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8/4/2019 Add Mth 12 Dan Skema f4 Final Mlk 2009
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NO.KAD PENGENALAN/I.C NUMBER- -
PEPERIKSAAN SELARAS AKHIR TAHUNSEKOLAH-SEKOLAH MENENGAH NEGERI MELAKA
KelolaanPEJABAT PELAJARAN DAERAH
JASIN * ALOR GAJAH * MELAKA TENGAHDengan kerjasama :
JABATAN PELAJARAN NEGERI MELAKATINGKATAN 4 2009
ADDITIONAL MATHEMATICSPaper 12 hours
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. Tuliskan nombor kad pengenalan, nama dan tingkatan anda pada ruang yang disediakan.
Write your I.C. number, name andclass in the space provided.
2. Calon dikehendaki membaca arahandi halaman 2 dan halaman 3
Candidates are required to read theinstructions on page 2 and 3 .
Kertas soalan ini mengandungi 15 halaman bercetak
Examiners Code
Full MarksQuestion
Marks Acquired
1 2
2 3
3 3
4 4
5 3
6 3
7 3
8 3
9 310 3
11 3
12 3
13 4
14 4
15 3
16 4
17 3
18 3
19 3
20 4
21 322 3
23 4
24 3
25 3
Total 80
3472/1Form FourAdditional MathematicsPaper 12009
2 hours Nama Calon :
Tingkatan : .
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SULIT 3472/1
3472/1 SULIT
2MAKLUMAT UNTUK CALON
1. Kertas soalan ini mengandungi 25 soalan.
2. Jawab semua soalan.
3. Bagi setiap soalan berikan SATU jawapan sahaja.
4.
Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalan.5. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda
untuk mendapatkan markah.
6. Sekiranya anda hendak menukarkan jawapan, batalkan kerja mengira yang telah dibuat.
Kemudian tuliskan jawapan yang baru.
7. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.
8. Markah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam
kurungan.
9. Satu senarai rumus disediakan di halaman 4 hingga 6.
10. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.
11. Kertas soalan ini hendaklah diserahkan di akhir peperiksaan.
INFORMATIONS FOR CANDIDATES
1. This question paper consists of 25 questions.
2. Answer ALL questions.
3. Give only ONE answer for each question.
4. Write your answer clearly in the spaces provided in the question paper.
5. Show your working. It may help you to get marks.
6. If you wish to change your answer, cross out the work that you have done. Then write down the
new answer.
7. The diagram in the questions provided are not drawn to scale unless stated.
8. The marks allocated for each question and sub-part of a question are shown in brackets.
9. A list of formulae is provided on pages 4 to 6.
10. You may use a non-programmable scientific calculator.
11. This question paper must be handed in at the end of the examination.
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SULIT 3472/1
[See overleaf]3472/1 SULIT
3
ALGEBRA
1 a
acbb x
242
= 8 ab
bc
ca log
loglog =
2 a m x a n = a m + n 9 Tn = a + (n -1)d
3 a m a n = a m n 10 S n = [ ]2 ( 1)2n
a n d +
4 ( a m )n = a m n 11 T n = 1nar
5 nmmn aaa logloglog += 12( 1) (1 )
, 11 1
n n
n
a r a r S r
r r
= =
6 nmnm
aaa logloglog = 13 , 11a
S r r
=
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7 (a) Midpoint of QR = (5,4) or m QR = 1 y = x + c passes through (5,4) y = x + 9 or equivalent
or
22 )5()6( + y x or 22 )3()4( + y x x2 12 x + 36 + y2 10 y + 25 = x2 8 x + 16 + y2 6 y + 9 y = x + 9 or equivalent
(b) 22 )3()4( + y x = 2x2 + y 2 8x 6y + 21 = 0
(c) x 2 + (9 x) 2 8x 6(9 x) + 21 = 0(x 4)(x 6) = 0(4,5), (6,3)
