PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPP

MATHEMATIC

FORM 5

MODUL 3

PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPP

TRANSFORMATIONS III

KEMENTERIAN PELAJARAN MALAYSIA

2

TRANSFORMATIONS III Arahan :

1. Modul ini mengandungi tiga puluh lima soalan. 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 mengisikan 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. Soalan 31 hingga 35 akan dibaca oleh guru. Murid perlu mendengar dengan

teliti dan menjawab di dalam kertas jawapan objektif.

7. Jawab semua soalan.

Modul ini mengandungi 23 halaman bercetak

D A B C E

3

Answer all questions given. 1. P ’ is the image of P under a 90o clockwise rotation at O. Which of the points A, B or C is the image of Q under the same rotation?

2. Translation M

23

moves an object P 3 units to the right and 2 units upwards.

Which of the following is the image of P ?

A

BC

.

...

. P’

Q

P . O x

y

A D

C B

P

4

3. The centre of an enlargement is determined by the intersection of the lines joining the points from an object to the corresponding points on its image. In the diagram, ∆P’Q’R’ is the image of ∆PQR under an enlargement. Which point represents the centre of the enlargement?

D

C

P'

Q' R'

B

A

R Q

P

5

4. The size and the shape of the image are the same as the object under an isometric transformation. Which of the following are isometric transformations? I II III IV

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

x

y

Object Image x

y Object

Image

x

y Image

Object x

y

Image

Object

6

5. The axis of reflection cuts the line joining the object G to its image G’ into two equal lengths at 90° Which of the following is the axis of reflection of G to G’? A PQ B RS C TU D VW

6. Which of the following is NOT an isometric transformation? A Rotation B Reflection C Translation D Enlargement

7. When all the points on a plane move the same distance in the same direction along a straight line, the transformation is called a

A rotation B reflection C translation D enlargement

P T R R

x

G

O

G’ V

y

U

W

Q S

..

7

8. Which of the following is a rotation? A B C D 9. In the diagram, triangle K’ is the image of triangle K under transformation W. What is transformation W?

A Rotation B Reflection C Translation D Enlargement

y

x

K’

K

O

x

y

Object

Image

O

x

y

Object Image

O

x

y

Object

Image

O

y

x

Object

Image

O

x

8

10. PQ is a combined transformation. Which of the following will change the orientation of the image.

P Q A Translation Enlargement B Rotation Translation C Translation Reflection D Rotation Enlargement

11. The image of an object under an enlargement lies on the opposite side of the centre of enlargement. What is the scale factor of this enlargement?

A 3 B 1

C 21

D -2

12. Under transformation V, the object and the image are inversed. What is transformation V?

A Rotation B Reflection C Translation D Enlargement

9

13. Diagram shows five pentagons drawn on square grids. Which of the pentagons A,B,C or D is the image of pentagon M under an enlargement with scale factor 2?

M

B

A

C

D

10

14. Diagram shows pentagon P and Q. Q is the image of P under a combined transformation. What are the transformations involved? A Reflection and translation B Enlargement and rotation C Enlargement and reflection D Translation and rotation 15. P’’ is the image of P under a combined transformation NM. Which of the following is an equivalent transformation of NM?

A Translation

− 50

B Reflection in the x-axis C Clockwise rotation at the origin through 90°

O

P

Q

xO

P P’

P”

y

11

16. Diagram shows a regular pentagon PQRST and its image PQ’R’S’T’ under an enlargement. Which of the following is the centre of this enlargement?

A P B Q C S D O

17. P undergoes a combined transformation MN where M is a translation

32

and N

a reflection in the x-axis. Which of the figures, A, B, C or D, is the image of P?

x

Q

O

Q’ P

T’ R’

R

S

T

S’

.

B

P

A

C

D

y

O

12

18. Diagram shows two polygons, M and M’ drawn on square grids. M’ is the image of M under a rotation of 180o. Which of the points A, B, C or D is the centre of rotation? 19. Diagram shows some points drawn on square grids.

Transformation M is a translation

25

Transformation N is a 90° anticlockwise rotation about the centre P. Point K undergoes transformation NM. Which of the points A, B, C or D is the image of K.

x

y

O

A

.BCM

M’

D

..

.

x

.

A

K P

B

C

DO

y

.

.

.

.

.

13

20. Diagram shows a right-angled triangle PQR.

W is a translation

− 87

and V is a reflection in the line MN.

