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SULIT 1449/
1449/2 [Lihat sebelahSULIT
JABATAN PELAJARAN NEGERI SABAH
SIJIL PELAJARAN MALAYSIA 1449/2EXCELMATHEMATICS Paper 2
2 Hours 30 Minutes Two hours and thirty minutes
JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU
1. Tulis nombor kad pengenalan dan angka giliran anda pada ruangan
yang disediakan.2. Kertas soalan ini adalah Bahasa
Ingers. 3. Calon dikehendaki membaca
maklumat di halaman 2.
Kod Pemeriksa
Bahagian Soalan MarkahPenuhMarkah
Diperolehi
A
1 32 4
3 4
4 5
5 3
6 67 5
8 5
9 7
10 4
11 6
B
12 1213 12
14 12
15 12
16 12Jumlah
Kertas soalan ini mengandungi 29 halaman bercetak.
NAMA : _______________________________
KELAS : ______________________________
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INFORMATION FOR CANDIDATES
1. This question paper consists of two sections : Section A and Section B ..2. Answer all questions in Section A and four questions from Section B .
3. Write your answers clearly in the space provided in the question paper.
4. Show your working. It may help you to get marks.
5. If you wish to change your answer, neatly cross out the answer that you have done. Then write down thenew answer.
.6. The diagram in the questions provided are not drawn to scale unless stated.
7. The marks allocated for each question and sub-part of a question are shown in brackets.
8. A list of formulae is provided on pages 3 to 4.
9. A booklet of four-figure mathematical tables is provided.
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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MATHEMATICAL FORMULAERUMUS MATEMATIK
The following formulae may be helpful in answering the questions. The symbols given are the ones commonlyused. Rumus-rumus berikut boloeh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasadigunaan.
1 nmnm aaa
2 nmnm aaa
3 mnnm aa )(
4
ac
bd
bcad A
11
5 Distance/ jarak
= 2212
21 )()( y y x x
6 Midpoint/ Titik tengah
2,
2),( 2121
y y x x y x
7
8 Mean =dataof number
dataof sum
9 Mean =sfrequencieof sum
frequency)mark class(of ums
10 Pythagoras Theorem / Teorem Pithagoras
222 bac
11
12 )(1)'( AP AP
1312
12
x x
y ym
14ercept xercept y
mintint
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SHAPES AND SPACE
1 Area of trapezium = heights21
sides parallelof um
Luas trapezium =
2 Circumference of circle = r d 2 Lilitan bulatan = d = 2 j
3 Area of circle = 2r Luas bulatan = j2
4 Curved surface area of cylinder = rh 2 Luas permukaan melengkung silinder = 2 jt
5 Surface area of sphere = 24 r Luas permuaan sfera = 4 j2
6 Volume of right prism = cross sectional area length Isipadu prisma tegak = luas keratan rentas panjang
7 Volume of cylinder = hr 2 Isipadu silinder = j2t
8 Volume of cone = hr 2
3
1
Isipadu kon =
9 Volume of sphere = 33
4r
Isipadu sfera = 33
4r
10 Volume of right pyramid =3
1 luas tapak tinggi
Isipadu piramid tegak =
11 Sum of interior angles of a polygon Hasil tambah sudut pedalaman poligon= 180)2(n
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12 360
centreatsubtendedanglecircleof ncecircumfere
lengtharc
13 360
centreatsubtendedanglecircleof areasectorof area
14 Scale factor,PAPA
k '
Faktor skala, k =
15 Area of image = 2k area of object Luas imej = k 2 luas objek
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Section A[52 marks ]
Answer all questions in this section .
1 The Venn diagram in the answer space shows sets, J , K and L such that the universalset, = J LK .
Gambar rajah Venn di ruang jawapan menunjukkan set J, set K and set L dengankeadaan set semesta = J LK .
