spm trial 2010 addmath q&a (melaka)
TRANSCRIPT
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SULIT
[ 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 are
shown 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 bolehdiprogram.
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 3
7 3
8 4
9 310 4
11 4
12 4
13 3
14 3
15 4
16 3
17 4
18 3
19 3
20 3
21 322 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
12 4
2
b b acx
a r
2 am u an = a m + n
3 am y an = a m - n
4 (am) n = a
nm
5 logamn = log am + logan
6 logan
m= log am - logan
7 log amn = n log am
8 logab =ab
c
c
loglog
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(, (rz 1)
13r
aS
f 1, r
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SULIT 2STATISTICS
1 Arc length, s = rT
( Panjang lengkok) s = j T
2 Area of sector ,L = 21
2rT
( Luas sektor L = T22
1j )
3 sin2A + cos
2A = 1
4 sec2A = 1 + tan
2A
5 cosec2A = 1 + cot2A
6 sin 2A = 2 sinA cosA
7 cos 2A = cos2A sin
2A
= 2 cos2A - 1
= 1 - 2 sin2A
8 tan 2A =A
A2tan1
tan2
TRIGONOMETRY
9 sin (ArB) = sinA cosB r cosA sinB
10 cos (ArB) = cosA cosB # sinA sinB
11 tan (ArB) =BtanAtan
BtanAtan
#1
r
12C
c
B
b
A
a
sinsinsin
13 a2
= b2
+ c2
- 2bc cosA
14 Area of triangle = Cabsin
2
1
( Luas Segitiga )
1 x =N
x
2 x =
f
fx
3 V =N
xx 2)(=
2_2
xN
x
4 V =
f
xxf 2)(=
22
xf
fx
5 m = Cf
FN
Lm
2
1
6 1
0
100Q
IQ
u
71
11
w
IwI
8)!(
!
rn
nP
r
n
9!)!(
!
rrn
nC
r
n
10 P(AB) = P(A)+P(B)- P(AB)
11 P (X= r) = rnrr
n qpC , p + q = 1
12 Mean = np
13 npqV
14 z =V
Px
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 pasangantertib { (-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 nilai nilai 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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3 The functionfis defined by f:x okx2 +p and the function g is defined by g:xo1 + 2x.Given the composite function fg :xox2 + x + 6, find the values of kandp.Fungsifditakrifkan sebagaif: x okx
2+ p dan fungsi g ditarifkan sebagai g: x o1+ 2x
Diberi fungsi gubahanfg : x ox2
+ 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
4
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SULIT 6
( 4, q )
5 Diagram 5 shows the graph of a quadratic functionf(x) = 3(x +p)2 + 2, wherep
is a constant. The curve y =f(x) has the minimum point (4, q), where q is a constant.Rajah 5 menunjukkan graf fungsi kuadratikf(x) = 3(x +p)
2 + 2 , dimana p ialah pemalar
Lengkung y =f(x) mempunyai titik minimum (4, q), dimana q ialah satu pemalar.
State,Nyatakan,
(a) the value ofp, nilai p
(b) the value ofq, nilai q
(c) the equation of the axis of symmetry.persamaan paksi semetri
[ 3 marks ][ 3 markah]
Answer: (a) ........................
(b) ........................
(c)..................................
For
examiners
use only
5
Diagram 5Rajah 5
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6 Find the range of values ofx for which 27)6( dxx .
Cari julat nilai- nilai x dimana 27)6( dxx
[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
examiner
use only
8
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 n terms of the geometric progression, 64, 32, 16, .. is 126.Hasil tambah n sebutan 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
examiner
use only
xy
x (12, 2 )
x ( 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
13
14
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15 Diagram 15 shows a triangle POQRajah 15 menunjukkan segitiga POQ
Diagram 15Rajah 15.
Given that OPo
= p and OQo
= 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 OPo = p dan OQo = 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) PYo
(b) QXo
[ 4 marks]
[4 markah]
Answer/Jawapan: (a) ..............................................
(b) ..............................................
O PX
C
Y
Q
4
15
For
examiner
use only
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SULIT 12
16 Given that T is an acute angle andq
pTsin , find in terms of p and /orq
Diberi bahawa T ialah sudut tirus danq
pTsin , cari dalam sebutanp dan/atau q
a) cos T kosT
b) tan ( 180 - T)
[3 marks][ 3 markah ]
Answer /Jawapan (a) .......................................
(b) .......................................
17 Solve 3cos 2T + 4 cos T +1 = 0 for
00
3600dd
T Selesaikan 3cos 2T + 4 cos T +1 = 0 untuk 00 3600 ddT
[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 S
8 cm
18 Diagram 18 shows a circleABC with centre O, of radius 8 cm. SR is an arc ofa circle with centerO. The reflex angleAOCis 1.6S radian.
Rajah 18 menunjukkan satu bulatanABC dengan pusat O dan berjejari 8 cm, SR ialah
lengkuk sebuah bulatan berpusat di O . Sudut reflekAOC ialah 1.6S radian.
Given thatA and C are midpoints ofOS and OR respectively, find the area of shadedregion, in terms ofS .Diberi bahawa A dan C ialah titik tengah kepada OS dan OR , cari luas kawasan berlorek
dalam sebutan S
[ 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
examiner
use only
19
3
18
Diagram 18
Rajah 18
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SULIT 14
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20 Given that5
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 1nx x x x .
