Hua Yi Sec Prelim 2024 A Math Paper 2_QP

[Turn Over HUA YI SECONDARY SCHOOL PRELIMINARY EXAM 2024 4-G3 / 5-G2 NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049/02 PAPER 2 (XX) 08 October 2024 2 hour 15 minutes Candidates answer on the Question Paper No Additional Materials is required. READ THESE INSTRUCTIONS FIRST Write your Name, Class, and Index Number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue, or correction fluid. 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. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in the brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. For Examiner’s Use 90 This document consists of 18 printed pages. © HYSS 2024 No part of this document may be reproduced in any form or transmitted in any form or by any means without the prior permission of Hua Yi Secondary School. Setter : Mdm Suzanne Lye

2 2024_4-G3 / 5-G2_PRELIMS_ ADDITIONAL MATHEMATICS _PAPER 2 [Turn Over 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0 , x = -b ± b2 - 4ac 2a Binomial expansion a + b( ) n = an + n 1 æ èç ö ø÷ an-1b + n 2 æ èç ö ø÷ an-2b2 + ...+ n r æ èç ö ø÷ an-rbr + ...+ bn , where n is a positive integer and n r æ èç ö ø÷ = n! r!(n - r)! = n(n -1)...(n - r +1) r! 2. TRIGONOMETRY Identities sin2 A+ cos2 A = 1 sec2 A = 1+ tan2 A cosec2 A = 1+ cot2 A sin( A ± B) = sin Acos B ± cos Asin B cos( ) cos cos sin sinA B A B A B= tan tantan( ) 1 tan tan ABAB AB = sin2A = 2sin Acos A cos2A = cos2 A- sin2 A = 2cos2 A-1= 1- 2sin2 A tan 2 A = 2 tan A 1- tan2 A Formulae for DABC a sin A = b sin B = c sinC a2 = b2 + c2 - 2bccos A Cabsin2 1=

3 2024_4-G3 / 5-G2_PRELIMS_ ADDITIONAL MATHEMATICS _PAPER 2 [Turn Over 1 Show that 𝑥 = 1 2 is a solution of the equation 2𝑥3 + 𝑥2 − 3𝑥 + 1 = 0 and hence solve the equation completely. [5]

4 2024_4-G3 / 5-G2_PRELIMS_ ADDITIONAL MATHEMATICS _PAPER 2 [Turn Over 2 (a) By considering the general term in the binomial expansion of (𝑝𝑥 + 1 𝑥3) 9 , where p is a constant, explain why there are no even powers of x in this expansion. [3]

5 2024_4-G3 / 5-G2_PRELIMS_ ADDITIONAL MATHEMATICS _PAPER 2 [Turn Over (b) Given that the coeffi