1. SULIT
1
1449/1
SULIT
1449/1
Kertas 1
Matematik
Kertas 1
Mei 2010
1 jam
UNIT PEPERIKSAAN & PENILAIAN
SEKOLAH MENENGAH KEBANGSAAN TUNKU BESAR BURHANUDDIN
71550 SERI MENANTI, NEGERI SEMBILAN
PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN 5 2010
MATEMATIK
Kertas 1
Satu jam lima belas minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
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 menukarkan jawapan, padamkan tanda yang telah
dibuat. Kemudian hitamkan jawapan yang baru.
6. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali
dinyatakan.
7. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.
Di Sediakan Oleh Di Semak Oleh
__________________________
(Sunita binti Mukhtar )
Kertas soalan ini mengandungi 15 halaman bercetak
1449/1@2010 [Lihat sebelah
SULIT
2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang
diberi adalah yang biasa digunakan.
PERKAITAN
m+n
1. a ×a = a
m n
.
2. am ÷ an = am−n
3. (a )
m n
= a mn
1 d − b
4. A−1 =
ad − bc − c a
n( A)
5. P ( A) =
n( S )
6. P ( A' ) = 1 − P ( A)
7. Jarak = ( x1 − x2 ) 2 + ( y1 − y2 ) 2
8. Titik Tengah
( x, y ) = x1 + x2 , y1 + y2
2 2
jarak yang dilalui
9. Purata laju =
masa yang diambil
hasil tambah nilai data
10. Min =
bilangan data
hasil tambah( nilai titik tengah × ke ker apan )
11. Min =
hasil tambah ke ker apan
12. Teorem Pithagoras
c 2 = a 2 + b2
y2 − y1
13. m=
x2 − x1
p int asan − y
14. m=−
p int asan − x
BENTUK DAN RUANG
2
3. 1
1. Luas trapezium = × hasil tambah dua sisi selari × tinggi
2
2. Lilitan bulatan = πd = 2πj
3. Luas bulatan = πj2
4. Luas permukaan melengkung silinder = 2πjt
5. Luas permukaan sfera = 4πj2
6. Isipadu prisma tegak = luas keratan rentas × panjang
7. Isipadu silinder = πj2t
1 2
8. Isipadu kon = πj t
3
4 3
9. Isipadu sfera = πj
3
1
10. Isipadu piramid tegak = × luas tapak × tinggi
3
11. Hasil tambah sudut pedalaman poligon = ( n − 2 ) × 180 0
panjang lengkok sudut pusat
12. =
lili tan bula tan 360 0
luas sektor sudut pusat
13. =
luas bula tan 360 0
PA '
14. Faktor skala, k =
PA
15. Luas imej = k 2 × luas objek
3
4. Answer All Questions
1 Round of 0.0040055 to three significant figures
A 0.004 C 0.00401
B 0.0040 D 0.004006
2 8.11 × 10 −4 =
A 0.0000811 C 81100
B 0.000811 D 811000
3 Express 351 000 in standard form
A 3.51 × 10 3 C 3.51 × 10 -3
B 3.51 × 10 5 D 3.51 × 10 -5
4 The area of rectangular plot is 7.2km2. Its width is 2 400m. The length, in m, of the
nursery plot is
A 3 × 103 C 4.8 × 103
B 3 × 104 D 4.8 × 104
5 Express 1768 as a number in base five
A 1015 C 2315
B 1265 D 10015
6 111012 + 11102 =
A 1000112 C 1011112
B 1110012 D 1010112
P T
7 y
Q S
R
W
x U
V
Diagram 1
4
5. In Diagram 1, PQRST is a regular octagon. QRUVW is a regular pentagon . Find the
value of x + y
A 153 C 175.5
B 165.5 D 243
8
P Q
T
yo
30
°
S R
Diagram 2
In Diagram 2, PQRS is a square and RQT is a isosceles. Find the value of y.
A 85 C 105
B 100 D 115
Q
9 C
A
O
12
8° xo
P B S
Diagram 3
In Diagram 3, PAQ dan PBS is a tangent to the circle centre
AC = BC. Value of x is
A 32 C 58
B 52 D 64
10 In Diagram 4 shows two vertical poles, PQ and YX , on the horizontal plane,
P
Y
25m
Q 10 m
X
Diagram 4 5
6. The angle of depression of vertex Y from vertecx P is 420. Calculate the angle
of elevation of vertex Y from vertex Q
A 32
B 410 59’
C 570 51’
D 680 11’
X
11 12 cm
A B C
6 cm
Y
Diagram 5
In Diagram 5 , ABC is a straight line. BC is 10. Find the value cos ∠ABX
1 3
A − C −
5 5
2 4
B − D −
5 5
12 Which one of the following graphs represents y = cos xo for 0° ≤ x ≤ 180 ° ?
A B
y y
1 1
x x
0 90° 180° 0 90° 180°
-1 -1
C D
y
y
1
1
x
x 0 90° 180°
0 90° 180°
-1
-1
6
7. 13 Diagram 6 shows a right prism with a horizontol base ELKG.
F J
E L
G K
DIAGRAM 6
Name the angle between line FK and the plane EFG.
