RVHS_9758_2024_Promo

RIVER VALLEY HIGH SCHOOL 2024 JC1 Promotional Examination Higher 2 NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Additional Materials: List of Formulae (MF27) Cover Page Answer Papers 9758/01 26 September 2024 3 hours READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Write your name, class and index number in the space at the top of this page. Write your name and class on the work you hand in. Write in dark blue or black pen on both sides of the paper. 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. 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. Up to 2 marks may be deducted for poor presentation in your answers. At the end of the examination, place the cover page on top of your answer paper and fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages and 2 blank pages.

2 9758 / 01 / 2024 1 A curve C has equation 2 abyc xx= + + , where a, b and c are constants. It is given that C passes through the point with coordinates 112, 2 −− and has a turning point at 1x= . The gradient of C is 3 2− at the point where 2x= . Find the values of a, b and c and state the equation of C. [5] 2 The diagram below shows the graph of ( )fyx= . The curve crosses the x-axis at the origin and at the point ( )6, 0 . The curve also has a minimum point at ( )2, 8− . The equations of the asymptotes of the curve are 1x=− and 2y= . On separate diagrams, sketch the following graphs, indicating clearly the coordinates of any points of intersections with both axes and any turning point(s), and the equations of any asymptotes where possible. (i) f (3 2)yx=+ [2] (ii) 1 f ( )y x= [3] 3 (i) Solve the inequality 2 9 15x −− exactly.