2023 Prelim - TMJC P1

Tampines Meridian Junior College 2023 JC2 Preliminary Examination H2 Mathematics CANDIDATE NAME: ___________________________________________________ CIVICS GROUP: _______________________________________________________ __________________________________________________________________________________ H2 MATHEMATICS 9758/01 Paper 1 13 SEPTEMBER 2023 3 hours Candidates answer on the question paper. Additional material: List of Formulae (MF26) ________________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name and Civics Group on all 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, 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. The total number of marks for this paper is 100. _________________________________________________________________________________ This document consists of 6 printed pages and 0 blank pages. TAMPINES MERIDIAN JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION For Examiners’ Use 1 2 3 4 5 6 7 8 9 10 Total [Turn Over

2 1 The hyperbola 1C has equation ( ) 2 2 22 2 1.32 x y− −= (a) Sketch 1C , labelling the equations of the asymptotes and coordinates of the axial intercepts. [3] The curve 2C has equation ( ) 2 222x yk−+= , where 0k > . (b) State the value of k such that 1C and 2C intersect exactly twice. [1] 2 (a) Differentiate 2 2exx+ with respect to x and hence find the exact value of ( ) 21 2 0 1e dxxxx ++∫ . [3] (b) Using the substitution sinxt= , where 0 2t π<< , find ( ) 3 2 2 1 d 1 x x− ⌠ ⌡ in terms of x. [4] 3 In an art lesson, wires are cut and bent to create a series of shapes. (a) Student A cuts a piece of wire of length 100 cm to create a series of squares. The perimeter of the smallest square is 5 cm and the perimeter of each succeeding square is increased by 3 cm. Find the maximum number of squares Student A can form. [3] (b) Student B cuts another piece of wire to create a series of 12 circles, such that the radius of the first circle is cmx . The circumference