SET 2 Koleksi Soalan dan Skema Jawapan SPM KBSM

SULIT 13 3472/1 For

12 A bag contains of six cards labelled 0, 1, 2, 3, 4 and 5. A card is taken out from the bag, examine s
use only

recorded and is replaced back. This process is repeated for 40 times and recorded in

table 1.

Sebuah beg mengandungi enam kad berlabel 0, 1, 2, 3, 4 dan 5. Satu kad dikeluarkan

daripada beg itu, dicatat dan dikembalikan semula. Proses ini diulangi sebanyak 40 kali

dan dicatatkan dalam jadual 1.

Card 012 3 45
Kad 349 5 a 11
Frequency
Kekerapan Table 1 / Jadual 1

Find
Cari

(a) the value of a, [4 marks]
nilai a, [ 4 markah]

(b) the standard deviation.
sisihan piawai.

Answer/Jawapan :

(a)

(b) 12
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For SULIT 14 3472/1
examiner
use only 13 Diagram 4 shows a major sector of OPRQ with centre O [3 marks]
Rajah 4 menunjukkan sebuah sektor major OPRQ dengan pusat O. [3 markah]

P
6 cm

0.8 rad
RO

Q

Diagram 4 / Rajah 4

Calculate
Hitung

(a) the minor angle of POQ in radians,
sudut minor POQ dalam radian,

(b) the major arc length of PRQ.
panjang lengkuk major PRQ.

Answer/Jawapan :
(a)

(b)

13 SULIT
3

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SULIT 15 3472/1 For

14 Diagram 5 shows a regular hexagon in a circle with centre N. examine s
use only

Rajah 5 menunjukkan heksagon sekata terterap di dalam sebuah bulatan berpusat di N.

(a) State angle PMQ in terms of radians,
Nyatakan sudut PMQ dalam sebutan radian,

(b) Hence, express the shaded area in terms of j, where j is the radius of the circle.
Seterusnya, ungkapkan luas kawasan berlorek dalam sebutan j di mana j adalah
jejari bulatan

M

PQ

N

Diagram 5 / Rajah 5

[ 4 marks ]
[ 4 markah ]

Answer/Jawapan :
(a)

(b) 14
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For SULIT 16 3472/1
examiner
use only 15 Given f (k) a(2k 1)5 and f '(k) 20(2k 1)b . Find the value of a and of b.

[2 marks]

Diberi f (k) a(2k 1)5 dan f '(k) 20(2k 1)b . Cari nilai a dan nilai b.

[2 markah]

Answer/Jawapan :

15

2

16 The gradient function of a curve is px2 qx , where p and q are constants. The curve has

a turning point at (3, 4) . The gradient of the tangent to the curve is 8 when x 1.

Find the value of p and of q. [4 marks]

Fungsi kecerunan suatu lengkung ialah px2 qx , dengan keadaan p dan q adalah

pemalar. Lengkung itu mempunyai titik pusingan pada (3, 4) . Kecerunan tangen

kepada lengkung itu ialah 8 apabila x 1. [4 markah]
Cari nilai p dan nilai q.

Answer/Jawapan :

16 SULIT
4

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SULIT 17 3472/1 For

17 The sixth term of an arithmetic progression is 47 and sum of the first ten terms is 410. examine s
use only

Find the first term and common difference of the progression. [3 marks]

Sebutan keenam bagi suatu janjang aritmetik ialah 47 dan hasil tambah sepuluh sebutan
pertama ialah 410. Cari sebutan pertama dan beza sepunya bagi janjang itu. [3 markah]

Answer/Jawapan :

17

3

18 It is given that x, 8, y + 5 are three consecutive terms of an geometric progression.
Diberi bahawa x, 8, y + 5 ialah tiga sebutan berturutan bagi suatu janjang geometri.
(a) Express y in terms of x.
Ungkapkan y dalam sebutan x.
(b) If y = 1, find the the sum to infinity of the progression.

Jika y = 1, cari hasil tambah ketakterhingaan janjang itu.
[4 marks]

[4 markah]
Answer/Jawapan :

(a)

(b) 18
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For SULIT 18 3472/1
examiner [3 marks]
use only 19 Find a 3 2 dx , in terms of a. [3 markah]
2 x2

Cari a 3 2 dx , dalam sebutan a.
2 x2

Answer/Jawapan :

19 SULIT
3

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SULIT 19 3472/1 For

20 Diagram 6 shows the shaded region P and Q with the area of 10 unit2. examine s
Rajah 6 menunjukkan rantau berlorek P dan Q dengan luas 10 unit2. use only

Diagram 6 / Rajah 6

(a) Using definite integral, write an expression to represent the area of P.
Menggunakan kamiran tentu, tulis ungkapan mewakili luas kawasan P.

(b) If the area of P is 6 unit2, find the value of k. [3 marks]
Jika luas kawasan P ialah 6 unit2, cari nilai k. [3 markah]

Answer/Jawapan :

(a)

(b) 20
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For SULIT 20 3472/1
examiner
use only 21 The variables x and y are related by the equation y p q , where p and q are
2 x x2

constants. Explain how the value of p and the value of q can be obtained from a suitable

straight line graph. [3 marks]

Pembolehubah x dan y dihubungkan oleh persamaan y p q , di mana p dan q
2 x x2

adalah pemalar. Terangkan bagaimana nilai p dan nilai q boleh diperolehi daripada

satu graf garis lurus yang sesuai. [3 markah]

Answer/Jawapan :

21 SULIT
3

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SULIT 21 3472/1 For

22 Diagram 7 shows two vectors, OA and OB on a Cartesian plane. examine s
Rajah 7 menunjukkan dua vektor OA dan OB pada satah Cartes. use only

y B(7, 5)
A(3, 4)

O x
Diagram 7 / Rajah 7
[3 marks]
(a) State OA in form of x [3 markah]
y

Nyatakan OA dalam bentuk x .
y

(b) Express AB in the form xi yj

Ungkapkan AB dalam bentuk xi yj

Answer/Jawapan :
(a)

(b) 22
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For SULIT 22 3472/1
examiner
use only 23 The following information refers to the vectors a and b .

