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[ Lihat sebelah
3472/1 SULIT
PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA
SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA
DENGAN KERJASAMA
JABATAN PELAJARAN MELAKA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2010
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Kertas soalan ini mengandungi 18 halaman bercetak
Nama : ....
Tingkatan: ..3472/1
Matematik Tambahan
Kertas 1
Sept 2010
2 jam
1. This question paper consists of25 questionsKertas soalan ini mengandungi 25 soalan.
2. Answer all questions.Jawabsemua soalan.
3.Give only one answer for each questionBagi setiap soalan berikan SATU jawapan sahaja.
4. Write the answers clearly in the space provided in the question paper.Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan.
5. Show your working. It may help you to get marks.Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh
membantu anda untuk mendapatkan markah.
6. If you wish to change your answer, cross out the work that
you have done. Then write down the new answer.Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telah
dibuat. Kemudian tulis jawapan yang baru.
7 The diagram in the questions provided are not drawn to scale unless
stated.Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinyatakan.
8. The marks allocated for each question and sub-part of a question areshown in brackets.Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan
dalam kurungan.
9.A list of formulae is provided on page 2 to 3Satu senarai rumus disediakan di halaman 2 hingga 3
10. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh
diprogram.
11.This question paper must be handed in at the end of the examination.Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan .
Kod
Pemeriksa
SoalanMarkah
Penuh
Markah
Diperoleh
1 2
2 2
3 4
4 3
5 3
6 37 3
8 4
9 3
10 4
11 4
12 4
13 3
14 3
15 4
16 3
17 418 3
19 3
20 3
21 3
22 3
23 3
24 3
25 3
Jumlah80
MATEMATIK TAMBAHAN
Kertas 1
Dua Jam
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2
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly
used.Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yang biasa
digunakan.
ALGEBRA
1
2 4
2
b b acx
a
2 am an= a m + n
3 am an = a m - n
4 (am)
n= anm
5 logamn = log am + logan
6 loganm = log am - logan
7 log amn
= n log am
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
rann
1
)1(
1
)1(, (r 1)
13r
aS
1
, r
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SULIT 2STATISTICS
1 Arc length, s = r( Panjang lengkok) s = j
2 Area of sector ,L = 21
2r
(Luas sektor L = 22
1j )
3 sin2A + cos
2A = 1
4 sec2A = 1 + tan
2A
5 cosec2A = 1 + cot
2A
6 sin 2A = 2 sinA cosA
7 cos 2A = cos2Asin
2A
= 2 cos2A - 1
= 1 - 2 sin2A
8 tan 2A =A
A2
tan1
tan2
TRIGONOMETRY
9 sin (AB) = sinA cosB cosA sinB
10 cos (AB) = cosA cosB sinA sinB
11 tan (AB) =BtanAtan
BtanAtan
1
12C
c
B
b
A
a
sinsinsin
13 a2 = b2 + c2 - 2bc cosA
14 Area of triangle = Cabsin2
1
( Luas Segitiga )
1 x =N
x
2 x = f
fx
3 =N
xx 2)(=
2_2
xN
x
4 =
f
xxf2)(
=2
2
xf
fx
5 m = Cf
FN
Lm
2
1
6 1
0
100Q
IQ
71
11
w
IwI
8 )!(
!
rn
n
Prn
9!)!(
!
rrn
nCr
n
10 P(A B) = P(A)+P(B)- P(A B)
11 P (X= r) = rnrr
nqpC
, p + q = 1
12 Mean = np
13 npq
14 z =
x
3
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SULIT 4
Answer all questions.
Jawab semua soalan
1 Diagram 1 shows the relation between two sets of number .Rajah 1 menunjukkan satu hubungan diantara dua set nombor.
Diagram 1Rajah 1
Based on the above information, the relation between P and Q is defined by the set
of ordered pairs { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.Berdasarkan maklumat diatas hubungan antara P dan Q ditarifkan sebagai set pasangan
tertib { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.
