2020 JC2_H2MATH_Prelim_P1_Questions

This document consists of 5 printed pages and 0 blank page. NANYANG JUNIOR COLLEGE Internal Examinations © NYJC 2020 [Turn Over NANYANG JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CT CLASS 1 9 Centre Number/ Index Number / MATHEMATICS 9758/01 Paper 1 28 August 2020 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name and class on 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, highlighters, 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 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 Question number Marks 1 2 3 4 5 6 7 8 9 10 11 12 Total

2 NYJC 2020 JC2 Preliminary examination  9758/01 1 A household's monthly utility bill is calculated by summing up the charges it incurs for its usage of electricity, gas and water based on the prevailing price rate per unit. The table below shows Mrs Ang’s household utilities usage for the months of April, May, June and July in a particular year. Monthly usage (units) April May June July Electricity 23 33 49 35 Gas 12 16 22 17 Water 16 21 33 26 The prevailing price rate per unit were unchanged for the period of April to June. However, in the month of July, the electricity rate was increased by 7%, the gas rate was reduced by 5% and the water rate remained unchanged. Given that Mrs Ang’s monthly utility bills for April, May and June were $103.00, $142.00 and $209.00 respectively, find her monthly utility bill for the month of July. [4] 2 (i) Sketch the graph of 2 4 7 1 2 3 xy x x  . Give the equations of the asymptotes and the coordinates of the turning points and the point(s) where the curve crosses the axes. [4] (ii) Find the range of values of k such that 2 4 72 31 x kx x   has only positive root(s). [1] 3 A curve C has parametric equations ,aaxt yt tt  , where t  , 0t  and a is a positive constant. (i) Find a cartesian equation of C. [2] (ii) The point P on C has parameter p. Show