On the diagram in the answer space, shadePada rajah di ruang jawapan, lorekkan
(a) J L ,
(b) ( ) ' J L K .[3 marks ]
[ 3 markah ]
Answer/ Jawapan :
(a) J K L
(b) J K L
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2 Calculate the value of p and of q that satisfy the following simultaneous linear equations:
Hitung nilai p dan nilai q yang memuaskan persamaan linear serentak berikut:
7612
343
q p
q p
[ 4 mar[4 marka
Answer /Jawapan :
3 Using factorization, solve the following quadratic equation. Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut.
)1(3222
x x [4 mar[4 marka
Answer/ Jawapan :
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4 Diagram 4 shows a trapezium PQRS drawn on a Cartesian plane . SR is parallel to PQ . Rajah 4 menunjukkan sebuah trapezium PQRS yang dilukis pada suatu satah Cartesan.SR adalah selari dengan PQ.
yS
R ( 6, 1)
xO
P ( -1,-2)
Q ( 4, - 3)
Diagram 4 Rajah 4
FindCari(a) the equation of the straight line SR
persamaan garis lurus SR
(b) the x-intercept of the straight line SR pintasan-x bagi garis lurus SR
[ 5 mark[ 5marka
Answer /Jawapan :
(a)
(b)
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5 Diagram 5 shows a pyramid. Base JKLM is a horizontal rectangle and VL is vertical. VLM is a rightangled triangle.
Rajah 5 menunjukkan sebuah piramid. Tapak segiempat tepat JKLM adalah mengufuk dan VL adalahmenegak. VLM adalah sebuah segitiga bersudut tegak.
V
3 cm
M L
5 cm
J 6 cm K
Diagram 5 Rajah 5
(a) Name the angle between the line KV and the plane LMV.
Namakan sudut di antara garis KV dengan satah LMV.
(b) Calculate the angle between the line KV and the plane LMV Hitung sudut di antara garis KV dengan satah LMV . [3 mar
[3 marka
Answer /Jawapan :(a)
(b)
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6 In Diagram 6, OABC and ODE are two sectors of circles with centre O .
Dalam Rajah 6, OABC and ODE ialah dua sektor bagi bulatan-bulatan berpusat O.
Diagram 6
Rajah 6
It is given that OA = 7 cm, OE = 14 cm , 104 , AOE and 36 . EOD Diberi bahawa OA = 7 cm, OE = 14 cm, 104 , AOE dan 36 . EOD
By using =7
22 , calculate
Dengan menggunakan =7
22 , hitung
(a) the area, in cm 2, of the whole diagram,luas , dalam cm 2, seluruh rajah itu ,
(b) the perimeter, in cm, of the whole diagram. perimeter, dalam cm, seluruh rajah itu. [6 mar
[6 markaAnswer /Jawapan :
(a)
(b)
D
C
B
A
OE
14cm
7cm
36o
104 o
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7 (a) Determine whether the following statement is true or false.
All multiples of 10 are multiples of 5
Tentukan pernyataan berikut betul atau palsu.
Semua nombor gandaan 10 merupakan nombor gandaan 5.
(b) It is given the sum of all interior angle of a regular polygon of n sides is 0( 2) 180n .Make one conclusion by deduction on the size of the sum of all interior angle of a regularoctagon.
Diberi bahawa jumlah sudut pedalaman sebuah polygon sekata dengan n sisi ialah0( 2) 180n .
Buat satu kesimpulan secara khusus tentang saiz jumlah sudut pedalaman sebuah octagon.
(c) State the premise in the following argument.Premise 1 : If x is a prime number, then x has two factors only.Premise 2 : . Conclusion : x is not a prime number.
Nyatakan premis yang sesuai dalam hujah berikut:Premis 1 : Jika x ialah suatu nombor perdana, maka x mempunyai dua faktor sahaja.
Premis 2 : . Conclusion : x bukan nombor perdana.
[5 marks[5 markah
Answer /Jawapan :
(a) .
(b)
.
(c) Premise 2 / Premis 2 ::
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8 The diagram 8 below shows six labeled cards in Box P and Box Q. Rajah 8 dibawah menunjukkan enam kad yang berlabel di dalam kotak P dan kotak Q.
Diagram 8 Rajah 8
A card is picked at random from each of the boxes.Sekeping kad dipilih secara rawak daripada setiap kotak itu.
(a) List the sample space.Senaraikan ruang sampel.
