Matematik Kertas 1

1449/1
Matematik
Kertas 1
Oktober
2006
1 ¼ jam

SEKTOR SEKOLAH BERASRAMA PENUH
BAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN
TINGKATAN 4 2006

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. Satu senarai rumus disediakan di halaman 2 hingga halaman 3.

8. Buku sifir matematik empat angka boleh digunakan.

9. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh
diprogram.

Kertas soalan ini mengandungi 16 halaman bercetak

[Lihat sebelah

SULIT 2 1449/1

MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols
given are the ones commonly used.

RELATIONS

1. am  an = am + n

2. am  an = am - n

3. (am)n = am n

( x 2  x1 ) 2   y 2  y1 
2
4. Distance =

5. Midpoint
 x  x 2 y1  y 2 
(x, y) =  1 , 
 2 2 
distance traveled
6. Average speed = time taken

sum of data
7. Mean = number of data

8. Pythagoras Theorem
c2 = a2 + b2

y 2  y1
9. m
x 2  x1

1449/1 © 2006 Hak Cipta Sektor SBP SULIT

SULIT 3 1449/1

SHAPE AND SPACE

1
1 Area of trapezium =  sum of parallel sides  height
2
2 Circumference of circle = d = 2r

3 Area of circle = r2

4 Curved surface area of cylinder = 2rh

5 Surface area of sphere = 4r2

6 Volume of right prism = cross sectional area  length

7 Volume of cuboid = length  width  length

8 Volume of cylinder = r2h

1 2
9 Volume of cone = r h
3

4 3
10 Volume of sphere = r
3

1
11 Volume of right pyramid =  base  height
3

12 Sum of interior angles of a polygon = (n – 2)  180°

13 arc length angle subtended at centre
=
circumference of circle 360°

area of sector angle subtended at centre
14 =
area of circle 360°

PA'
15 Scale factor, k =
PA

16 Area of image = k2  area of object.

[Lihat sebelah

SULIT 4 1449/1

Answer all questions

1 Round off 0.0608 correct to two significant figures.
A 0.060
B 0.061
C 0.0610
D 0.0600

2 The side of a cube is 4.3 cm. The volume, in cm³, of the cube correct to three
significant figures is
A 80.0
B 79.5
C 79.50
D 79.500

3 Express 0.0007023  108 as a number in standard form.
A 0.7023  1011
B 7.023  1012
C 7.023  104
D 7023  101
605
4 0.0368  
50000
A 4.89  10–2
B 4.89  10–3
C 4.89  10–4
D 4.89  10–5

5 In Diagram 1, AB is a tangent to the circle at point P and ASR is a straight line.
R Q
y°

S B
87° 62°
P

DIAGRAM 1
A
Find the value of y.
A 25
B 31
C 48
D 53


SULIT 5 1449/1

6 The area of a rectangular nursery plot is 1.08 km². Its width is 1 200 m. The
length of the nursery plot, in m, is
A 9  10–1
B 9  10–2
C 9  102
D 9  104

7 In Diagram 2, O is the centre of the circle. AB and CB are tangents to the circle
at A and C respectively.
A

40° B
E 80°
O
y°
D C

DIAGRAM 2
Find the value of y.

A 110
B 115
C 120
D 125

8 In Diagram 3, PQRST is a pentagon. STU is a straight line.
T
S U
32°

y° P

x°

R Q
DIAGRAM 3
Find the value of x + y.
A 212
B 362
C 384
D 392

[Lihat sebelah

SULIT 6 1449/1

9 In Diagram 4, PQRSTU and PVWXQ are regular hexagon and pentagon
respectively.
R
X
Q
S

W

T P
m°
V
U
DIAGRAM 4
The value of m is

A 24
B 32
C 48
D 50

10 Diagram 5 shows the graphs of y = sin x and y = cos x.
y
1

O 360°

–1 P

DIAGRAM 5
The x-coordinate of point P is
A 270°
B 225°
C 215°
D 180°

11 It is given that cos  = –0.454 where 180° ≤  ≤ 270°, find the value of .
A 117°
B 207°
C 243°
D 297°


SULIT 7 1449/1

12 In Diagram 6, KLMN is a straight line and JK = KM.
J

x°
K N
12 cm L 3 cm M

DIAGRAM 6
The value of tan x is
1
A 
4
1
B 
3
C –3
D –4

13 Simplify p  (2p–1)3 ÷ 2p –4.
A 3p
B 3p2
C 4p
D 4p2

14 Diagram 7 shows a triangle KLM and a shaded triangle, drawn on square grids.

M

D C

A
L
B

K

DIAGRAM 7

Triangle KLM is the image of the shaded triangle under an enlargement.
Which of the points, A, B, C or D, is the centre of the enlargement?

[Lihat sebelah

SULIT 8 1449/1

2u  1 2  w
15 Express  as a single fraction in its simplest form.
uw w

1  uw
A
uw
uw  1
B
uw
2u  uw  1
C
uw
2u  1
D
uw

1 3
16 32  18 2  2 2  =

A 36
B 54
C 108
D 162

3 1
4  (5 ) 4
2 2
17 
4

A 2
B 5
C 37.5
D 50

18 8pq – (3p + q)2 =
A 3p2 + q2 + 5pq
B 3p2 – q2 + 3pq
C –9p2 – q2 + 2pq
D –9p2 – q2 + 10pq


SULIT 9 1449/1

19 Diagram 8 shows a right prism with rectangular base KLMN.
P
Q

5 cm N

M
K 6 cm
8 cm
L
DIAGRAM 8

Calculate the angle between the line PL and the base KLMN.