State,Nyatakan,
(a) the image of 2.imej bagi 2
(b) the object of 0.imej bagi 0
[2 marks][ 2 markah ]
Answer/Jawapan: (a) ..
(b) ...
2 Given the function g :x x2
+1 , find the values of g-1
(10)Di beri g :x x
2+1 . Cari nilainilai bagi g
-1(10)
[ 2 marks ][ 2 markah ]
Answer/Jawapan: ......2
2
For
examiners
use only
P ={ -3, -2, -1, 0, 1, 2 }
Q ={ -1, 0, 1, 2, 3 }
2
1
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SULIT
3 The functionfis defined by f:x kx2
+p and the function g is defined by g:x1 + 2x.
Given the composite function fg :xx2
+ x + 6, find the values of kandp.
Fungsifditakrifkan sebagaif: x kx2
+ p dan fungsi g ditarifkan sebagai g: x 1+ 2x
Diberi fungsi gubahanfg : x x2 + x + 6, cari nilai k dan nilaip
[4 marks]
[ 4 markah]
Answer/ Jawapan : k =....p=
4 Given thatp
1is one of the roots of the quadratic equation px
2+ 7x 2p = 0, find the values ofp.
Diberi bahawap
1ialah salah satu punca bagi persamaan kuadratikpx
2+ 7x 2p = 0, cari nilai-nilai
bagip
[ 3 marks ][ 3 markah ]
Answer /Jawapan: ....
For
examiners
use only
4
3
3
4
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6 Find the range of values ofx for which 27)6( xx .
Cari julat nilai- nilai x dimana 27)6( xx
[3 marks][ 3 markah]
Answer/Jawapan: ................................
7 Solve the equation 02781 321 xx .
Selesaikan persamaan 02781 321 xx [ 3 marks ]
[ 3 markah]
Answer /Jawapan: x = ...
8 Given log7 2 = h and log7 5 = k. Express log7 2.8 in terms of h and k.Diberi log7 2 = h dan log7 5 = k. Ungkapkan log7 2.8 dalam sebutan h dan k.
[ 4 marks ]
[ 4 markah ]
Answer /Jawapan : = .................................
For
examiners
use only
4
8
3
6
3
7
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SULIT 8
9 Solve 1)1(log)4(log 33 xx
Selesaikan 1)1(log)4(log 33 xx
[3 marks][ 3 markah]
Answer/Jawapan: ..........
10 The first three terms of an arithmetic progression are 6, t 2, 14,....Tiga sebutan pertama satu janjang arithmatik ialah 6, t 2, 14,....
find,cari,
(a) the value of t,nilai t
(b) the sum of the first ten term .hasil tambah sepuluh sebutan pertama
[ 4 marks ][ 4 markah ]
Answer /Jawapan: (a)......
(b) .............
11 The sum of the first nterms of the geometric progression, 64, 32, 16, .. is 126.Hasil tambah nsebutan pertama suatu janjang geometri, 64, 32, 16, .. ialah 126
Find,
Cari,
(a) the value ofn,nilai n
(b) the sum to infinity of the geometric progression.hasiltambah ketakterhingaan janjang geometri ini,
[ 4 marks ]
[ 4 markah]
Answer/Jawapan: (a) n = .
(b).
4
10
For
examiners
use only
3
9
4
11
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12 x andy are related by the equationm
x nyx
, where m and n are constants.
A straight line is obtained by plottingxy againstx2, as shown in Diagram 12 .
x dany dihubungkan oleh persamaanm
x nyx
, dimana m dan n ialah pemalar.
Satu garislurus diperolehi dengan memplotkan xy melawan x2, sebagaimana ditunjukkan
dalam Rajah 12
Calculate the value ofm and ofn.Kira nilai m dan nilai n
[4 marks][ 4 markah]
Answer/Jawapan: m=
n =.....
