EJC_H2_2020_Prelim_P1

EUNOIA JUNIOR COLLEGE JC2 Preliminary Examinaton 2020 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CLASS INDEX NO. MATHEMATICS Paper 1 [100 marks] 9758/01 28 August 2020 3 hours Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, civics group and question number 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 paper clips, highlighters, glue or correction fluid. Answer all 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 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. This document consists of 28 printed pages (including this cover page) and 2 blank pages. For markers’ use: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Total

1 The curve C has equation 22 ( 3)x y y x   . Find the coordinates of the points on C at which the tangents are parallel to the y-axis. [4] 2 State the derivative of 2tan x . Hence, or otherwise, find 3 2 2sec dx x x . [4] 3 [It is given that a sphere of radius r has surface area 24 r and volume 34 3 r .] Air is being blown into a spherical balloon at a constant rate of 12 3cm per minute. Initially there is no air in the balloon. (i) Find the rate at which the radius of the balloon is changing when the radius of the balloon is 5 cm. [2] (ii) Find the rate at which the surface area of the balloon is changing 10 minutes after air is blown into the balloon. [4] 4 (i) On the same axes, sketch the graphs of 1 aby x  and y b x a , where a and b are positive constants such that 01 ab   . It is given that the two graphs intersect exactly twice. [3] (ii) Hence, solve the inequality 1 axa x  . [3] 5 You are given that e d.ee x xxFx   (i) Use the substitution exy to find another expression for F. [2] (ii) By considering e (e e ) (e e )x x x x xAB     where and AB are real constants to be determined, find an expression for F. [3] (iii) Show algebraically that your answers to parts (i) and (ii) differ by a constant. [1] 6 The functions f and g are defined by   2f: 3xa xa  for , ,x x a 2 g : 1 22 aaxx    for 0x where a is a positive constant. (i) Define, in a similar form, the in