[FMS] [2023] 4E EM 4052 Prelims P1_MS

Pg 1 Fairfield Methodist School (Secondary) Secondary 4 Express / 5 Normal (Academic) Mathematics Paper 1 Marking Scheme Preliminary Examinations 2023 Qn No. Workings Description Mark Allocation AO 1(a) B1 AO1 1(b) m = 2 n = 5 B1 AO1 2(a) 901.16 B1 AO1 2(b) B1 AO1 3(a) 37 B1 AO1 3(b) 9 + 4n B1 AO1 3(c) Let 318 = 9 + 4n 4n = 309 n = 77 ¼ Since n is not a positive integer, 318 is not a term of the sequence. B1 AO3 4(a) 72 + 2x + 75 + 69 + x = 360 3x + 216 = 360 3x = 144 x = 48 B1 AO2 4(b) B1 AO1 5 y-intercept = 5( 2 5 )=2 Gradient of line graph 2 2 5 5 vert horizontal=− =− =− Equation of line is y = - 5x + 2 M1 M1 A1 AO2

Pg 2 Qn No. Workings Description Mark Allocation AO 6 Distance travelled by fuel in 24 mins = 2×24×60=2880m Capacity of fuel tank 2 3 822880 ( ) 100 14.476 14.5 (3 ) 145000 (3 ) m sf l sf = = = = M1 M1 A1 AO2 7a ( ) 3 4 4 3 3 4 3 3 4 4 33 3 81 1 () 81 11 (3 ) 11 3 1 27 x x x x x − −= = = = Apply () m n mnaa = M1 A1 AO1 7b 1 1 5 4 1 1 53 5 4 3 4 3 1 4 32 2 8 (2 ) 2 (2 ) 2 2 2 22 31 4 3 14 1 4 x x x x x x + = = = = += =− =− Apply () m n mnaa = M1 A1 AO1 8(a)(i) {3, 6, 9, 12, 15, 18, 21} No { } will result to no marks awarded B1 AO1 8(a)(ii) {4, 8, 10, 14, 16, 20, 22} B1 AO1 8(b)(i) B1 for each correct answer B1 B1 AO1 8(b)(ii) n[ ] = 5 B1 AO1

Pg 3 Qn No. Workings Description Mark Allocation AO 9 M1 for factorising out either common factor correctly M1 for factorising m2 – 5mn + 4 n2 correctly M1 M1 A1 AO1 10 M1 for converting to linear equation correctly M1 for expanding either side correctly M1 for simplifying either algebraic terms or constants correctly M1 M1 M1 A1 AO2 11a cos cos65 180 65 115 x x =−  = − =  B1 AO1 11b 1 1Area of ( )( )sin 2 115 (10)(6)sin2 15 30sin 15sin 30 15sin ( )30 30° or 150 PQR PQ PR QPR QPR QPR QPR QPR − = = = = = = M1 M1 A1 for both ans AO1 12a A2 = 4 6 4 6 0 2 0 2      −−   = 16 12 04   B1 AO1

Pg 4 Qn No. Workings Description Mark Allocation AO 12b A = 2B 46 02   − =2 2 01 k  − 46 02   − = 42 02 k  − 2k = 6 k = 3 B1 AO1 13a S = 34000 20100 14500 30000   B1 AO1 13b ( ) ( ) 34000 2010011 14500 30000 48500 50100   = B1 AO1 13c The total/combined sales in 2021 and 2022 (or for the 2 years) for IMic and Lenovo Laptops respectively • Keywords: Total/Combined , respectively, • 2021 and 2022 or past 2 years B1 AO2 14a Angle x = 180○ – 112○(int. angles, AB//CD) = 68○ Deduct 1 mark – wrong or missing reasons B1