Download - Mat K1 SPM
JABATAN PELAJARAN NEGERI SELANGOR
SULIT
1449/11449/1
Matematik
Kertas 1
September
jam22SULIT 1449/1
23SULIT 1449/1
PROGRAM PENINGKATAN PRESTASI SAINS & MATEMATIK
SIJIL PELAJARAN MALAYSIA
MATEMATIK
Kertas 1
Satu jam lima belas minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak.INFORMATION FOR CANDIDATES
1 This question paper consists of 40 questions.
2. Answer all questions.
3. Answer each question by blackening the correct space on the answer sheet.
4. Blacken only one space for each question.
5. If you wish to change your answer, erase the blackened mark that you have done.
Then blacken the space for the new answer.
6. The diagram in the questions provided are not drawn to scale unless stated.
7. A list of formulae is provided on pages 3 to 6.
8. You may use a non-programmable scientific calculator.MAKLUMAN UNTUK CALON
1. Kertas soalan ini mengandungi 40 soalan.
2. Jawab semua soalan.
3. Jawab dengan menghitamkan ruangan yang betul pada kertas jawapan.
4. Bagi setiap soalan hitamkan satu ruangan sahaja.
5. Sekiranya anda hendak menukar jawapan, padamkan tanda yang telah dibuat.
Kemudian hitamkan jawapan yang baru.
6. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.
7. Satu senarai rumus disediakan di halaman 3 hingga 6.
8. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.
MATHEMATICAL FORMULAEThe following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
RELATIONS1
2
3
4
5
6
7 Distance =
8 Midpoint,
9 Average speed =
10 Mean =
11Mean =
12Pythagoras Teorem
13
14
Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.
PERKAITAN1
2
3
4
5
6
7Jarak =
8Titik tengah
9Purata laju =
10 Min =
11Min =
12Teorem Pythagoras
13
14
SHAPES AND SPACE
1 Area of trapezium = sum of parallel sides height2 Circumference of circle =
3 Area of circle =
4 Curved surface area of cylinder =
5 Surface area of sphere =
EMBED Equation.3 6 Volume of right prism = cross sectional area length7 Volume of cylinder =
8 Volume of cone =
9 Volume of sphere =
10 Volume of right pyramid = base area height11 Sum of interior angles of a polygon = (n 2)
12 =
13 =
14 scale factor
15 Area of image = area of objectBENTUK DAN RUANG15 Luas trapezium = hasil tambah dua sisi selari tinggi
16 Lilitan bulatan =
17 Luas bulatan =
18 Luas permukaan melengkung silinder =
19 Luas permukaan sfera
=
EMBED Equation.3 20 Isipadu prisma tegak = luas keratan rentas panjang
21 Isipadu silinder =
22 Isipadu kon =
23 Isipadu sfera =
24 Isipadu piramid tegak = luas tapak tinggi
25 Hasil tambah sudut pedalaman poligon = (n 2)
26 =
27 =
28 Faktor skala,
29 Luas imej = luas objekAnswer all questions.1 Round off 48 008 correct to four significant figures. [ Bundarkan 48 008 kepada empat angka bererti . ]
A 48 00
B 48 01
C 48 000
D 48 0102 Express 5.72 x 10-3 as a single number . [ Ungkapkan 572 10-3 sebagai satu nombor tunggal . ]
A 0000572
B 000572
C 00572
D 0572
3 Calculate and express the answer in standard form. [ Hitungkan dan ungkapkan jawapan dalam bentuk piawai . ]
A 85 10-1 B 85 10-2 C 8.5 10-3
D 8.5 10-4
4 The population of town D is 7.8 x 105 and the population of town Z is 5.3 x 104 .
The difference in population between the two towns is
[ Populasi Bandar D ialah 7.8 x 105 dan populasi Bandar Z ialah 5.3 x 104
Perbezaan populasi di antara dua bandar itu ialah ]
A 2.5 x 104 B 2.5 x 105 C 7.27 x 104
D 7.27 x 1055 What is the value of the digit 2 , in base ten, in the number 1248 ? [ Apakah nilai bagi digit 2, dalam asas sepuluh, dalam nombor 1248 ? ]