Satu set nombor1 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 1nx x x x
.
[ 3 marks ][ 3 markah]
Answer/Jawapan : median = ..
variance =...
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examiners
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20
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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 ialah7
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 teachersand 12 students.Satu kumpulan ekspedisi mengandungi 10 ahli yang akan dipilih daripada kumpulan 4orang 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
22
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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
P and a standard deviation of 2. If the value ofXis 85 when the Z-score is k,
find the value of P.
Xialah pembolehubah rawak selanjar yang bertabur secara normal piawai dengan min
P dan sisihan piawai 2. Jika nilaiXialah 85 bila skor- Z ialah k, cari nilai P .
[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 25
Rajah 25
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SULIT 18
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SULIT 3472/2
[ Lihat sebelah
3472/2 SULIT
3472/2
Matematik
Tambahan
Kertas 2
Sept
2010
2 jam
PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA
SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA
DENGAN KERJASAMA
JABATAN PELAJARAN MELAKA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2010
MATEMATIK TAMBAHAN
Kertas 2
Dua jam tiga puluh minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. This question paper consists of three sections : Section A, Section BandSection CKertas soalan ini mengandungi tiga bahagian : Bahagian A, Bahagian B dan Bahagian C.
2. Answer all questions in Section A, four questions from Section B and two
questions from Section C.Jawab semua soalan dalam Bahagian A, empat soalan daripada Bahagian B, dan dua soalan
daripada Bahagian C.
3. Give only one answer/solution to each question.
Bagi setiap soalan, berikan satu jawapan / penyelesaian sahaja.4. 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.
5. The diagrams in the questions provided are not drawn to scale unless stated. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan,
6. The marks allocated for each question and sub-part of a question are shown in
bracketsMarkah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan.
7. A list of formulae is provided on pages 2 and 3.Satu senarai rumus disediakan di halaman 2 dan 3.
8. A booklet of four-figure mathematical tables is provided.Buku sifir matematik empat angka boleh digunakan.
9. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.
Kertas soalan ini mengandungi 17 halaman bercetak
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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
42
b b acxa
r
2 am u an = a m + n
3 am y 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(, (rz 1)
13
r
aS
f1
, r
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SULIT
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SULIT
3
STATISTICS ( STATISTIK)
1 Arc length , s = rT
(Panjang lengkok, s = jT)
2 Area of sector ,A =21
2rT
(Luas sektor , L =21
2j T )
3 sin2A + cos
2A = 1
4 sek2A = 1 + tan2A
5 cosec2A = 1 + cot2A
6 sin2A = 2 sinAcosA
7 cos 2A = cos2A sin2A= 2 cos2A-1= 1- 2 sin
2A
8 tan2A =A
A2
tan1
tan2
TRIGONOMETRY
9 sin (ArB) = sinAcosB r cosAsinB
(sin (ArB) = sinAkosB r kosAsinB)
10 cos (ArB) = cosAcosB # sinAsinB(kos (ArB) = kos AkosB # sinAsinB )
11 tan (ArB) =BA
BA
tantan1
tantan
#
r
12C
c
B
b
A
a
sinsinsin
13 a2
= b2
+c2
- 2bc cosA
( a2 = b2 +c2 - 2bckosA )
14 Area of triangle ( Luas segitiga) = Cabsin2
1
1 x =N
x
2 x = f
fx
3 V =N
xx 2)(=
2_2
xN
x
4 V =
f
xxf2
)(=
22
xf
fx
5 m = Cf
FN
Lm
2
1
6 1
0
100Q
IQ
u
71
11
w
IwI
8 )!(
!
rn
n
Prn
9!)!(
!
rrn
nC
r
n
10 P(AB)=P(A)+P(B)-P(AB)
11 P(X=r) = rnrr
n qpC , p + q = 1
12 Mean, = np
13 npqV
14 z =V
Px
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SULIT
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SULIT
Section A
[40 marks]
[ 40 markah]Answerall questions in this section .
Jawabsemua soalan dalam bahagian ini.
1 Solve the following simultaneous equations:
Selesaikan persamaan serentak berikut
284 2 nmmnm[5 marks]
[5 markah]
2 Solution by scale drawing will not be acceptedPenyelesaian secara lukisan berskala tidak diterima.
Diagram 2 shows the rhombusABCD with vertexA( -1, 5). The vertexB lies on thex-axis.Rajah 2 menunjukkan sebuah rombusABCD dengan bucuA( -1, 5). BucuB terletak pada paksi x
0
y
x
E
D
C
B
A(-1,5)
Diagram 2Rajah 2
The equation of the straight lineBD is x + 2y = 4. The diagonalsACandBD intersect at pointE.Persamaan bagi garislurusBD ialah x + 2y = 4. Garis pepenjuruACdanBD bersilang pada titikE.
FindCari
(a) the equation of the straight lineAC [3 marks]persamaan bagi garislurusAC [3 markah]
(b) the coordinates of the pointE [2 marks]koordinat bagi titikE [2 markah]
(c) the coordinates of the point C [2 marks]koordinat bagi titikC [2 markah]
4
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3 (a) Sketch the graph of y = 3sin 2x + 1 for S2
30 ddx [4 marks]
Lakarkan graf y = 3sin 2x + 1 bagi S2
30 ddx [4 markah]
(b) Hence, using the same axes, sketch a suitable straight line to find the numberof solutions for the equation xx 22sin3 S for S
2
30 ddx . State the number of solutions
[3 marks]Seterusnya, gunakan paksi yang sama, lakarkan garislurus yang sesuai untuk mencari bilangan
penyelesaian persamaan xx 22sin3 S bagi S2
30 ddx .