4
12
For
examiners
use only
xy
(12, 2 )
( 6, 0) x
2
Diagram 12Rajah 12
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SULIT 10
13 Given that the point P 3,2 divides the line segment that joining ),4( tA and )8,(rB inthe ratio AP : PB = 1 : 4. Find the value ofrand of t.
Diberi bahawa titik P 3,2 membahagi segmen garis yang menghubungkan),4( tA dan )8,(rB dalam nisbah AP : PB = 1 : 4. Cari nilai r dan nilai t.
[3 marks][3 markah]
Answer/Jawapan: ..
14 Given that 2 2a i j , 2 3b i j and 2c a b .
Diberi bahawa 2 2a i j , 2 3b i j dan 2c a b .
Find,
Cari,
(a) c
(b) unit vector in the direction ofc .
vektor unit dalam arah c
[3 marks][3 markah]
Answer: (a)
(b) ...
For
examiners
use only
3
13
3
14
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15 Diagram 15 shows a triangle POQRajah 15 menunjukkan segitiga POQ
Diagram 15Rajah 15.
Given that OP
= p and OQ
= q .PointX is lies on OP where OX:XP = 2 : 1 and point Y
is lies on OQ where OY: YQ = 3 : 1 . Straight line QXand line PYintersect at point C.
Diberi OP
= p dan OQ
= q . TitikX terletak pada OP di mana OX:XP = 2 : 1 dan titikYadalah
titik pada OQ di mana OY: YQ = 3 : 1 . Garis lurus QXdan garis lurus PY bersilang pada titikC.
Express in terms of p and q
Ungkapkan dalam sebutan p dan q
(a) PY
(b) QX
[ 4 marks]
[4 markah]
Answer/Jawapan: (a) ..............................................
(b) ..............................................
O PX
C
Y
Q
4
15
For
examiners
use only
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SULIT 12
16 Given that is an acute angle andq
psin , find in terms ofp and /or q
Diberi bahawa ialah sudut tirus dan
q
psin , cari dalam sebutanp dan/atau q
a) cos kos
b) tan ( 180 - )[3 marks]
[ 3 markah ]
Answer /Jawapan (a) .......................................
(b).......................................
17 Solve 3cos 2 + 4 cos +1 = 0 for 00 3600
Selesaikan 3cos 2 + 4 cos +1 = 0 untuk00 3600
[4 marks][4 markah]
Answer/Jawapan: ...........
4
17
For
examiners
use only
3
16
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SULIT
A
C
R
S
OB 1.6
8 cm
18 Diagram 18 shows a circleABC with centre O, of radius 8 cm. SR is an arc of
a circle with center O. The reflex angleAOCis 1.6 radian.
Rajah 18 menunjukkan satu bulatanABC dengan pusat O dan berjejari 8 cm, SR ialah
lengkuk sebuah bulatan berpusat di O . Sudut reflekAOC ialah 1.6 radian.
Given thatA and C are midpoints ofOS and OR respectively, find the area of shaded
region, in terms of .Diberi bahawa A dan C ialah titik tengah kepada OS dan OR , cari luas kawasan berlorek
dalam sebutan
[ 3 marks][ 3 markah ]
Answer / Jawapan : . cm2
19 The radius of circle decreases at the rate of 10.5cms . Find the rate of change of the
area of a circle when the radius is 4 cm. .[ Given the area of a circle is A= r2
]Jejari sebuah bulatan berkurang dengan kadar 0.5 cms-1.Cari kadar perubahan luas
bulatan apabila jejarinya ialah 4 cm, [ Diberi luas bulatan A= r2]
[ 3 marks][ 3 markah]
Answer/Jawapan:
For
examiners
use only
3
19
3
18
Diagram 18Rajah 18
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SULIT 14
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20 Given that
5
1
( ) 5g x dx , find the value of m if5
1
[ 2 ( )] 3mx g x dx m
Diberi bahawa
5
1
( ) 5g x dx , cari nilai m jika5
1
[ 2 ( )] 3mx g x dx m
[ 3 marks ]
[ 3 markah ]
Answer / Jawapan :................................................