(d) Replacing point (5,4) to equation of locus P.No
111
1
11
11
111
11
3
2
3
2
8 (a) h =2
24
xor curved surface area of cone = 2 x2 or curved
surface area of cylinder = 2 x(2
24 x
)
Total surface area = 2 x2 + 2 x( x24
) + x2
= 3 (x2 + x16 )
(b) 6 x -2
48
x
= 0
x = 2A = 36
(c)dt dA
dAdx
dt dx
=
=
2
486
1
x x
(42 )
= 2
1
1
1
1
11
1
1
3
3
2
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(d)2
486(
x x A
= )(0.003)
= 0.063
11 2
9 (a) Identify Q 1 class = 6 10 or L = 5.5
5.5 + )5(5
3)17(41 + k
= 7.5
k = 3
(b) x =20
255 or 2 x = 4175
2)20
255(
204175
=
= 6.796
(c) Complete histogramUsing X to determine the modeMode = 11.75
1
1
1
1
1
1
211
3
3
4
10 (a) 60
(b) s = 8(20 x180
)
= 2.973 cm
(c) AB 2 = 8 2 + 8 2 2(8)(8)Cos 100AB = 12.26 cm
Perimeter = 26.21 cm
1
11
111
1
2
3
Mode=11.75
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(d) Segment 1 = (8 2)(1.745) (8)(8) sin 100Segment 2 = (8 2)(1.047) (8)(8) sin 60Shaded region = 24.33 5.791
= 18. 54 cm 2
1111 4
11(a) AC m = 2 or ABm =
2
1
1** = AB AC mm 11 2
(b) midpoint AC = (0 , 0)
D ( x , y) =
+
21
,2
7 y x
02
7=
+ xor 0
21
= y
x = 7 or y = 1 D = ( 7, 1)
Area of parallelogram =21
12
71
12
71
=21 *
1629
=2
13unit 2
(c) Centre = midpoint BC
= E (3 ,23
)
Distance EC or Distance EB or Distance ED
( )2
2
23
3
++ y x = ( )2
2 223
13
+++ or
( )2
2
23
3
++ y x = ( )2
2
23
137
++
053622 =++ y x y x
1
1
1
1
1
1
1
1
2
2
4
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12 (a) PR 2 = 12 2 + 20 2 2(12)(20) Cos 72 0
PR = 19.89 (at least 3 s.f, correct round off)
(b) Use16
48Sin*89.19
SinS 0=
S = 67.49 0 , 112.51 0 (must 2 d.p, correct round off
(c) (i) P = 180 48 0 67.49 0 *
= 64.51 0
48Sin16
*49.67Sin*89.19
*51.64SinRS
== or use Cosine
Rule in PRS
RS = 19.43
( ii) 00 72sin)12)(20(x21
or48sinx*)43.19*)(89.19(x21
Area = 143.60 + 114.13
Area = 257.73
1
1
1
1,1
1
1
1
1
1
2
3
5
13(a) i) 125 = 100x
P32RM
06or equivalent
P06 = RM25.60
ii) Use I 08/04 =100
xII 04 / 0606 / 08 or equivalent
=100
140x115
= 161
1
1
1
1
1 5
(b)
Item I W IW
P 125 30 3750
Q 120 10 1200
R x 20 20x
S 115 40 4600
= 100W += x209550IW
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i) += x IW 209550
Use100
IWI 06 / 08 = *
100209550
5.124 x+
=
x = 145
ii) Use 100xCostCost
I06
0806 / 08 = or equivalent
or Cost 08 =100
14x5.124RM
= RM 17.43
1
1
1
1
15
14 (a) i) PR 2 = 6 2 + 14.5 2 2(6)(14.5) Cos 48 0
PR = 11.39 (at least 3 s.f, correct round off)
ii)*39.11
110Sin8.4
SinPRQ0
= or equivalent
S = 23.33 0
(must 2 d.p, correct round off, decimal form better than
minutes form)
1
1
1
1 4
(b) i)
Must correct labeled, angle P is obtuse
ii) P = 180 110 0 23.33 *
= 46.67 0
1
1
Q
P
R
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*33.23Sin
8.4*33.133Sin
QR*67.46Sin
QR==
QR = 8.817 / 8.82
000 33.2333.133180QR'P =
= 23.34 0
Area PQR = *034.23sinx*)82.8()8.4(x21
= 8.386
1
1
1
1 6
15(a) Use I 04/00 = 100x
PP
00
04
x = 125, y = 2.08, z = 0.72
(b) i)
Item I W IW
A 125* 80 10000*B 130 100 13000
C 160 140 22400
D 125 40 5000
= 360W = 50400IW
= 50400IW
Use360
IWI 00 / 04 = or
360*50400
I 00 / 04 =
= 140
ii) Use 100xCostCost
I00
0400 / 04 = or
Cost 00 =140
100x50.128RM
= RM20.36
1
1, 0
1
1
1
1
1
2
5
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(c) 130I 04 / 08 =
Use I 08/04 =100
xII 00 / 0404 / 08 or
=100
140x130
= 182
1
1
13
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