A 8
B 16 C 20 D 326 110112 + 10012 =
A 1001002 B 1011012 C 1000102 D 1010102
7 Diagram 1 shows a pentagon ABCDE. Lines AB and FED are parallel.
Diagram 1 [ Rajah 1 ]
Find the value of
[ Rajah 1menunjukkan pentagon ABCDE. Garis lurus AB adalah selari dengan
FED. Carikan nilai ]
A 2160 B 2220 C 2500 D 26008 In Diagram 2, the tangent PQR touches the circle at Q,
P Diagram 2 [ Rajah 2]
Find the value of y x [Dalam Rajah 2 , tangent PQR menyentuh bulatan pada Q. Carikan nilai y x ] A 480 B 550 C 770 D 10309 Diagram 3 [ Rajah 3]
Diagram 3 shows five triangles drawn on a square grid. Which of the figures A, B, C or D is not the image of J under reflection?[Rajah 3 menunjukkan lima segitiga dilukis pada grid segiempat sama. Antara segitiga A, B, C dan D yang manakah bukan imej bagi segitiga J di bawah satu pantulan?]10In Diagram 4 , M' is the image of M under a certain translation. T' is the image of T under the same translation.
Diagram 4 [ Rajah 4 ]
The coordinates of T is [ Dalam Rajah 4, M' adalah imej bagi M di bawah satu translasi. T' adalah imej bagi T di bawah translasi yang sama. Koordinat bagi T ialah ]
A ( -3, 0 ) B ( 0, -3 ) C ( 5 , 4 )
D ( 5 , 0 )
11 In Diagram 5, ABC is a right angled triangle. H is the midpoint of AB.
Diagram 5 [Rajah 5] Find the value of tan [Dalam Rajah 5,ABC ialah sebuah segitiga sudut tegak. H ialah titik tengah AB.
Carikan nilai bagi tan ]
A
B
C
D
12 In Diagram 6, KLM is a straight line. It is given that cos (NKL = .
Diagram 6
Find the value of cos (NLM.
[ Dalam Rajah 6, KLM ialah garis lurus. Diberi kos (NKL = . Hitungkan kos (NLM. ] A
B
C
D
13Which of the following represents the graph y = sin x for 0o x 180o Antara yang berikut, yang manakah mewakili graf bagi ?]
A B
C D
14Diagram 7 shows a cuboid with a horizontal base PQTS. Name the angle between the plane TWQ and the plane RTQU
Diagram 7 [ Rajah 7] [Rajah 7 menunjukkan sebuah kuboid dengan satah mengufuk PQTS. Namakan sudut di antara satah TWQ dengan satah RTQU]
A. RWT
B RWQ
C RTQ
D RTW
15In Diagram 8, RT and AF are two vertical poles on a horizontal plane. S is a point on RT such that ST = AF
Diagram 8 [Rajah 8]
. The angle of elevation of point R from point A is [ Dalam Rajah 8, RT dan AF adalah dua batang tiang tegak pada satah mengufuk. S adalah satu titik di atas RT dengan keadaan ST = AF. Sudut dongak titik R dari titik A ialah ] A ARS
B SAR
C TFR
D TAF16 In Diagram 9, SQ and TP are two vertical poles on a horizontal plane .
Diagram 9 [Rajah 9] The angle of depression of S from T is 420. Calculate the value of h, in m.. [Dalam Rajah 9, SQ dan TP adalah dua tiang tegak di atas satah mengufuk.
Sudut tunduk puncak S dari T ialah 420 . Hitungkan nilai h, dalam m ] A 18.0 B 22.2 C 26.0 D 30.217 M , N and P are three points on a horizontal plane. N is due south of M. The bearing of P from M is 150o and the bearing of N from P is 230o.
Which of the following diagrams shows the position of M , N and P?[ M, N dan P ialah tiga titik pada satah mengufuk. N berada di selatan M. Bearing P dari M ialah 150o dan bearing N dari P ialah 230o. Antara rajah berikut, yang manakah menunjukkan kedudukan M, N, dan P?]
