Sembawang Secondary 4051/01 MS 2025

Prepared By: Ms Adeline LimPage 1 of 2 SEMBAWANG SECONDARY SCHOOLSEC 4NA PRELIMINARY EXAMINATION 2025 ADDITIONAL MATHEMATICS P1 MARKING SCHEMEQnSolution1(i)375723737157576279713729229137222(a)2 Aq24q 222tan1seccos144AqAAqqqq2(b)222sin22sincos224444AAAqqqqq

Prepared By: Ms Adeline LimPage 2 of 2 32222221212From2: 213Sub3 into1: 212220202102 or 13 or 3xyyyxxyyyyyyyyyyyyyxx 4220.52When 0.8, 20.81.280.51.280.51.280.51.280.124m/hdVdtdVxdxdVxdxdVdVdxdtdxdtdxdtdxdtdxdt5(a)432432f3:233193303633361f3:2331933318212:21899mnmnmnmnmnnnm

Prepared By: Ms Adeline LimPage 3 of 2 5(a)By long division method:22f92133211xxxxxxxx 62232(1)11xABCxxxxx23211xAxBxxCx When x = 0,–2 = AWhen x = 1, C = 1When x = 2, B = 22232221111xxxxxx

Prepared By: Ms Adeline LimPage 4 of 2 72(3)2yxx122(3)2yxx11222d1322(2)d2yxxxxx When x = 2, 11222d1322222(2(2))d2yx = 334Gradient of normal 3314 = 433When x = 2, 2(32)22y = 2Sub x = 2 and 2y into 433yxc42(2)33c 7433cEqn of normal : 4743333yx8(a)Amplitude = 3 Period = 180°

Prepared By: Ms Adeline LimPage 5 of 2 8(b)Correct Shape Amplitude, period x, y intercepts 922cos27sin4012sin7sin402sin7sin302sin1sin301sin or sin3 rejected23030,150xxxxxxxxxxBasicx 10(a)2323232f34434 =432 = 2451246f246xxxdxxxxcxxxcccxxxx

Prepared By: Ms Adeline LimPage 6 of 2 10(b)2321 21432246d4322212222622643431011222643xxxxxxxx 11(a)(i)411(a)(ii)311(b)Since principal value of 1cosis between 0 and ,it is not possible for the principal value of 12cos2 to be 4.Or principal value of 12cos2 is 34so it cannot be 4.11(c)(i)222211sin1sin1sin1(sin1) (sin1)(sin1)2= sin12 1cos12cos2secxxxxxxxxxx

Prepared By: Ms Adeline LimPage 7 of 2 11(c)(i)222113sin21sin212sec233sec222cos232cos23basic angle = 0.615479 20.61547, 2.52611, 3.75707, 5.66771 0.308, 1.26, 1.88, 2.83 ( to 3s.f.)xxxxxxxx12(a)7162661223723723723 or dxdxxxxxxx 12(b) 6411247177641 72323243231122327xdxxxxxdxx

Prepared By: Ms Adeline LimPage 8 of 2 13(a)22222229292119110110yxxyxxyxxyxyx Maximum value: 10mx = 1 13(b)2211001101104.16 m or 2.16xxxxx It takes 4.16m for the stone to reach sea level