Nyatakan bilangan penyelesaian. markah]
4 The gradient function of a curve is kx2
x, where k is a constant. The equation of the normal tothe curve at point (1, - 2) is 5y +x = 7.Fungsi kecerunan bagi suatu lengkung ialah kx2 x, di mana k ialah pemalar. Persamaan garis normal
kepada lengkung di titik (1, - 2) ialah 5y +x = 7.
Find
Cari
(a) the value ofk, [4 marks]nilai k, [4 markah]
(b) the equation of the curve, [3marks] persamaan lengkung itu, markah]
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6
5 Table 5 shows the frequency distribution of the ages of a group of villagers in a village.Jadual 5 menunjukkan taburan kekerapan umur bagi sekumpulan penghuni di sebuah kampung.
Table 5Jadual 5
(a) (i) Without drawing an ogive, calculate the third quartile [3 marks]
Tanpa melukis ogif, hitungkan kuartil ketiga [3 markah]
(ii) Calculate the standard deviation of the distribution [3 marks]Hitungkan sisihan piawai bagi taburan itu. [3 markah]
(b) If two villagers with the ages of 20 and 40 years old respectively were shifted out from the
village, find the new variance. [2 marks]Sekiranya dua orang penghuni kampung itu yang berumur 20 dan 40 tahun masing-masing telah
berpindah keluar dari kampung itu, cari varians yang baru.
[2 markah]
Age/Umur
(year/tahun)
Number of villagers/
bilangan penghuni kampung1 - 10 25
11 - 20 32
21 - 30 28
31 - 40 9
41 - 50 6
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6 Diagram 6 shows the waves formed when a stone is thrown into the water. Each wave has theshape of a circle and is rcm away from the one before it.Rajah 6 menunjukkan gelombang yang terbentuk apabila seketul batu telah dibaling ke dalam air. Setiap
gelombang berbentuk bulatan dengan jaraknya rcm jauh daripada bulatan sebelumya.
Diagram 2Rajah 2
r cmr cmr cm
(a) show that the circumferences of the waves form an arithmetic progression and find the common
difference. [3 marks]Tunjukkan bahawa lilitan bulatan gelombang itu membentuk satu janjang aritmatik dan carikan beza
sepunya. [3 markah]
(b) If the radius of the smallest wave is 4 cm, find the radius of the tenth wave . Hence, find its
circumference in terms of S . [3marks]Sekiranya jejari bagi gelombang terkecil ialah 4 cm, hitungkan jejari bagi gelombang yang kesepuluh.
Seterusnya, cari lilitan bulatan gelombang kesepuluh dalam sebutan S . [3 markah]
Diagram 6
Rajah 6
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Section B
[40 marks]
[ 40 markah]
Answerfour questions from this section.Jawab empat soalan dalam bahagian ini
7 Table 7 shows the values of two variables,x andy, obtained from an experiment. The
variables are related by the equation pyx k 5 , where kandp are constants.Jadual 7 menunjukkan nilai-nilai bagi dua pembolehubah,x dany, yang diperoleh dari suatu
eksperimen. Pembolehubah-pembolehubah itu dihubungkan oleh persamaan pyx k 5 ,di mana kdanp adalah pemalar.
x 1.4 1.9 2.5 3.2 4.1 5.5
y 3.3 5.3 7.9 12 15.8 26.3
Table 7
Jadual 7
(a) Based on Table 7, construct a table for the values of log10y and log10x
[2 marks]Berdasarkan Jadual 7, bina satu jadual bagi nilai-nilai log10y and log10x
[ 2 markah]
(b) Plot log10y against log10x by using a scale of 2 cm to 0.1 unit on the log10x- axis and 2 cm to
0.2 unit on the log10y- axis. Hence, draw the line of best fit.[3 marks]
Dengan menggunakan skala 2 cm kepada 0.1 unit pada paksi- log10
x and 2 cm kepada 0.2 unit pada
paksi-log10y, plot log10y lawan log10x dan seterusnya lukiskan garis penyuaian terbaik.
[3 markah]
(c) Use your graph in (a) to find the value ofGunakan graf anda di (a) untuk cari nilai
(i) k
(ii) p[5 marks]
[5 markah]
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8 Diagram 8 shows ODC, OEA,BDEandACB are straight lines.Rajah 8 menunjukkan ODC, OEA, BDEdanACB ialah garis-garis lurus.
E
D
C
B
AO
Diagram 8Rajah 8
It is given that xOA 6 , yOB 3 , OE: OA = 1 : 3, andDE= 3BD.
Diberi bahawa xOA 6 , yOB 3 , OE : OA = 1 : 3, danDE= 3BD.
(a) Express in terms ofx and y
Ungkapkan dalam sebutan x dan y
(i) AB
(ii) OD
[3 marks] [3 markah]
(b) If ODmOC and BAnBC , where m and n are constants. Find the value ofm and n.