A
B
C
D18P (77 N, 35 E) and S are two points on the surface of the earth with PS as the diameter of the earth. The position of S is[ P (77 U, 35 T) dan S adalah dua titik di atas permukaan bumi dengan keadaan PS ialah diameter bumi. Kedudukan bagi S ialah ]
A (77 S, 145 W)
B (77 S, 35 E)
C (77 N, 145 W)
D (77 N, 35 E )19
A
B
C
D
20 Simplify
A
B
C
D 4
21 Given that , express m in terms of n.
[Diberi , ungkapkan m dalam sebutan n.]
A
B
C
D
22 Given that , then =
[Diberi , maka = ]
A
B
C
D
23 Simplify
[ Ringkaskan ]
A
B
C
D
24 List all the integers which satisfy both the inequalities
and
[Senaraikan semua integer yang memuaskan kedua-dua ketaksamaan
and ]
A -2, -1, 0 , 1, 2
B -2, -1, 0, 1
C -1, 0, 1, 2
D -1, 0, 1
25Diagram 10 is a pictograph showing the number of tourists who visited Pangkor Island in March and April. The number of visitors in January and February are not shown.
January
February
March
April
represents 2500 tourists
DIAGRAM 10 A total of 55000 tourists had visited Pangkor Island in those four months.
The number of tourists in January was two third the number of tourists in
February.
The number of tourists in February was[ Rajah 10 ialah piktograf yang menunjukkan bilangan pelancung ke Pulau Pangkor dalam bulan Mac dan April. Bilangan pelancung dalam bulan Januari dan Februari tidak ditunjukkan.]
Sejumlah 55000 pelancung telah melawat Pulau Pangkor dalam empat bulan
itu. Bilangan pelancung dalam bulan Januari adalah dua pertiga bilangan pelancung dalam bulan Februari.
Bilangan pelancung dalam bulan Februari ialah ]
A 10 000
B 15 000
C 20 000
D 25 00026Table 1 shows the number of children in 30 families in a village.
The median of the distribution is
Number of children
01234
Frequency
411762
TABLE 1
[ Jadual 1 menunjukkan bilangan anak bagi 30 buah keluarga dalam sesuatu kampung.
Median bagi taburan ini ialah ]
A 1.5
B 2
C 2.5
D 3
27 Diagram 11 shows a set of six pieces of data where and are integers.
3, 5, , , 4, 5
DIAGRAM 11The mean for the data is 4 and the median is 4.
Two new pieces of data, 4 and 6 were put into the set.
Determine the mode for these eight pieces of data.
[ Rajah 12 menunjukkan sekumpulan enam data dengan keadaan mewakili
satu integer
Min bagi data tersebut ialah 4 dan median ialah 4. Dua data baru, 4 and 6 dimasukkan ke dalam kumpulan data itu. Tentukan mod bagi lapan data itu.]
A 3
B 4
C 5
D 6
28Which of the following graphs represents the graph of
[ Antara yang berikut, yang manakah mewakili graf bagi ]
A
29It is given that the universal set , { is an integer } and
set R = { is a number such that the difference between the two digits is a prime number} .
Find set R.
[ Diberi bahawa set semesta ,{ ialah integer } dan set R = { ialah nombor dengan keadaan beza antara dua digitnya ialah nombor perdana} . Carikan set R.]
A { 16, 18, 20, 22, 24 }
B { 16, 18, 20, 24, 25 }
C { 15, 17, 19, 21, 22, 23 }
D { 16, 18, 20, 21, 24, 25 }
30Diagram 12 is a Venn Diagram showing the universal set , and set P and Q.
The region is equivalent to the region
[Rajah 12 ialah gambarajah Venn yang bawah menunjukkan set semesta dan set-set P and Q.]
Rantau setara dengan rantau ]
A
B
C
D
31Table 2 shows the data obtained from a survey of favourite drinks of 40 students in a class. Diagram 13 is a Venn Diagram that represents part of the information given in Table 2.
DrinksNumber
of Students
Tea15
Coffee27
Tea and Coffee only4
Tea and Milo7
Milo and Coffee9
Milo only5
Table 2
Diagram 13Find the number of students who like one type of drink only.
[Jadual 2 menunjukkan data yang diperoleh daripada satu kaji selidik minuman yang digemari oleh 40 pelajar dalam sebuah kelas. Rajah Venn dalam Gamabarajah 13 mewakili sebahagian maklumat dalam Jadual 2. Carikan bilangan pelajar yang suka hanya sejenis minuman sahaja]
A 9
B 15
C 19
D 23
32 Point Q lies on a straight line with gradient -3 and passes through the point
P (-1,2 ).
