2. slaid selanjutnya.... teknik jawab k2 math pmr

8/3/2019 2. Slaid Selanjutnya.... Teknik Jawab K2 Math PMR

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SAMBUNGAN SELEPAS SLAID KE 85


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LOCI IN TWO DIMENSIONS

(Lokus Dalam Dua Matra)


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Draw a locus W such that its distance from point Q and point S

are the same.

Q

S

P

R


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are the same.

Q

S

P

R

Tajam


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are the same.

Q

S

P

R

Tajam


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are the same.

Q

S

P

R

Jawapantak tepat


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are the same.

Q

S

P

R

Jangan gunakan

compasses untukmembina lokus.

Letak pembaris

dan lukis garis

PR


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E

DC

B

A

Diagram 6 in the answer space shows a regular pentagon ABCDE,

draw the locus of W such that it is equidistant from point B and point C.


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E

DC

B

A



tajam


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E

DC

B

A



tajam


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E

DC

B

A




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E

DC

B

A

Tak perlu nak gunakan kaedah construct, kita tahu bahawa

ia pasti melalui titik E dan melalui titik tengah antara titik

B dan titik C.

Tandakan titik tengah BC, sambungkan ke titik E.

.


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Garis terus :

tidak boleh garis putus-putus.


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Diagram 2 shows a square PQRS. A, B, C dan D are midpoints of line PQ, QR,

RS and SP respectively. X, Y and Z are three points which move within the

diagram.

(a) X is a moving point in the square such that it is always equidistant from the

straight lines PQ and SR.

By using the letters in the diagram, state the locus of X.

Q

DO

P

C

A

BDiagram 2

S R


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DB atau BD

D to B atau from D to BD ke B atau dari D ke B


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D and B

D or B

D,B

D.B


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(b) On the diagram 2, draw

(i) The locus Y which move such that it is equidistant from

AC and BD,

(ii) The locus of Z such that SZ = SP.

(c) Hence, mark with the symbol the intersection of the locus of Y

and the locus of Z.


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P Q

D

C

B

A

O

S R

Gunakan

pembaris dan

pensil


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P Q

D

C

B

A

O

S R

Untuk

membina

lengkok,

gunakancompasses.


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P Q

D

C

B

A

O

S R


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P Q

D

C

B

A

O

S R

Dapat 1 markah sahaja iaitu lokus Y

Lokus Z tak dapat markah

Automatik intersection pun tak dapat markah


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P Q

D

C

B

A

O

S R

Tidak di

ambil kira


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Describe

Beri dengan selengkapnya.

Circlemust be have centre and radius

circle, radius 3 units, centre O

Linestraight line, name of line

straight line PQ

Arcmust be have centre, radius or name of

arc

arc, radius 3 units, centre O

or arc AB or arc ABD


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GEOMETRICAL

CONSTRUCTIONS(Binaan Geometri)


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Garis/lengkok sebagaibantuan

jangan dipadam


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(b) Diagram 4 shows a quadrilateral KLMN.

(i) Using only a ruler and a pair of compasses, construct quadrilateral

KLMN as shown in diagram 4 using the straight lines KL and LM

provided in the answer space.(ii) Hence, construct angle bisector of theKNM such that point P lies

on the line KL.

(iii) Measure the length, in cm, of NP.

60o

N

ML

K


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M

K

L


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M

K

L

Setelah siap dibina, sukat

sudut LMN(60o) dengan

protractor.Jika tak tepat, buat

semula.


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M

L

K


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M

L

K

Sukat sudut LKN(90o

)dengan protractor.

Jika tak tepat, buat

semula.


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M

L

K

Biarkan semua garis-garis dan lengkok-lengkok tersebut

jangan dipadamkan


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GRAPH OF

FUNCTION

(Graf Fungsi)


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i. Jadual bagi nilai x dan y diberisepenuhnya.

x 3 2 1 0 1 2 3 4

y 34 14 0 8 10 6 4 20


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ii. Paksi x tersedia dilukis dengan

skalanya.

Paksi y tersedia dilukis garisnya

sahaja.


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0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

x

y

-1 3210-2-3


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iii. Skala bagi paksi y hendaklahditulis dengan betul dan seragam

seperti yang diberi dalam soalan.

(1 markah untuk tandaan paksiyang betul)

(1 markah dipotong jika

menggunakan skala yang lain)


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iv. Tandaan untuk semua titikmesti tepat.

(2 markah untuk semua

tandaan titik yang betul,

1 markah jika 1 atau 2

kesilapan)


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-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

-4 -2 0 2 4 6x

y


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Tandaan dot lebih selamatdaripada tandaan pangkah


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v. Graf mesti licin danberterusan dalam julatnya.

