SET 1 Koleksi Soalan dan Skema Jawapan SPM KBSM

SULIT 30 1449/1
33 Diagram 15 is a Venn diagram with the universal set, , set P set Q and set R.

Rajah 15 ialah gambar rajah Venn dengan set semesta, , set P set Q dan set R.



P Q




R







Diagram 15
Rajah 15

Set P = { Egg Sandwich }

Set Q = { Tuna Sandwich }
Set R = {Sardine Sandwich }
It is given that n( ) = 260, n(P) = 100, n(Q) = 120, n(R) = 20 and n(P Q) = 10.

Find the difference between the number of students who did not take any of the sandwiches

with the number of students who took Sardine sandwich only.
Set P = { Sandwich Telur }
Set Q = { Sandwich Telur }

Set R = { Sandwich Sardin }
Diberi n( ) = 260, n(P) = 100, n(Q) = 120, n(R) = 20, dan n(P Q) = 10.

Cari beza di antara bilangan murid yang tidak mengambil mana-mana sandwich dengan
bilangan murid yang mengambil sandwich Sardin sahaja.


A 10

B 12

C 15

D 18







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SULIT 31 1449/1


34 Which of the following graphs represents ?

Antara graf berikut, yang manakah mewakili ?


A B
y y


x
x






C D
y y



x x



3




























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SULIT 32 1449/1
35 Diagram 16 shows a straight line which intercepts the x-axis and y-axis on a Cartesian plane.

Rajah 16 menunjukkan suatu garis lurus yang memotong paksi-x dan paksi-y pada suatu
satah Cartes.




y

(4, 2)

x
q



( , )




Diagram 16
Rajah 16

The value of q is
Nilai bagi q ialah

A



B



C


D

















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SULIT 33 1449/1
36 There are 80 red shirts and 32 green shirts in a container. A shirt is chosen at random from

the container. Find the probability that the shirt chosen is a green shirt.
Terdapat 80 helai baju berwarna merah dan 32 helai baju berwarna hijau di dalam sebuah

bekas. Sehelai baju dipilih secara rawak dari bekas itu. Cari kebarangkalian bahawa sehelai
baju berwarna hijau dipilih.

A


B


C


D



37 In a book shelf there are 40 Science books and a number of Geography books. The probability

that a Geography book is chosen at random from the shelf is .


How many Geography books are there in the bookshelf?
Di dalam sebuah rak buku terdapat 40 buah buku Sains dan beberapa buah buku Geografi.


Kebarangkalian bahawa sebuah buku Geografi dipilih secara rawak ialah . Berapakah

buku Geografi yang ada di rak itu ?


A 15

B 24

C 55

D 65


















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SULIT 34 1449/1
38 It is given that p varies inversely as square root of q and p = 3 when q = 64.

Calculate the value of p when q = 16.
Diberi bahawa p berubah secara songsang dengan punca kuasa dua q dan p = 3 apabila

q = 64.
Hitung nilai p apabila q =16.

A



B



C 12

D 6


39 The volume of a prism varies directly as the length and the height of the prism. Given that
3
the volume of the prism is 450 cm when the length and the height of the prism is 10 cm and
5 cm respectively.
Calculate the volume of the prism with the length 12 cm and height 7 cm.
Isipadu sebuah prisma berubah secara langsung dengan panjang dan tinggi prisma itu.

3
Diberi isipadu prisma ialah 450 cm apabila panjang dan tingginya ialah 10 cm dan 5 cm
masing masing.

Hitung isipadu sebuah prisma dengan panjang 12 cm dan tinggi 7 cm.

A 378

B 387

C 756

D 765




















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SULIT 35 1449/1
40
It is given that is the inverse matrix of .

Find k + m.

1 2 k
Diberi ialah matriks songsang bagi .
m 1 3

Cari nilai k + m.

A 2

B 6

C 10

D 14






















END OF QUESTION PAPER
KERTAS PEPERIKSAAN TAMAT











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SULIT 36 1449/1

INFORMATION FOR CANDIDATES
MAKLUMAT UNTUK CALON

1. This question paper consists of 40 questions.
Kertas soalan ini mengandungi 40 soalan.

2. Answer all questions.
Jawab semua soalan.

3. Answer each question by blackening the correct space on the objective answer sheet.
Jawab setiap soalan dengan menghitamkan ruangan yang betul pada kertas jawapan
objektif.