The coordinates of point Q could be
[Titik Q terletak pada garislurus dengan kecerunan -3 dan melalui titik P (-1,2 ).
Koordinat-koordinat titik Q yang mungkin ialah ]
A (2, 7)
B (2, 6)
C (2, 5)
D (2, -7)
33In Diagram 14, EF is a straight line with gradient .
Diagram 14Find the intercept of the straight line EF.
[Dalam Rajah 15, EF ialah garis lurus dengan kecerunan .
Carikan pintasan - bagi garis lurus EF ]A 2
B -2
C
D
34It is given that set G is { 1,2,3,5,6,7,8,10,12,14,15 }. A number is chosen at random from the elements of set G. Find the probability that the number chosen is a factor of 30.
[Diberi bahawa set G { 1,2,3,5,6,7,8,10,12,14,15 }. Satu nombor dipilih secara rawak daripada unsur-unsur set G. Carikan kebarangkalian bahawa nombor yang terpilih ialah faktor bagi 30.]
A
B
C
D
35 A box contains 3 bottles of soya sauce, 10 bottles of tomato sauce and a few bottles of chilli sauce. A bottle is chosen at random from the box. The probability of choosing a bottle of tomato sauce is
Find the probability of choosing a bottle of chilli sauce.
[Sebuah kotak mengandungi 3 botol kicap, 10 botol sos tomato dan beberapa botol sos cili. Sebuah botol dipilih secara rawak daripada kotak itu . Kebarangkalian bahawa sebuah botol sos tomato dipilih ialah Carikan kebarangkalian bahawa sebuah botol sos cili dipilih.]
A
B
C
D
36It is given that varies inversely with the square of and = 9 when = . Calculate the value of when = 25.
[Diberi bahawa berubah secara songsang dengan kuasa dua dan = 9 apabila = . Hitungkan nilai p apabila = 25.]
A
B
C 4
D 10
37It is given that and = 2 when = 9.
Calculate the value of when = 4 .
[Diberi bahawa
EMBED Equation.3 dan = 2 apabila = 9.
Hitungkan nilai apabila = 4 ]
A 12
B 16
C 24
D 36
38Table 3 shows two sets of values of , and which satisfy .
Calculate the value of
873
414w
TABLE 3
[Jadual 3 menunjukkan dua set bagi nilai and yang memuaskan
Hitungkan nilai ]
A 0.75
B 1.25
C 1.30
D 1.33
39
A
B
C D
40If then =
[Jika maka = ]
A 1
B 2
C
D
END OF QUESTION PAPER
distance travelled
time taken
sum of data
number of data
sum of (class mark EMBED Equation.3 frequency
sum of frequencies
y-intercept
x-intercept
jarak yang dilalui
masa yang diambil
hasil tambah nilai data
bilangan data
hasil tambah nilai titik tengah kelas EMBED Equation.3 kekerapan
hasil tambah kekerapan
pintasan - y
pintasan - x
arc length
circumference of circle
angle subtended at centre
EMBED Equation.3
Angle subtended at centre
EMBED Equation.3
area of sector
area of circle
panjang lengkok
lilitan bulatan
sudut pusat
EMBED Equation.3
luas sektor
luas bulatan
sudut pusat
EMBED Equation.3
F
E
D
600
1100
C
EMBED Equation.3
EMBED Equation.3
B
A
y0
x0
550
480
Q
R
0
2
EMBED Equation.3
EMBED Equation.3
4
2
4
EMBED Equation.3
EMBED Equation.3
x4
y
M'
T'
M
-2
-4
-2
A
B
C
17 cm
4 cm
H
M
N
L
K
O
90
180
o
y
x
1
-1
O
90
180
y
x
1
-1
y
O
90
180
y
x
1
-1
1
x
o
180
90
O
-1
R
V
T
Q
U
P
S
W
F
R
T
S
A
S
Q
T
P
h
8 m
20 m
M
N
P
North
M
N
P
North
N
M
P
North
N
M
P
North
y
y
B
8
O
x
8
O
x
y
y
D
C
O
O
x
x
-2
-2
DIAGRAM 12
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
TeaTea
Coffee
4
5
MiloTea
y
O
E
-3
F
EMBED Equation.3
