pmr 2010.ppt

TAJUK-TAJUK TINGKATAN 1, 2 DAN 3

TAJUK UTAMA

JADUAL ANALISISSOALAN MATEMATIK

2004 - 2008

NILAIAN MARKAH

MATEMATIK PMRBil Perkara Kertas 1 Kertas 21 Jenis Instrumen Objektif Subjektif2 Jenis Item Aneka Pilihan Respons Terhad3 Bilangan Soalan 40

Jawab Semua20 Jawab Semua

4 Jumlah Markah 40 605 Tempoh Ujian 1 jam 15 minit 1 jam 45 minit6 Wajaran

Konstruk40% Pengetahuan 60% Kemahiran

30% Pengetahuan 65% Kemahiran 05% Nilai

MATEMATIK PMRBil Perkara Kertas 1 Kertas 2

7 Cakupan Konteks

Tingkatan 1 : 12 Tingkatan 2 : 11 Tingkatan 3 : 10

Tingkatan 1 : 6 Tingkatan 2 : 9 Tingkatan 3 : 9

8 Aras Kesukaran

R:S:T = 5:3:2R:S:T = 5:4:1 R:S:T = 5:2:3

9 Alatan Tambahan

Kalkulator Saintifik Sifir Matematik Alat Geometri

Sifir Matematik Alat Geometri

MATEMATIK KERTAS 1

PENILAIAN MENENGAH RENDAH

MATEMATIK KERTAS 1 ANALISIS MASA

40 SOALAN: 75 MINIT

MATEMATIK KERTAS 1 ANALISIS MASA

40 SOALAN: 75 MINITBUKAN

1 SOALAN: 1.875 MINIT

MATEMATIK KERTAS 1 ANALISIS MASA

40 SOALAN: 75 MINITBUKAN

1 SOALAN: 1.875 MINITSEBENAR

BACA+FAHAM+KIRA: 1.5 MINIT MENGHITAM: 0.375 MINIT

MATEMATIK KERTAS 2

PENILAIAN MENENGAH RENDAH

MATEMATIK KERTAS 2 ANALISIS MASA

20 SOALAN: 105 MINIT

MATEMATIK KERTAS 2 ANALISIS MASA

20 SOALAN: 105 MINITBUKAN

1 SOALAN: 5.25 MINIT

MATEMATIK KERTAS 2 ANALISIS MASA

20 SOALAN: 105 MINITBUKAN

1 SOALAN: 5.25 MINITSEBENAR

60 MARKAH: 105 MINIT 1 MARKAH: 1.75 MINIT

MATEMATIK KERTAS 2 PERINGATAN

1. Jawapan Sebenar 6 : (-2)(-3) Tidak dikira

2. Jawapan Sebenar : Tidak dikira

3. Jawapan Sebenar 0 : Tidak dikira

4. Jawapan Sebenar 15.2 : 10+5.2 Tidak dikira

5. Jawapan Sebenar : Tidak dikira

32

-3 -202

12

36

MATEMATIK KERTAS 2 PERINGATAN

6. Jawapan Sebenar Tidak dikira

7. Jawapan Sebenar Tidak dikira

23:

23

52:

52

MATEMATIK KERTAS 2 PERINGATAN

1. Nombor Perpuluhan Berulang:

Misalan 1.222222222 TERIMA 1.22 Ditulis: 2 Tempat perpuluhan/2 Kali Nombor

Berulang

2. Pecahan Tidak Wajar

Misalan TERIMA Untuk 372

12

Format soalan kertas 2• Dalam Bahasa Inggeris dan

Bahasa Melayu /Dwibahasa

Format soalan kertas 2• Dalam Bahasa Inggeris dan

Bahasa Melayu /Dwibahasa

• Markah maksima ialah 60 markah dan markahnya dalam pelbagai iaitu 1 markah, 2 markah hingga 6 markah bagi sesuatu soalan.

Format soalan kertas 2• Dalam Bahasa Inggeris dan Bahasa

Melayu /Dwibahasa

• Markah maksima ialah 60 markah dan markahnya dalam pelbagai iaitu 1 markah, 2 markah hingga 6 markah bagi sesuatu soalan.

• Setiap jawapan perlu ditunjukkan jalan mengira yang jelas dalam ruang jawapan yang disediakan sahaja.