4. Blacken only one space for each question.
Hitamkan satu ruangan sahaja bagi setiap soalan.

5. If you wish to change your answer, erase the blackened mark that you have done. Then
blacken the space for the new answer.

Sekiranya anda hendak menukar jawapan, padamkan tanda yang telah dibuat.
Kemudian hitamkan jawapan yang baharu.

6. The diagram in the questions provided are not drawn to scale unless stated.
Rajah yang mengiringi soalan tidak dilukis megikut skala kecuali dinyatakan.
7. A list of formulae is provided on page 2 to 4.

Satu senarai rumus disediakan di halaman 2 hingga 4.
8. You may use a scientific calculator.

Anda dibenarkan menggunakan kalkulator saintifik.































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PROGRAM GEMPUR KECEMERLANGAN
SIJIL PELAJARAN MALAYSIA 2020


SIJIL PELAJARAN MALAYSIA 2020

MATHEMATICS 1449/2
Kertas 2
Peraturan Pemarkahan
Oktober





PERATURAN PEMARKAHAN

Question Solution and Mark Scheme Mark Total


1 (a) ( X Z)' Y or X ' Z' Y . Accept P1 1



(b)
K2 2













Note:

1. (P Q ) correctly shaded seen, award K1

3


2 3x 2 7x 6 0 K1
(x 3 )( 3x ) 2 0 or equivalent K1
OR

( ) 7 ( ) 7 2 3 ( 4 )( ) 6
(K1)
) 3 ( 2
3 N1
2
3 N1
Note:
1.
2. Accept three correct terms on the same side, in any order
4

3 2x y 40 or 3x 2y 65 P1

4x 2y 80 or equivalent K1
Note:
1. Accept any two different variable .
2. Attempt to equate the coefficient of one of the unknowns
award K1
OR
40 y
y 40 2 x or x or equivalent (K1)
2
Note:
Attempt to make one of the unknowns as the subject with two terms
on other side, award K1.
K1
x 15 or y 10 or equivalent
N1
x 15 N1
y 10
(x = mass of Wafiq and y = mass of Khalish)



5



4 (a)

or P1
or


(b)


80 120 2 80 2
sin or cos or K1
120 120

80
tan or equivalent
120 2 80 2
41.8 or N1


3

Question Solution and Mark Scheme Mark Total

5 4x 12y 72 or equivalent P1
10x 20y 140 or equivalent P1



4 12 x 72
or equivalent P1
10 20 y 140


1 20 12 72 or equivalent K1
( 4 20 ) 12 ( 10 ) 10 4 140


Note :

Inverse 72
1. award K1
matrix 140
Inverse 4 12 Inverse 1 0
2. Do not accept or
matrix 10 20 matrix 0 1

N1
x 6 N1
y 4


Note :
1. Accept any two different symbol for price of a white tile and price
of a black tile.
x 6
2. as the final answer, award N1.
y 4
3. Do not accept any solution solved not using matrix method. 6

6 (a) Some // Sebilangan P1 1

(b) Implication 1 // Implikasi 1: P1
If number of subset for set P is 8 then n(P) = 3
Jika bilangan subset bagi set P ialah 8 maka n(P) =3

Implication 2 // Implikasi 2 : P1 2
If n(P) = 3 then number of subset for set P is 8
Jika n(P) =3 maka bilangan subset bagi set P ialah 8

(c) ( 7 ) 2 180 or 5 180 or 900 K2 2
Note :
If K0, 7( ) 2 180 or 5 180 or 900 seen, award K1 5

7 (a) 3 P1
m 2
3 K1
*
4 ( )( ) 8 c or c 8
2
3
3 N1
y x 8
2
(b) 0 * ( 3 x ) 8 or equivalent
2 K1
16
3 N1 2

5


8 (a) 178 P1 1

(b) 350 K1
7 or equivalent
50 N1 2

(c)
or equivalent
K1
2.07 N1 2

5


9 (a)
Tempat / Langkawi Pulau Pinang Cameron
Baucer (L) (P) Highlands
(C)
50 ( L, 50) ( P , 50 ) ( C , 50)
80 ( L, 80) ( P , 80 )
100 ( L, 100) ( P , 100) ( C, 100)
150 ( P , 150) ( C , 150) P2 2

