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

Copyright reserved Please turn over NATIONAL CERTIFICATE AUGUST EXAMINATION MATHEMATICS N6 5 AUGUST 2016 This marking guideline consists of 17 pages. MARKING GUIDELINE
MARKING GUIDELINE -2- T900(E)(A5)T MATHEMATICS N6 Copyright reserved Please turn over ✓= 1⁄2 MARK TOTAL: 100 2 200  NOTE: Do not subtract marks for incorrect units or units omitted QUESTION 1 1.1 z = ) cos (3 4 4 x  y 4cos (3 4 ). ( 4)sin(3 4 ) 3 x y x y y z        16cos (3 4 )sin(3 4 ) 3  x  y x  y (4) 1.2 3 x  ln u u y e 3  at the point where u = 1 du u dx 3  u e du dy 3  3 du dx du dy dx dy  u e u 3 3 3   e u dx dy u . 3  dx du dx dy du d dx d y         2 2   3 . 3 u e u du d u   3 ( 3 . ) 3 3 u e e u u u    3 . 3 . 3 3 2 e u e u u u   3 3 3 3 e  e   26,781 or 3 4 3 e  (8) [12]            
MARKING GUIDELINE -3- T900(E)(A5)T MATHEMATICS N6 Copyright reserved Please turn over QUESTION 2 2.1 x c x x x c x x x dx x or x x x x x x x y x x dx                                                                  1 2 1 2 2 2 2 2 2 2 2 2 ( 1) 2 69 2 2( 1) 2 69 ( 1) sin 2 69 2 ( 1) 2 69 2 ( 1) 2 69 ( 1) sin 2 69 2 ( 1) 2 69 2 ( 1) ] 2[34,5 ( 1) ] 2 69 2[ ] 2 69 2[( 1) 1] 2 67 2[( 1) ) 2 67 2( 2 2 4 67 67 4 2 OR x x c x        1 2 0,707( 1) 34,5 ( 1) 5,874 ( 1) 48,79sin (8)        
MARKING GUIDELINE -4- T900(E)(A5)T MATHEMATICS N6 Copyright reserved Please turn over 2.2 x c x x x dx x x x x x dx x x x x dx x x x x x g x x f x f x x g x x y x x dx                                     ln( 1) 6 1 2 . 3 1 .tan 3 ) 1 ( 3 1 .tan 3 3 1 1 .tan 3 ) 3 ( 1 1 .tan 3 3 ( ) 1 1 '( ) ( ) tan '( ) arctan . 2 2 1 3 2 1 3 2 3 1 3 3 2 1 3 3 2 1 2 2 (6) 2.3 y tan 7x.tan 7xdx 3 2   tan 7x.(sec 7x 1)dx 3 2          tan 7x.sec 7x)dx  tan 7xdx 3 2 3      (tan7x) .7sec 7xdx  tan 7x.tan7xdx 7 1 3 2 2      x  xdx x (sec 7 1).tan7 4 tan 7 . 7 1 2 4      x xdx  xdx x sec 7 .tan7 tan7 28 tan 7 2 4   x c x x    ln(sec7 )  7 1 2 tan 7 . 7 1 28 tan 74 2 x c x x    ln(sec7 )  7 1 14 tan 7 28 tan 74 2 (10)       x x x x x x     1 3 2 3