• Memberikan tumpuan 100% dalam proses P&P

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi

• Menguji soalan berdasarkan contoh

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi

• Menguji soalan berdasarkan contoh• Membuat latihan yang diberi oleh

guru

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi

• Menguji soalan berdasarkan contoh• Membuat latihan yang diberi oleh

guru• Membuat latihan soalan-soalan lain

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi

• Menguji soalan berdasarkan contoh• Membuat latihan yang diberi oleh guru• Membuat latihan soalan-soalan lain• Mencari soalan bagi format yang sama

dari soalan PMR yang lalu

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi

• Menguji soalan berdasarkan contoh• Membuat latihan yang diberi oleh guru• Membuat latihan soalan-soalan lain• Mencari soalan bagi format yang sama

dari soalan PMR yang lalu• Berbincang dan bertanya rakan sebaya

KAEDAH BELAJAR

• Memberikan tumpuan 100% dalam proses P&P

• Membuat salinan contoh-contoh yang diberi• Menguji soalan berdasarkan contoh• Membuat latihan yang diberi oleh guru• Membuat latihan soalan-soalan lain• Mencari soalan bagi format yang sama dari

soalan PMR yang lalu• Berbincang dan bertanya rakan sebaya• Merujuk kepada guru bagi soalan sukar

diselesaikan

KAEDAH BELAJAR

CIRCLES IICIRCLES II

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC. CENTRE

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC. CENTRE

CHORD

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC. CENTRE

CHORD

MINOR ARC

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC. CENTRE

CHORD

MINOR ARCMINOR SEGMENT

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC. CENTRE

CHORD

MINOR ARCMINOR SEGMENT

MAJOR SEGMENT

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

ARC. CENTRE

CHORD

MINOR ARCMINOR SEGMENT

MAJOR SEGMENT

MAJOR ARC

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

a)The radius that is perpendicular to a chord bisects the chord and vice versa

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

b)The perpindicular bisectors of two chords intersect at the centre of the circle

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

0

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

0

c)Two chords that are equal in length are equidistant from the centre and vice versa

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

3.1b PROPERTIES

CHORD-is a straight line drawn across a circle with both ends on the circumference

d)Chpords of the same length cut arcs of the same length

PYTHAGORAS THEOREM

A

B C

8cm

6cm2 2 2

2 2 2

2

2

8 6

64 36

100

10010

AC BA BC

AC

AC

AC

ACAC

PYTHAGORAS THEOREM

A

B C

8cm 10cm

2 2 2

2 2 2

2

2

10 8

100 64

36

366

BC AC AB

BC

BC

BC

BCBC

PYTHAGORAS THEOREM

A

B C6cm

10cm

2 2 2

2 2 2

2

2

10 6

100 36

64

648

AB AC BC

AB

AB

AB

ABAB

PROPERTIES OF ANGLES IN CIRCLES

a)Angles subtended at the circumference by the same arc are equal

PROPERTIES OF ANGLES IN CIRCLES

a)Angles subtended at the circumference by the same arc are equal

PROPERTIES OF ANGLES IN CIRCLES

a)Angles subtended at the circumference by the same arc are equal

PROPERTIES OF ANGLES IN CIRCLES

a)Angles subtended at the circumference by the same arc are equal

Same angles

PROPERTIES OF ANGLES IN CIRCLES

b)Arcs of equal length subtend equal angles-at the circumference-at the centre

PROPERTIES OF ANGLES IN CIRCLES

b)Arcs of equal length subtend equal angles-at the circumference-at the centre

PROPERTIES OF ANGLES IN CIRCLES

b)Arcs of equal length subtend equal angles-at the circumference-at the centre

Same angles

PROPERTIES OF ANGLES IN CIRCLES

b)Arcs of equal length subtend equal angles-at the circumference-at the centre Same angles

PROPERTIES OF ANGLES IN CIRCLES

c) The angle subtended by an arc at the centre is twice the angle at the circumference

PROPERTIES OF ANGLES IN CIRCLES

c) The angle subtended by an arc at the centre is twice the angle at the circumference

0 centre

a

b

PROPERTIES OF ANGLES IN CIRCLES

c) The angle subtended by an arc at the centre is twice the angle at the circumference

0 centre

x

2x

PROPERTIES OF ANGLES IN CIRCLES

d)The angle subtended at the circumference in semicircle is90

PROPERTIES OF ANGLES IN CIRCLES

d)The angle subtended at the circumference in semicircle is90

PROPERTIES OF ANGLES IN CIRCLES

d)The angle subtended at the circumference in semicircle is90

PROPERTIES OF ANGLES IN CIRCLES

d)The angle subtended at the circumference in semicircle is90

3.3b)IDENTIFIYING INTERIOR OPPOSITE ANGLES

Cyclic Quadrilateral-a quadrilateral whose 4 vertices lie on the circumference

3.3b)IDENTIFIYING INTERIOR OPPOSITE ANGLES

Cyclic Quadrilateral-a quadrilateral whose 4 vertices lie on the circumference -the sum of the interior opposite angles is 180

3.3b)IDENTIFIYING INTERIOR OPPOSITE ANGLES

Cyclic Quadrilateral-a quadrilateral whose 4 vertices lie on the circumference -the sum of the interior opposite angles is 180-the exterior angle is equal to its corresponding interior opposite angle