21 A set of numbers 1 2 3 4, , , ,..., nx x x x x has a median of 5 and a standard deviation of 2.
Find the median and the variance for the set of numbers
1 2 36 1,6 1,6 1,.......,6 1n x x x x .
Satu set nombor 1 2 3 4, , , ,..., nx x x x x mempunyai median 5 dan sisihan piawai 2.
Cari median dan variance bagi set nombor 1 2 36 1,6 1,6 1,.......,6 1n x x x x .
[ 3 marks ][ 3 markah]
Answer/Jawapan : median = ..
variance =...
For
xaminers
use only
3
20
3
21
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SULIT 15
[Lihat sebelah
3472/1 SULIT
22 A box contains 6 black balls andp white balls. If a ball is taken out randomly from the
box, the probability of getting a white ball is7
4. Find the value ofp.
Sebuah kotak mengandungi 6 biji bola hitam danp biji bola putih . Jika sebiji bola diambil
secara rawak dari kotak itu kebarangkalian mendapat sebiji bola putih ialah 7
4
. Cari nilai p.
[ 3 marks ][3 markah]
Answer/Jawapan: ............
23 An expedition team consisting of 10 members to be chosen from a group of 4 teachers
and 12 students.Satu kumpulan ekspedisi mengandungi 10 ahli yang akan dipilih daripada kumpulan 4
orang guru dan 12 orang pelajar.
(a) Calculate the number of teams that can be formed.Kira bilangan kumpulan yang boleh dibentuk .
(b) If the team must consist of at least 2 teachers, calculate the numbers of teams thatcould be formed.Jika kumpulan ekspedisi itu mesti mengandungi sekurang-kurangnya 2 orang guru kira
bilangan kumpulan yang boleh dibentuk.
[3 marks][ 3 markah]
Answer/ Jawapan: (a) .......
(b) ..................................
For
examiners
use only
3
23
3
22
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SULIT 16
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24 In a survey, the probability that a family having one unit of computer is 0.6.
Nfamilies were selected at random. The standard deviation of the numbers of
family having one unit of computer is5
24
Dalam satu tinjauan , kebarangkalian sebuah keluarga mempunyai satu unit komputer
ialah 0.6. N keluarga dipilih secara rawak . Sisihan piawai keluarga yang mempunyai
komputer ialah5
24
Find,
Cari,
(a) the value ofNnilai N
(b) the mean of the numbers of family having one unit of computer.min keluarga yang mempunyai satu unit komputer
[3 marks][ 3 markah]
Answer/Jawapan: (a) ..
(b) ........................................
3
24
For
xaminers
use only
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SULIT 17
[Lihat sebelah
3472/1 SULIT
25 Diagram 25 shows a standard normal distribution graph.Rajah 25 menunjukkan graf taburan normal piawai
The probability represented by the area of the shaded region is 0.803.Kebarangkalian yang diwakili oleh kawasan berlorek ialah 0.803
(a) Find the value of P( Z > k)Cari nilai P( Z > k)
(b)X is a continuous random variable which is normally distributed with a mean of
and a standard deviation of 2. If the value ofXis 85 when the Z-score is k,
find the value of .
Xialah pembolehubah rawak selanjar yang bertabur secara normal piawai dengan min
dan sisihan piawai 2. Jika nilaiXialah 85 bila skor- Z ialah k, cari nilai .
[3 marks][ 3 markah]
Answer: (a)
(b) .
