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]