[5 marks]
Jika ODmOC and BAnBC , di mana m dan n ialah pemalar. Cari nilai bagi m dan n.[5 markah]
(c) Given that 4x unit and the area of the triangle OBEis 20 unit2. Find the perpendicular
distance fromB to OA
[2 marks]
Diberi bahawa 4x unit dan luas segitiga OBEialah 20 unit2. Kirakan jarak serenjang dariB ke OA.
[2 markah]
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9 Diagram 9 shows OQRS is a sector of a circle with centre O. SOP is a straight line and OPQ is a
right angle tringle.Rajah 9 menunjukkan OQRS ialah sebuah sektor bulatan yang berpusat di O. SOP ialah garislurus dan
OPQ ialah sebuah segitiga bersudut tegak.
Given that OP = 12 cm, q 30OPQ and the length of the arc QR is cm2
S.
Diberi OP = 12 cm, q 30OPQ dan panjang lengkok QR ialah cm2
S.
Find,Cari,
(a) the length, in cm, of OQ [2 marks] panjang , dalam cm, bagi OQ [2markah]
(b) QOR , in radians, [2 marks]
QOR , dalam radian, [2 markah]
(c) the area, in cm2, of the sectorROS, [3 marks]
luas, dalam cm2, bagi sektorROS, [3 markah]
(d) the perimeter, in cm, of the shaded region. [3 marks] perimeter, dalam cm, bagi rantau berlorek. [3markah]
Diagram 9Rajah 9
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10 Diagram 10 shows the straight liney = -x + k touching the curvey = 3x x2
at pointA.Rajah 10 menunjukkan garislurusy = - x + k menyentuh lengkungy = 3x x2pada titikA.
Diagram 10Rajah 10
Find,Cari,
(a) the value ofk [2 marks]nilai k [2 markah]
(b) the coordinates of pointA [2 marks]titik koordinatA [2 markah]
(c) the area of the shaded region [3 marks]luas rantau berlorek [3 markah]
(d) the volume generated,in terms ofS , when the region bounded by the curvey = 3x x2
and thex-axis
is revolved through 360 about thex-axis. [3 marks]isipadu janaan apabila rantau yang dibatasi oleh lengkungy = 3x x2 dan paksi -x dikisarkan melalui 360
pada paksi -x. [3 markah]
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11 (a) In a survey carried out in a school, it is found that 3 out of 5 students have computer at home. If10 students from that school are chosen at random, calculate the probability thatDalam suatu soalselidik yang telah dijalankan di sebuah sekolah, didapati 3 daripada 5 orang pelajar
mempunyai komputer di rumah. Sekiranya 10 orang pelajar dipilih secara rawak, hitung kebarangkalian
(i) exactly 7 students have computer at home
tepat 7 orang pelajar mempunyai komputer di rumah(ii) at least 2 students have computer at home
sekurang-kurangnya 2 orang pelajar mempunyai komputer di rumah
[ 5 marks] [5 markah]
(b) The mass of a packet of cake produced by a factory is normally distributed with the mean of
350g and a variance of 25g2.
Jisim bagi sebungkus kek yang dihasilkan oleh sebuah kilang bertaburan normal, dengan minnya ialah
350g dan varians 25g2.
Find,
Cari,(i) the probability that the mass of a packet of cake chosen at random will be less than 345g,
kebarangkalian sebungkus kek yang dipilih secara rawak mempunyai jisim kurang daripada
345g,
(ii) the number of the packet of cakes whose masses exceed 342g if the factory produced
1500 packets of cake daily.Bilangan bungkus kek yang berjisim lebih daripada 342g yang dapat dihasilkan oleh kilang itu
jika ia menghasilkan 1500 bungkus kek sehari.
[5 marks] [5 markah]
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13
Section C
[20 marks]
[ 20 markah]
Answertwo questions from this section.
Jawabdua soalan dalam bahagian ini
12 A product is make up of four components,A,B, CandD .Table 12 shows the prices of the four
components in the year 2004 and 2005 as well as their respective weightages.Suatu keluaran dihasilkan daripada gabungan empat komponen iaituA,B, CdanD. Jadual 12 menunjukkan
harga setiap komponen pada tahun 2004 dan 2005 serta pemberat masing-masing.
Componentkomponen
Price/harga(RM) Price index for the year 2005based on the year 2004
Index harga tahun 2005
berasaskan tahun 2004
WeightagepemberatYear/tahun
2004
Year/tahun
2005
A 90 x 150 2
B 60 90 150 m
C y 100 125 4
D 30 42 z 8
Table 12Jadual 12
(a) Calculate the values ofx,y danz [3 marks]Hitungkan nilai bagix,y, danz [3 markah]
(b) Given that the composite index of the product in the year 2005 based on the year 2004 was 141,
find the value ofm. [3 marks]
Diberi indeks gubahan bagi keluaran itu pada tahun 2005 berasaskan tahun 2004 ialah 141, Cari nilai m.[3 markah]
(c) If the product is sold for RM350 a unit in the year 2004. Calculate the selling price of the
product in the year 2005 in order to maintain the same profit. [2 marks]Sekiranya keluaran itu dijual dengan harga RM350 pada tahun 2004. Hitungkan harganya pada tahun 2005
jika keuntungan yang sama dikekalkan. [markah]
(d) If the prices of all components of the product was increased by 50% from the year 2004 to theyear 2006, find the composite index of the product in the year 2006 based on the year 2005.