(b) List all the outcomes of the events and find the probability thatSenaraikan semua kesudahan peristiwa dan cari kebarangkalian bahawa
(i) both cards are labelled with an odd number,kedua-dua kad dilabel dengan nombor ganjil.
(ii) a card is labelled with number 7 or the card with an even number is picked.satu kad dilabel dengan nombor 7 atau kad berlabel nombor genap dipilih.
[5 marks[5 markah
Answer /Jawapan :
(a)
(b)(i)
(ii)
Box Q Kotak Q
Box P Kotak P
765 328
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9.The inverse of
3 2
6 7
is7 21
2 3mk
Matrix songsang bagi3 2
6 7
ialah7 21
2 3mk
a) Find the value of m and of k Cari nilai m dan nilai k
b) Using matrices, calculate the value of x and of y that satisfy the following matrix equation: Menggunakan kaedah matriks, hitung nilai x dan nilai y yang memuaskan persamaan matriksberikut:
3 2 1
6 7 8
x
y
[7 marks
[7 markah
Answer/ Jawapan :
(a)
(b)
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10 Diagram 10 shows a solid mass in the shape of a half cylinder with a half cone taken out. The height of the cone is half of the length of the cylinder. The diameter of the half cylinder is 7cm and the length of cylinder is 12cm.
Rajah 10 menunjukkan sebuah pepejal berbentuk separuh silinder dengan separuh kon dikeluarkan.Tinggi kon adalah separuh daripada tinggi silinder tersebut. Diameter separuh silinder adalah 7cm dan
panjang silinder adalah 12cm.
Diagram 10 Rajah 10
Calculate the volume, in cm 3 , of the remaining solid. Hitung isipadu, dalam cm 3 , pepejal yang tinggal itu.
[ Use /Guna =7
22] [1
marks ][10 markah
Answer/ Jawapan :
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11 Diagram 11show the distance-time graph of a lorry and a taxi. Rajah 11 menunjukkan graf jarak masa bagi perjalanan sebuah lori dan sebuah taxi.
Diagram 11 Rajah 11
The graph ABCD represents the journey of the lorry from town Y to town X. Graph PQ represents the journey of the taxi from town X to town Y. The lorry and the taxi depart at the same time and travelalong the same road.
Graf ABCD mewakili perjalanan lori dari bandar Y ke bandar X. Graf PQ mewakili perjalanan taxi daribandar X ke bandar Y. Lori dan taxi itu bertolak pada masa yang sama dan melalui jalan yang sama.
(a) State the length of time, in minutes, during which the lorry is stationary. Nyatakan tempoh masa, dalam minit, lori itu berhenti.
(b) (i) If the journey starts at 2.00 p.m., at what time do the vehicles meet? Jika perjalanan itu bermula jam 2.00 p.m., pukul berapakah kedua-dua kenderaan itubertemu?
(b) (ii) Find the distance, in km, of the two vehicles from town Y when they meet.Cari jarak, dalam km, dari bandar Y bila kedua-dua kenderaan itu bertemu.
(c) Calculate the average speed, in kmh -1 , of the lorry for the whole journey.Kirakan purata laju, dalam kmj -1 , lori itu bagi keseluruhan perjalanan. [6 marks
[6 markahAnswer/ Jawapan :
(a)
(b)(i)
(b) (ii)
(c)
Time / Masamin
Town Y Bandar Y
60
40
0 10 25 50 80
A
B C
D
Q
P
Town X Bandar X
Distance/ Jarak km
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Section BBahagian B
[ 48 marks/markah]Answer any four questions from this section.
Jawab mana-mana empat soalan daripada bahagian ini.
12 (a ) Complete Table 12 in the answer space for the equation 12 y x
by writing down the values of y
when x = 2 and x = 3.5. [2 marks ]
Lengkapkan Jadual 12 di ruang jawapan bagi persamaan12
y x
dengan menulis nilai-nilai y
apabila x = 2 dan x = 3.5 . [2 markah ]
(b) For this part of question, use the graph paper provided on page 19.You may use a flexible curve rule.Untuk ceraian soalan ini, guna kertas graf pada halaman 19.
Anda boleh guna pembaris flesible.
Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of 12
y x
for . [4 marks ]
Menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 2 cm kepada 2 unit pada paksi-y, lukis
graf 12
y x
untuk . . [4 markah ]
(c) From the graph in 12 (b), find Dari graf di 12 (b) , cari
(i) the value of y when x = 2.5,nilai y apabila x = 2.5,(ii) the value of x when y = 10.
nilai x apabila y = 10. [2 marks ][2 markah ]
(d ) Draw a suitable straight line on the graph in 12(b) to find the values of x which satisfy the equation24 12 0 x for . .
State the values of x. [4 marks ] Lukis satu garis lurus yang sesuai pada graf di 12 (b) untuk mencari nilai-nilai x yang memuaskan persamaan 24 12 0 x untuk . . Nyatakan nilai-nilai x ini. [4 markah ]
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Answer / Jawapan :
(a ) x -4 3 2 -1.2 1 2 3 3.5 4
y 3 4 10 -12 -6 -4 -3
Table 12 Jadual 12
(b) Refer graph on page 19. Rujuk graf di halaman 19.
(c) (i) y = .
(ii) x = .
(d ) x = , .
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Graph for Question 12Graf untuk Soalan 12
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13 (a ) Transformation R is a clockwise rotation of 90 o about the centre (0, 2).
Transformation T is a translation2
2
.
Penjelmaan R ialah putaran 90o ikut arah jam pada pusat (0, 2).
Penjelmaan T ialah translasi 22
.
State the coordinates of the image of the point (-1, 5) under these transformations : Nyatakan koordinat imej bagi titik (-1 ,5) di bawah penjelmaan:
(i) T 2
(ii) TR [4 marks ][4 markah ]
(b) Diagram 13 shows three pentagons, ABCDE, FGHIJ and FMNPQ , drawn on a Cartesian plane. Rajah 13 menunjukkan tiga pentagon , ABCDE, FGHIJ dan FMNPQ , dilukis pada suatu satahCartesan .
Diagram 13 Rajah 13
(i) FMNPQ is the image of ABCDE under a combined transformation WV . FMNPQ ialah imej bagi ABCDE di bawah gabungan penjelmaan WV .
Describe in full the transformation Huraikan selengkapnya penjelmaan(a) V ,(b) W . [ 5 marks ]
4
y
A
B
C
D
0
M
E F
H
G
2 4
2
4 8
2
4
6
x
I
J Q
P
2 6
N
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[5 markah ](ii) It is given that the region FMNPQ represents a region of area 20.5 m 2.
Calculate the area, in m 2, of the shaded region. Diberi bahawa kawasan FMNPQ mewakili luas 20.5 m 2. Hitung luas , dalam m2, kawasan berlorek.
Answer / Jawapan :
(a ) (i)
(ii)
(b) (i) (a ) V :
(b) W :
(ii)
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14 The data below shows the life span, in hours, of 32 batteries tested.
Data di bawah menunjukkan jangka hayat, dalam jam, 32 buah bateri yang telah diuji .
20 40 37 26 30 42 28 35
31 25 41 36 35 38 30 36
35 39 32 48 33 27 44 22
49 29 42 40 51 36 48 34
(a ) Based on the data, complete Table 14 in the answer space. [5 marks ] Berdasarkan data itu, lengkapkan jadual 14 pada ruang jawapan. [5 markah ]
(b) State the modal class. [1 marks ]Nyatakan kelas mod. [1 markah ]
(c) For this part of the question, use the graph paper provided on page 24.Untuk ceraian soalan ini, gunakan kertas graf yang disediakan di halaman 24 .
By using a scale of 2 cm to 5 hours on the x-axis and 2cm to 5 batteries on the y-axis, drawan ogive based on the data. [4 marks ]
Dengan menggunakan skala 2cm kepada 5 jam pada paksi x and 2cm kepada 5 bateri pada paksi y, lukiskan satu ogif berdasarkan data yang diberi. [4 markah ]
(d) From the ogive in (c) Dari ogif di (c)
(i) Find the median [1 marks ]Cari median, [1 markah ]
(ii) Find the third quartile, [1 marks ]Cari kuartil ketiga , [1 markah ]
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Answer / Jawapan :
(a )
Class
intervalSelang kelas
Upperboundary Sempadan
atas
Frequency Kekerapan
CumulativeFrequency
Kekerapan longgokan
15-19 19.5 0 0
20-24 24.5
25-29
30-34
35-39
40-4445-49
50-54
Table 14 Jadual 14
(b)
(c) Refer graph on page 24. Rujuk graf di halaman 24.