Graf mesti melalui semuatitik yang sepatutnya.

(1 markah untuk graf ini)


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Jangan sambungkan titik-titik dengan

pembaris

SALAH


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pembaris


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pembaris


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atau menjadi lonjong


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Bentukkan lengkung yang sesuai


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STATISTICS

(Statistik)


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BAR CHARTS


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13

12

11 10

9

8

7

6

5

4

3

2

1 Bas Basikal Kereta


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13

12

11 10

9

8

7

6

5

4

3

2

1 Bas Basikal Kereta


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PICTOGRAPH

(PMR 2004)


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Table 1 shows the number of books in the reading corners of three

classes.

Kelas Bilangan Buku

Aman 75

Bestari 60

Cerdas 90

The information of Bestari class is shown fully in the pictograph in

the answer space.

Complete the pictograph to represent all the information in Table 1.[3 marks]


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Aman

Bestari

Cerdas

Number of books in the reading corners

represent.. 30. books

75

60

90


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Aman

Bestari

Cerdas

Number of books in the reading corners


75

60

90


HANYA SATU SIMBOL SAHAJA


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30

15

atauatau

Ketiga-tiganya boleh


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30

15

atauatau

Ini tak boleh


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LINE

GRAPH


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Skala ditulis dengan betul1 markah

Semua titik diplot dengan betul2 markah Graf garis dilukis betul1 markah

**************************************

* Garis putus-putus @ lakaran0 markah

* Garis disambung ke titik lain0 markah


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43210 5

100

80

60

40

20

Takboleh!


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43210 5

100

80

60

40

20

Takboleh!


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43210 5

100

80

60

40

20

Takboleh!


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PIE

CHART

Table shows the number of students who play four


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types of games.

Types of game Number of studentsPing Pong 8

Badminton 15

Hockey 25

Hand Ball 12

(PMR 2005)



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types of games.

Types of game Number of studentsPing Pong 8

Badminton 15

Hockey 25

Hand Ball 12

60


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The information for badminton is shown fully in the

pie chart in the answer space. Complete the pie chart

to represent all the information in table.

90o

Badminton


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Kirakan sudut sektor

yang mewakili setiap

unsur atau perkara.

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Calculate the angle of sector.

Ping pong

Hockey

Hand Ball

4836060

8

o150360

60

25

o72360

60

12


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Binakan sektor bagi

setiap unsur atau

perkara tersebut

dengan tepat.4/27/2012 68


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90o

Badminton48o

72o

150o


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Lebelkan setiap sektor

dengan betul.

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90o

Badminton

PingPong

Hockey

Hand

BallSaiz sudut

tidak perlu

ditulis


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INEQUALITY

(Ketaksamaan)

(a) Solve the inequality 2 + x 5

(b) Li ll h i l f hi h i f b h h i li i


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(a) x 5 2

x 3

(b)

132

x

312

x

42

x

8x

3 x

x 3

x = 4, 5, 6, 7, 8

(b) List all the integer values of x which satisfy both the inequalities

and 3x 0.[4 marks]


(b) Li t ll th i t l f hi h ti f b th th i liti


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(a) x 5 2

x 3

(b)

132

x

312

x

42

x

8x

x


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(a) x 5 2

x 3

(b)

132

x

312

x

42

x

8x

3 x

x 3

3 < x 8


and 3x 0.[4 marks]


(b) Li t ll th i t l f hi h ti f b th th i liti


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(a) x 5 2

x 3

(b)

132

x

312

x

42

x

8x

3 x

x 3

x = 4, . . . . . ., 8


and 3x 0.[4 marks]


(b) S l b th f th i liti


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(a) x 5 2

x 3

(b)

132

x

312

x

42

x

8x

3 x

x 3

3 < x 8

(b) Solve both of the inequalities

and 3x 0.[4 marks]




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(a) x 5 2

x 3

(b)

132

x

31

2

x

42

x

8x

3

xx 3


and 3x 0.[4 marks]

| | | | | | | |

2 3 4 5 6 7 8 9


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TRIGONOMETRY

(Trigonometri)


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1312

5

6

8 10

54

3


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In Diagram 1, C is the midpoint of the straight line BD

[2 marks]Find the value of tan xo.

13 cm5 cm

xo

DCB

A

Rajah 1

BD = 12 cm

BC = 6 cm

Tan xo =5

6


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In Diagram 1, C is the midpoint of the straight line BD

[2 marks]Find the value of tan xo.Tan xo =

5

6

13 cm5 cm

xo

DCB

A

Rajah 1

66


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BD2 = 13252

BD2 = 16925

BD2

= 144BD =

BD = 12

144

tan x =AB

BC

5

6

TAK PERLU BUATPENGIRAAN MENCARI

PANJANG BD


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