2023 Springfield 3G3 Mathematics (4052) (P2-MS)

22 Marking Scheme 3Exp P2 1a 50 8 4 5  = M1 A1 AO1 1b 31 3 1 0.65 10 10 0.65 10 10 6500 a a a − −  =  = = M1 A1 AO1 2a 52 5 2 0 7 7 1 77 5 2 0 5 2 k k k k − −+ = = − + = = M1 A1 AO2 2b 3 5 15 2 22 3 5 15 2 , 15 2 22 5 20 , 7 3 74 , 3 7 43 x x x x x x x xx xx x −  −  + −  − −  +  −   − −   M1 M1 A1 AO2 2c B1 3a Based on the perimeter, the various combination for Length and Breadth are: 1. 4+4+9+9 2. 5+5+8+8 3. 6+6+7+7 6320 2 5 320 2 2 2 2 2 2 5 8 5 = =       from the prime factorisation of 320, the perimeter combination should be 5+5+8+8. Thus the height of the cuboid will be 8 cm M1 M1 A1 AO3 -3 -2 1 3 4 5 -1 0 2 7 3−

23 [Turn Over 3b n = 20 B1 AO2 4a 16 oC B1 AO1 4b 16 8850 m 88501 16 1 553.125 m 5 553.125 2765.625 m C C C → → → = M1 A1 AO2 5a Let x be the length and y be the breadth ( )( ) area new area 1.1 0.82 new area 0.902 0.902% change 100% % change 9.8% xy xy xy xy xy xy = = = −= =− M1 M1 A1 AO2 5b amt in Yen 32400 6200 amt in Yen 38600 total amt in Yen 1.05 38600 total amt in Yen 40530 40530total amt in SGD 106.80 total amt in SGD $379.49 =+ = = = = = M1 M1 A1 AO2 6a 3000 x B1 AO1 6b 3000 6x− B1 AO1 6c 2 2 3000 3000 50 69 3000 3000( 6) 50 ( 6) 9 18000 50 ( 6) 9 162000 50 300 6 3240 0 xx xx xx xx xx xx −=− −− =− =− =− − − = M1 M1 A1 AO2

24 6d ( ) 2 2 6 3240 0 ( 6) 6 4(1)( 3240) 2(1) 60 or 54( ) 3000no. of kg of vegetable 60 6 no. of kg of vegetable 55.6 kg xx x x x rej − − = − −  − − −= = =− = − = M1 M1 A1 AO2 7a 2 2 3 31.5 1.5 4.25 yx x a a =+ =+ = B1 AO1 7b Correct plotting of points – 2 mark [correct 6 out of 8 points – 1 mark] Smooth curve – 1 mark AO2 7c Drawing of line y = 9 2.8 0.05x= M1 A1 AO1

25 [Turn Over 7d Drawing of tangent Grad = 5.67 0.1 M1 A1 AO1 7e Drawing of tangent 3.9 0.1y= M1 A1 AO3 8a 17 12 5 5cos 17 72.895 72.9 OB AOB AOB AOB = − = =  =   =  M1 A1 AO1 8b reflex 360 72.9 2 reflex 214.2 214.2major arc length 2 (17)360 major arc length 63.554 major arc length 63.6 cm AOC AOC   = −   =  =  = = M1 M1 A1 AO2 8c 2 2 145.8area of sector (17) 360 area of sector 367.71 area of sector 368 cm OAEC OAEC OAEC =  = = M1 A1 AO1 8d 2 1area of minor segment 367.71 (17)(17)sin( 72.9 2)2 area of minor segment 286.49 area of minor segment 286 cm ABEC ABEC ABEC = −  = = M1 A1 AO2 9a AO2 B O A D

26 35cos30 40.415 40.4 cm AD AD AD = = = M1 A1 9b 40.415 12 28.415 cm BG BG =− = M1 A1 AO1 9c 2 2 2 40 28.415 49.065 49.1 cm AG AG AG =+ = = M1 A1 AO2 9d sin 30 28.415 14.208 14.2 cm HG HG HG = = = M1 A1 AO2 9e 2 1area of triangle 2 1area of triangle 40.415 402 area of triangle 808.3 cm GAD AD AB GAD GAD =   =   = M1 A1 AO1 A F 30o 35 cm A B G 40 28.415 30o B H G 28.415

27 [Turn Over 10a 53 3 3 5 3 5 3 53 3 x y z x y z x z y zyx + = += =− −= M1 A1 AO2 10b 53 3 5( 3) 3(2) 3 7 zyx x x −= −−= =− B1 AO1 11a 1645 h B1 AO1 11b 20 km B1 AO1 11c 80speed 1 speed 80 km/h = = M1 A1 AO1 11d 160avg speed 2.5 avg speed 64 km/h = = M1 A1 AO1 12a (vert. opp ) (alt ) triangle is similar to triangle (AA te st) BDC EDF BCD EFD BDC EDF  =   =  M1 A1 AO2 12b 2 Area of triangle Area of triangle Area of triangle 9 Area of triangle 4 BDC BD EDF ED BDC EDF = = M1 A1 AO1 12c 2 2 Area of triangle Area of triangle Area of triangle 9 Area of triangle 25 54 9 Area of triangle 25 Area of triangle 150 cm BDC BD AFC AF BDC AFC AFC AFC = = = = M1 M1 A1 AO1 12d Area of triangle 54 Area of trapezium 150 54 Area of triangle 9 Area of trapezium 16 BDC ABDF BDC ABDF = − = M1 A1 AO2

28 13a 6 litres/min B1 AO1 13b 6 full flushes, 6 half flushes + 4 full flushes 3 15 18 63 litres =  + = M1 A1 AO2 13c 19% 8208 100% 43200 litres → → M1 A1 AO2 13d 3 43200 litres 0.001 43200 43200 litres 43.2 m Tariff 1.52 43.2 Tariff $65.66 Water conservation tax 0.65 65.66 Water conservation tax $42.68 Water bill 65.66 42.68 Water bill $108.34 → → = = = = =+ = M1 M1 M1 A1 AO2 13e 3 First answer: highest usage 49.75 m Tariff 1.52 49.75 Tariff $75.62 Water conservation tax 0.65 75.62 Water conservation tax $49.15 Water bill 75.62 49.15 Water bill $124.77 Second answer: 49.75average usage = = = = = =+ = = 349 48.75 49.25 48.25 49 m5 Tariff 1.52 49 Tariff $74.48 Water conservation tax 0.65 74.48 Water conservation tax $48.41 Water bill 74.48 48.41 Water bill $122.89 + + + + = = = = = =+ = M1 M1 M1 A1 [M1] [M1] [M1] [A1] AO3