State the coordinates of the image of point P under the transformation WV.

A (2, -3)

B (2, -5)

C (8, -3)

D (16, -3)

21. Given the point (4, -2) is the image of the point (-3, 5) under a translation

kh

.

Find the value of h and k.

A h = 1, k = 3 B h = -1, k = 3 C h = 7, k = -7 D h = -7, k = 7

N

O x

M

P

Q R 2

4

6

-2

-4

-6

2 4 6 8 10 12 14 16 18

y

14

-1

22. P” is the image of P under a combined transformation MN. N is an enlargement with a scale factor of 2 at (1,-1).

Which of the following is transformation M?

A Reflection on the x-axis

B Reflection on the line y = x

C 90° clockwise rotation at O

D 90° anticlockwise rotation at O

x

y

-4 -3

-2

5

4

32

1

6 5 -5 -4 -3 -2 -1 4 3 21P

P’’

O

15

23. Diagram shows five triangles drawn on square grids. Given that R is

a translation

−23

and S is an enlargement at the origin with scale factor -2,

what is the image of P under the combined transformation RS?

y

Ox

A

B

C

D

P

16

24. T’ is the image of T under an enlargement with scale factor 3. Given that the

area of T’ is 81 cm2 , find the area, in cm2 , of T.

A 729 B 243 C 27 D 9

25. Diagram shows triangle PQR and triangle PTS. Triangle PTS is the image of

triangle PQR under a reflection in the line PR followed by an enlargement.

Given that PR: RS = 1: 2, and PQ = 6 cm, find the length of PT.

A 2 cm B 3 cm C 12 cm D 18 cm

S R

T

Q

P

17

26. In the diagram, P’ is the image of P under a transformation M. Describe transformation M.

A A reflection in the y-axis B An enlargement at O with scale factor 1 C A clockwise rotation at O through 90° D A translation of three units to the right and one unit upwards

x

y

O

P’P

18

27. Diagram shows transformation W. Stements below describe some transformations. I The distance between the object and the axis of reflection is equal to the distance between the image and the axis of reflection. II The object and the image have the same shape and size. III The orientation of the object and the image are the same. IV The image may be bigger or smaller than the object. Describe the characteristics of transformation W. A I and II B I and III C I and IV D II and III

axis

P P’ Q Q’

R’

S’ T’

R

S T

19

28. State a characteristic of the image under an enlargement at point O with scale factor -2? A The image is twice the size of the object. B The orientation of the image is inversed. C The image lies on the same side as the object with respect to O. D The distance of the image from O is equal to the distance of the object from O.

29. The translation

− 43

can be described as

A 3 units upwards and 4 units to the left. B 3 units to the right and 4 units downwards. C 3 units downwards and 4 units to the right. D 3 units to the left and 4 units downwards. 30. Triangle P’Q’R’ is the image of triangle PQR under a 90° clockwise rotation. The statements below describe the steps to determine the centre of rotation. I Draw a straight line from Q to Q’ II Draw a straight line from P to P’ III Construct the perpendicular bisectors of PP’ and QQ’ IV Determine the point of intersection of the two perpendicular bisectors State the steps in the correct sequence. A I, IV, II, III B II, I, III, IV C III, IV, I, II D IV, III, II, I

20

From Question 31 – 35, the teacher reads the questions to the students. Student choose the correct answer. 31. 32.

A 21

B 2 C 6 D 8

P

P’

Q

A

B C

D

21

33. A -1

B 1

C 5

34. A (-5, 5)

B (6, -4)

C (1, 1)

D (-1, 5)

x

y

O -4 -2

-2

-4

2

2

4

4

6

6

8

8 L .

22

35. A 42

B 24

C 18

D 12

END OF QUESTION PAPER

Q R

Q’ R’

P

6 cm2

Tahun/ Tingkatan : 5 Mata Pelajaran: MATHEMATIC

Nama Pelajar:

Nama Sekolah: Modul:

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

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

Konstruk No. Soalan Jumlah Soalan

Bilangan Soalan Gagal Dijawab

Kegunaan Guru

K1

K3

K5

K6

K7

K8

K10

1 - 5

6 - 9

10 - 14

15 - 19

20 - 25

26 - 30

31 - 35

5

4

5

5

6

5

5

1

9

2

3

10

4

5

6

7

8