2024 HYSS Prelim Sec 4G2 Math MS P1

Name: Index Number: Class: HUA YI SECONDARY SCHOOL Preliminary Examination 2024 MATHEMATICS Paper 1 For Examiner’s Use This document consists of 6 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. [Turn Over 4G2 4G2 MARK SCHEME

2 4G2 Prelim 2024_Mathematics_P1_MARK SCHEME Qn Suggested Solution Mark Allocation 1 5( 2) 8xx+ = − 5 10 8 62 1 3 xx x x + = − =− =− --- M1 (expansion) --- A1 (will not accept 3sf) 2 0.6 , 0.60 , 5 8 , 5  --- B1 3a 0.000845 48.45 10 −= --- B1 3bi ( ) ( ) 1 2.5 10 4.9 10 12.25 10 1.225 10 10 1.225 10 m n m n mn mn + + ++    =  =   = 1.225a= --- B1 3bii 1b m n= + + --- B1 4 5.9 24.2 6 20 0.333 0.3 400 20   = = --- M1 (any 2 correct) --- A1 5a --- B1 (5 sides drawn) --- B1 (correct interior angles) 5b Interior angle of pentagon ( )5 2 180 5 108 −  = = Interior angle of polygon 360 108 108 144 = − −  = Exterior angle of polygon 180 144 36 = −  = 360 36 10 n = = --- M1 --- M1 (ecf)(if students measure the int. angle of polygon, can award them the mark) --- M1 (or if they use int. angle formula) --- A1

3 4G2 Prelim 2024_Mathematics_P1_MARK SCHEME 6a 2 1 1 5 1 5 25 ( 5)( 5) ( 5)( 5) 6 ( 5)( 5) x x x x x x x x xx ++ = +− − − + − + += −+ --- M1 (same denominator) --- A1 6b 1 ()3a h k b=+ 3 ( ) 3 3 a h k b a hkb ahk b =+ =+ =− --- M1 --- A1 7a 65 60 803 x++  Or 65 60 240x+ +  *Students don’t have to simplify/solve. If they did and did it wrongly, they will still be awarded full marks if they had formed the inequality correctly. --- B1 7b 65 60 240 115 x x + +   Mary is wrong because the maximum mark is 100. --- B1 (must have both answer and conclusion) 8a-c --- B1 --- B2 8d 4.6cm ( 0.1 )cm --- B1 9a 1 )3(4 )2(5 = −− −− --- M1, A1 9b y mx c=+ Substitute x = 4, y = 5, then c = 1. Equation of PQ: y = x + 1 --- M1 (ecf from (a)) --- A1 9c (0, )Ry (0,1)R --- B1 (ecf) (8a) 1m for CAB , 1m for BC (must show arc) (8b) & (8c) Correct construction with arcs shown

4 4G2 Prelim 2024_Mathematics_P1_MARK SCHEME 9d Since the line l is parallel to PQ, gradient of line l = 1 Sub 4, 5, 54 9 xy y mx c c c = =− =+ − = + =− Equation of line l: 9−= xy --- M1 --- A1 10a 2( 3) 5 8( 3) 4 5 20 20 5 8 24 20 3 24 20 x x x x xx x −−− = − −+= −+= --- M1 (expansion) --- A1 10b 2210 8 10 15 3 15 3 8 25 4 x y x x y y y x x  =  = --- M1 --- A1 11a Since the no. of workers and the time taken for completing the building are inversely proportional, workers days 50 120 1 6000 20 300 No. of days Or --- B1 11b workers days 50 120 6000 1 60 100 No. of workers needed Or Or use (a) to find the 60 workers No. of more workers required --- M1 --- A1 12a 10 3(20) 50− =− --- B1 12bi 45n− --- B1 12bii 4 5 121 4 126 31.5 n n n −= = = 121 is not a term in this sequence because n is not an integer/whole number/is a decimal. --- M1 --- A1

5 4G2 Prelim 2024_Mathematics_P1_MARK SCHEME 13 100% $8 300% $24 − − 92% $24 22.08= 98% $22.08 $21.6384 $21.64 = = --- M1 --- M1 --- A1 14a 2 18xy−= 92xy+= --- B1 --- B1 14b 92 29 xy xy += =− 2(2 9) 18 4 18 18 3 36 12 yy yy y y  − − = − − = = = 2(12) 9 15 x=− = --- M1 --- A1 15a 17.5 2.57 = --- B1 15b 16 2.5 6.4 a= = --- B1 16a 22 2 6 20 ( 3) 9 20 ( 3) 29 3, 29 x x x x ab − − = − − − = − − =− =− --- M1 --- A1 (ecf) 16b 2 2 ( 3) 29 0 ( 3) 29 3 29 8.39 2.39(2 ) x x x x or dp − − = −= − = =− --- M1 (ecf) --- A1 17a *For Qn 17, overall deduct one mark for wrong/missing reason 126p= Reason: corresponding angles --- B1 17b 38q= Reason: interior angles --- B1 17c 88r = Reason: vertically opp. angles/ alternate angles --- B1

6 4G2 Prelim 2024_Mathematics_P1_MARK SCHEME 18a sin 0.75 48.590 x x = = Obtuse angle x 131.4 (1 )dp= --- B1 18b 8tan 0.5 14.6439 AC AC = = 2 1 14.6439 82 58.5756 Area of OAC cm  =   = 0.52 1.07079 AOC rad  = − − = 2 2 1sec 8 1.07079 2 34.2652 Area of tor AOB cm =   = 2 58.5756 34.2652 24.3104 24.3 (3 ) Area of shaded region cm sf =− = = --- M1 --- M1 --- M1 --- M1 --- A1 19a 7 --- B1 19b 4 --- B1 19c 2(3) 3(2) 4(4) 5(6) 6(6) 3.923 2 4 6 6 94 3.9221 94 3.92 82.32 2.92 11.68 4 a a a a aa a a + + + + + =+ + + + + + =+ + = + = = --- M1 --- A1 19d 1.63 (3sf) --- B1