kami juara
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PROGRAMPROGRAM`̀
KAMI JUARAKAMI JUARA´́
2010 2010
MATEMATIK PMRMATEMATIK PMR(KERTAS 2)(KERTAS 2)
Tingkatan 1 & 2Tingkatan 1 & 2
Dewan SMK (A) Sharifah RodziahDewan SMK (A) Sharifah Rodziah16 Mac 201016 Mac 2010
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APAKAH AKTIVITI KITA HARI INI? APAKAH AKTIVITI KITA HARI INI? Analisis ringkas soalanAnalisis ringkas soalan--soalan Matematik soalan Matematik
PMR bagi Tingkatan 1 & 2 (2005PMR bagi Tingkatan 1 & 2 (2005 ² ² 2006).2006).
-- Apakah topik yang disoal?Apakah topik yang disoal?-- Bila dan bagaimanakah bentuknya?Bila dan bagaimanakah bentuknya?
-- Berapa kerap ia disoal?Berapa kerap ia disoal?
Latih tubi & teknik menjawabLatih tubi & teknik menjawab Sesi soal jawabSesi soal jawab
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JUMLAH MARKAH DIPERUNTUKKANJUMLAH MARKAH DIPERUNTUKKANUNTUK TOPIK TINGKATAN 1 & 2UNTUK TOPIK TINGKATAN 1 & 2
JUMLAH MARKAH KESELURUHANJUMLAH MARKAH KESELURUHAN
KERTAS 1 : 40 MARKAHKERTAS 1 : 40 MARKAHKERTAS 2 : 60 MARKAHKERTAS 2 : 60 MARKAHJUMLAH : 100 MARKAHJUMLAH : 100 MARKAH
MARKAH KERTAS 2 UNTUK TINGKATAN 1 & 2
2525 ±± 30 DARIPADA KESELURUHAN MARKAH (K2)30 DARIPADA KESELURUHAN MARKAH (K2) MENYUMBANG KEPADA 40% KE 50% MARKAHMENYUMBANG KEPADA 40% KE 50% MARKAHKESELURUHAN KERTAS 2.KESELURUHAN KERTAS 2.
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TOPIK² PENTING MATEMATIK PMR TOPIK² PENTING MATEMATIK PMR (Tingkatan 1 & 2)(Tingkatan 1 & 2)
BILBIL TOPIKTOPIKPMR PMR
0505 0606 0707 0808 0909
1 INTEGERS / DIRECTED NUMBERSINTEGERS / DIRECTED NUMBERS
2 WHOLE NUMBERS / FRACTIONS /WHOLE NUMBERS / FRACTIONS /DECIMALSDECIMALS
3 SQUARES, SQUARE ROOTS,SQUARES, SQUARE ROOTS,CUBES & CUBE ROOTSCUBES & CUBE ROOTS
4 LINEAR EQUATIONS ILINEAR EQUATIONS I
5 ALGEBRAIC EXPRESSIONS I & IIALGEBRAIC EXPRESSIONS I & II
6 TRANSFORMATIONSTRANSFORMATIONS
7 STATISTICS ISTATISTICS I
8 SOLID GEOMETRY I & IISOLID GEOMETRY I & II
9 LOCI IN TWO DIMENSIONSLOCI IN TWO DIMENSIONS
10 GEOMETRICAL CONSTRUCTIONSGEOMETRICAL CONSTRUCTIONS
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SOALANSOALAN--SOALAN TAHUN LALU PMRSOALAN TAHUN LALU PMRMENGIKUT TOPIK DAN TAHUN.MENGIKUT TOPIK DAN TAHUN.
(2005 (2005 ²² 2009)2009)
Kertas Soalan Latih TubiKertas Soalan Latih Tubi
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INTEGERS / DIRECTED NUMBERSINTEGERS / DIRECTED NUMBERS1
YearYear TopicTopic
20052005 Directed NumbersDirected Numbers
20062006 Directed NumbersDirected Numbers
20072007 IntegersIntegers20082008 --
20092009 Directed NumbersDirected Numbers
[ 2 marks][ 2 marks]
Kertas Soalan Latih TubiKertas Soalan Latih Tubi
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Q.1: Directed Numbers (2005)Q.1: Directed Numbers (2005)
5.18.026.4 v!
5.1408.3 !
908.4!
4.26 x 0.8 ± ¹ º
¸©ª
¨
2
11
and express the answer correct to two decimal places.
91.4!
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Q.2: Directed Numbers (2006)Q.2: Directed Numbers (2006)
3
2)6.0(14 z
326.014 z!
2
36.014 v!
9.014 !
9.14!
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Q.3: Integers (2007)Q.3: Integers (2007)
± 24 ÷ 8 ± 14
= ± 24 ÷ 8 ± 14
= ±3 ± 14
= ±17
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Q.4: Directed Numbers (2009)Q.4: Directed Numbers (2009)
)16(4
1115 z
164515 z!
16
5
415 v!
1612 !
= ±4
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3
4)24.06( z!
Q.5: Directed Numbers (2009)Q.5: Directed Numbers (2009)
4
3
76.5 v!
344.1 v!
(6 ± 0.24)3
4z
and express the answer correct to two decimal places.
32.4!
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WHOLE NUMBERS / FRACTIONS /WHOLE NUMBERS / FRACTIONS /DECIMALSDECIMALS2
YearYear TopicTopic
20052005 Whole NumbersWhole Numbers
20062006 FractionsFractions20072007 DecimalsDecimals
20082008 FractionsFractions
20092009 --
[ 2 marks][ 2 marks]
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Q.1: Whole Numbers (2005)Q.1: Whole Numbers (2005)
96 ± 3(12 + 48 ÷ 6)
=96 ± 3(12 + 8)
=96 ± 3(20)
=96 ± 60
=36
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Q.2: Fractions (2006)Q.2: Fractions (2006)
¹ º
¸©ª
¨ v!
