NJC_9758_2024_Promo

* © NJC 2024 [Turn_over NATIONAL JUNIOR COLLEGE SENIOR HIGH 1 Higher 2 NAME SUBJECT CLASS 1ma2 REGISTRATION NUMBER MATHEMATICS 9758 Term 4 Promotional Examination 25 September 2024 3 hours Candidates answer on the Answer Booklet. Additional Materials: List of Formulae (MF27) Printed Answer Booklet READ THESE INSTRUCTIONS FIRST Write your name, class and registration number on the work you hand in. Write in dark blue or black pen. 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 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 must show all necessary working clearly. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. 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 2 blank pages.

2 © NJC 2024 1 Without using a calculator, solve the inequality 2 3 12 x xx + +− − . [4] 2 The region bounded by siny xx= , the x-axis, and the lines 0x= and πx= is rotated through 2π radians about the x-axis. Find the exact volume of the solid generated. [5] 3 (i) Given that k is a positive constant, s ketch the curve E with equation ( ) 2y x x k=− , labelling the coordinates of the points where the curve cuts the axes. [2] (ii) Hence, find, in terms of k, the area of the region (s) bounded by E and the x-axis for 02 x k . [3] 4 (a) The diagram shows the curve f ( )yx= that passes through the origin and (1,0). It has a minimum point 1 2 , 1 2  −   and asymptotes 1x=− and 3.y = ( )fyx= 3y= O ( )1, 0 1x=− 1 2 , 1 2  −   x y Sketch the curve ( ) 1 ,fy x= showing clearly the coordinates of any stationary points, axial intercepts and equations of all asymptotes. [3]

3 © NJC 2024 [Turn_over (b) A curve with equation h( )yx= undergoes the following sequence of transformations. Step 1: A translation of 2 units in the positive direction of the x-axis.