1449/1 2007 Hak Cipta JPNS [Lihat sebelah
SULIT1449/1 SULIT1449/1 [Lihat sebelah SULIT
_1144822798.unknown
_1235887375.unknown
_1235898636.unknown
_1235973581.unknown
_1235984292.unknown
_1235993379.unknown
_1235993457.unknown
_1235999519.unknown
_1235999671.unknown
_1235993519.unknown
_1235993401.unknown
_1235993329.unknown
_1235993349.unknown
_1235993304.unknown
_1235981650.unknown
_1235984252.unknown
_1235984275.unknown
_1235984238.unknown
_1235975093.unknown
_1235979987.unknown
_1235981630.unknown
_1235977543.unknown
_1235979466.unknown
_1235977516.unknown
_1235974989.unknown
_1235898655.unknown
_1235907427.unknown
_1235933932.unknown
_1235934866.unknown
_1235934905.unknown
_1235934966.unknown
_1235935057.unknown
_1235934887.unknown
_1235934830.unknown
_1235934845.unknown
_1235934810.unknown
_1235907587.unknown
_1235908661.unknown
_1235908671.unknown
_1235912867.unknown
_1235908329.unknown
_1235908371.unknown
_1235907539.unknown
_1235907574.unknown
_1235907441.unknown
_1235898929.unknown
_1235906720.unknown
_1235907412.unknown
_1235898939.unknown
_1235898820.unknown
_1235898867.unknown
_1235898878.unknown
_1235898810.unknown
_1235897329.unknown
_1235898619.unknown
_1235898178.unknown
_1235898598.unknown
_1235897346.unknown
_1235890104.unknown
_1235891180.unknown
_1235891225.unknown
_1235891300.unknown
_1235891324.unknown
_1235890125.unknown
_1235890852.unknown
_1235887675.unknown
_1235887897.unknown
_1235889015.unknown
_1235889976.unknown
_1235887927.unknown
_1235887830.unknown
_1235887404.unknown
_1234116507.unknown
_1234204419.unknown
_1234287699.unknown
_1234288583.unknown
_1234289672.unknown
_1235885852.unknown
_1235887331.unknown
_1235887353.unknown
_1234289840.unknown
_1234289998.unknown
_1234290027.unknown
_1234289714.unknown
_1234288740.unknown
_1234288904.unknown
_1234288611.unknown
_1234287764.unknown
_1234288529.unknown
_1234287742.unknown
_1234287443.unknown
_1234287610.unknown
_1234287677.unknown
_1234287469.unknown
_1234287387.unknown
_1234287413.unknown
_1234286755.unknown
_1234117836.unknown
_1234202981.unknown
_1234204306.unknown
_1234204366.unknown
_1234204267.unknown
_1234120955.unknown
_1234177779.unknown
_1234117877.unknown
_1234116824.unknown
_1234116939.unknown
_1234116983.unknown
_1234116901.unknown
_1234116580.unknown
_1234116755.unknown
_1234116537.unknown
_1173793127.unknown
_1234116140.unknown
_1234116362.unknown
_1234116455.unknown
_1234116178.unknown
_1234116035.unknown
_1234116108.unknown
_1208802782.unknown
_1234115948.unknown
_1178526188.unknown
_1178526378.unknown
_1178526012.unknown
_1144823160.unknown
_1173793018.unknown
_1173793126.unknown
_1173792988.unknown
_1144823417.unknown
_1144823039.unknown
_1144823107.unknown
_1144822847.unknown
_1144820056.unknown
_1144822537.unknown
_1144822657.unknown
_1144822693.unknown
_1144822739.unknown
_1144822594.unknown
_1144822577.unknown
_1144822321.unknown
_1144822433.unknown
_1144822482.unknown
_1144822364.unknown
_1144821222.unknown
_1144821948.unknown
_1144821177.unknown
_1144821068.unknown
_1144819504.unknown
_1144819807.unknown
_1144819889.unknown
_1144819748.unknown
_1144819353.unknown
_1144819431.unknown
_1144819270.unknown