[2 marks]
Sekiranya harga bagi semua komponen keluaran itu meningkat sebanyak 50% dari tahun 2004 ke tahun2006, cari indeks gubahan bagi keluaran itu pada tahun 2006 berasaskan tahun 2005.
[2 markah]
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14
13 Diagram 13 shows a pyramid with a triangular base. The peakVis vertically above P.Rajah 13 menunjukkan sebuah piramid dengan tapak berbentuk segitiga. PuncakVterletak tegak di atas P.
V
6 cm
8 cm
11 cm
Q
R
P
Diagram 13Rajah 13
Given that PR = 8 cm, PV= 6 cm, VQ = 11 cm and q 40PQR ,
Diberi PR = 8 cm, PV= 6 cm, VQ = 11 cm dan q 40PQR ,
Find,Cari,
(a) the length, in cm, ofPQ; correct to 2 decimal places [2 marks] panjang PQ, dalam cm; betul kepada 2 tempat perpuluhan [2markah]
(b) the length, in cm, ofQR [4 marks]panjang QR, dalam cm [4 markah]
(c) the area, in cm2, of the inclined plane QVR [4 marks]
luas , dalam cm2 bagi permukaan condong QVR [4 markah]
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15
14 Use graph paper to answer this question.Gunakan kertas graf untuk menjawab soalan ini.
On a particular ferry trip to Langkawi, the passengers in the ferry comprisex adults andy
children, with each adult paying a fare of RM40 and each children paying a fare of RM30. Thisparticular ferry trip is based on the following constraints.
Pada suatu perjalanan feri pergi ke Langkawi, penumpang feri itu mengandungix orang dewasa danyorang kanak-kanak di mana setiap dewasa dan kanak-kanak perlu membayar tambang RM40 dan RM30
masing-masing. Perjalanan feri itu perlu mematuhi syarat-syarat berikut.
1 : The ferry can accommodate up to 40 passengers onlyFeri itu boleh muat sebanyak 40 orang penumpang sahaja.
11 : The amount collected from the passengers fares must at least RM360, in
order for the ferry company to make profit.Jumlah tambang yang dikutip daripada penumpang mesti sekurang-kurangnya
RM360 supaya syarikat feri itu boleh memperoleh keuntungan daripada perjalanan
itu.
III : The number of adult passengers is not more than twice the number of childrenBilangan penumpang dewasa tidak lebih daripada dua kali ganda bilangan penumpangkanak-kanak.
(a) Write three inequalities, other than 0tx and 0ty , which satisfy the above constraints.
[3 marks]Tulis tiga ketaksamaan, selain daripada 0tx dan 0ty , yang mematuhi syarat- syarat di atas.
[3 markah]
(b) Using a scale of 2 cm to 5 passengers on both axes, construct and shade the region R, which
satisfies all the above constraints. [3 marks]Dengan menggunakan skala 2 cm kepada 5 orang penumpang bagi kedua-dua paksi, bina dan lorekkan
rantau R yang mematuhi semua syarat-syarat di atas. [3 markah]
(c) By using your graph from (b), findDengan menggunakan graf anda dari (b), cari
(i) the minimum number of passengers on this ferry trip if there are five adult passengers
only.bilangan minima penumpang dalam perjalanan feri ini jika hanya ada lima orang penumpang
dewasa sahaja.
(ii) the maximum amount collected from the fares of the passengers.amaun maksima tambang penumpang
[4 marks][4 markah]
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16
15 A particle moves along a straight line and passes through a fixed point O. Its velocity, V ms-1
,is given by v = t
2- 9t+ 18, where t is the time in second after passing through O.
[Assume motion to the right is positive]Suatu zarah bergerak sepanjang garislurus dan melalui titik tetap O. Diberi halaju zarah itu, Vms-1, ialah
v = t2 - 9t+ 18, Di mana t ialah masa dalam saat selepas zarah itu melalui titikO.
