SPM 2016 Matematik Tambahan (Soalan Ramalan)


SPM 2016 Matematik Tambahan (Soalan Ramalan)

Bahagian A
[40 markah]
Jawap semua soalan.

Soalan 1
Selesaikan persamaan-persamaan serentak:
2(xy) = x + y – 1 = 2x2 – 11y2

[5 markah]
Jawapan serta penyelesaian:
2(xy) = x + y – 1
2x – 2y = x + y – 1
x = 3y – 1 ---- (1)

x + y – 1 = 2x2 – 11y2
2x2 – 11y2 x y + 1 = 0 ---- (2)

Gantikan (1) ke dalam (2):
2(3y – 1)2 – 11y2 – (3y – 1) y + 1 = 0
2(9y2 – 6y + 1) – 11y2 – 3y + 1 y + 1 = 0
18y2 – 12y + 2 – 11y2 – 4y + 2 = 0
7y2 – 16y + 4 = 0
(7y – 2)(y – 2) = 0
y= 2 7     atau    y=2
  
Daripada (1):
apabila y= 2 7 , x=3( 2 7 )1 x= 6 7 1= 1 7
  
apabila y = 2,
x = 3(2) – 1 = 5

Maka penyelesaian ialah,  x= 1 7 ,y= 2 7  atau x=5,y=2



Soalan 2
Diberi f:x 5x mx3 ,x 3 2  dan g:x34x. Cari
(a)    nilai bagi m,                                                                                                           [2 markah]
(b)   gf-1 (–2),                                                                                                                 [3 markah]
(c)    fungsi h jika hg (x) = 12x + 5                                                                                [3 markah]

Jawapan serta penyelesaian:
(a)
mx3=0 m( 3 2 )3=0 m=3× 2 3 =2

(b)
Katakan y= 5x 2x3 2xy3y=5x 2xy5x=3y x( 2y5 )=3y              x= 3y 2y5 f 1 ( y )= 3y 2y5 f 1 ( x )= 3x 2x5 f 1 ( 2 )= 3( 2 ) 2( 2 )5 = 2 3
g f 1 ( 2 )=g( 2 3 )               =34( 2 3 )               = 1 3  

(c)
hg (x) = 12x + 5
h [g(x)] = 12x + 5
h (3 – 4x) = 12x + 5
Katakan u = 3 – 4x
x= 3u 4 h( u )=12( 3u 4 )+5 h( u )=93u+5 h( u )=143u h( x )=143x  

0 comments:

Post a Comment