TMJC 9758 2025 Prelim P2

Tampines Meridian Junior College 2025 JC2 Preliminary Examination H2 Mathematics CANDIDATE NAME: ___________________________________________________ CIVICS GROUP: _______________________________________________________ __________________________________________________________________________________ H2 MATHEMATICS 9758/02 Paper 2 22 SEPTEMBER 2025 3 hours Additional materials: Printed Answer Booklet List of Formulae and Results (MF27) ________________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Answer all the questions. Write your answers in the spaces provided in the Printed Answer Booklet. Follow the instructions on the front cover of the Printed 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 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. _________________________________________________________________________________ This document consists of 7 printed pages and 1 blank page. TAMPINES MERIDIAN JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION [Turn Over

2 Section A: Pure Mathematics [40 marks] 1 (a) Without using a calculator, solve the inequality 2 5 12 5 3 x xx + − + + . [4] (b) Hence, solve exactly the inequality 2 cos 5 12cos 5cos 3 x xx + − + + for 0 x  . [2] 2 It is given that ( ) 2f a b c  = + + , where a, b and c are real constants. The curve with equation ( )fy = passes through the point with coordinates ( )0,1 and has a turning point at 31,.32 − (a) Find the exact values of a, b and c. [3] (b) In a triangle ABC, 1AB= , 3AC= and angle 6BAC =+ radians. Given that  is sufficiently small for 3 and higher powers of  to be neglected, show that ( ) 2 f.BC  [3] (c) Hence, show that 2331. 28BC  + + [3] 3 The function f is defined by ( ) 2 for 4 1,f for 1 . 4 2 2 x x xx x −  −= −   + + It is given that ( ) ( )f f 6xx=+ for all real values of .x (a) Sketch the graph of ( )fy x= for .6 6x−  [3] (b) Hence sketch the graph of ( )f12y x= − for .6 6x−  [3]

3 4 A viral trend on social media gains popularity rapidly but eventually slows down due to oversaturation. Let P represent the popularity score of the trend at time t (measured in days), where 0 100.t The change in th