JPJC 2021 J1 H2 Maths promo Exam Questions

Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC1 End-of-Year Examination 2021 MATHEMATICS 9758/01 Higher 2 29 September 2021 Paper 1 3 hours Additional materials: Answer Paper Cover Page List of Formulae (MF 26) 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 5 printed pages and 1 blank page. [Turn over Answer all the questions. 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 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 The parametric equations of a curve C are 2e , 2 e , 2.t tx t y t t      (i) Sketch C. [2] (ii) Find the equation of the normal to the curve at the point P where t = 0. [4] 2 A curve C has equation 3 ay bx cx   , where a, b and c are constants. It is given that C passes through the point with coordinates (1, 3) and has a stationary point (5, 21). (i) Find the values of a, b and c. [4] (ii) Hence find the equations of the asymptotes of C. [2] 3 It is given that 2 1 3tan 4x y y   . Find d d y x in terms of x and y. [4] Hence, find the exact value of d d y x when y = 1 , given that x > 0. [3] 4 (i) Sketch the curve with equation ln( 1), 1y x x   , stating the equation of asymptote and intercepts with the axes. On the same diagram, sketch the curve with equation 29 , 3 3,y x x     stating the intercepts with the axes. [4] (ii) Use your answer in part (i), solve the inequality 2ln( 1) 9x x   . [2] (iii) Hence solve the inequality 2 4ln( 1) 9x x   . [3] 5 The function f is de