Note :
1. Allow two mistakes for P1


(i) L , 50 , , L 80 , , L 100 , , L 150 , , P 100 , , C 100 K1

6 1 N1 2
or
12 2

(b) , L 50 , , L 80 , L 100 , L 150 , P 50 , P 80 , , P 100 , P 150 , K1
(ii) , C 50 , , C 80 , , C 100
2

11
= N1
12

Note :
1. Accept correct answer without working from listing.
2. Accept correct listing without brackets and commas


6

10 (a) 5 22 9 2 t or equivalent
9 7 K1

1 4 22 3
2 3 7 9 or equivalent K1

5 22 1 4 22
3
9 2 t = 9 K1
9 7 2 3 7

10.8 cm
N1
Note :

1. Accept for K mark
2. Accept correct value from incomplete substitution for K mark
3. Correct answer from incomplete working, award Kk2


4

Question Solution and Mark Scheme Mark Total
11 (a) 270 22 90 22 K1
360 2 7 15 or 360 2 7 10 or equivalent

270 22 90 22
360 2 7 15 + 360 2 7 10+15 + 15 + 10 + 10 K1

or equivalent

955 3
7 or 136 or 136.4 N1 3
7


270 22 90 22
2
2
(b) 15 or 10 or equivalent K1
360 7 360 7

270 22 90 22
15 - 10 or equivalent K1
2
2
360 7 360 7

6325 11
or 451 or 451.6 451.8 N1 3
14 14
6

NOTE:

1. Accept for K mark
2. Accept correct value from incomplete substitution for K mark
3. Correct answer from incomplete working, award Kk2

Question Solution and Mark Scheme Mark Total

12 (a) 4 K1
0 K1 2

(b) Axes drawn in correct directions with uniform scale for x P1
and 10 y 14.
All 5 and *2 points correctly plotted or curve passes through all the K2
points for x 10 y 14.
Note:
5 or 6 points are correctly plotted,award K1

Smooth and continuous curve without any straight line passes
through all 7 correct points using the given scale for x N1 4
10 y 14

(c) (i) 5.8 P1
(ii) 2
P1

(d) A straight line is correctly drawn.
(Check any two points are plotted or the straight line passed through K2
( 0,0), (1 ,4), ( 2 1 square grid
2
vertically)

Note:
Identify equation award K1

N1
N1
4

Note:
1. Allow P mark or N mark if values of x and y are shown on the
graph.
2. Values of x and y are obtained by calculations, award P0 or
N0.
3. Values of x and y are obtained from the wrong graph award
P0 or N0.

12

Graph for Question 12 / Graf untuk Soalan 12
y
14




12




10




8




6




4




2




x
-3 -2 -1 0 1 2 3


- 2




- 4




- 6




- 8





-10

Question Solution and Mark Scheme Mark Total
13 (a) (i) (0, 5) P1

(ii) ,6 2 P2 3
Note:
(6, - 2) marked on the diagram or 6, 2 seen or (6, 2) marked on
the diagram, award P1.

(a) V = Rotation 90 clockwise centre 2 , 2 //Putaran 90
o
o
(b)(i)
ikut arah jam pusat 2 , 2 P3

Note:
o
1. Rotation 90 clockwise or Rotation centre (-2,2)// Putaran
o
90 ikut arah jam or Putaran pusat (-2,2), award P2
2. Rotation // Putaran award P1
P3 6
(b) W = Enlargement of scale factor 3 with centre E 5 , 3
or equivalent
Pembesaran dengan faktor skala 3 pada pusat E 5 , 3
Note :
1. Enlargement of scale factor 3// Enlargement with centre
E (-3, 5) award P2
Pembesaran dengan faktor skala 3 // Pembesaran pada pusat
F (-3, 5)
2. Enlargement // Pembesaran award P1
OR equivalent.

x 248 ) 3 ( 2 x or equivalent
(b)(ii)
OR
248 5 . 2 (K2)
20 K2
OR
248 4 (K2)

