2. MODULE 13: TRIGONOMETRY
Arahan:
1. Modul ini mengandungi tiga puluh lima soalan. Semua soalan adalah dalam
bahasa Inggeris.
2. Modul merangkumi tujuh konstruk yang diuji
K1 - Memahami soalan dalam bahasa Inggeris
K3 - Memahami istilah matematik dalam bahasa Inggeris
K5 - Menguasai konstruk pengetahuan
K6 - Menguasai konstruk kefahaman
K7 - Menguasai konstruk kemahiran
K8 - Mengungkapkan idea/informasi dalam bahasa Inggeris
K10 - Memahami pengajaran dan pembelajaran dalam bahasa Inggeris
3. Murid hendaklah menulis maklumat diri dalam kertas jawapan objektif disediakan.
Murid juga perlu memastikan maklumat konstruk, nombor soalan dan jumlah
soalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam kertas
jawapan objektif sebelum ujian.
4. Bagi soalan objektif, anda perlu menandakan jawapan dengan menghitamkan
pilihan jawapan pada pilihan jawapan A , B , C atau D pada kertas jawapan
objektif.
Contoh:
Antara berikut, yang manakah haiwan?
A. Pokok B. Kambing C. Kereta D. Pen
A B C D E
5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan
yang disediakan oleh guru.
6. Jawab semua soalan.
Modul ini mengandungi 19 halaman bercetak
2
3. 1 The hypotenuse of a right-angled triangle is the side opposite to the right angle.
P
S
R
Q
T
What is the hypotenuse in the diagram?
PQ
A
QR
B
PR
C
PS
D
∆ XYZ shows the sides of a right-angled triangle with reference to angleθ .
2
Z
Hypotenuse
θ
X Adjacent
Opposite
Y
The tangent of angle θ is the ratio of the opposite side to the adjacent side.
R
θ
M N
State the tangent of angle θ for the ∆ MNR.
A MN
NR
B NR
MN
C MR
NR
D NR
MR
3
4. A right-angled triangle is a triangle in which one of its angles must be 90 o .Which of
3
the following shows a right-angled triangle?
A
P
R Q
B
P
R Q
C
P
Q
R
D
P
Q
R
1
The value of sin 30o is equal to the value of cos 60 o . Since sin 30 o =
4 , what is the
2
value of cos 60 o ?
A 1
5
B 3
5
C 1
3
D 1
2
4
5. 5 Sine of an angle is the ratio of the opposite side to the hypotenuse.
K
θ
M
L
In the triangle above, KL is the adjacent side, LM is the opposite side and KM is the
hypotenuse with respect to angle θ .
What is sine θ ?
KL
A
LM
LM
B
KM
LM
C
KL
KL
D
KM
P
6
70°
60° 50°
L
T
The angles P, T and L are known as
A right angles
B acute angles
C obtuse angles
D corresponding angles
5
6. 7 The cosine of an angle is
A the ratio of the adjacent side to the hypotenuse
B the ratio of the opposite side to the adjacent side
C the ratio of the adjacent side to the opposite side
D the ratio of the hypotenuse side to the opposite side
8 Name the hypotenuse in the diagram below.
S
T
θ
P R
Q
A PR
B PT
C TQ
D SR
9 The ratio of the opposite side to the hypotenuse in a right-angled triangle is called
A the cosine of the angle
B the sine of the angle
C the tangent of the angle
D the cotangent of the angle
10 The diagram below shows the right-angled triangle PQR.
R
P
θ
Q
With reference to the angle θ , PR is known as the
A adjacent side
B opposite side
C hypotenuse
6
7. Name the adjacent side with reference to the angle θ in the diagram below.
11
R
S
θ
P Q
A PR
B PQ
C QR
D PS
12 The diagram shows the right-angled triangle PRS.
S R
θ
P
What is tan θ ?
A PS
RS
B PS
PR
C SR
PS
D SR
PR
7
8. 13 The diagram shows a right-angled triangle.
c
a
θ
b
What is cos θ ?
a
A
b
a
B
c
b
C
c
c
D
a
What is the value of tan 45° ?
14
1
A
2
1
B 2
3
C 2
D 1
8
9. 15 The diagram shows a right-angled triangle PQR.
R
5 cm
4 cm
P Q
3 cm
Find the value of tan ∠ RPQ.
3
A
5
3
B
4
4
C
3
4
D
5
16 The diagram shows a rectangle RSTU with diagonal RT.
R U
x
S T
Based on the diagram, which of the following trigonometric ratios are true?
ST
tan x =
I
SR
RS
sin x =
II
RT
RS
cos x =
III
ST
RU
tan x =
IV
TU
A I and II
B I and III
C II and III
D I and IV
9
10. 17 The diagram shows a right-angled triangle PQR.
P
x
R
Q
Given that PQ : PR = 12:13, what is the value of sin x?
