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SMK PENDING KUCHING
SUMMATIVE ASSESSMENT 1
MATHEMATICS T
UPPER 6 SCIENCE 2016
Answer all questions. (60 marks)
Answers may be written in either English or Bahasa Malaysia. All
necessary working should be
shown clearly. Scientific calculators may be used. Programmable
and grahics dislay calculators are rohibited.
!. Sketch the grah of the function k " where
( )
>+−≤−
=#"$#
#"#$
$
x x x
x x x xk
%ind( ) xk
x −→#lim
and( ).lim
#
xk x
+→
&ence"show that k is not continuous at oint
.#= x ' marks
*etermine whether k is continuous at oint .+= x
'# marks
$. A cur,e is defined by the arametric equations"
!-
! # −= t x and
.$
!t y =
f the normal to the cur,e at the oint where at =
meets the y/a0is at the oint ( )"1"+ P
show
that .+(2-!$# $( =−+− aaa '2 marks
#. 3i,en that"+"
sin$
>= x x
x y
ro,e that( ) .+$- $
$
$
$ =+++ y xdx
dy x
dx
yd x
' marks
-. 4sing integration by arts" show that∫ −=-
$.#$ln!-ln dx x x
'2 marks
. E0ress $
$
- x
x
− in artial fractions.
&ence" show that"ln
-
!
+ $
$
nmdx x
x−=
−∫ stating the ,alues of m and n. '!+ marks
2. %ind the oint of intersection of the cur,e xe y
$−= and the line .e y = &ence"
show that the
area bounded by the cur,e" e y = and
the y-a0is is.
$
!
5alculate also the ,olume of the solid
formed when the bounded area is rotated about the x/a0is.
'!+ marks
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1. 3i,en that the cur,e.
-#
#$
$
−−
−=
x x
x x y
(a) State equations of the asymtotes. '- marks
(b) %ind the coordinates of the turning oints. ' marks
(c) Show that the region where the grah does not e0ist is.!
$(
6
≤< y '- marks(d) &ence" sketch the cur,e. '$
marks
END OF THE QUESTION PAPER
MATHEMATICAL FORMULAE
Differentiation
•
( )$
!
!
!sin
x x
dx
d
−=−
•
( )$
!
!
!tan
x x
dx
d
+=−
•
( ) ( )[ ] ( ) ( ) ( ) (
) x g x f x g x f x g x f dx
d ′+′=
•
( )
( )
( ) ( ) ( ) ( )
( )[ ] $ x g
x g x f x g x f
x g
x f
dx
d ′−′=
•
( )$
!
!
!cos
x x
dx
d
−
−=−
•
