2024 RI H2 Math Prelim P1 (Qn)

This document consists of 21 printed pages and 3 blank pages. RAFFLES INSTITUTION  RI2024 Mathematics Department [Turn over CANDIDATE NAME CLASS 24 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 P aper. You may use the blank page s on page 22, 23 and 24 if necessary and you are reminded to indicate the question number(s) clearly. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. 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. For Examiner’s Use Only Q1 Q2 Q3 Q4 Q5 Q6 / 4 / 5 / 8 / 8 / 8 / 7 Q7 Q8 Q9 Q10 Q11 TOTAL / 10 / 12 / 12 / 14 / 12 / 100 RAFFLES INSTITUTION 2024 YEAR 6 PRELIMINARY EXAMINATION CHairperson

2 H2 MA 9758/2024 RI Year 6 Preliminary Examination Paper 1 1 A function f is defined by 32f( ) .x ax bx cx d= + ++ The graph of f( )yx= passes through the points ( 3,4)− and (1, 8). Given that the graph of 1 f( )y x= has a turning point at 1 4(2, ), find the values of , , and .abc d [4] CHairperson

3 H2 MA 9758/2024 RI Year 6 Preliminary Examination Paper 1 [Turn over 2 [The volume of a sphere with radius r is given by 34 3 rπ and the surface area of a sphere with radius r is given by 24 rπ .] (a) The volume of an expanding sphere is increasing at a constant rate of 315 cm s .− Show that, at any instant, the rate of increase of the surface area is 21cm s ,k r − where r is the radius of the sphere and