Paper 1 SPM 2004

 

SPM 2004 1.

Dia Diagra gram m 1 shows shows the relati relation on be betwe tween en set set P  and  and set Q.

. w 

 

  d   .

.  x 

  e  .

. y 

  f   . . .

. z

Set P  Set P 

Set Q

State (a) the range of the relation, (b) the type of relation.  1 (a) !ange " # $ , y % (b) many&to&one many&to&one relation '

2.

i ie en n the the f* f*n+ n+ti tion on h    x  x   4 x  x  - m and h &1  $  2kx 2kx  -

/ .

, where m and k  are  are +onstants, find the al*e of 

m and of k . 2

m " & /2

 " 1 '

3

.

i ie en n the the f* f*n+ n+ti tion on h(  x) x) "

 ,  , x  x    0 and the +omposite f*n+tion hg (  x) x) "  x  x,, find  x

(a) (a) g   g ( x)  x) (b) the al*e of x of x when  when gh  gh(( x)  x) " /.   (a) g($) " 2$ , $  0 , (b) $ " 1/ 1/ '

4.

5orm the 6*adr 6*adrati+ ati+ e6*ation e6*ation whi+ whi+h hh has as the roots 7  and 8 . 2 ie yo*r answer in the form ax  - bx bx - c  "0, where a,b a,b and  and + are +onstants.  4 2$2 - /$ 7  " 0 '

/.

5i 5ind nd th thee rran ange ge of a al* l*es es of of x  x for  for whi+h  x  x (  ( x  x 7  7 4 ) 9 12  / & 2 : $ : 3'

3.

Dia Diagra gram m 2 shows shows the gra graph ph of the the f*n+t f*n+tion ion y  y "  " 7 ( $ 7 k   ))2 7 2 , where  is a +onstant. y  0  – 3

 

 x  (2 ,– 3 )

Diagram 2

 

5ind (a) the al*e of k , (b) the e6*ation of the a$is of symmetry, (+) the +oordinates o off the ma$im* ma$im*m m point.  3(a)  " 1 (b) $ " 1

(+) Ma$ point ( 1 , & 2 ) '

;. Sole the e6*ation e6*ation 2 4$ " 4 $- 3.  

; $"'

. ien that log/ 2 " m and log / ; " p " p,, e$press log/ 4.< in terms of m and and p  p..  

  log / 4.< " 2p 7 m 7 1 ' 4