3.3b)IDENTIFIYING INTERIOR OPPOSITE ANGLES

Cyclic Quadrilateral-a quadrilateral whose 4 vertices lie on the circumference -the sum of the interior opposite angles is 180-the exterior angle is equal to its corresponding interior opposite angle (a=b)

a

b

ex:In the figure, ABCD is a cyclic quadrilateral. BAE is a straight line. Finda)Angle BCDb)Angle ABC

A

BC

D

F50

135

ex:In the figure, ABCD is a cyclic quadrilateral. BAE is a straight line. Finda)Angle ABCDb)Angle ABC

A

BC

D

F50

135)

135

solutiona BCD EAD

ex:In the figure, ABCD is a cyclic quadrilateral. BAE is a straight line. Finda)Angle ABCDb)Angle ABC

A

BC

D

F50

135)

135

solutiona BCD EAD

Ex:In the diagram, 0 is the centre of the circle.Find the value y

Y

70

105

0

PQ

RS

Ex:In the diagram, 0 is the centre of the circle.Find the value y

Y

70

105

0

PQ

RS

180 702

55

solutionORQ OQR

Ex:In the diagram, 0 is the centre of the circle.Find the value y

Y

70

105

0

PQ

RS

180 702

55

solutionORQ OQR

180

105 180

55 105 180

180 160

20

solution

SRQ SPQ

Y ORQ

Y

Y

MODUL

33

Y

X

33

Y

X

sama

33

Y

X

sama

2x sudut x

33

Y

X

sama

2x sudut x

33+294=327

GRAPHS OF FUNCTIONSGRAPHS OF FUNCTIONS

3. Answer/Jawapan:

Kedua-dua paksi-x dan paksi-y dilukis betul, dengan skala yang seragam dan betul.

K1

40

30

20

10

-2 -1 0 1 2 3

-10

-20

-30

-3

-40

K1

3. Answer/Jawapan:

Kedua-dua paksi-x dan paksi-y dilukis betul, dengan skala yang seragam dan betul.

Kesemua tujuh titik ditanda betul @ lengkung melalui semua titik.

Nota:

Lima atau enam titik ditanda betul, beri K1

K1

K2

40

30

20

10

-2 -1 0 1 2 3

-10

-20

-30

-3

-40

× ×

×

×

×

×

×

K1

K2

20. Answer/Jawapan:

Kedua-dua paksi-x dan paksi-y dilukis betul, dengan skala yang seragam dan betul.

Kesemua tujuh titik ditanda betul @ lengkung melalui semua titik.

Nota:

Lima atau enam titik ditanda betul, beri K1

Lengkung licin, tidak tebal melalui semua titik betul.

Nota:

Jika skala lain tolak 1 markah dari markah diperolehi.

K1

K2

N1

40

30

20

10

-2 -1 0 1 2 3

-10

-20

-30

-3

-40

× ×

×

×

×

×

×

K1

K2

N1

MODUL

Table 16 shows the values of two variables x and y of a function.Jadual 16 menunjukkan nilai-nilai dua pembolehubah, x dan y bagi suatu fungsi.

(a) By using a scale of 2 cm to 2 units, complete and label the y-axis.Dengan menggunakan skala 2 cm kepada 2 unit, lengkap dan labelkan paksi-y itu.

Table 16 shows the values of two variables x and y of a function.Jadual 16 menunjukkan nilai-nilai dua pembolehubah, x dan y bagi suatu fungsi.

(a) By using a scale of 2 cm to 2 units, complete and label the y-axis.Dengan menggunakan skala 2 cm kepada 2 unit, lengkap dan labelkan paksi-y itu.(b) Based on Table , plot the points on the graph paper.Berdasarkan Jadual , plot titik-titik itu pada kertas graf itu.(c) Hence, draw the graph of the function.Seterusnya, lukis graf fungsi itu.

LOCI IN TWO DIMENSIONSLOCI IN TWO DIMENSIONS

NOTES

1.Locus is the path of a moving point that satisfies given condition

NOTES

1.Locus is the path of a moving point that satisfies given condition

2.It can be found by joining all the points that satisfy given conditions and then determined the pattern formed

Patterna) The locus of a moving point is at a

constant distance from a fixed point 0 is a circle with centre 0

LOCI IN TWO DIMENSION

• 1 DISTANCE 1 POINT=CIRCLE

.

.

LOCI IN TWO DIMENSION

• 1 DISTANCE 1 POINT=CIRCLE

=3 cm from A =Locus X that is constantly 5 units

from point A =Locus X such that AX=3cm =Locus X such that AX= AB

.

.

LOCI IN TWO DIMENSION

• 1 DISTANCE 1 POINT=CIRCLE

.

.

.

