student's copy module 13

8/6/2019 Student's Copy Module 13

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MODULE 13: TRIGONOMETRY

Arahan:

1. Modul ini mengandungitiga puluh lima soalan. Semua soalan adalah dalam

bahasa Inggeris.

2. Modul merangkumitujuh konstruk yang diuji

K1 - Memahami soalan dalam bahasa InggerisK3 - Memahami istilah matematik dalam bahasa InggerisK5 - Menguasai konstruk pengetahuanK6 - Menguasai konstruk kefahamanK7 - Menguasai konstruk kemahiranK8 - Mengungkapkan idea/informasi dalam bahasa InggerisK10 - 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 jumlahsoalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam kertasjawapan objektif sebelum ujian.

4. Bagisoalan objektif, anda perlu menandakan jawapan dengan menghitamkanpilihan jawapan pada pilihan jawapan A , B , Catau D pada kertas jawapanobjektif.

Contoh:

Antara berikut, yang manakah haiwan?

A. Pokok B. Kambing C. Kereta D. Pen

5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasinganyang disediakan oleh guru.

6. Jawab semua soalan.

Modul ini mengandungi19 halaman bercetak

DA B C E


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1 The hypotenuse of a right-angled triangle is the side opposite to the right angle.

What is the hypotenuse in the diagram?

2 XYZshows the sides of a right-angled triangle with reference to angle .

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

State the tangent of angle for theMNR.

A

NR

MN

BMNNR

C

NR

MR

D

MR

NR

A PQB QRC PRD PS

P

S

RQT

N

R

M

Hypotenuse

Adjacent

Opposite

Z

X

Y


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3 A right-angled triangle is a triangle in which one of its angles must beo

90 .Which of

the following shows a right-angled triangle?

A

B

C

D

4 The value of sino

30 is equal to the value of coso

60 . Since sino

30 =2

1, what is the

value of coso

60 ?

A

5

1

B

5

3

C

3

1

D

2

1

R

P

Q

R

P

Q

P

QR

P

QR


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

In the triangle above, KL is the adjacent side, LMis the opposite side and KMis the

hypotenuse with respect to angle.

What is sine ?

ALM

KL

BKM

LM

CKL

LM

DKM

KL

6

The angles P, Tand L are known as

A right anglesB acute anglesC obtuse anglesD corresponding angles

K

L M

70

60 50

P

LT


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7 The cosine of an angle is

A the ratio of the adjacent side to the hypotenuseB the ratio of the opposite side to the adjacent sideC the ratio of the adjacent side to the opposite sideD the ratio of the hypotenuse side to the opposite side

8 Name the hypotenuse in the diagram below.

A PRB PTC TQD SR

9 The ratio of the opposite side to the hypotenuse in a right-angled triangle is called

A the cosine of the angleB the sine of the angleC 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 , PR is known as the

A adjacent sideB opposite sideC hypotenuse

P

T S

RQ

Q

P R


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

A PRB PQC QR

D PS

12 The diagram shows the right-angled triangle PRS.

What is tan ?

A

RS

PS

B

PR

PS

C

PSSR

D

PR

SR

Q

R

P

S

P

R

S


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13 The diagram shows a right-angled triangle.

What is cos ?

Ab

a

Bc

a

Cc

b

Da

c

14 What is the value of tan 45 ?

A 2

1

B 2

1

C 2

3

D 1

ac

b


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15 The diagram shows a right-angled triangle PQR.

Find the value of tan RPQ.

A5

3

B4

3

C3

4

D5

4

16 The diagram shows a rectangle RSTU with diagonal RT.

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

I tanSR

STx=

II sin

RT

RSx=

III cosST

RSx=

IV tanTU

RUx=

A I and IIB I and IIIC II and IIID I and IV

R

4 cm5 cm

P

R

Q3 cm

x

TS

U


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

A12

13

B13

12

C12

5

D13

5

18 The diagram shows a right-angled triangle.

The value of cosxis

A4

3

B5

2

C5

3

D5

4

3

x2

5

2

P

Q R

x


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19 In the diagram, PQRis a right-angled triangle.

Given that cosx=5

4, tanx=

A53

B4

3

C4

5

D3

4

P

Q Rx


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Given that, sinx=5

3, what is the length ofQR?

21 The diagram shows the right-angled triangle PQR.

Given that tan4

3=x , find the length, in cm, ofPQ.

A 8B 9C 10

D 12

A 3 x 3

B 4 x 3

C 5 x 3

D 4 x 5

15 cm

P

QR

x

QP

R

x

6 cm


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

Find the value of tan x.

A7

3

B 5

3

C4

3

D5

4

23 The diagram shows a right-angled triangle KLM.

Find the length, in cm, ofKL.

A 2.12

B 4.72C 6.40D 7.55

TP

SR

Q

x

10 cm6 cm

M

32

L

K

4 cm


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24 The diagram shows two right-angled triangles PQTand QRS. Tis the mid-point of

QSand QR= 2PQ.

Find the value of tan y.

A2

1

B5

3

C4

3

D3

4

25 The diagram below shows trapezium RSTU.

Given that tan =5

12, find the length ofRS.

A 10

B 17

C 22

D 26

R

R

TS

U

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 thehypotenuse.

28 The diagram shows the right-angled triangleABC.

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


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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. Studentschoose the correct answer.

31

A13

5

B12

5

C5

12

D5

13

K

L M


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32

A 6

B 8

C 9

D 11

33

A 8 sino60

B 8 coso60

C 8 tano60

D 8

P Q

R

12

E

G

F

10

f


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34

A 0.6

B 0.8

C 0.75

D 1.2

P

R Q


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35

Ar

p

Bp

q

Cq

p

Dr

q

END OF QUESTION PAPER


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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 MALAYSIA

KERTAS JAWAPAN OBJEKTIFUjian Diagnostik

51

52

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

56

57

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

46

47

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

41

42

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 DijawabKegunaan 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

student's copy module 13

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