ACSI 2016 Y3 Core Mathematics Paper 2

Anglo - Chinese School (Independent) FINAL EXAMINATION 2016 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY 10th October 2016 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. 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/Y3IPCoreMathPaper2/2016/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: 9] (a) Simplify 183 36 2   p p . [2] (b) Solve for x, given that 023 4 5 2  xx [2] (c) Make k the subject of the formula h khm 22  . [2] (d) Simplify            xx 2 1 3 2 2 123 1 as a single fraction. [3] 2 [Maximum mark: 7] (a) Solve the inequality 212 12386  xx . [5] (b) Hence, write down (i) the least value of x, [1] (ii) the greatest integer value of x. [1] 3 [Maximum mark: 6] (i) Sketch the curve ( 1 )( 6)y x x   , indicating clearly the x- and y-intercepts and the coordinates of the turning point of the curve. [3] (ii) The tangent to the curve ( 1 )( 6)y x x   at the point where 1x has a gradient of 3. Find the equation of the line perpendicular to the tangent at this point. [3] 4 [Maximum mark: 7] (a) If 6416 1 x , find the value of 11 3 x . [3] (b) Solve  22 1345  xxx [4]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2016/FinalExamination 3 5 [Maximum mark: 5] (a) Find the range of values of x for which 2124 xx  . [2] (b) Find the range of values of m for which the expression 3)2(22  mxmmx is negative for all real values of x. [3] 6 [Maximum mark: 6] (i) The points of intersection of the graphs of 3xy and xy 2 1 are A and B. Find the coordinates of A and B. [3] (ii) Sketch the graphs of 3xy and xy 2 1 on the same axes for 33  x . Indicate clearly the points of interse