(d ) (i)
(ii)
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Graph for Question 14Graf untuk Soalan 14
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15 You are not allowed to use graph paper to answer this question. Anda tidak dibenarkan menggunakan kertas graf untuk menjawab soalan ini .
(a ) Diagram 15(i) shows a solid right prism with a rectangular base ABCD on a horizontal plane. Thesurface ABRUFE is the uniform cross-section of the prism. The rectangle RBCS is an inclinplane. The rectangles EFGH and RSTU are horizontal planes. The edges EA and FU are vertical.
Rajah 15(i) menunjukkan sebuah pepejal berbentuk prisma tegak dengan tapak segiempat tepat ABCD yang terletak di atas satah mengufuk. Permukaan ABRUFE ialah keratan rentasseragamnya. Segiempat tepat JRBCS ialah satah condong. Segi empat tepat EFGH dan RSTU ialah satah mengufuk. Tepi EA dan FU adalah tegak.
Diagram 15(i) Rajah 15(i)
Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X .
Lukis dengan skala penuh, dongakan pepejal itu pada satah mencancang yang selari dengan ABsebagaimana dilihat dari X .
[3 marks[3 markah
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Answer /Jawapan :(a )
(b) A solid cuboid of length 4cm, width 3cm and height 2cm is removed from the prism and theremaining solid is shown in Diagram 15(ii). PQML is a horizontal plane. FP, JL, NM and RQ arevertical edges.
Sebuah pepejal berbentuk kuboid dengan panjang 4cm, lebar 3cm dan tinggi 2cm, dikelaurkandaripada prisma itu . Pepejal yang tinggal seperti ditunjukkan pada Rajah 15(ii). PQML ialahsatah mengufuk. Tepi FP, JL, NM dan RQ adalah tegak .
Diagram 15(ii) Rajah 15(ii)
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Draw to full scale, Lukis dengan skala penuh,
(i) the plan of the remaining solid, pelan pepejal yang tinggal ,
[4 marks[4 markah
(ii) the elevation of the remaining solid on a vertical plane parallel to BC as viewed from Y .dongakan pepejal yang tinggal pada satah mencancang yang selari dengan BC sebagaimana dilihat dari Y. [5 marks
[5 markahAnswer /Jawapan :(b) (i), (ii)
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16 P (42 oN, 65 oW), Q and R are three points on the surface of the earth. PQ is the diameter of the parallel of latitude 42 oN. PR is the diameter of the earth.P (42 oU, 65 oB), Q dan R adalah tiga titik pada permukaan bumi. PQ ialah diameter selarian latitud 42oU . PR ialah diameter bumi.
(a ) State the position of Q. Nyatakan kedudukan Q.
[3 marks[3 markah
(b) Calculate the shortest distance, in nautical mile, from P to Q measured along the surface of theearth,
Hitung jarak terpendek , dalam batu nautika, dari P ke Q diukur sepanjang permukaan bumi ,[2 marks
[2 markah
(c) An aeroplane took off from P and flew due east to Q along the parallel of latitude. It then flew duesouth to R.Sebuah kapal terbang berlepas dari P arah ke timur ke Q sepanjang selarian latitude dankemudian terbang arah ke selatan ke R.
Calculate/ hitung (i) the distance, in nautical mile, from P to Q measured along the common parallel of latitude,
jarak , dalam batu nautika, dari P ke Q diukur sepanjang selarian latitude sepunya ,[3 marks
[3 markah
(ii) The time, in hours, taken for the whole flight if its average speed is 630 knots. Masa, dalam jam, yang diambil bagi seluruh penerbangan itu jika purata lajunya ialah 63knot.