Patternb) The locus of a moving point that is at equidistant from 2 fixed points is the

Perpendicular bisector of the line

LOCI IN TWO DIMENSION

• 1 DISTANCE 2 POINT=PERPENDICULAR

BISECTOR

.

.A

.B

Patternc) The locus of a moving point that is a constant distance from a straight line are

2 straight lines parallel to the first line

• 1 DISTANCE 1 LINE=PARALLEL LINE

BA

Patternd) The locus of a moving point that is at equidistant from 2 intersecting lines is a

Pair of straight lines which is perpendicular to each other and bisect the angles between the 2 intersecting lines.

• 1 DISTANCE 2 LINE=BISECTOR ANGLE

Example (i)X, y and z are 3 moving points in the diagramDrawa) The locus of x such that it is 3 units from B

A B

CD

.0

Example (i)X, y and z are 3 moving points in the diagramDrawa) The locus of x such that it is 3 units from B

A B

CD

.0

Exercise (iii)

Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

Exercise (iii)

Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of y such that it esequidistant from points P and J

Exercise (iii)

Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and J

Exercise (iii)

Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and J

iii)The locus of c that it is constantly 1 cm from the straight line NL

Exercise (iii)

Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and J

iii)The locus of c that it is constantly 1 cm from the straight line NL

Exercise (iii)Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and Jiii)The locus of c that it is constantly 1 cm from the straight line NL

Exercise (iii)Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and Jiii)The locus of c that it is constantly 1 cm from the straight line NLiv)Hence, marks with the symbol the intersection of the locus A and C

Exercise (iii)Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and Jiii)The locus of c that it is constantly 1 cm from the straight line NLiv)Hence, marks with the symbol the intersection of the locus A and C

Exercise (iii)Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and Jiii)The locus of c that it is constantly 1 cm from the straight line NLiv)Hence, marks with the symbol the intersection of the locus A and C

Exercise (iii)Diagram in the answer space shows four square, PKJN, KQLJ and JLRM. A, B and C are 3 moving points in the diagram. On the diagram draw.i)The locus of A such that AJ=2cm

P K Q

NJ

L

S M R

ii)The locus of B that it is equidistant from points P and Jiii)The locus of c that it is constantly 1 cm from the straight line NLiv)Hence, marks with the symbol the intersection of the locus A and C

MODUL

(a) PR or straight line PR or diagonal PR.

Y

R

S

Y

R

S

Z

Y

R

S

Z

Y

R

S

Z

GEOMETRICAL GEOMETRICAL CONSTRUCTIONCONSTRUCTION

NOTES1.Construct line segment• Using a ruler draw a straight line• Mark a point on the line and label• Using compasses, set it to the radius

needed• With the centre of the marked point,

draw and arc to cut the straight line

Draw a line AB 5 cm long

Draw a line AB 5 cm long

A

Draw a line AB 5 cm long

A

NOTES

2. CONSTRUCT ANGLE BISECTOR•Using a ruler, draw 2 straight line which intersect each other.•With the intersection as the centre, draw arc to cut both lines.•Without changing the radius and the point of the intersection of the line and arc, draws arc that cut each other•Joint the intersection of two lines and the intersection of two arc

1. Construct a bisector from the angel below

A

C

B

ANGLE ACB

1. Construct a bisector from the angel below

answer

1. Construct a bisector from the angel below

answer

1. Construct a bisector from the angel below

answer

1. Construct a bisector from the angel below

answer

3. Construct angle 60º•With the centre of the marked point , draw a big arc to cut the straight line.•Using the same radius and the intersection of the arc and the straight line as the centre, draw another arc.•Joint the first point and the intersection of two arc to get 60º angle.

a) Construct 60º angle from the point A on the line

A

a) Construct 60º angle from the point A on the line

A

a) Construct 60º angle from the point A on the line

A

a) Construct 30º angle from the point A on the line

A

a) Construct 30º angle from the point A on the line

A

a) Construct 30º angle from the point A on the line

A

b) Construct 30º angle from the point A on the line

A

b) Construct 30º angle from the point A on the line

A

b) Construct 30º angle from the point A on the line

A

4. Construct perpendicular bisector•Follow rule how to construct line segment.•Set the compasses to a radius slightly over half the marked point•Using the left point, draw arcs above and below the line.•Using the right point, draw arc above and below the line again to cut the arcs drawn from the left point.•Joint the intersection of the two arcs.

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

a) Construct a perpendicular line (90) from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

b) Construct 45 from the point A on the line below

A

A

c)Construct perpendicular line (90) from the point A below

.

A

c)Construct perpendicular line (90) from the point A below

.

A

c)Construct perpendicular line (90) from the point A below

.

A

c)Construct perpendicular line (90) from the point A below

.

A

c)Construct perpendicular line (90) from the point A below

.

MODUL

• Construct angle 90 at point B correctly.