[Anggap gerakkan ke kanan sebagai positif]
Find,Cari,
(a) the initial velocity, in ms-1
, of the particle. [1 mark]halaju awal, dalam ms-1, bagi zarah itu [1markah]
(b) the maximum velocity , in ms-1
, of the particle. [3 marks]halaju maksima, dalam ms-1, bagi zarah itu [3markah]
(c) the range of values of t when the particle moves to the left [2 marks]Julat nilai t apabila zarah itu bergerak ke arah kiri [2 markah]
(d) the total distance, in m, travelled by the particle in the first 5 seconds [4 marks]Jumlah jarak, dalam m, yang dilalui oleh zarah itu dalam 5 saat pertama [4 markah]
END OF QUESTION PAPER
KERTAS SOALAN TAMAT
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3472/1
Additional
Mathematics
Paper 1
Sept
2010
PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA
SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA
DENGAN KERJASAMA
JABATAN PELAJARAN MELAKA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2010
ADDITIONAL MATHEMATICS
Paper 1
MARKING SCHEME
This marking scheme consists of 5 printed pages
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PAPER1
QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
1
(a) 3
(b) 1
1
1
2
2
3,3
x2+1=10or 11 xg
2
B1 2
3
4
23
4
1 pandk
4
23
4
1 pork
614 pkork
pxk 2)21(
4
B3
B2
B1
4
4
2 , -2
028
pp
02)
1
(7)
1
(
2 pppp
3
B2
B1
3
5
a) -4
b) 2
c) x = 4
1
1
1
3
6
3 9x d d
2
( 9)( 3) 0
6 27 0
x x
x x
d
d
3
B2
B13
7
2
13x
4 4 6 9x x
033 )32(3)1(4 xx
3
B2
B1
3
3 9or or -3 and 9
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QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
8
7 7 7
7 7
7
1
log 2 log 7 log 5
log 2 log 7
28
log 10
h k
4
B3
B2
B1
4
9
1
4log
31
4
3
3x
x
x
x
x
3
B2
B13
10
a)t=12
t8=16t
b)240
10
[(2(6) 9(4)]2
2
B1
2
B1
4
11
a) n=6
5.01
)5.01(64
126
n
b) 128fs
5.01
64
fs
2
B1
2
B1
4
12
m = -6 and n = 3
m = -6 or n = 3
n
m
n 6
0 and n
m
n 12
2
n
m
n
60 or
n
m
n
122
4
B3
B2
B1
4
13
r=6and7
4t
3
3
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QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
4
7t orr=6
5
)4(42
r or
5
843
t
B2
B1
14 (a) 10
6 8i j
b) )43(5
1ji
2
B1
1
3
15(a) PY
o= p +
3
4q
PY
o= OQPO
o
o
4
3
(b) QXo
=q+2
3p
QXo
= OPQOo
o
3
2
2
B1
2
B1
4
16a)
q
pq 22
b) 22 pq
p
22 pq
p
1
2
B1
3
17 70.53 ,180 , 289.47$ $ $
B3: 70.53 ,180$ $
B2:(3cosT 1)(cosT +1)=0
B1:2cos2T 1
4
B3
B2
B1
4
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QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
18
2 2
38.4
1 116 0.4 8 0.4
2 2
S
S Su u u u
2 21 116 0.4 8 0.42 2
orS Su u u u
3
B2
B1
3
19
4
2 (4)( 0.5)
2dA
rdr
S
S
S
3
B2
B1
3
2023
B2:
2 25 1[ ] 10 3
2 2m 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
B2
B1
3
22
pp
p
p
p
6
7
4
6
8
3
B2
B1
3
23 (a) 8008
(b) 7062
B1:4 12 4 12 4 12
2 8 3 7 4 6C C C C C C Or
4 12 4 12
1 9 0 108008 C C C C
3
2
B1
3
or12.57
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QUESTION
NUMBERSWORKING MARKS
FULL
MARKS
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
orP
1
2
B1
3
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Additional
Mathematics
Paper 2Sept
2010
PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA
SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA
DENGAN KERJASAMA
JABATAN PELAJARAN MELAKA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2010
ADDITIONAL MATHEMATICS
Paper 2
MARKING SCHEME
This marking scheme consists of 13 printed pages
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Question Mark Scheme of Paper 2 Trial SPM 2010 Melaka Sub
Marks
Total
Marks
1.n= -6 4m or n = m2 +m-2 or
4
6 nm
m2+m+6+4m=2 or 4m+m2+m-2+8=2 or 2)4
6(2)4
6( nnn
(m+4)(m+1)=0 or (n-10)(n+2)=0 or use formula/completing the square
m= -4, -1 or n=10, -2
n=10, -2 or m= -4, -1
P1
K1
K1
N1
N1
5
2.(a)
(b)
(c)
m2 = 2
y -5= 2(x+1) or equivalent
y = 2x +7
Solve simultaneous equations: 22
172 xx
E( -2, 3)
)3,2()2
5,2
)1((
yx
C( -3, 1)
K1
K1
N1
K1
N1
K1
N1
7
3.(a)
(b)
Shape of sin x
Graph of sin x shifted up 1 unit
Miximum = 4, minimum = -2
1 cycles in S
2
30 ddx
12
xyS
or equivalent
Sketch the straight line involves x and y
Number of solutions = 4
P1
P1
P1
P1
N1
K1
N1
7
4.(a) Gradient of tangent = 5
kx2-x = 5
substitute x = 1 to kx2-x = 5
K1
K1
K1
xSx
4x
1
-2
02
S
2
3S
3
y
