2025 YIJC Prelim H2 Maths Papers 1&2 (QP & Soln)

This document consists of 5 printed pages and 1 blank page. [Turn Over YISHUN INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CG MATHEMATICS Paper 1 Additional Materials: Printed Answer Booklet List of Formulae and Results (MF27) 9758/01 29 August 2025 3 hours READ THESE INSTRUCTIONS FIRST Write your CG, index number and name on the work you hand in. Answer all questions. Write your answers on the Printed Answer Booklet. Follow the instructions on the front cover of the answer booklet. 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 must present the mathematical steps using mathematical notations and not calculator commands. You must show all necessary working clearly. 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.

2 ©YIJC 9758/01/JC2PE/25 1 Show that the differential equation 24 d 2d e xx yxyy x §· ¨¸©¹ can be reduced by the substitution 24e xzy to 2 d2 d ex zx x . Hence, find the general solution in the form 2 fyx . [4] 2 Ronald is writing a novel. He began his new novel on 1 March 2025, writing 23 pages on the first day. On each subsequent day, he writes 90% of the number of pages he has written the previous day. (a) Find the total number of pages Ronald will have written by 31 March 2025. [1] Sam is also writing a novel. He began writing his novel on 8 March 2025, writing 2 pages on the first day. On each subsequent day, he writes 1 more page than the day before. (b) Find the first date on which Sam writes more pages in a day than Ronald. [2] (c) Find the first date on which Sam’s total num ber of pages written exceeds Ronald’s. [2] 3 (a) Find the series expansion of 1 15 x , up to and including the term in x2. State the range of values of x for which the expansion is valid. [3] (b) Hence, use the substitution 1 20x to obtain an approximation of 5, expressing your answer as a fraction. [2] (c) Without any further calculation, explain whether using the substitution 4 25x gives a better approximation of 5 than the substitution used in part (b). [1] 4 A curve has parametric equations 34 3 txt , 23yt t . (a) For the part of the curve where 0,x! find the equation of the tangent to the curve which is parallel to the y-axis. [3] (b) Find the coordinates of the point where the tangent meets the curve again. [2] 5 (a) Without using a calculator, solve the inequality 2 98 2 23 x xx t

. [4] (b) Hence solve the inequality 2 9ln 8 2 ln 2ln 3 x xx t

. [2]

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