7/25/2019 Senior Three Revision Midterm Kulai July
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Senior Three Revision (Chapter 2,3 ) Midterm Exam
Attempt all the question :
! "a#torise $x%& 'x3 %x2 3x 3 , *iven that there is a
repeated linear +a#tor !
2! iven
y z z x x yc
ay bz az bx ax by
+ + += = =
+ + +
, -here a , . , # are real num.ers , prove that
2c
a b=
+
!
3! "a#torise (i) (x/0) (x/ /0 0x ) & x/0 (ii) a2(.#)3 .2(
#a)3 #2(a.)3
%! Solve the equation (i) 2x' & x%& 1x3& 1x2& x
2 (ii) x% 4x3 %x2 4x
'! 5rove that , 3x2 02& 6x/ & 2/0 2x0 %/2never ne*ative
+or real values o+ x , / and 0 !
6! 7hen the pol/nomial +(x) is divided ./ x2 x 2 and x3 , the
remainders are 3x2 and
3 , +ind the remainder -hen +(x) is divided ./ (x2 x 2 ) ( x 3 )
!
4! Solve
2 23 ' 3 3 2x x x x + =
(ans : , % )
1! Sho- that expression
2
2
3 %
3 %
x x
x x
+
+ +
lie .et-een 84 and 4 +or real values o+ x !
$! "ind the minimum (or maximum) value o+ 2x2 1x/ $/22x 21/ 3
and the values o+ x and
/ #orrespondin* to this minimum ( or maximum) !
! Solve the equation x% 2x3& x2& 2x & 1 , *iven that
the produ#t o+ t-o o+ its roots is 2 !
! 9+ x2& x & 6 is a +a#tor o+ +(x) x % mx3& 'x2 nx 6
, +ind the values o+ m and n , hen#e
+a#torise +(x) #ompletel/ ! ( ans : m 3 , n 3 )
2! iven that x / 0 ' , x/ /0 0x 2 , x/0 4 , +ind the values
o+
(i) x3 /3 03 (ii)
z x y
xy yz zx+ +
(iii) (x/) (/0) (0x )
3! Solve
2 2 2
3
2 3 %
2 2 3 6
x x y x y z
x y z x y z
+= =
+ + + =
7/25/2019 Senior Three Revision Midterm Kulai July
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%! Solve2 % 2 3x x+ + =
( ans : $86 )
'! "a#torise (. & #) (.#)3 ( # &a ) (#a)3 (a.) (a.)3
6! 7hen the pol/nomial +(x) is divided ./ x2&x 2 and x2 ,
the remainder are %x4 and x%
respe#tivel/ ! "ind the remainder -hen +(x) is divided ./ (x2 )
(x 2 ) ! (ans : 3x2 x )
4! Solve the equation x% 2x3& x22x & 1 , *iven that the
produ#t o+ t-o o+ its roots is 2 !
1! "a#torise
2
2
2
a.
a a bc
b b ac
c c
$! Sho- that
2 2
2 2
2 2
a ab b
b bc c
c ca a
(a2&.# ) (.2a) (#2&a.)
2! "ind the ratio x : / : 0 i+ 3x%/20 x 2/ 0 and x/0 ! ( ans : 1
: ' : 2 )
2! 9+
2 3
3 % 2
2 3
x y
x y
x y k
+ =
+ = + =
are #on#urrent , +ind the value o+ ; ! ( ans : ; ' )
22! "ind the real value o+ +or -hi#h
2
3
3
x y z
x y z
x y z
+ + =
+ + = + + =
, -here x , / , 0 are not all 0ero , are
#onsistent !