A 20° 18 
B 24° 16 
C 24° 22 
D 26° 34 

20 The angle of elevation of the peak of pole P from the peak of pole Q is 60°. The
two poles are vertically planted in a horizontal ground. Which diagram below
represents the situation described?
P
Q
A C 30°
60°

P Q

Q
B D
P

60° 30°
P Q

[Lihat sebelah

SULIT 10 1449/1

21 Diagram 9 shows a pole, PR on a horizontal plane.

P

160°

R Q
DIAGRAM 9

Calculate the angle of depression of Q from vertex P.

A 70°
B 60°
C 30°
D 20°

h
22 Given that v   , then h =
t

vt
A

vt
B
2
v2
C
 2t
v 2t
D
2

23 There are two helicopters X and Y at height 300 m and 340 m above sea level
respectively. If the angle of elevation of helicopter Y from helicopter X is 41°,
calculate the horizontal distance, in m, between the two helicopters.

A 26.2
B 30.2
C 34.2
D 46.0


SULIT 11 1449/1

w
24 Given that y  , express w in terms of y.
1 w
y
A w
1 y
y
B w
1 y
1 y
C w
y
1 y
D w
y
25 In Diagram 10, Q is the image of P under a reflection.

P K
L

N M
H

Q

DIAGRAM 10

The axis of reflection is the straight line that joins H and

A K
B L
C M
D N

m 1 2m
26 Express  as a single fraction in its simplest form.
n 3n

3m  1
A
4n
3m  1
B
3n 2
m 1
C
3n
5m  1
D
3n

[Lihat sebelah

SULIT 12 1449/1

k
27 The solution for 1   k  3 is
2

A k≥4
8
B k≥
3
5
C k≥
2
5
D k≥
3

28 The solution for simultaneous linear inequalities 3n + 1 > –11 and 20 ≤ 8 – 4n is

A 3<n ≤4
B –4 < n ≤3
C –3 < n <4
D –4 < n ≤ –3

29 Diagram 11 is a pie chart showing the colours of t-shirts chosen by a number of
students.

Red
Yellow
60°
190°
Blue

DIAGRAM 11

If 18 students chose yellow t-shirts, find the number of students who chose red
t-shirts.

A 108
B 72
C 36
D 33


SULIT 13 1449/1

30 Table 1 shows the frequency distribution of the scores obtained by a group of
pupils in a competition.

Time (min) 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35

Frequency 4 10 12 9 5

TABLE 1

Calculate the mean of the distribution.

A 21.375
B 22.875
C 23.125
D 25.250

31 Diagram 12 is a bar chart showing the number of candidates who obtained
scores 1 to 5 in a Mathematics test.

Number of
Candidates
20
15

10

5

1 2 3 4 5 Score

DIAGRAM 12

If the passing score is the mean score, calculate the percentage of students who
pass the test.

A 90
B 70
C 60
D 50

[Lihat sebelah

SULIT 14 1449/1

32 It is given that the universal set  = {x : 1  x  20, x is an integer},
set P = {2, 3, 6, 7, 9, 11, 13, 17}, set Q = {x : x is a prime number} and
set R = {x : x multiple of 3}.
Find n[(P  R)’  Q].
A 5
B 6
C 7
D 9

33 Diagram 13 is a Venn diagram showing the sets P, Q and R such that the
universal set  = P  Q  R.
P Q
R

DIAGRAM 13

The shaded region represents the set
A P’  (Q  R)
B P  (Q  R)’
C P  (Q  R)’
D P’  (Q  R)

34 Diagram 14 is an incomplete Venn diagram showing the elements in sets P, Q
and R.

P R Q
.s
.c .y
.m
.w
.g .q
.k

DIAGRAM 14
It is given that the universal set,  = P  Q R, n(Q) = 6 and n(PR) = 3.
Find n(P’ Q  R).
A 8
B 10
C 11
D 12


SULIT 15 1449/1

2x 5y
35 Find y-intercept of the straight line   3.
3 6
18
A 
5
4
B 
5
18
C
5
4
D
5

36 The straight line PQ has gradient –2 and passes through the point (3, –5). It is
parallel to the straight line y + mx – 4 = 0.
Find the value of m.

A –3
B –2
C 2
D 3

37 Diagram 15 shows two straight lines, OR and QR, on a Cartesian plane.

y
Q

R(1, 8)

P O x

DIAGRAM 15

The distance and the x-intercept of PQ is 15 units and –9 respectively.
Find the gradient of QR.

A –1
B –4
C –7
D –8

[Lihat sebelah

SULIT 16 1449/1

38 Table 2 shows the distribution of a group of students playing a game.

Form One Form Two

Girls x 12

Boys 8 6

TABLE 2

A student is chosen at random from the group to start the game. The probability
2
that a girl from Form One will be chosen is . Find the value of x.
15
A 2
B 4
C 6
D 8

39 A box contains a number of yellow marbles and 10 red marbles. A marble is
chosen at random from the box. The probability of choosing a yellow marble is
3
. Then, a number of red marbles is put in the box. If a marble is now selected
5
1
at random from the box, the probability that a red marble chosen is . How
2
many red marbles are there in the box?

A 15
B 20
C 25
D 30

40 A dice is rolled twice and the sum of the number shown is noted. Find the
probability that the sum of the numbers being 7.

1
A
6
1
B
4
1
C
3
1
D
2

END OF QUESTION PAPER


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