AMKSS_PRELIM_2023_4NA_EMath_P2_Marking Scheme

Marking Scheme 4NA PRELIM 2023 EM Paper 2 4045/02 Qn Working Note 1a 342 $9.5036 = 1bi 1.5 $9.50 $14.25= for 10 hours = $142.50 2 $9.50 $19.00= for 2 hours = $38.00 Total = 342 + 142.50 + 38 = $522.50 1bii 636.50 342 $294.50 $294.50 $142.50 $152 $152 $19 8 36 10 8 54 hours −= −= = + + = 2a 3509.2 32.2100= 2b 48 5.58 5.5 100 550 km = = 2c 200 km: 9.2 2 18.4 l= 160 km: 8.0 1.6 12.8 l= 360 km: 31.2l 1 km: 31.2 0.0867360 l= Minus one mark for 0.087 (less than 3sf) 3ai 10 km 3aii 22 22 12 14 3 12 cm km cm km cm km −−−−−− −−−−− −−−−− 3aiii 22 22 1 0.5 1000 0.5 1000000 0.25 18000000 4.5 km cm m cm m cm m cm −−−−− −−−− −− −− 3b 10 550000 1 $81444.73100 81444.73 50000 $31444.73 A = + =  −= 4ai 0 4aii 2 5 [B1] [M1] [B1] [M1, A1] [M1] [A1] [M1, A1] [A1] [M1] [A1] [M1] [A1] [M1] [A1] [M1] [M1,A1] [B1] [B1]

4aiii 3 5 4bi 08 26 4bii 484000 5 49 min 484000 20940 23.1 / h ms = = Conversion from 484 km to 484000m [M1] 5ai ( )( )99x y x y−+ 5aii ( ) ( ) ( )( ) 10 15 6 9 5 2 3 3 2 3 5 3 2 3 px qx py qy x p q y p q x y p q − + − = − + − = + − 5b ( ) ( ) ( )( ) 2 2 35 12 2 1 3 2 1 5 2 2 2 1 6 3 5 10 2 4 2 2 4 15 0 4 136 4 3.92 1.92 xx x x x x x x x x x xx x or −=−+ + − − = − + + − + = + − − − − = = =− Must show this step with 136 for M1 6a Volume of hemisphere 314 323 56.54866776 56.5 =    = = Did not deduct marks for those who went to comvert to cm2 but did wrongly. Marked correct so long as they showed 56.5 in working. 6b Curve surface of hemisphere ( ) 2 43 2 56.54866776 = = Big circle – small circle ( ) ( ) 22 3 0.25 28.07798434 =− = Curved surface of pole 2 0.25 2 3.141592654 =   = Total surface area = 87.76824476 Disagree because he would need more than 8 litres of paint to cover 87.8 m2. [M1] [A1] [A1, A1] [B1] [B1] [M1] [M1] [A1] [M1] [M1] [M1] [M1] [M1, M1] [M1] [A1] [B1] [M1] [A1]

7 180 144 36 2 1 130 2 129 64.5 x x x − =  += = = 8a 1y= 8bi 1 2 8bii 1 12yx=+ 9a When x = 3, 2y=− When x = 6, 6.5y= 9b points smooth curve Graph at bottom 9c x = 4.7 0.1 Draw 2y= 9d Draw tangent Gradient = 2.088 0.5 Drawing tangent [B1] L [B2] [B1] [B1] [A1] [M1] [M1] [A1] [B1] [B1] [5 points B1, all points B2] [B1] [B2, or M1, A1] [M1] [M1] [M1]

10 20 4990 $998100 212 24 $5088 998 5088 $6086Total = = = + = Extra amount 6086 4990 $1096 =− = 1096 100% 21.96 22.0%4990 = = Accept 22% 11ai 0.7 Angles in the same segment 11aii 1.4 Angle and centre = 2 angles at circumference 11bi Area of minor sector 21 6 1.42 25.2 =   = 11bii Area of triangle 1 10.76 12 sin 0.72 41.5906... 41.6 =    = = 12ai 80 26 54 − = 12aii 550 12aiii 680-420 = 260 12b 10 26 13 80 79 316= 12c The interquartile range f