8/11/2019 STPM Trials 2009 Math T Paper 1 (Terengganu)
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Name:
a
8/11/2019 STPM Trials 2009 Math T Paper 1 (Terengganu)
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1. Show that for all real values of x, the function of82
422
2
++
=xx
xxy does not have values
between9
2and 2. [5]
2. Solve the equation 3110 = xx [6]
3. Using the definitions of set }:{ AxxA = and set }:{' AxxA , prove that''')( BABA = . Hence, simplify )()( ' BABA . [7]
4. Given that yx tan1tan += , finddx
dyin terms of x and y. Hence show that when
xyyxx 2,4
10++= where 0y is the value when
4
1=x . [7]
5. Find dxx
x
2
1
02
2
1 in terms of by using the substitution sin=x [7]
6. Find the distance from the point )6,5(A to the line 217 =+ yx . Hence find the equation of
the circle with centre )6,5(A which touches the line 217 =+ yx . Find also the coordinates
of the point of contact. [7]
7. The functions f and g are defined as
0,ln2: >xxxf
0,: xxxg
(i) Sketch the graph of f , and give a reason why the inverse function 1f exists.
(ii) Find1f , and state its domain.
(iii) Find the composite function1gf and state its range. [8]
8. Given that the quadratic equation 02 =++ cbxax has roots and . Show thata
b=+
and
a
c= . [4]
Find in terms of and the roots of the equation 0)2( 2222 =+ cyacbya [5]
9. The function f is defined by )1ln(3635: 2 + xxf and has domain 2x .
(a) Determine the value of x for which f is stationary. [4]
(b) The second derivative of )(xf is ).('' xf Find the range of '.'f [6]
8/11/2019 STPM Trials 2009 Math T Paper 1 (Terengganu)
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CONFIDENTIAL*
950/1, 954/1
*This question paper is CONFIDENTIAL until the examination is over.[ Turn over ]
CONFIDENTIAL*
10. a) Given that X =
ab
ba
0
010
0
, find a in terms of b if X is singular. [3]
b) If
=
541
213
421
A and ,
7611
10917
8613
=B find AB
Hence , solve the simultaneous equations138613 =+ rqp 2010917 =+ rqp
147611 =+ rqp [7]
11. Express( )( )2
2
212
141710
xx
xx
+
+in partial fractions in the form
( )221212 xC
x
B
x
A
+
++
.
Hence expand
( )( )
2
2
212
141710
xx
xx
+
+in ascending powers of x until the term in 2x .
State the range of values of x where the expansion is valid. [10]
12. State the asymptotes for the curvex
xy
+=
2. Hence sketch the curve. [3]
Find the area enclosed by the curve, the x-axis and the line x = 1 by usingi) trapezium rule with 5 ordinatesii) integrationGive your answer correct to 4 decimal places and calculate the percentage error in the
estimation when the trapezium rule is used. [8]
Find also the volume of the solid formed when this area is rotated completely about thex-axis. [3]
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