Maklumat berikut adalah berkaitan dengan vektor a dan vektor b .

a 9 , b 3
r2 1

2

It is given that a k b , where a is parallel to b and k is a constant.
Diberi bahawa a k b , dengan keadaan a adalah selari dengan b dan k adalah
pemalar.

Find the value of
Cari nilai

(a) k, [3 marks]
(b) r. [3 markah]

Answer/Jawapan :
(a)

(b)

23 SULIT
3

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SULIT 23 3472/1 For

24 Solve the equation 2(1 cos x) sin2 x for 0 x 360 . examine s
Selesaikan persamaan 2(1 cos x) sin2 x bagi 0 x 360 .
[3 marks] use only

[3 markah]

Answer / Jawapan:

24
3

25 It is given that sin x k , where k is a constant and 0 x 90 .
Diberi bahawa sin x k , dengan keadaan k adalah pemalar dan 0 x 90 .

Express in terms of k
Ungkapkan dalam sebutan k

(a) sin ( x) , [3 marks]
(b) sec x. [3 markah]

sek x.

Answer/Jawapan :
(a)

(b)

Kertas Soalan Tamat 25

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SULIT 2 3472/1

MARK SCHEME FOR ADDITIONAL MATHS. MPP2 (PPT)
PAPER 1

No Mark Scheme Marks

15 2
3 x 10 2
x
B1
2 17
m 5 4n 3
3m n(12) B2 3
B1
3 p 2 q2
4 2
2
( 2q)2 4(2)(1 2 p) 0
B1

4 h 100 , k 100 (both) 4
B3
h 100 or k 100 B2

1 log10 h 1 or log10 k 2 B1 4
4 2

log10 y log10 k x2 log10 h OR m 1 and c 2
4 2

5 (a) h = 1 1
23
(b) k 9 B1
2
2
62 4(1)(2k) 0 B1 3

6 (a) q = 9, p = 1 (both ) 1
p(4 1 )2 + 9 = 0

(b) 0 f (x) 9

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SULIT 3 3472/1

7 a 3, 3 (both) 3
b 9 and b 2 B2 3
b2 7b 18 or equivalent B1

8 (a) 1 2
4p
B1
log6 1 and log6 1 4
9
62 2

(b) 1 p B1

log6 6 3
3 B2
B1 4
9 (a) AB:BC = 1:2 1
m1
4
n2 3 B3
5n m B2 4

mn B1
(b) r = 6
1
10 Wrong and y-intercept = 1 23
y-intercept = 1 B1
y 2x 1 OR y ( 3) 2
01
(1, 3) and m 2 OR

x ( 1) 2 y ( 4) 2 x 3 2 y ( 2) 2

11 (a) 17
(b) 8
46 38

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SULIT 4 3472/1
4
12 (a) 8 1 3
(b) 1.609 3
4
12(4) 22(9) 32(5) 42(8) 52(11) 1(4) 2(9) 3(5) 4(8) 5(11) 2 B2 2
40 40 4

1(4) 2(9) 3(5) 4(8) 5(11) B1
40

13 (a) 1.542 1
(b) 28.45 2
6 2 1.542 B1

14 (a) 2 1
3 3
B2
(b) j2 3 j2 B1
32

2( j2 3 j2 )
64

1 j2 atau 1 j2 sin
232 3

15 a = 2, b = 4 (both) 2
10a(2k 1)4 B1

16 p 2, q 6 (both) 4
Solve the linear simultaneous equation in one unknown B3
9 p 3q 0 and p + q = 8 B2
9 p 3q 0 or p + q = 8 B1

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SULIT 5 3472/1
4
17 a = 13 , d = 12 ( both ) 3
a = 13 or d = 12 B3
Solve the linear simultaneous equation in one unknown B2
T6 = a + 5d = 47 or S10 = B1

18 (a) y 64 5x 2
x B1

8 y5 4
2
x8 B1

(b) 32 16 3
s
1 B2 3
1 2
B1
19 3 6a 5
a 2 1
3
3a 1 2a 3 21 2 2
1 1 2
B1
3x 1 2x
1

20 k k
(a) f (x)dx (2x)dx

0 0

(b) 2

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SULIT 6 3472/1
3
21 plot xy against 1 , m 2q and c 2 p or equivalent 3
x B2 3
B1 3
plot xy against 1 or m 2q and c 2 p 3
x 1 3
2
xy 2q 1 2 p or equivalent B1
x
2
22 (a) 3 B1
4
1
(b) 4i j
3
3i 4 j 7i 5 j OR 3 7 B2
4 5 B1

23 (a) k=3 1
2
3k=9 OR r 2 3 1 B1
2

(b) r 7
2

24 0 , 360 (both)
cos x 3 cos x 1 0
2(1 cos x) 1 kos2 x

25 (a) k
(b) 1
1 k2
1 k2

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