Tiêu đề Copy of T900 - MATHEMATICS N6 MEMO NOV 2016.pdf ✅

Copyright reserved Please turn over NATIONAL CERTIFICATE NOVEMBER EXAMINATION MATHEMATICS N6 24 NOVEMBER 2016 This marking guideline consists of 20 pages. MARKING GUIDELINE
MARKING GUIDELINE -2- T900(E)(N24)T MATHEMATICS N6 Copyright reserved Please turn over  full mark TOTAL: 100 2 200  NOTE: Do NOT subtract marks for incorrect units or units omitted QUESTION 1 1.1 1.1.1 tan( ) cosec( ) 3 2 2 z  x y  xy 3 sec ( ) cosec( ) cot( ) 2 2 2 3 2 2 2 2 x y x y y xy xy x z     (4) 1.1.2 2 sec ( ) 2 cosec( ) cot( ) 3 2 3 2 2 2 x y x y xy xy xy y z     (2) 1.2 2 x  t 5 y  2t t dt dx  2 4 10t dt dy  t t dt dx dt dy dx dy 2 10 4   3  5t dx dt dx dy dt d dx d y          2 2   t t dt d 2 1 5 3   or t t t t 7,5 2 15 2 1 15 2    (6) [12]            
MARKING GUIDELINE -3- T900(E)(N24)T MATHEMATICS N6 Copyright reserved Please turn over QUESTION 2 2.1 y = sin 3xdx 1  2 1 1 (3 ) 3 '( ) ( ) sin 3 x f x f x x     g x x g x   ( ) '( ) 1   = dx x x x x 2 1 1 9 3 .sin 3 .     = x x x x dx 2 1 1 2 .sin 3 3 .(1 9 )        2 1 (1 9 ) . 18 3 .sin 3 2 1 2 1 x x x      x x   x  c 1 2 1 9 3 1 . sin 3 (4) 2.2 y = dx sec 2x 2  4 = 2 cos 2xdx 4   = x dx 2 cos 4 ) 2 1 2 1 2 (    = x cos 4x)dx 2 1 2 1 cos 4 )( 2 1 2 1 2 (    = x cos 4x)dx 4 1 cos 4 2 1 4 1 2 ( 2          = c x x x x                16 sin 8 4 2 1 4 sin 4 . 2 1 4 1 2 = c x x x x          64 sin8 8 8 sin 4 4 1 2 = c x x x x     32 sin 8 4 4 sin 4 2 1 c x x  x    32 sin 8 4 sin 4 4 3 (8)
MARKING GUIDELINE -4- T900(E)(N24)T MATHEMATICS N6 Copyright reserved Please turn over 2.3 y = dx 4x 12x 24 1 2    2 2 2 2 2 2 2 3 15 4 4 15 2 3 4 2 3 6 2 3 4 4( 3 6) 4 12 24                                                         x x x x x x x dx 4x 12x 24 1 2    = dx x 2 2 3 15 4 1          c x     15 ) 2 3 2( tan 2 15 1 1 or c x     3,873 2 3 0,129 tan 1 Or y = dx 4x 12x 24 1 2    = dx 4(x 3x 6) 1 2      = dx x x 6 2 3 2 3 3 1 4 1 2 2 2                  = dx x 4 15 2 3 1 4 1 2            c x                 4 15 ) 2 3 ( tan 4 15 1 4 1 1 or c x                 2 15 ) 2 3 ( tan 2 15 1 4 1 1 (8)            