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MATHEMATICS

FORM 3

MODULE 8

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TRANSFORMATIONS II

MINISTRY OF EDUCATION MALAYSIA

2

MODULE 8: TRANSFORMATIONS II 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 In an enlargement with scale factor 2, the length of the image is twice the length

of the object.

Find the length of the image under this enlargement when the length of the object

is

3 cm.

2 The image under an enlargement is on the same side as the object if the scale

factor is greater than 0. In which region A, B, C or D does the image of the object

under an enlargement with scale factor 5 lie?

A 4 cm B 5 cm C 6 cm D 9 cm

A

B C

D

Centre of enlargement

Object

4

3 In an enlargement, all the straight lines that join a point on the object and the

corresponding point on the image, meet at the centre of enlargement. PQ’R’S’ is

the image of PQRS under an enlargement.

Determine the centre of this enlargement.

4 Two geometrical shapes are similar if their corresponding angles are equal and

their corresponding sides are proportional.

Which of the following A, B, C or D is similar to P?

A P B Q C R D S

Q’ R’

S’ S P

Q R

A

DC

B

P

5

5 In an enlargement, if the scale factor is 3, the distance of the image from the

centre of enlargement is three times the distance of the object from the centre of

enlargement.

Which of the following is the image of line PQ under an enlargement with scale

factor 3?

A RS B TU C VW D VY

Centre of enlargement

Q

S

U

W

Y

P R T V X

6

6 In the diagram, the corresponding angles of P and Q are equal and the sides are

proportional.

P and Q are

7 What is the type of transformation shown in the diagram?

A similar B equal C identical D congruent

A Rotation B Reflection C Translation D Enlargement

image

object

O

P

Q

7

8 In an enlargement, P’Q’ is the image of PQ

The ratio PQ

'Q'P is known as

9 Under an enlargement, all the points of an object move from a fixed point at a

constant ratio.

The fixed point is known as the

10 ∆LMN undergoes a transformation to become N'.M'L'∆ N'M'L'∆ is known as

the

A scale B length C scale factor D centre of enlargement

A ratio of enlargement B scale of enlargement C image of enlargement D centre of enlargement

A image B object

C subject

D shadow

N’ M’ M N

L

L’

8

11 The diagram shows two similar triangles. Which of the following is false?

12 Which of the following is true about an enlargement?

13 The table shows the relationship between the scale factor, k and the size of the

object and its image. Which of the following is false ?

A PQR is the object B P’Q’R’ is the image C OPP’ is a straight line D R is the centre of enlargement

A The object and the image are similar B The image is always larger than the object

C The scale factor cannot be less than one

D The centre of enlargement must be a point on the object

Scale factor, k Comparison of size

A k > 1 Image > object

B k = 1 Image = object

C k =21

Image < object

D k = -2 Image < object

P’

Q’ R’

P

Q R

O

9

14 The diagram shows triangles P, Q, R and S.

Which of the following is a pair of similar triangles?

15 In the diagram, JKL is a triangle and JL is parallel to RS.

Which of the following sides are proportional?

A P and Q B P and R

C Q and R

D R and S

A KR and KJ B RS and KS

C KR and KS

D JL and SL

J

L

R

S K

65°

55°

60°

P

65°

60°

55° Q

45°

65°

70° R

75°

60°

45°

S

10

16 The diagram shows rectangle EFGH and its image E’F’G’H’.

Find the scale factor of the enlargement.

A 184

B 186

C 4

18

D 6

18

E’ F’

H’ G’

12 cm

18 cm

F

G H

E

4 cm

6 cm

11

17 In the diagram, KL, KP, LN and PN are straight lines, and KL is parallel to NP. Which of the following is true?

A MNKM

LNKP

=

B PMLM

MNKM

=

C MNLM

PNKL

=

D PMKM

KLPN

=

K

N

P

M

L

12

18 The diagram shows quadrilateral PQRS and its image P’Q’R’S’ under an

enlargement.

Which of the following is the scale factor, k?

19 The area of an object is q cm2. Express the area of the image under an

enlargement with a scale factor p in terms of p and q.

A Q'P'

PQ

B R'S'

SR

C PS

S'P'

D RP'

PR'

A qp2

B 2qp

C qp2

D 2pq

P Q

S R

P’ Q’

S’ R’

13

20 Given the area of∆PQR is 10 cm2, find the area of the image of ∆PQR under an enlargement with scale factor 3.

21 Trapezium RSTU in the diagram undergoes an enlargement with scale factor 2. Find the area of the image.

A 3 x 10

B 32 x 10

C 3 x 102

D 6 x 10

A 144 B 80 C 72 D 36

R

U

T

8 cm 10 cm

4 cm

S

14

22 In the diagram, AB’C’D’ is the image of ABCD under an enlargement.

Find the value of p.

23 PQR is the image of triangle LMN under a certain enlargement. Given the area of triangle PQR is 36 cm2, calculate the area, in cm2, of triangle LMN.

A 6 B 4 C 3 D 2

A 6 B 12 C 16 D 24

D

C

8 cm

12 cm

D’

C’

B

B’

A p

2 cm

L

N

M

P

R

Q

2 cm 3 cm

15

24 In the diagram, PTUV is the image of PQRS under an enlargement with centre P.

Find the area, in cm2, of the shaded region given that the area of PQRS is 10

cm2.

25 In the diagram, P’Q’R’S’T’ is the image of pentagon PQRST under a certain

enlargement. Find the scale factor of the enlargement

A 30 B 40 C 80 D 90

A 31

B 91

C 3 D 9

8 cm4 cmP

V

S R

Q

U

T

P’

Q’

R’

S’

T’

P

Q

R

S T

12 cm 4 cm

3 cm

16

All questions from number 26 to number 30 must be answered in words. 26 Explain how to determine the centre of an enlargement. . 27 Explain the concept of similarity. 28 Give two properties of enlargement. 29 Explain how to find the scale factor of an enlargement. 30 What can you say about the image and object when the scale factor is negative?

17

From Question 31 to 35, the teacher reads the questions to the students. Students choose the correct answer. 31

32

A 41

B 21

C 2

D 4

A 100 cm2 B 50 cm2 C 20 cm2 D 10 cm2

8 cm

16 cm

Picture M

2 cm

4 cm

Picture N

18

33

34

A 144 B 72 C 18 D 9

A 60 cm2 B 120 cm2 C 180 cm2 D 400 cm2

19

35

A 5 B 3

C 51

D 31

50° P ’

3 cm 50° 40°

P

15 cm

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: 8