[4 marks[4 markah
Answer / Jawapan :(a )
(b)
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(c) (i)
(c) (ii)
END OF QUESTION PAPERSOALAN TAMAT
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Question Solution and Mark Scheme Marks
1 (a)
(b)
J KK L
J KL
P1
P2
32
2
12p 16q = 12 o r 9 p - 12 q= 9 or 24 p-12q = 14 or
equivalent
Note :Attempt to equate the coefficient of one of the unknowns, award K1
-10q= 5 or -15p = -5 or equivalent
OR
p = 134
q or q=43
43
p or p127
21
q or q =67
2 p or
equivalent
Attempt to make one of the unknowns as the subject, award K1
K1
K1
K1
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-10q= 5 or -15p = -5 or equivalent
OR
7
3
312
46
)12)(4(6)3(1
q
p
Note :
Award K1 if
1.
7
3*
Matrix
Inverse
q
p or
7
3
612
43
q
p
2. Do not accept
*inverse
matrix
=
612
43 or
1 0
0 1
31
p
21
q
Note :
21
3
1
q
pas final answer, award N1
K1
K2
N1
N1
4
3 2 x2-3 x - 5=0 K1
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(2 x- 5) ( x + 1) =0 or equivalent
x = 2.5 or 2
5
x = -1
Note :
1. Accept without =0
2. Accept three terms on the same side, in any order
3. Do not accept solutions solved not using factorization
K1
N1
N1
4
4(a)M PQ =M SR =
)1(4)2(3
or5
1
=1 = * (6)SR M c or equivalent
y =5
1151
x or equivalent
P1
K1
N1
4(b)0 =
1 115 5
x or equivalent
11
K1
N1
5
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5(a)
(b)
6(a)
(b)
Identify KVL or LVK
tan KVL =3
5or equivalent
59.04 or 59 2
777
22360220
or36 22
14 14360 7
777
22360220
+36 22
14 14360 7
32155
45cm 2 or
7007
45cm 2 or 155.71 cm 2
77
222
360220
or36 22
2 14360 7
77
222
360220
+36 22
2 14 14 7 7360 7
3163
45cm or
286645
cm or 63.69 cm
Note:
1. Accept for K mark.2. Correct answer from incomplete working, award KK2
P1
K1
N1
K1
K1
N1
KI
K1
N1
3
6
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8(a)
(b) (i)
(ii)
{(5,2), (5,3),(6,2),(6,3),(7,2),(7,3),(8,2),(8,3)}
{(5,3),(7,3)}
2
8 @ 1
4
{(5,2),(6,2),(6,3),(7,2),(7,3),(8,2),(8,3)}
7
8
Note: Accept answer without working for K1N1
P1
K1
N1
K1
N1
9. (a)
(b)
k = 9
2m = -6m= -3
7 2 116 3 8(3)(7) (2)(6)
x
y
1
2
x
y
x = -1 y = 2
P1
P2
K2
N1N1
7 (a)
(b)
(c)
True
0(8 2) 180 1080 o
x has more than two factors / x does not has two factors
P1
P1N1
K2
5
5
7
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Note:
1. * 1
8
x inverse
y matrix
or7 2 116 3 8(3)(7) (2)(6)
