YJC P1 MS

Yishun Junior College  JC2 Preliminary Examination 2012  H2 Mathematics 9740/1 Pg 1 of 10 1 3 541 xx       2 2 3 5 4 01 3 5 9 4 01 4 9 2 01 4 1 2 01 xx xx x xx x xx x            1 or 1 24xx    Let sinxy , 1sin or 1 sin 2 (rejected)4 0.253 or 2.89 yy yy           2 (i) 2 sin 2 d 2 sin 2 4 cos 2 dx x xe x x e x e x x 2 sin 2 4 cos 2 2 sin 2 d 2 sin 2 4 cos 2 4 2 sin 2 d x x x x x x e x e x e x x e x e x e x x            5 2 sin 2 d 2 sin 2 4 cos 2 12 sin 2 d 2 sin 2 4 cos 25 x x x x x x e x x e x e x C e x x e x e x C           (ii) 2 2 2 2 1 2 2 1d d d2 5 2 5 2 5 xx x x xx x x x x x                 2 2 2 21 1ln 2 5 d 12 11ln 2 5 tan 22 x x x x xx x C              2 1 1 4 2 + + – –

Yishun Junior College  JC2 Preliminary Examination 2012  H2 Mathematics 9740/1 Pg 2 of 10 3 (a)   5 32 1 0zi   311 25 42 3211 20 510 2 2 , where 2, 1, 0,1, 2 ik ki ze z e k         (b) 3zi 2 cos sin 66 i                 2 cos sin 66 2 cos sin66 n n n zi nn i                     Since nz is purely imaginary,     cos 06 21 , where 62 6 3, n kn k n k k         4 (i)   1 2 1 4 4 x x    1 1 2 2 2 2 141 4 1 1 312 8 128 1 1 3 2 16 256 x xx xx             Range of x: 44 x   (ii) 2 1 1 1 4 3 4 2 16 5 256 544 5              1 1 1 3 2 20 40016 5 5 223 4 400 2235 100      

Yishun Junior College  JC2 Preliminary Examination 2012  H2 Mathematics 9740/1 Pg 3 of 10 5 (i) 40 2 3yx 320 2yx Area, 21 sin(60 )2A xy x  = 213 22xy x   2 22 2 3 1 320 2 2 2 3320 24 3320 (Shown)42 x x x x x x xx              (ii) dA 3 320 2d 4 2 xx     3320 2 0 42 9.37218 x x     2 2 d 3 3 20d 4 2 A x     A has a maximum value when 9.37218x . Max A     23320 9.37218 9.3721842     93.7218 93.72 (to 2 d.p)   6 (i)  fyx  B(– 4, 0) A(– 2, 0) y = 0 x = 0 x y

Yishun Junior College  JC2 Preliminary Examination 2012  H2 Mathematics 9740/1 Pg 4 of 10 (ii)   1 fy x (iii)  f1yx 7 (i) ln , 1, 0x t t y t t     d 1 d1 , 1, dd xy t t t   d1 1d1 1 yt xt t   Since 0, 1 0, tt   d 0 for all > 0d1 yt txt Hence C does not have a stationary point (ii) When x = 0, ln 0tt 0.5671432904t (by g.c.) (0, 1.567) y=1 A (– 2, 1) y = 0 x y B (– 4, 1 3 ) C: x = –5 y = 0 x = –1 x y

Yishun Junior College  JC2 Pre