2019 J2 TJC H2 Math Prelim (with ans)

TEMASEK JUNIOR COLLEGE, SINGAPORE JC 2 Preliminary Examination 2019 CANDIDATE NAME CG MATHEMATICS 9758/01 Higher 2 Paper 1 30 Aug 2019 Candidates answer on the Question Paper. 3 hours Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your Civics group and name on all the work that you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 significant figur es, or 1 decimal place in the case of angles in degrees, unless a differ ent level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate . Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 10 11 Total Marks www.KiasuExamPaper.com 741

2 © TJC 2019 9758/01 1 The diagram below shows a shape which is symmetrical about the x- and y-axes. The shape is made up of four curves, A, B, C and D. The curve A has equation 1xy for 01 xdd and 01 ydd . (i) State the equations and the range of values of x and y for curves B and C. [3] (ii) The curves A and B are scaled by a factor 1 2 parallel to the x-axis and the curves C and D are scaled by a factor 2 parallel to the y-axis. Sketch the resulting shape. [2] 2 The position vectors of A, B, C and D a r e 1 5 D§· ¨¸ ¨¸ ¨¸ ©¹ , 1 2 1 §· ¨¸¨¸ ¨¸ ©¹ , 2 3 1 §· ¨¸ ¨¸ ¨¸ ©¹ and 1 7 E §· ¨¸ ¨¸ ¨¸ ©¹ respectively, where α and β are real numbers. Given that BD is a perpendicular bisector of AC, find the values of α and β. [5] 3 The hyperbola C passes through the point (2, 0) and has oblique asymptotes 2yx and 2yx . ( i) Sketch C, showing the relevant features of the curve. [2] (ii) Write down the equation of C. [1] (iii) By adding a suitable curve to your sketch in part (i), solve the inequality 2 114 x x . [3] 1 1 x y 0 −1 −1 A B C D www.KiasuExamPaper.com 742

3 © TJC 2019 9758/01 4 A curve C has equation ex y xk , x ≠ k, where k is a positive real number. Show algebraically that C has exactly one stationary point, and show that the stationary point lies in the first quadrant. [3] Sketch C for x > k, indicating clearly the