seen, award K1
2. Do not accept*inverse
matrix
=
3 2
6 7
or1 0
0 1
3.1
2
x
y
as final answer, award N1
4. Do not accept any solutions solve not using matrices.
10. 1 1 22 3.5 3.5 62 3 7
OR 1 22 3.5 3.5 122 7
1 223.5 3.5 12
2 7 -
1 1 223.5 3.5 6
2 3 7
96.25 cm 3 @ 96 cm 3
K1
K2
N14
11(a)
(b)(i)
(ii)
(c)
40 or 40 m or 40 min
2.25pm or 1425 or 2.25
20km or 20
8060
60
45kmh -1 // 45 kmj -1 or 45
P1
P1
P1
K2
N16
12(a) (a) 6 K1
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3.43 K1 2
(b) Graph1. Axes drawn in correct direction with uniform scales in
3 x 4 and 12 y 82. All 6 points and *2 points correctly plotted or curve passes
through all the points for 3 x 43. A smooth and continuous curve without any straight line and
passes through all points
Note :6 or 7 points correctly plotted award K1 N0
P1
K2
N1
4
(c) (i)
(ii)
y = 4.8 4.5 5.1 y , and
x = -1.21.1 1.3 x
Note :
1. Allow P mark if value of x and of y are shown on graph
2. Value of x and of y obtained by calculation, award P0
P1
P1 2
(d) Identify equation 24 y x
Straight line 24 y x correctly drawn(Check any two points (-1,4), (0,0), (1,- 4),)
1.65 1.85 x
1.85 1.65 x
Note:
1. Allow N mark if value of x shown on graph
2. Value of x obtained by calculation, award N0
K1
K1
N1
N1
4
12
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3613(a)(i) (3,1) P2
y
x
8
-8
-10
-12
Graph for Question 12Graf untuk Soalan 12
-4 -3 -2 -1 0 1 2 3 4 x
10
8
6
4
2
-2
-4
-6
-8
-10
-12
y = -4x
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(ii) (5,1) P2 4
(b) (i) (a) V : Reflection in the line x = 3
Note :
1. Reflection / Pantulan , award P1
P2
(b) W : Enlargement with scale factor1
2at centre F/ (-3,1)
Note :
1. Enlargement with scale factor1
2// Pembesaran dengan faktor skala
1
2
or Enlargement at centre F (-3,1) // Pembesaran pada pusat F
(-3,1), award P2
2. Enlargement // Pembesaran, award P1
P3 5
(b) (ii) 22 20.5
22 20.5 - 20.5
61.5
K1
K1
N1 3
12
14(a)
Class Upper Frequency Cumulative
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intervalSelang kelas
boundary Sempadan
atas
Kekerapan Frequency Kekerapanlonggokan
15-19 19.5 0 0I 20-24 24.5 2 2II 25-29 29.5 5 7III 30-34 34.5 6 13IV 35-39 39.5 9 22V 40-44 44.5 6 28VI 45-49 49.5 3 31VII 50-54 54.5 1 32
Upper boundary : (II to VII) P1Frequency : (I to VII) P2Cumulative Frequency : (I to VII) P2 5
Note :1. Allow two mistakes in frequency for P12. Allow two mistakes in cumulative frequency for P1
(b) 35-39 P1 1
(c) Graph1. Axes drawn in correct direction with uniform scales in
19.5 x 54.5 and 0 y 322. All points correctly plotted and curve passes through using at
least correct 6 correct upper boundary
3. Smooth and continuous curve without any straight line passesthrough all correct points using the given scales
Note :5* points plotted correctly award K1 N0
P1
K2
N1
4
(d) (i) 36 37 x P1 1
(ii) 40.5 41.5 x P1 112
Graph for Question 14Graf untuk Soalan 14
CumulativeFrequency
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15(a)
Correct shape with prism AEFURB.All solid lines .
AE=AB>RB>RU=FU>EF
Measurement correct to 0.2 cm (one way) and all angles at the verticesof rectangles = 90 o 1 o.
K1
K1
N1 3
15 (b) (i)
Correct shape with rectangle ADGF, LTSN,FLNR,RSCB.All solid lines .
CD=AB>AD=BC=FG=RS>FL=RN>ST=FR=JN>GJ=SN
K1
K1
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Measurement correct to 0.2 cm (one way) and angle A, angle B andangle K= 90 o 1 o.
N2 4
15 (b) (ii)
Correct shape with rectangle REGS and ARSC.All solid lines.
Note :Ignore dotted line NM and QM.
N and M as well as Q and M joined with dotted line to form rectangleQRNM
AE=DH>EG=RS=AC>RN>NS
Measurement correct to 0.2 cm (one way) and all angle at the verticesof rectangles = 90 o 1 o.
K1
K1
K1
N2 5
12
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16 (a) (42 oN, 115 oE) // (42 oU, 115 oT)
Note :
1. 42 oN // 42 oU or 115 oE // 115 oT, award P22. 42 o or 115 o, award P1
P3 3
(b) (180 o-42 o-42 o)x60=96 x 60=5760 n.m.
K2
N1 3
(c)(ii) 180 60 cos 42 o
Note : Using cos42 o or * cos42 o , award K1
8025.96 n.m.
K2
N1 3
(ii) (5760 8025.96)630
21.88
K2
N1 3
12
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