AMKSS_PRELIM_2023_4NA_EMath_P1_Marking Scheme

Marking Scheme 4NA PRELIM 2023 EM Paper 1 4045/01 Qn Working Note 1 3  , 3 2 , 73% , 0.63 , 3 7 Cover one and all correct (1 mark) All correct 2 marks 2a 2444466.947 = 2444000 2b 62.444 10 Accept their (a) changed to standard form 3 3 4 ( ) 22 5 5 25 5 25 7 7 5 33 33 35 2 qxp p qx q x x x x qx q pq p p − +−+=− + − = = − =− =− + = 5a ( ) 2 2 2 2 2 10 5 10 5 5 5 5 30 5, 30 xx xx x ab +− = + + − − = + − = =− If answers wrong, accept M1 for this step 5b ( ) 2 5 30 5 30 30 5 or 30 5 0.48, 10.48 x x xx x += + = = − =− − =− If answers wrong, accept M1 for this step 6a 6b 2 3 3 1 15 14 3 4 :4 y y y Ans − +   − − − [M1] [A1] [B2] [B1] [B1] [A1] [B1, B1] [B1, B1] [B1] [M1] [A1]

7 : 9 : 4 27 :12 : : 27 :12 : 7 xy x y z == = 8a 3 33 33 168 2 3 7 540 2 3 5 2 3 5 7 7560LCM =   =   =    = 8b 22 5 50= 9 3 3 3 3 3 2 24 24 24 3 48 ky x k k y x y = = = = == 10a 24, 29−− 10b 56n−+ 10c 110 5 6 5 116 116 23.25 n n n − =− + = == Since 23.2n= which is not an integer, 110− is not a term in this sequence. 11a 89 11b 63 11c 52 11d 7 100% 35%20= Yes, student A is correct as only 7 out of 20 failed , which is 35%. 12 Answer behind 13a ( ) 24 2 10 36 6 u u u = − − = = [M1] [M1] [A1] [A1] [M1, A1] or B2 [B1] [M1] [B1] [A1] [B1] [B1] [B1] [B1] [B1] [B1]

13b 22 22 22 2 2 2 u v t t v u vut =− =− −= 14a 40 14b 0930 to 1030 The gradient is gentler. 14c 100 66.71.5 = km/h 15a The table only shows the percentage of participants. 15b 35 360 126100 =  16a $1 = 106.5 JPY 16b $1 AUD ------ $0.90 $1080AUD – 0.9 x 1080 = $972 € 0.68 ------- $1 € 1 ----------- 1 0.68 €620 ----------- 1 620 $911.760.68= Yes, he should ask his Spanish friend to buy as it is cheaper by $$60.24 to buy the wallet in Spain than in Australian. Must state that is it $60.24 cheaper. 17 1sin 0.723 46.3 ,180 46.3 46.3 ,133.7 x x x −= =  −  =   18a 23 32 2 3 32 10 5 3 25 10 4 15 8 xy y x xy x y xy − = = 18b ( )( ) ( ) 2 2 2 3 7 3 7 2 9 42 49 18 84 98 xx xx xx − + + =− + + =− − − 18c ( )( )2 3 4xx+− [M1] [B1] [M1] [A1] [M1] [A1] [B1] [B1] [M1, A1] [B1] [M1, A1] [B1] [M1] [M1] [A1] [M1] [A1 or B1,B1] [A1]

19 Curved surface area 6 19 114   =   = Base ( ) 2 2 6 36 r   = = = Total = 114 36 471.238898 471+ = = Aceept 3 sf or more ( 471.238898 ) 20 Answer at the back 21ai ( )8 2 180 1358 − = 21aii 360 458 = 21aiii 180 135 22.52 135 22.5 112.5 HAG BAG − = =   = − =  21b Parallelogram 22 Area of sector AOB 2120 14360 205.25072 =   = 14tan 60 14 tan 60 OC OC = =  Area of AOC 1 142 1 14 142 tan 60 56.58032638 OC=   =   = Area of shaded region 205.25072 56.58... 148.67 149 = − = = [M1, A1] [M1] [M1] [