TMJC 9758 2025 Prelim P1

Tampines Meridian Junior College 2025 JC2 Preliminary Examination H2 Mathematics CANDIDATE NAME: ___________________________________________________ CIVICS GROUP: _______________________________________________________ __________________________________________________________________________________ H2 MATHEMATICS 9758/01 Paper 1 16 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 6 printed pages and 0 blank page. TAMPINES MERIDIAN JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION [Turn Over

2 1 (a) On the same diagram, sketch the graphs of y x a=− and 1 ,y xa= − where a is a real constant such that 1.a You should show clearly the equations of any asymptotes and axial intercepts of both graphs. [3] (b) Hence, or otherwise, solve the inequality 1 .xa xa− − [3] 2 A curve C has equation 22 e. xy x y=+ (a) Show that ( ) 22 d2 e 1 2 e .d xx yyy x− = + [2] (b) Find the equations of the tangents to C at the points where 0.x= [4] 3 Find the following integrals. (a) 2 2 31 d41 xx xxx −− −+  , [3] (b) ( )ln dx kx x , where k is a real constant, [2] (c) sin d2cos 2 1  +  , using the substitution cos .x = [4] 4 An arithmetic series has first term a and common difference d, where a and d are non-zero real constants. A convergent geometric series has first term b and common ratio r, where 0b and r is a non-zero real constant. The sum of the first n terms of the geometric series is denoted by S. It is given that the 7th, 10th and 11th terms of the arithmetic series are equal to the 3rd, 6th and 10th terms of the geometric series respectively. (a) Show that r satisfies the equation 733 4 1 0rr− + = . Solve this equation, giving your answer correct to 4 decimal places. [4] (