2024 HYSS_S4-5 G3 MA Prelim_Paper 2_MS

[Turn Over HUA YI SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 4-G3 / 5-G2 NAME CLASS INDEX NUMBER MATHEMATICS 4052/02 PAPER 2(XX) 19 August 2024 2 hour 15 minutes Candidates answer on the Question Paper. MARKING SCHEME . For Examiner’s Use 90 This document consists of 25 printed pages and 1 blank page. © 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: Ms Jasmine Tan

2 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over Mathematical Formulae Compound interest Total Amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over 1 (a) Express as a single fraction in its simplest form 21 7 3 6xx−−− . ( )( ) ( )( ) ( )( ) 2 1 2(6 ) (7 3 ) 7 3 6 6 7 3 12 2 7 3 1 [expand numerator correctly]6 7 3 5 16 7 3 xx x x x x xx Mxx x Axx − − −−=− − − − − − += −−−−− += −−−−− Answer ………………………. [2] (b) It is given that 35 92 wv w −=+ + . (i) Find v when 6w=− . ( )3 5 6 39 0.75 16 2 4v or B−−= + = −−−−+ Answer ………………………. [1] (ii) Rearrange the formula to make w the subject. ( )( ) 35 92 2 9 3 5 1 [remove bases] 9 2 18 3 5 4 21 2 1 [group - terms on 1 side] 21 2 4 21 2 14 wv w w v w M wv w v w wv w v A w vw v v Av −=+ + + − = − −−− − + − = − − = − −−− −= − −=− −−−−

4 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over Answer w = .…………………. [3] (c) Solve the equation 2 5 3 1 2 4 7xx −=−− . Give your solutions correct to two decimal places. ( )( ) ( ) ( ) 2 2 2 2 53 1 24 7 5( 2) 3 1 1 [puts to common base]2 2 7 7(5 10 3) 4 35 53 0 1 [simplifies accurately quad. eqn.] 35 35 4(1)( 53) 12(1) 1.45389 36.45389 xx x Mxx xx x x M xM x or x −=−− +− = −−−+− + − = − − − = −−− − −  − − −= −−− =− = 1.45 1 36.45 1 [accept 2 d.p. only]x A or x A=− −−− = −−− Answer x = ……...… , x = …….…… [5]

5 2024_4-G3 / 5-G2_PRELIMINARY EXAMINATION_MATHEMATICS_PAPER 2 [Turn Over 2 C is the point ( )9,1− and D is the point ( )7,4 . 2 8CE −= . (a) Calculate the length of the line CD. ( ) ( ) 22 Length 9 7 1 4 1 265 16.3 1 CD M A = − − + − −−− = = −−− Answer ……………… units [2] (b) Determine the coordinates of point E. ( ) 29 81 11,9 1 CE OE OC OE EB =− −−   +=        − −−− Answer E (………. , …….….) [1] (c) Find the equation of the line DE.