A ∠KFE C ∠KFG
B ∠KEF D ∠KGF
14 110112 + 1112 =
A 1000102 C 1100112
B 1011002 D 1111012
15 Diagram 7 , M’ is the image of M under a translation. T’ is the image of T under a same
translation.
Diagram 7
A (-4, 7) C (4, 1)
B (-2, 5) D (6, -1)
16 In Diagram 8, the triangle PQR is the image of the triangle SQT under an enlargement
7
8. Diagram 8
Find the scale of the enlargemet
1 1
A C
3 2
B 2 D 3
17 Diagram 9 shows two straight lines, ST and S’T’ drawn on a square grid
S’T’ is the image of ST under a rotation. Which of points A, B, C, D is the centre
of the rotation
Diagram 9
18 (2 x)(3 y ) − 2( x − 3 y ) 2 =
A − 2x 2 + 18 xy + 18 y 2
B − 2x 2 + 18 xy − 18 y 2
C − 2x 2 + 6 xy − 18 y 2
D − 2x 2 − 6 xy + 18 y 2
2
19 − 3 = 5, then p =
p
1 1
A C
16 4
1 1
B D
8 2
4u − v 8 − v
20 − =
uv 2v
1
A
2u
u−2
B
2u
u+2
C
2u
−u −2
D
2u
8
9. r 5
21 Given that − = 3r. Express r in terms of s.
s 3s
5 5
A C
3(1 − 3s ) 3(1 + 3s)
5 3(3s − 1)
B D
3(3s − 1) 5
( )
4
22 Simplify m 2 ÷ m5
A m C m11
13
B m3 D m
23 The gradient of the straight line 4x - 2y = 3
A -4 C 2
B -2 D 4
9
Given that 3 =
x
24 2x , find the value of x
3
2
A 2 C
3
1
B 1 D
2
25 List all the integers of t that saticfy the inequlities 3t − 8 < t ≤ 5 + 4t
A 0, 1, 2, 3 C -1, 0, 1,2,3,4
B -1, 0, 1, 2 ,3 D -2, -1, 0, 1, 2,3,4
1 2 − 1
26 +3 − =
4 5 6
4 8
A
3 C
1
6 8
B
13 D
13
27 The region defined by the inequalities y ≥ 2 x + 4 .
A B
y y
4 x
2 9
x
-2 -4
10. C y D
y
4 4
x x
2 2
4 − 4 12
28 If ( − 1 q ) =
p 2 , then p + q =
− 6
A -5 C 1
B -1 D 2
4 4 2 3
29 =
2 2 −1 2
8 16 4 16
A C
−2 10 2 10
14 2 4 8
B
3 0 D
9 10
30 Which graph represents y = x3 + 4?
A y B y
4
4
x x
O O
C D
y y
x
O x
O
-4
-4
31 Find the x-intercept of the straight line 3 y + 5 x = 5
A −2 C 1
10
11. B −1 D 2
32 Given that P ∪ Q = Q, R ∩ Q = R, and P '∩ R = R. the Venn diagram that represents
these relationships is
A B
R Q
P R P
Q
C D
Q R
P P
R Q
33 Diagram 10 is a venn diagram which shows the universal set ξ = P and set Q
ξ P Q
Diagram 10
The shaded region in the venn diagram represents the sets
A P’ ∩ Q’ C P ∩ Q’
B P’ ∩ Q D P ∩Q
34 Diagram 11 is venn diagram which shows the elements of sets P,Q and R
11
12. .5 .6 .4 .3 .1
Diagram 11 2
If the universal set ξ = P ∪ Q ∪ R, then set Q ' . is
A { 1,2 } C {1,2,5 }
B { 3, 6 } D {3,4,6 }
x2
35 It is given that T ∝ and T = 32 when x = 4 and w = 6. Express T in terms of w and
w
x.
3x 2 24 x 2
A B
w w
x2 12 x 2
C D
12 w w
1 1
36 Given that Q ∝ and Q = 45 when R = and S = 6 . Calculate value of S when
RS 2
1
R= and Q = 27.
3
A 9 C 36
B 15 D 135
37 Diagram 12 shows some number cards
1321 27 29 33 35
Diagram 12
A card is picked at random. State the probability that a prime number is picked
A 3/2 C 1/2
B 1/3 D 1/6
38 Class 5 Bestari consists of male students and female srudents. The number of male
students in the class is 16. If one student is chosen at random, find the probability of
choosing a male student is 4 / 9. Determine the number of female in 5 Bestari ?
A 20 C 28
B 24 D 36
12
13. 39 Table 1 shows the number of cars that visited a service centre for 5 consecutive
days
Days Number of cars
Monday 20
Tuesday 40
Wednesday 50
Thursday 30
Friday 40
Table 1
The mean is
A 35 C 40
B 36 D 50
40 Table 2 shows the distribution of the scores of 40 students in a health quiz
Score 1 2 3 4
Frequency 6 17 13 4
Table 2
If the above data is represented using a pie chart, then the angle of the
sector of the modal score is
A 900 C 1530
B 1170 D 2700
END OF THE QUESTIONS PAPER
13
