2024_HYSS_Prelim_Sec 4G2_Math_MS_P2

Name: Index Number: Class: HUA YI SECONDARY SCHOOL Preliminary Examination 2024 MATHEMATICS Paper 2 For Examiner’s Use This document consists of 7 printed pages including the cover 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. [Turn Over 4G2 4G2 MARK SCHEME

2 4G2 Prelim 2024_Mathematics_P2_MARK SCHEME Qn Suggested Solution Mark Allocation 1ai Not all the powers of the prime factors are even numbers/multiples of 2. --- B1 1aii 22 3 11 726 k =   = --- B1 1bi 2 2100 2 1050 3 525 5 175 5 35 7 7 1 222100 2 3 5 7=    --- M1 --- A1 1bii 223 12 HCF = = --- B1 (ecf) 2 (70 2.5) (2 ) 804.5 175 2 360 2 185 92.5 x x x x + = += = = --- M1 ---M1 --- A1 3 2 2 10506.25 10000 1 100 1.050625 1 100 1 1.025100 2.5 p p p p =+  =+ += = --- M1 --- M1 --- A1 4a *M1 – multiplication frame 22 9 5 (2 1)( 5)x x x x− − = + − --- M1 --- A1 4b 2 2 2 2 22 2 18 2( 9 ) 2 (3 ) 2( 3 )( 3 ) x y x y xy x y x y − = − =−  = + − ---M1 ---A1

3 4G2 Prelim 2024_Mathematics_P2_MARK SCHEME 5a 5 :1 5 :100000 1: 20000 cm km cm cm --- B1 5b 22 22 5 :1 25 :1 200 :8 cm km cm km cm km Or 22 22 5 :1 1 : 0.2 1 : 0.04 200 :8 cm km cm km cm km cm km --- M1 --- A1 6a 2 2 2 2 22 20 99 10201 101 10201 XZ XY YZ + = + = == Since 2 2 2XZ XY YZ+= , XYZ is a right-angled triangle. --- B1 6b 99cos 101 11.4211 XYZ XYZ = = Or using area Let the shortest distance from X to YZ be h. sin11.4211 99 19.603 19.6 (3 ) h h h m sf = = = --- M1 --- M1 --- A1 7a --- A1 (for the 6 outcomes for the die) --- A1 (for the outcomes for the coin) *wont penalise students if they write the probabilities/write the probabilities wrongly 7bi 31 12 4= --- B1 7bii 0 --- B1 8a 3 --- B1

4 4G2 Prelim 2024_Mathematics_P2_MARK SCHEME 8b 1m --- at least 8 points plotted correctly 1m --- smooth curve drawn 8c 2.1,4.6( 0.1)x=−  --- B2 8d The minimum/lowest point of the curve is at 7y=− , so there will not be any point below 7y=− . --- B1 8e Drawing of tangent correctly 1 ( 12) 4.2 0 3.0952 3.10(3 ) gradient sf −−= − = = --- B1 --- B1 9ai 300$ x   --- B1 9aii 300$ 1.5x  + --- B1 9b ( ) 2 2 300 1.5 30 360 9000300 1.5 45 360 9000 1.5 105 0 9000 1.5 105 0 70 6000 0 xx xx xx xx xx  + − = − + − = − + − = − + − = − − = --- M1 (form eqn) --- M1 (expansion) --- A1 9c 2 70 6000 0 ( 120)( 50) 0 120 50 xx xx x or x − − = − + = = =− --- M1 (or any other method) --- A1 9