Crest Sec 4NA Prelim MS Paper 1

2024 4NA Mathematics Prelim Paper 1 Marking Scheme Qns Workings Mark Allocation 1a 0.00220 B1 1b 32.195 10 − B1 2 52 32 2 x= 552 2 2 55 10 x x x = += = M1 convert 32 = 25 A1 3 3 15 15 3 5 y y y −  − − Largest integer: 6y=− M1 A1 4a y = (2x + 1) (x – 1) y = 2x2 – x – 1 a = 2 B1 4b 0.5 1 0.252 −+ = x = 0.25 B1 5 $35.90 $29.90 $6−= 6 100%35.90 16.7130919% 16.7%  = = M1 A1 Accept 25616 %359 6 ( ) 22(4 0) 2 6 8.94427191 8.94 − + − − = = M1 A1 7a 233780 2 3 5 7=    B1 7b 23 22 3780 2 3 5 7 2 5 7 2450 mm m m =     =   = B1 8 235 45 LCM LCM = = After 45 minutes, the next timing will be 0815. M1 A1

9 5 2 19 (1) 3 3 (2) (2) 5 : 5 15 15 (3) (3) (1) (5 15 ) (5 2 ) 15 19 17 34 2 3( 2) 3 63 3 xy xy xy x y x y y y x x x − = −−−−− + =− −−−−−  + =− −−−−− − + − − =− − =− =− + − =− − =− = M1 Substitution/Elimination B1 B1 10 ( )( ) ( ) ( ) 170 0.5 70 90 512 35 80 51 80 16 0.2 0.2 0.5 0.7 t t t t  + + = += = = += M1 M1 A1 11a 1: 35000 20 : 700000 700000 100000 = 7 km B1 11b 1 cm : 0.35 km 1 cm2 : 0.1225 km2 2.1 0.1225= 17.142857 = 17.1 cm2 or 117 7 cm2 M1 A1 12 ( )( ) ( )( ) 2 2 2 7 5 1 3 2 7 5 3 2 3 2 2 6 4 0 2 2 2 0 2 2 0               2 0                   1      x x x x x x x xx xx x x OR x x OR − = + − − = − + − − + = − − = = −− = == M1 expansion M1 factorise A1

13a 2 2 2 10 (0.5) 2.5 2.5 kR C k k R C = = = = M1 A1 13b 2 2 2 2 2.5 2.540 2.5 40 10.0625 /16 10.25 / 4 R C C C C C = = = = = B1 14 ( ) 2 1 1685.40100 61 1685.40100 1.1236 1685.40 1685.40 1.1236 1500 n rP P P P P += += = = = M1 M1 A1 15 Let x m be the distance from cliff to A and y m be the distance from cliff to B. 350tan 60 350 tan 60 202.0725942 x x x = =  = 350tan 42 350 tan 42 388.7143802 y y y = =  = 388.7143802 – 202.0725942 = 186.641786 M1 tangent M1

= 187 m A1 16a 180(8 2) 1358 − = B1 16b 180 135 22.52 − = B1 16c 360 458 = B1 17a 20 members B1 17b 35% B1 17c 9 111 20 20−= B1 18a 89250 750 119= B1 18b 33201 119 279= 349 – 279 = 70 I do not agree with Jen. The same luggage cost $70 cheaper (or 8330 ¥ more expensive) in Japan than in Singapore. M1 ecf/convert $349 to JPY M1 difference A1 disagree 19a 5 : 4 = 15 : 12 6 : 1 = 12 : 2 15 : 12 : 2 M1 for either ratio A1 19b 6 29 872= M1 for 1 unit – 3 A1 20a 2 2 2 22 4 3 ( 2) 2 3 4 3 ( 2) 1 x x x x x x + + = + − + + + = + − a = 2, b = – 1 B1 each 20b 2 2 2 4 3 0 ( 2) 1 0 ( 2) 1 2 1 2 1 13 xx x x x or x x or x + + = + − = += + = + =− =− =− M1 A1 22a 9 B1 22b 3 + 10 – 7 – 4 = 2 B1 22c 1(3) 2(10) 3(8) 4( ) 5(4) 33 10 8 4 67 4 325 67 4 75 3 75 67 8 x x x x xx x x + + + + =+ + + + + =+ + = + =− = M1 A1

23a 1 5cos 13 5cos 13 1.176005207 1.