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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.