32
Note:
1 248 248
1. 8 or seen OR OR award K1 3
8 20 32

31
N1 12

Question Solution and Mark Scheme Mark Total
14 (a) Class interval Cumulative Frequency Midpoint
(marks) frequency Kekerapan Midpoint
Selang kelas Kekerapan
(markah) Longgokan

I 61 65 0 0 63
II 66 70 2 2 68
III 71 75 6 4 73
IV 76 80 17 11 78
V 81 85 32 15 83
VI 86 90 40 8 88
VII 91 95 45 5 93
VIII 96 100 48 3 98
P2
Frequency : I to VIII P1 3
Midpoint : I to VIII

(b) * 2 68 4 * 73 * 11 78 * 15 83 8 * 88 5 * 93 3 * 98
48 K2

Note :
1. Allow two mistakes in *frequency for K1
2. Allow two mistakes for multiplication of *frequency and
midpoint for K1
1997 5
24 or 83 24 or 83.21 N1 3
Note :
Correct answer from incomplete working, award Kk2.
e.g 3994
48

(c) Histogram
Axes are drawn in the correct directions with uniform scales for P1
65 5 . x 100 5 . and 0 y * 15
*8 bars are correctly drawn using correct values of class K2
boundaries/class interval/midpoint.

Note: N1 4
*6 or *7 bars are correctly drawn, award K1.
Correct histogram using the given scale.
(d)
*35.42
Note : K2 2
*17 seen award K1
Do not accept answer without histogram
12

Graph for question 14
Graf untuk soalan 14














Frequency/
Kekerapan





16




14




12



10




8




6




4



2





0 68 73 78 83 88 93 98 Marks
Markah

Question Solution and Mark Scheme Mark Total
15 Note:
1. Accept drawing only (Not sketch)
2. Accept diagram without labels and ignore wrong labels.
3. Accept correct rotation of diagram.
4. Lateral inversions are not accepted.
5. If more than 1 diagram are drawn, award mark to the correct
ones only.
6. For extra line (dotted/dashed or solid) except construction
lines, no KN mark is awarded.
7. If other scale is used, award K marks only.
8. Accept small gaps or extension.
For each part attempted:
(i)
mark from the N mark obtained.
(ii) If > 0.4 cm, no N mark is awarded.
9. If construction lines cannot be differentiated from the lines:
(i) Dotted line
If outside the diagram, award the N mark.
If inside the diagram, award N0.
(ii) Solid line
If outside the diagram, award N0.
If inside the diagram, no KN mark is awarded.
10. For double line, non collinear lines, bold lines and crooked
lines, deduct 1 mark from the N mark obtained, for each part
attempted.
11. If drawn on graph paper, award K mark only.

(a)


6 cm
A B
E 4



5 cm




F G
4 cm
Correct shape trapezium ABGF. All solid line. No right angle in all K1
vertices.
K1
JK > AB > FG, AF = BG
N1 3
Measurement ± 0.2 cm (one way)




(b) N P

3 cm


B C


8 cm







G 7 cm S 2 cm Q


Correct shape with rectangle BCSG and rectangle NPQS. All solid K1
line.
PQ > GS > BG > NC > NP K1

Measurement ± 0.2 cm (one way), and all angles at vertices 4
90 1 N2

(ii) L P

2 cm

D M H N







7 cm







A 1 cm F 4 cm G 1 cm B

Correct shape with rectangle LPNM and rectangle DNBA. All solid K1
line.
(Ignore line MF and line HG)

M-F and H-G are joined with dotted line to form rectangles ADMF,
FMHG and GHNB K1

DA > LP > FG > LM > AF = GB K1

Measurement ± 0.2 cm (one way), and all angles at vertices N2 5
90 1

Question Solution and Mark Scheme Mark Total
16 (a) ( 40 , S 106 E ) //( 40 , S 106 T ) P1P2 3
Note:
( 40 , S E ) //( 40 , S T ) or 40 S , 106 W ) //( 40 , S 106 ) B award
(
P1P1




(b) ( 180 40 40 ) 60 K1

6000 N1 2


(c)
( 25 106 ) 60 cos 40 K2
Note:
( 25 106 ) or cos 40° correctly used, award K1


N1 3
6021




(d) ( 80 60 ) K1

*6021 80 60 K2

500

Note:
*6021 + (80 60) award K1

21.64 N1 4


12

SAINS