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MATHEMATICS

FORM 3

MODULE 13

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TRIGONOMETRY

MINISTRY OF EDUCATION MALAYSIA

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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

5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan

yang disediakan oleh guru.

6. Jawab semua soalan.

Modul ini mengandungi 19 halaman bercetak

D A B C E

3

1 The hypotenuse of a right-angled triangle is the side opposite to the right angle. What is the hypotenuse in the diagram? 2 ∆XYZ shows the sides of a right-angled triangle with reference to angleθ .

The tangent of angle θ is the ratio of the opposite side to the adjacent side.

State the tangent of angle θ for the∆MNR.

A NRMN

B MNNR

C NRMR

D MRNR

A PQ B QR C PR D PS

P

S

R Q T

N

R

M θ

Hypotenuse

Adjacent Opposite

θ Z

X

Y

4

3 A right-angled triangle is a triangle in which one of its angles must be o90 .Which of

the following shows a right-angled triangle?

A

B

C

D

4 The value of sin o30 is equal to the value of cos o60 . Since sin o30 = 21

, what is the

value of cos o60 ?

A 51

B 53

C 31

D 21

R

P

Q

R

P

Q

P

Q R

P

Q R

5

5 Sine of an angle is the ratio of the opposite side to the hypotenuse.

In the triangle above, KL is the adjacent side, LM is the opposite side and KM is the hypotenuse with respect to angleθ . What is sine θ ?

A LMKL

B KMLM

C KLLM

D KMKL

6

The angles P, T and L are known as

A right angles B acute angles C obtuse angles D corresponding angles

K

L M

θ

70°

60° 50°

P

L T

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.

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.

With reference to the angle θ , PR is known as the

A adjacent side B opposite side C hypotenuse

θ P

T S

RQ

Q

P R

θ

7

11 Name the adjacent side with reference to the angle θ in the diagram below.

A PR B PQ C QR D PS

12 The diagram shows the right-angled triangle PRS. What is tan θ ?

A RSPS

B PRPS

C PSSR

D PRSR

θ Q

R

P

S

P

R

θ

S

8

13 The diagram shows a right-angled triangle. What is cos θ ?

A ba

B ca

C cb

D ac

14 What is the value of tan °45 ?

A 21

B 21

C 23

D

1

a c

b θ

9

15 The diagram shows a right-angled triangle PQR.

Find the value of tan ∠RPQ.

A 53

B 43

C 34

D 54

16 The diagram shows a rectangle RSTU with diagonal RT.

Based on the diagram, which of the following trigonometric ratios are true?

I tanSRSTx =

II sinRTRSx =

III cosSTRSx =

IV tanTURUx =

A I and II B I and III C II and III D I and IV

R

4 cm 5 cm

P

R

Q 3 cm

x

T S

U

10

17 The diagram shows a right-angled triangle PQR.

Given that PQ : PR = 12:13, what is the value of sin x?

A 1213

B 1312

C 125

D 135

18 The diagram shows a right-angled triangle.

The value of cos x is

A

43

B

52

C

53

D

54

3

x 2

5

2

P

Q R

x

11

19 In the diagram, PQR is a right-angled triangle.

Given that cos x = 54

, tan x=

A

53

B

43

C

45

D

34

P

Q Rx

12

20 The diagram shows a right-angled triangle PQR.

Given that, sin x = 53

, what is the length of QR?

21 The diagram shows the right-angled triangle PQR.

Given that tan 43

=x , find the length, in cm, of PQ.

A 8 B 9 C 10 D 12

A 3 x 3

B 4 x 3

C 5 x 3

D 4 x 5

15 cm

P

Q R

x

Q P

R

x

6 cm

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22 The diagram shows a square, PQRS and a right-angled triangle PST.

Find the value of tan x .

A 73

B 53

C 43

D 54

23 The diagram shows a right-angled triangle KLM.

Find the length, in cm, of KL.

A 2.12 B 4.72 C 6.40 D 7.55

TP

S R

Q x°

10 cm 6 cm

M 32°

L

K

4 cm

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24 The diagram shows two right-angled triangles PQT and QRS. T is the mid-point of

QS and QR = 2PQ.

Find the value of tan y.

A 21

B 53

C 43

D 34

25 The diagram below shows trapezium RSTU.

Given that tan θ = 5

12, find the length of RS.

A 10

B 17

C 22

D 26

R

R

T S

U θ

24 cm

S

P

5 cm

Q

T

y

3 cm

12 cm

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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. Explain how to determine the value of sin y. 29 Explain how to determine the value of tan 14.7°, using a scientific calculator.

C

3

4

y B

A

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

A 135

B 125

C 5

12

D 5

13

K

L M

17

32

A 6

B 8

C 9

D 11

33

A 8 sin o60 B 8 cos o60 C 8 tan o60 D 8

P Q

R

12

E

G

F 10

f

18

34

A 0.6

B 0.8

C 0.75

D 1.2

P

R Q

19

35

A rp

B pq

C qp

D rq

END OF QUESTION PAPER

θ

16 17

18

19

20

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

21 22

23

24

25

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

26 27

28

29

30

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

Tahun/ Tingkatan : 3 Mata Pelajaran: MATEMATIK

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

KEMENTERIAN PELAJARAN MALAYSIAKERTAS JAWAPAN OBJEKTIF

Ujian Diagnostik

5152

53

54

55

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

5657

58

59

60

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

4647

48

49

50

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

4142

43

44

45

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

31 32

33

34

35

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

36 37

38

39

40

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

1 2

3

4

5

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

6 7

8

9

10

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

11 12

13

14

15

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

Konstruk No. Soalan Jumlah Soalan

Bilangan Soalan Gagal Dijawab

Kegunaan Guru

K1

K3

K5

K6

K7

K8

K10

1-5

6-10

11-15

16-20

21-25

26-30

31-35

5

5

5

5

5

5

5

1

9

2

3

10

4

5

6

7

8

Nama Pelajar:

Nama Sekolah: Modul: 13