13
A
12
12
B
13
5
C
12
5
D
13
18 The diagram shows a right-angled triangle.
x
2
5
2
3
The value of cos x is
3
A
4
2
B
5
3
C
5
4
D
5
10
11. 19 In the diagram, PQR is a right-angled triangle.
P
x
Q R
4
Given that cos x = , tan x=
5
3
A
5
3
B
4
5
C
4
4
D
3
11
12. 20 The diagram shows a right-angled triangle PQR.
P
15 cm
x
Q R
3
Given that, sin x = , what is the length of QR?
5
A 3x3
B 4x3
C 5x3
D 4x5
21 The diagram shows the right-angled triangle PQR.
PQ
x
6 cm
R
3
Given that tan x = , find the length, in cm, of PQ.
4
A 8
B 9
C 10
D 12
12
13. 22 The diagram shows a square, PQRS and a right-angled triangle PST.
Q P
T
x°
6 cm 10 cm
R S
Find the value of tan x .
3
A
7
3
B
5
3
C
4
4
D
5
23 The diagram shows a right-angled triangle KLM.
L
4 cm
32°
K M
Find the length, in cm, of KL.
A 2.12
B 4.72
C 6.40
D 7.55
13
14. 24 The diagram shows two right-angled triangles PQT and QRS. T is the mid-point of
QS and QR = 2PQ.
S
5 cm
T
y
PR Q 3 cm
Find the value of tan y.
1
A
2
3
B
5
3
C
4
4
D
3
25 The diagram below shows trapezium RSTU.
R
θ
U
12 cm
S T
24 cm
12
Given that tan θ = , find the length of RS.
5
A 10
B 17
C 22
D 26
14
15. All questions from number 26 to number 30, must be answered in words.
26 Explain how to determine the sine of an angle.
27 In a right-angled triangle, explain how you would determine the side which is the
hypotenuse.
28 The diagram shows the right-angled triangle ABC.
A
3
y
C
B 4
Explain how to determine the value of sin y.
29 Explain how to determine the value of tan 14.7°, using a scientific calculator.
15
16. 30 Explain how to identify the opposite side and the adjacent side of a given angle
in a right-angled triangle.
From question 31 – 35, the teacher reads the questions to the students. Students
choose the correct answer.
31
K
L M
5
A
13
5
B
12
12
C
5
13
D
5
16
17. 32
R
E
f
12
G
10
F
Q
P
A 6
B 8
C 9
D 11
33
A 8 sin 60 o
B 8 cos 60 o
C 8 tan 60 o
D 8
17
19. 35
θ
p
A
r
q
B
p
p
C
q
q
D
r
END OF QUESTION PAPER
19
20. KEMENTERIAN PELAJARAN MALAYSIA
KERTAS JAWAPAN OBJEKTIF
Ujian Diagnostik
Nama Pelajar:
Tahun/ Tingkatan : 3 Mata Pelajaran: MATEMATIK
Modul: 13
Nama Sekolah:
GUNAKAN PENSIL 2B ATAU BB SAHAJA.
TENTUKAN TIAP-TIAP TANDA ITU HITAM DAN MEMENUHI KESELURUHAN RUANG.
PADAMKAN HINGGA HABIS MANA-MANA TANDA YANG ANDA UBAH
SILA HITAMKAN JAWAPAN DI BAWAH MENGIKUT HURUF JAWAPAN YANG ANDA PILIH
A A A
B C D E B C D E B C D E
1 31 46
A A A
2 32 47
B C D E B C D E B C D E
A A A
B C D E B C D E B C D E
3 33 48
A A A
B C D E B C D E B C D E
4 34 49
A A A
B C D E B C D E B C D E
5 35 50
A A
B C D E B C D E
6 36 51
A B C D E
A A
7 37 52
B C D E B C D E
A B C D E
A A
B C D E B C D E
A
8 38 53
B C D E
A A
B C D E B C D E
A
9 39 54
B C D E
A A
B C D E B C D E
10 40 55
A B C D E
A A
B C D E B C D E
A 41 56
B C D E
11
A A
42 57
B C D E B C D E
A
12 B C D E
A A
B C D E B C D E
A B C D E 43 58
13
A A
B C D E B C D E
A B C D E 44 59
14
A A
B C D E B C D E
A 45 60
B C D E
15
Jumlah Bilangan Soalan
Konstruk No. Soalan Kegunaan Guru
A B C D E
16
Soalan Gagal Dijawab
A
17 B C D E
A K1 1-5 5
B C D E 1
18
A B C D E
19
K3 6-10 5
2
A B C D E
20
K5 11-15 5
3
A B C D E
21
K6 16-20 5
4
A
22 B C D E
A B C D E
23
K7 21-25 5
5
A B C D E
24
A B C D E
25 26-30 5
K8
6
31-35 5
K10
7
A B C D E
26
A
27 B C D E
8
A B C D E
28
A B C D E 9
29
A B C D E
30
10