END OF THE QUESTION PAPER
KERTAS SOALAN TAMAT
3
25
For
examiners
use only
-k k z
f(z))
0.803
Diagram 25Rajah 25
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3472/1 SULITSULIT
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SULIT 19
[Lihat sebelah
3472/1 SULIT
3472/1
Additional
Mathematics
Paper 1
Sept
2010
PERSIDANGAN KEBANGSAAN
PENGETUA-PENGETUA
SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA
DENGAN KERJASAMA
JABATAN PELAJARAN MELAKA
PEPERIKSAAN PERCUBAANSIJIL PELAJARAN MALAYSIA 2010
ADDITIONAL MATHEMATICS
Paper 1
MARKING SCHEME
This marking scheme consists of 5 printed pages
PAPER1
QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
1
(a) 3
(b) -1
1
1
2
2
3 , - 3
x2
+1 = 10 or 11 xg
2
B1
2
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SULIT 20
3472/1 SULIT
QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
3
4
23
4
1 pandk
4
23
4
1 pork
614 pkork
pxk 2)21(
4
B3
B2
B14
4
2 , -2
028
pp
02)1
(7)1
( 2 ppp
p
3
B2
B1
3
5
a) -4
b) 2
c) x = 4
1
1
1
3
6
3 9x
2
( 9)( 3) 0
6 27 0
x x
x x
3
B2
B1
3
72
13x
4 4 6 9x x
033 )32(3)1(4 xx
3
B2
B1 3
8
7 7 7
7 7
7
1
log 2 log 7 log 5
log 2 log 7
28log
10
h k
4
B3
B2
B1
4
9
1
4log
31
4
3
3x
x
x
x
x
3
B2
B1
3
10 a) t = 12t8 = 16t
2B1
-3 9o
or -3 and 9
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SULIT 21
[Lihat sebelah
3472/1 SULIT
QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
b) 240
10[(2(6) 9(4)]
2
2
B1 4
11
a) n = 6
5.01
)5.01(64126
n
b) 128s
5.01
64
s
2
B1
2
B1
4
12
m = -6 and n = 3
m = -6 or n = 3
n
m
n
60 and
n
m
n
122
n
m
n
60 or
n
m
n
122
4
B3
B2
B1
4
13
r= 6 and7
4t
4
7t or r= 6
5
)4(4
2
r
or 5
84
3
t
3
B2
B1
3
14 (a)10
6 8i j
b) )43(5
1ji
2
B1
1
3
15(a) PY
= p +
3
4q
PY = OQPO 4
3
(b) QX
= -q +2
3p
QX
= OPQO
3
2
2
B1
2
B1
4
16
a) q
pq22
1
2
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SULIT 22
3472/1 SULIT
QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
b) -22
pq
p
22pq
p
B1
3
17 70.53 ,180 , 289.47
B3: 70.53 ,180
B2 : ( 3 cos -1)(cos +1)=0
B1: 2 cos2
-1
4
B3
B2
B1
4
18
2 2
38.4
1 116 0.4 8 0.4
2 2
2 21 116 0.4 8 0.4
2 2or
3
B2
B1
3
19 4
2 (4)( 0.5)
2
dA
rdr
3
B2
B1
3
20 2
3
B2:2 25 1
[ ] 10 32 2
m m
B1:
5 52
1 1
2 ( )2
mxor mx dx g x dx
3
B2
B1 3
21
2
2
31 var 144
6(5) 1 6 (4)
6(5) 1 6 (4)
median and iance
and
or
3
B2B1
3
22
p
p
p
p
p
6
7
4
6
8
3
B2
B1
3
or - 12.57
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SULIT 23
[Lih b l h
QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
23 (a) 8008
(b) 7062
B1:4 12 4 12 4 12
2 8 3 7 4 6C C C C C C Or4 12 4 12
1 9 0 108008 C C C C
3
2
B1 3
24 (a)20
B1 : )4.0)(6.0(N =5
24
(b)12
2
B1
1
3
25 (a)0.0985
(b)82.42
B1:85
1.292
or
1
2
B1
3
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