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SEKOLAH BERASRAMA PENUHBAHAGIAN PENGURUSAN
SEKOLAH BERASRAMA PENUH / KLUSTER
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2008
Kertas soalan ini mengandungi 15 halaman bercetak
For examiners use only
Question Total MarksMarks
Obtained
1 3
2 3
3 34 3
5 3
6 3
7 3
8 3
9 3
10 4
11 4
12 4
13 4
14 3
15 2
16 3
17 4
18 3
19 3
20 3
21 3
22 3
23 3
24 4
25 3
TOTAL 80
M A T E M A T I K T A M B A H A N
Kertas 1
Dua jam
J A N G A N B U K A K E R T A S SO A L A N IN I
S E H IN G G A D IB E R IT A H U
1 This quest ion paper consists of 25 quest ions.
2 . Answer a ll quest ions.
3. Give only one answer for each qu est ion.
4. Write your answers clearly in the spaces provided in
the quest ion paper.
5. Show yo ur working. I t may help you to get marks.
6. If you wish to change your answ er, cross out the work
that you have done. Then wri te down the newanswer .
7. The diagrams in the quest ions provided are not drawn to scale unless stated.
8. The marks al located for each quest ion and sub-part
of a quest ion are shown in brackets.
9. A l ist of formulae is provided on pages 2 to 3.
10. A bo oklet of four- f igure m athematical tables isprovided.
.11 You may use a n on-programm able scient if ic
calculator.
12 This quest ion paper must be handed in at the end of
the examinat ion .
Name : ..
Form : ..
3472/1
Matematik Tambahan
Kertas 1
Ogos 2008
2 Jam
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The following formulae may be helpful in answering the questions. The symbols given are the onescommonly used.
ALGEBRA
1
24
2
b b acx
a
=
2 am an = a m + n
3 am an = a m - n
4 (am)
n= a
nm
5 loga mn = log am + loga n
6 logan
m= log am - loga n
7 log a mn = n log a m
8 logab =a
b
c
c
log
log
9 Tn = a + (n-1)d
10 Sn = ])1(2[2
dnan
+
11 Tn = arn-1
12 Sn =r
ra
r
ra nn
=
1
)1(
1
)1(, (r 1)
13r
aS
=
1, r
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3
STATISTIC
1 Arc length, s = r
2 Area of sector ,L = 212
r
3 sin2A + cos
2A = 1
4 sec2A = 1 + tan
2A
5 cosec2A = 1 + cot
2A
6 sin 2A = 2 sinA cosA
7 cos 2A = cos2A sin
2A
= 2 cos2A - 1
= 1 - 2 sin2A
8 tan 2A =A
A2
tan1
tan2
TRIGONOMETRY
9 sin (A B) = sinA cosB cosA sinB
10 cos (A B) = cosA cosB sinA sinB
11 tan (A B) =BA
BA
tantan1
tantan
m
12C
c
B
b
A
a
sinsinsin==
13 a2
= b2
+ c2
- 2bc cosA
14 Area of triangle = Cabsin2
1
1 x =N
x
2 x = f
fx
3 =N
xx 2)(=
2_2
xN
x
4 =
f
xxf 2)(=
22
xf
fx
5 m = Cf
FN
Lm
+ 2
1
6 1
0
100Q
IQ
=
71
11
w
IwI
=
8 )!(
!
rn
n
Prn
=
9!)!(
!
rrn
nC
r
n
=
10 P(AB) = P(A)+P(B)- P(A B)
11 P (X= r) =rnr
r
n qpC , p + q = 1
12 Mean = np
13 npq=
14 z =
x
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2
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Answer all questions.
1. A functionfmaps the elements from set { 3, 4, 9,16, 25}P m=
to set Q = { 0, 3, 8, 15, 24 } as shown below in ordered pairs :
{ ( 3m , 0), (4, 3), (9, 8), (16, 15), (25, 24) }(a) Write down the function notation forf.
(b) State the value ofm.
(c) State the codomain.
[ 3 marks ]
Answer: ( a )..
( b )......
( c )..................................
2. Given that function : 3, 0f x ax a < and 2 : 16f x x b , find the value ofa and ofb.
[ 3 marks ]
Answer: a =.
b =..............................3
2
3
1
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4
3. Given that function : 3 , 0k
f x xx
, and 1 4: ,f x x hx h
+
, find the value ofh
and of k.
[ 3 markah ]
Answer: h =.........
k=.....................................
4. Given m and -3 are the roots of a quadratic equation 22 4 1x x k = , find the valueofm and ofk.
[ 3 marks ]
Answer: m =.........
k =.....................
