Paper 2 MS

Name: Index Number: Class: HUA YI SECONDARY SCHOOL Preliminary Examination 2022 MATHEMATICS Paper 2 2022 2 h 30 min Candidates answer on the Answer Space provided. Mark Scheme This document consists of 15 printed pages including the cover page. © HYSS 2022 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 4E 4E 4048/2 Setter: Ms Lee Hui Ling

2 Sec 4E Preliminary Examination 2022 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = l rπ Surface area of a sphere = 24 rπ Volume of a cone = h r2 3 1π Volume of a sphere = 3 3 4 rπ Area of triangle ABC C absin2 1 Arc length = θr , where θ is in radians Sector area = θ2 2 1 r , where θ is in radians Trigonometry C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Statistics Mean = f fx ∑ ∑ Standard deviation = 22       ∑ ∑−∑ ∑ f fx f fx

3 Sec 4E Preliminary Examination 2022 Mathematics Paper 2 Answer all the questions. 1. (a) 42 x ------B1 (b) 42 0.5x+ -----B1 (c) (i) 2 2 42 42 1 10.5 4 84 0.5 1 2 168 0 1 Mxx xx M xx A − = −−−−−+ = + −−−−− + − = −−−−−− (ii) ( ) 21 1 4(2)( 168) 12(2) 8.919 8.92(3 )------A1 9.419 9.42 31 xM x sf or sf A −± − −= −−−−− = = − =− −−−−−− (iii) 42 4.459 4.46 (3 ) 18.919 0.5 = 4 h 28 min -------A1 h h sf M= = −−−−−+ 2. (a) (i) 1.25 ---------B1 (ii) Find area of triangle AOC: 0.5 (12)( 8 )( sin 1.25) = 45.55 ----M1 ecf Find area of sector AOB: 0.5 (122 )(1.25) = 90 ------M1 ecf Area of shaded region = 44.45 ----------A1 (iii) Find AC using cosine rule = 12.14 ---------M1 Perimeter = 31.1 ( 3sf) --------A1

4 Sec 4E Preliminary Examination 2022 Mathematics Paper 2 (b) (i) 32+38 = 70 ( isosceles triangle AOD and AOB ) (ii) 140 ( angle at center = twice angle at circumference ) (iii) Find DCB using opposite angle of cyclic quad ( M1 ecf ) Angle ODC = 180 – angle DCB ( interior angles, // lines ) =180-110 =70-------A1 3. (a) . AD 2 = 42+ 122 --------M1 AD = 12.649 ( shown ) -----A1 (b) Area of ABCD = 96 -------M1 Lateral area = ( 10+12+6+12.649) x 16 =650.384 --------M1 Surface area = 842.384 =842 ( 3sf) -----A1 (c) Volume of prism = 96 ( 16) -----M1 = 1536 -----A1

5 Sec 4E Preliminary Examination 2022 Mathematics Paper 2 4.