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(b)
k = 6
cxx
y 23
6 23
c2
)1(
3
)1(62
23
2
7
22
23
xxy or equivalent
N1
K1
K1
N1 7
5.(a)(i)
(ii)
(b)
L = 20.5 F = 57 fQ3 = 28
1028
57)100(4
3
5.203
Q
= 26.93
100
)5.45(6)5.35(9)5.25(28)5.15(32)5.5(25 x
=19.4
222222
4.19100
)5.45(6)5.35(9)5.25(28)5.15(32)5.5(25
V
= 11.30
222
2
98
20401940
98
204050415
V
= 126.02
P1
K1
N1
K1
K1
N1
K1
N1
8
6. (a)
(b)
d = 2r or 2r, 4r, 6r
d = 4r - 2r = 6r - 4r
2r = 2r
T10 = 4 + 9(4) or T10 = 2r + 9 (2r )= 40 = 20 (r)
Circumference = 2(40) = 20 (4)
= 80 = 80
P1
K1
N1
K1
N1
N1
6
7.(a)
(b)
(c)
(i)
(ii)
log10x 0.15 0.28 0.40 0.51 0.61 0.74
log10y 0.52 0.72 0.90 1.08 1.20 1.42
Refer to the appendix
One point correctly plotted with uniform scales
6 points correctly plotted with uniform scales
Line of best fit
xkpy 101010 log5loglog
-5k=1.52
35.025.0 lk
log10p = 0.29
N1
N1
K1
N1
N1
P1
K1
N1
K1
N1
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0.29.1 lp 10
8(a)(i)
(ii)
(b)
(c)
OBAOAB or equivalent
yx 36
xyOD 2
1
4
9
)2
1
4
9( xymOC
)36( yxnBC
)36()2
1
4
9(3 yxnxymy
5
6m
10
1n
x 8 x h = 20
h = 5
K1
N1
N1
P1
P1
K1
N1
N1
K1
N1
10
9(a)
(b)
(c)
(d)
1230sin
OQq or equivalent
OQ = 6
TS
62
QOR rad12
ST // 0.2618 rad
radradROS 833.1/127/1051560180 Sqqqq
Area of sector ROS = ROSuu 262
1
=32.99 or 10.5
Perimeter of shaded region = )5.52sin6(2)12
7(6 qS
=20.52
K1
N1
K1
N1
P1
K1
N1
K1K1
N1
10
10(a)
(b)
(c)
Use b2 4ac = 0
(-4)2 4(1)k =0
k = 4
Solve equation : (x 2)(x 2) = 0
A(2, 2)3
2
32
32
3
xx
3
2
2
)2(3
3
3
2
)3(3 3232
K1
N1
K1
N1
K1
K1
N1
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(d)
=6
7
3
0
543
54
6
3
9
xxxS
= 05
34)3(6
3)3(9
543
S
= 8.1
K1
K1
N1
10
11(a)(i)
(ii)
(b)(i)
(ii)
377
10 )4.0()6.0(C
= 0.215
1 P(x=0) P(x=1) or P(x=2)+P(x=3)+P(x+4)+ .+P(x=10)
= 91110100
010 )4.0()6.0()4.0()6.0(1 CC
= 0.9983
)5
350345(
zP
= 0.1587 // 0.15866
P(x >342) = 1 P(z > 1.6) or other valid method
Number of cakes = 0.9452 x 1500
= 1417 // 1418
K1
N1
P1
K1
N1
K1
N1
K1
K1
N1
10
12(a)
(b)
(c)
(d)
Use 100
0
1 u
P
PI
x = 135, y = 80, z = 140
141842
)8(140)4(125150)2(150
m
m
m = 6
141100350
2005 uP
P2005 = 493.50
100141
11502005/2006 uuI
= 106.38
K1
N2,1,0
K1K1
N1
K1
N1
K1
N110
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Substitute t = 3 or t = 5 into ttt
s 182
9
3
23
S3 = 22.5
S5 =6
119
Total distance traveled= )
6
1195.22()05.22(
6
525
OR5
3
233
0
23
182
9
318
2
9
3
ttt
tt
)3(18
2
)3(9
3
3)5(18
2
)5(9
3
50)3(18
2
)3(9
3
3232323
=6
525
K1
K1
N1
K1K1
K1
N1
10
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7(a)
14(b)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8 lg y
(0.15,0.52)
(0.28,0.72)
(0.40,0.90)
(0.51,1.08)
(0.61,1.20)
(0.74,1.42)
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Rx+y=40
x2y
4x+3y=36
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1
PEPERIKSAAN PERCUBAAN SPM TAHUN 2010
KERTAS SELARAS NEGERI MELAKA
JADUAL SPESIFIKASI UJIAN MATEMATIK TAMBAHAN
(PAPER 1 & PAPER 2)
TOPICSTotal
Question
s PAPER 1PAPER 2
Section A Section B Section C
No
Marks
No
Marks
No
Marks
No
Marks
1) A1 Functions (F4) 3
1 2
2 4
3 3
2) A2 Quadratic Equations (F4) 1 4 3 2 7
3) A3 Quadratic Functions (F4) 25 2
6 3
4) A4 Simultaneous Equations (F4) 1 - - 1 5
5) A5 Indices and Logarithms (F4) 27 3
8 3
6) A6 Progressions (F5) 3
9 3 6 6
10 2
11 4
7) A7 Linear Law (F5) 1 - - 8 10
8) T1 Circular Measure (F4) 1 12 4 10 10
9) G2 Vectors (F5) 213 4 5 8
14 4
10) G1 Coordinate Geometry (F4) 1 15 3 9 10
11) T2 Trigonometric Functions (F5) 216 3 4 617 3
12) C2 Integration (F5) 218 3 7 10
19 4
13) C1 Differentiation (F4) 1 20 3 3 7
14) S2 Permutations/Combinations (F5) 1 21 4
15) S3 Probability (F5) 1 22 3
16) Statistics ( F4) 1 23 3
17) S4 Probability Distributions (F5) 324 3 11 10
25 4
18) AST1 Solution of Triangles (F4) 1 - - 12 1019) ASS1 Index Number (F4) 1 - - 13 10
20) AST2 Motion Along a Straight Line
(F5)1 - - 15 10
21) ASS2 Linear Programming (F5) 1 - - 14 10
TOTAL 25 80 6 40 5 50 4 40
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2
TEST SPECIFICATION TABLE
KERTAS SELARAS NEGERI MELAKA
JADUAL SPESIFIKASI UJIAN MATEMATIK TAMBAHAN
(PAPER 1 & PAPER 2)
Paper 1
Question Topics Construct Level ofDifficulty Marks
1 Functions
Knowledge
Interpret from ordered pairs.
