JPJC_9758_2022_Promo_QP.pdf

Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC1 Year End Examination 2022 MATHEMATICS 9758/01 Higher 2 29 Sept 2022 Paper 1 3 hours Additional materials: Answer Paper Cover Page List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name and civics class on all 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. This document consists of 6 printed pages. [Turn over Answer all the questions. Give non-exact numerical answers co rrect 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 ans wers 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. At the end of the examination, fasten all your work securely together. The number of marks is given by [ ] at the end of each question or part question.

2 1 (i) On the same axes, sketch the graphs of 1 2y x  and 42yx , indicating clearly the equations of the asymptotes and the coordinates of the axial intercepts. [2] (ii) Hence, or otherwise, solve the inequality 1 422 xx  . [3] 2 (a) Differentiate the following with respect to x. (i)   3ln 9 3e x , [1] (ii) 42sin x , [2] (iii) 1sec3 sin 2xx  . [3] (b) A curve has equation 32 4 9 10 0y y x x     . Find d d y x in terms of x and y. [2] 3 By using the substitution 31,ut find the exact value of   2 5 33 0 d 1 t t t   without using a calculator. [5] 4 The curve C has equation 2 4 1 x kxy x   , where k is a constant. (i) Find the range of values of k if C has two distinct stationary points. [3] For the rest of this question, use 4k  . (ii) Sketch the graph of C, indicating clearly the equations of any asymptotes and the coordinates of any turning points and axial-intercepts. [3] (iii) Usin