RVHS_9758_2025_Prelim_P2

1 ©RIVER VALLEY HIGH SCHOOL 9758/02/2025 RIVER VALLEY HIGH SCHOOL 2025 JC2 Preliminary Examination Higher 2 NAME CLASS INDEX NUMBER MATHEMATICS Paper 2 Additional Materials: Printed Answer Booklet List of Formulae (MF27) 9758/02 19 Sep 2025 3 hours READ THESE INSTRUCTIONS FIRST This document consists of 8 printed pages and 0 blank page. Write your class, index number and name 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 on the Printed Answer Booklet. Follow the instructions on the front cover of the answer booklet. 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 must show all necessary working clearly. 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.

2 ©RIVER VALLEY HIGH SCHOOL 9758/02/2025 Section A: Pure Mathematics [40 marks] 1 A sequence is such that 1uN= where N is a constant, and 1 38nnuu+ =− , for 1n . (a) Describe how the sequence behaves when (i) 4N = , [1] (ii) 3N = . [1] (b) Find the value of N for which 5 409u = . [2] (c) The sequence ( ) ( )1 n nnv u k= − + for 1n where k is a constant, is convergent when 1 4u = . State the value of k . [1] 2 The points A , B and C represent the complex numbers 5 6iAz =+ , 9 3iBz =+ and Cz respectively. ABC is an isosceles triangle labelled in a clockwise direction where 90CAB =  . (a) Find Cz . [3] (b) The point D representing the complex number Dz , is such that ABDC is a parallelogram. Find Dz . [2] 3 (a) The region A is bounded by the curves 22 5xy+= and 2 1yx=+ for 1y . Find the volume when A is rotated π radians about the y-axis. [2] (b) The region B is bounded by the curve 2 2 47 y xx = −+ , the line 2yx=− , the line 1x = and the x-axis. Find the exact volume when B is rotated 2π radians about the x-axis. Give your answer in the form 23ππab + , where a and b are constants to be determined. [6]

3 ©RIVER VALLEY HIGH SCHOOL 9758/02/2025 4 The dos