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4
3
3
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5. Given that quadratic equationx(3x p) = 2x 3 has no roots, find the range of values
ofp.
[ 3 marks ]
Answer: .................................
___________________________________________________________________________
6. Diagram 1 shows the graph of a curve qpxxf ++= 2)(2)( , wherepand q are constants.
Diagram 1
Given the straight line 3=x is the axis of symmetry of the curve and parallel to they-axis. Find
(a) the value ofp,
(b) the value ofq,
(c) the turning point of the curve )(xf .
[3 marks]
Answer: (a) .........................
(b) ........................
(c)..................................
3
5
3
6
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x
qpxxf ++= 2)(2)(
8
O
3=x
f(x)
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6
7. Find the range of the values of x for which )52(2)12(3 + xxx .[3 marks]
Answer: ..................................
8. Solve the equation 23
2
1
8 +
= xx
.
[3 marks]
Answer: . ..................................
9. Solve the equation xx 2log1)25(log 55 = .[3 marks]
Answer: ....................................
7
3
9
3
8
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10. Given that 2log2log 927 = qp , expressp in terms ofq.[4 marks]
Answer: .........
11. An arithmetic progression has 9 terms. The sum of the first four terms is 24 and the
sum of all the odd number terms is 55. Find
a) the first term and the common difference,
b) the seventh term.
[4 marks]
Answer: ( a )............
( b).....................................
10
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11
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8
12. For a geometric progression, the sum of the first two terms is 30 and the third
term exceeds the first term by 15. Find the common ratio and the first term
of the geometric progression.
[4 marks]
Answer: .............___________________________________________________________________________
13. Diagram 2 shows the graph ofxy against2x .
The variablesx andy are related by the equationx
kxy +=2 , where kis a
constant. Find the value ofh and ofk.[4 marks]
Answer: h = .
k = ......4
13
4
12
For
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(0 , h)
2x
(7 , 2)
O
xy
Diagram 2
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14. In Diagram 3 below, the equation of straight lineLM is 6
x1
4=
y. The points
L and M lie on thex-axis andy-axis respectively.
Find the equation of a straight line which is perpendicular toLMand passes
through the pointM.
[3 marks]
Answer : .
15. In Diagram 4, OA a
= and OB b
= . On the same square grid , draw the line that
represents the vector 3OC a b = + .[ 2 marks ]
2
15
3
14
For
examiners
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x
y
0
M
L
Diagram 3
O
A
B
Diagram 4
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10
16. Given (2, 5), (3, 4)A B and ( , )C p q . Find the values ofp and q such that
~ ~
2 9 5AB BC i j
= .
[3 marks]
Answer: ......
___________________________________________________________________________
17. Solve the equation 3sin2cos4 =+ xx for 3600 x .
[4 marks]
Answer: ............4
17
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18. Diagram 5 shows a sectorBOCof a circle with centre O.
Given the perimeter of the sectorBOCis 24.5 cm, calculate
(a) the radius of the sector
(b) the area of the sector.
[3 marks]
Answer: a)...
b) .
___________________________________________________________________________
19. Given3
)35(
2)(
xxf
= , find the value of (2)f .
[3 marks]
Answer:
3
19
3
18
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B
O
C
0.45 rad
Diagram 5
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20. Find the equation of normal to the curve xxy 53 += at the point when 1=x .
[ 3 marks ]
Answer: ............
___________________________________________________________________________
21. Given that
=
2
5
6)( dxxf , calculate dxx
xf
5
2 4
)( .
[3 marks]
Answer: ..
22. It is given that the sum of 5 numbers is . The mean of the sum of the square is 200and the variance is 3 2 . Express in terms of .
[3 marks]
Answer: ..
3
20
3
21
3
22
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23. A pack of present containing three pens are chosen from 4 blue pens and 5 black pens.
Find the probability of getting at least one black pen in the pack of present.
[3 marks]
Answer: ............
___________________________________________________________________________
24.
Diagram 6
Diagram 6 shows six cards of different letters.
(a) Find the number of possible arrangements beginning with P.
(b) Find the number of these arrangements in which the vowels are separated.
[ 4 marks ]
Answer: ( a )
( b )
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4
24
3
23
P O L I T E
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25. Xis a random variable which is normally distributed with mean and standard
deviation of 6. Find
(a) the value of , if thez-value is 1.5 whenx = 42,
(b) P(X < 47 ).
[3 marks ]
Answer: ( a)............
( b )...................................
END OF QUESTION PAPER
3
25
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