown in the diagram below. Find the value of x y z+− . [4] (b) Two squares have a combined area of 300 m2. The sum of the perimeter of the squares is 80 m. Form and solve a pair of simultaneous equations. Hence, find the dimensions of the squares. [5] A B C D E

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2018/FinalExamination 3 4 [Maximum mark: 10] In the diagram, P, Q and R are points on level ground. The bearing of Q and R from P are 058o and 208o respectively. Given that QR = 125 m and the bearing of R from Q is 225o, (a) find the bearing of P from R, [2] (b) find the length of PR, [3] (c) calculate the shortest distance from P to QR. [3] (d) A vertical tower of 30 m is built at P. Find the largest angle of elevation of the top of the tower from a point along RQ. [2] 5 [Maximum mark: 13] (a) Let 3 3 3