Find object and determine the type of relation.Find the range of relation
L 2
2 FunctionsUnderstanding
Inverse function and composite function.L 4
3. Function
Understanding
Determine one of the functions in a given
composite function given the other related
function..
L 3
4QuadraticEquations
Understanding
Find the roots for the equation that cannot be
factorized.
I 3
5QuadraticFunctions
Understanding
Find the range of values for quadratic
inequalities.
I 3
6Quadratic
Functions
Application
Find the axis of symmetry and minimum point
from completing the square method.
H 3
7Indices and
LogarithmsApplication
Solving equation involving indices.L 3
8Indices andLogarithms
ApplicationSolve problems involving the change of base and
laws of logarithms
H 3
9 ProgressionsApplication
Find the value a and Sun to n terms for API 3
11 Progressions
Application
Find the value of n, given the sum of the first nterms of G P
I 4
12 ProgressionApplication
Geometric Progression: Sum to infinityI 2
13 Linear LawApplication
Given the line of best fit; convert to linear formand find the gradient andy-intercept .
H 4
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4
ADDITIONAL MATHEMATICS
PAPER 2
TEST SPECIFICTION TABLE
Question Topics Construct Level of Difficulty Marks
1 SimultaneousEquations
Application
Solving two simultaneous equations :
one linear equation and one non-linear
equation.
L 5
2 Integration (a) Application
Find the unknown from gradient
function.
(b) Application
By integration, find the the equation
of the curve.
L
I
3
3
3 Progressions (a) Problem Solving / Application
Find the a from Tn.
Application
(b) Find the Sn(c) Find n from given Tn
L
I
I
2
2
2
4 Trigonometric
Functions
(a) Application
Prove the identity.
(b) Application
Sketch the trigonometric graph and a
straight line.Find the number of solutions from the
graph.
L
H
2
6
5 Coordinate
Geometry
Application
(a) Find the coordinate of a point
divides a segment internally at a
ratio.
(b) Find the equation of a
perpendicular line.
(c) Find the area of parallelogram
L
I
I
2
3
3
6 Statistics (a) Application
Find the mean and standard deviation
from the Histogram.
(b) Understanding
The effect of change to the mean and
standard deviation.
I
L
4
3
7 Linear Law (a) Understanding
Plot the graph and draw the line of best
fit.
(b) Application
Change the equation to linear form.
Use the gradient and y-intercept to find
the unknowns.
I
H
4
6
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5
8 Vectors (a) Application
Find the resultant vector using polygon
law.
(b) Application
Express a vector as a combination ofother vectors.
(c) Understanding
Solve simultaneous equations to find theconstants.
(d) UnderstandingNegative vector.
L
I
I
L
2
3
4
1
9 Circular
Measure
(a) Application
Find the angle of sector using
trigonometry.
(b) Application
Find the perimeter of shaded region.
(c) Application
Find the area of triangle.
(d) ApplicationFind the area of shaded region.
L
I
L
H
2
3
2
3
10 Progressions (a) Understanding
Show the areas form a geometric
progression.
(b) Problem Solving/Application
(i) Find n from Tn.
(ii) Find the sum of specific terms.
(iii) Find Sum to Infinity
L
I
I
L
2
3
3
2
11 Probability
Distributions
(a) Application
Find the area of the shaded region.(b) Application
Find the minimum point of the curve.
(c) Application
Find the volume generated.
H
I
H
3
3
4
12 Solutions of
Triangle
(a) Application
Use the Sine Rule or Cosine Rule to find
the length.(b) Application
Use the Sine Rule or Cosine Rule to find
the angle.
(c) Application
Use the area formula to find the area oftriangle.
(d) Application
Use the Cosine Rule to find the length.
L
L
L
H
2
3
2
3
13 Index Number Problem solving(a) (i) Find the price of the base year.
(ii) Find the price index.
(b) (i) Given the composite function,
find the price index.
(ii) Find the cost of item in the base
L
H
I
L
2
3
3
2
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6
year, given the composite index.
14 Motion Along a
Straight Line
Problem solvinga). Determine displacement of a particlefrom a fixed point.b). Determine the total distance traveledby a particle over a time interval using
graphical methodc). Determine velocity function of aparticle by differentiation.d) Determine instantaneous velocity of aparticlee ) Determine acceleration function of aparticle by differentiation
L
L
H
L
H
2
2
2
2
2
15 Linear
Programming
Problem solving
a) writing linear inequalities and
equations describing asituation.
b) shading the region of feasible
solutions.
c) determining and drawing the
objective functionax + by = k where a, b and k
are constants.
d) determining graphically the
optimum value of the
objective function.
L
L
H
H
3
3
2
2
Level of Difficulty : L LowI Intermediate
H- High
JOB DISTRIBUTION
Paper 1
No 1 - 7 Horsiah No 8 - 14 Saripah
No 15 20 GanNo 21 24 Kee
Paper 2
Part A and B
No 1 4 Horsiah
No 5 7 Saripah
No 8 9 KeeNo 10 - 11 Gan
Paper 2
Part C
No 12 Horsiah
No 13 Kee
No 14 GanNo 15 Saripah
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3(56,'$1*$1.(%$1*6$$13(1*(78$3(1*(78$
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