2019 Y6 RI H2 Math Prelim (with ans)

¤ RI2019 [Turn over CANDIDATE NAME CLASS 19 MATHEMATICS 9758/01 PAPER 1 3 hours Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name and class on all the work 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 different 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 unle ss a question specifically states otherwise. Where unsupported answers from a graphing calculator are not all owed in a question, you are required to present the mathematical steps using mathematical n otations 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 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Total This document consists of 6 printed pages. RAFFLES INSTITUTION Mathematics Department RAFFLES INSTITUTION 2019 YEAR 6 PRELIMINARY EXAMINATION www.KiasuExamPaper.com 578

2 H2 MA 9758/2019 RI Year 6 Preliminary Examination Paper 1 1 A curve C has equation 3 ayb x cx  , where a, b and c are constants. It is given that C has a stationary point  1.2, 6.6 and it also passes through the point 2.1, 4.5 . (i) Find the values of , and ab c , giving your answers correct to 1 decimal place. [4] (ii) One asymptote of C is the line with equation x = 0. Write down the equation of the other asymptote of C. [1] 2 Two variables u and v are connected by the equation 11 1 20uv . Given that u and v both vary with time t, find an equation connecting dd , , and .dd uv uvtt Given also that u is decreasing at a rate of 2 units per second, calculate the rate of increase of v when u = 60 units. r [4] 3 Fig. 1 Fig. 2 Fig. 1 shows a square sheet of metal with side a cm. A square x cm by x cm is cut from each corner. The sides are then bent upwards to form an open box as shown in Fig. 2. Use differentiation to find, in terms of a, the maximum volume of the box, proving that it is a maximum. [6] a x www.KiasuExamPaper.com 579

3 H2 MA 9758/2019 RI Year 6 Preliminary Examination Paper 1 4 A curve C has parametric equations   22 1, 2 1.xt y t   (i) Find the coordinates of the point A where the tangent to C is parallel to the x-axis. [4] (ii) The line yx d  intersects C at the point A and another point B. Find the exact coordinates of B. [4] (iii) Find the area of the triangle formed by A, B and