15
1012
8
9
15
2
8
9v!
20
3!
¹ º
¸©ª
¨v3
2
5
4
8
11
express the answer as a fr action in its lowest term.
¹ º
¸©ª
¨v3
2
5
4
8
11
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Q.3: Decimals (2007)Q.3: Decimals (2007)
9.0
72.0!
9.0
18.04v
9
2.7!
= 0.8
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Q.4: Fractions (2008)Q.4: Fractions (2008)
¹ º
¸©ª
¨v!
15
4
2
5
3
2
1
1v!
3
2!
express the answer as a fr action in its lowest term.
¹ º
¸©ª
¨
v15
59
2
5
¹ º
¸©ª
¨v3
1
5
3
2
5
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SQUARES, SQUARE ROOTS, CUBES,SQUARES, SQUARE ROOTS, CUBES,CUBE ROOTSCUBE ROOTS
3
[ 1 + 2 =3 marks][ 1 + 2 =3 marks]
(2005 (2005 -- 2009) 2009) YearYear
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Q.1: Squares,Square Roo ts,Q.1: Squares,Square Roo ts,Cubes, Cube Roo ts (2005)Cubes, Cube Roo ts (2005)
232.4 z!
24.1!
(ii)
96.1!
64
1
4
1
4
1
4
1
4
13
!¹ º
¸©ª
¨v¹
º
¸©ª
¨v¹
º
¸©ª
¨!¹
º
¸©ª
¨(i)
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Q.2: Squares,Square Roo ts,Q.2: Squares,Square Roo ts,Cubes, Cube Roo ts (2006)Cubes, Cube Roo ts (2006)
3
14
5¹ º
¸©ª
¨!
3
4
1¹ º
¸©ª
¨!
(ii)
64
1!
7.07.07.049.0 !v!(i)
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3
362
1¹ º
¸©ª
¨v!
3
62
1¹ º
¸©ª
¨ v!
(i)
(ii) 33!
Q.3: Squares,Square Roo ts,Q.3: Squares,Square Roo ts,Cubes, Cube Roo ts (2007)Cubes, Cube Roo ts (2007)
4)4()4()4(64 33 !vv!
= 27
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2916 !
2
7!
(i)
(ii)
49!
Q.4: Squares,Square Roo ts,Q.4: Squares,Square Roo ts,Cubes, Cube Roo ts (2008)Cubes, Cube Roo ts (2008)
3
1
3
1
3
1
3
1
27
133 !¹
º
¸©ª
¨v¹
º
¸©ª
¨v¹
º
¸©ª
¨!
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23 87 !
2
)2(7
!
(i)
(ii)
227 !
Q.5: Squares,Square Roo ts,Q.5: Squares,Square Roo ts,Cubes, Cube Roo ts (2009)Cubes, Cube Roo ts (2009)
9.09.09.081.0 !v!
25!
= 25
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LINEAR EQUATIONS ILINEAR EQUATIONS I
4
[ 1 + 2 =3 marks][ 1 + 2 =3 marks]
(2005 (2005 -- 2009) 2009) YearYear
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Q.1: Linear Equations I (2005)Q.1: Linear Equations I (2005)
432 ! nn
4! n
4!n
(a)
(b) k k 73)2(5 !
k k 7310 !3710 !k k
317 !k
173!k
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1
312!
n
n312 !
3
12!n(a)
(b) 3)1(2 ! k k
322 ! k k 232 ! k k 5!k
Q.2: Linear Equations I (2006)Q.2: Linear Equations I (2006)
4!n
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410 ! x
104 ! x
6! x
(a)
(b)
13
45 x x!
x x 345 !
435 ! x x
42 ! x
2! x
Q.3: Linear Equations I (2007)Q.3: Linear Equations I (2007)
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115 ! p
511! p
16! p
(a)
(b)
2
31
!
x x
3)1(2 ! x x
322 ! x x
232 ! x x
5! x
Q.4: Linear Equations I (2008)Q.4: Linear Equations I (2008)
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186 !k
6
18!k
3!k (a)
(b) 72
34 !
m
472
3!
m
233 v!m
63 !m
2!m
Q.5: Linear Equations I (2009)Q.5: Linear Equations I (2009)
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q pq p 532 !
)5(32 q pq p !
qq p p 532 !
Q.1: Algebraic Expressions I & II (2008)Q.1: Algebraic Expressions I & II (2008)
Simplify:Simplify:
q p 8!
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Q.2: Algebraic Expressions I & II (2009)Q.2: Algebraic Expressions I & II (2009)
3102 ! n
Simplify:Simplify:
3)5(2 n
72 ! n
(a)(a)
(b)(b) )5()34(3 mk k m
mk k m ! 5912
k k mm 5912 !
k m 1413 !
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TRANSFORMATIONS ITRANSFORMATIONS I6
YearYear TopicsTopics MarksMarks
20052005 ReflectionsReflections Translations & Translations &
RotationsRotations
2+4=62+4=6
20062006 ReflectionsReflections TranslationsTranslations 2+2=42+2=4
20072007 ReflectionsReflections -- 22
20082008 ReflectionsReflections RotationsRotations 44
20092009 ReflectionsReflections -- 22
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PART APART A
REFLECTIONS
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Q.(a): Transf ormation I (2005)Q.(a): Transf ormation I (2005)
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Q.(b): Transf ormation I (2006)Q.(b): Transf ormation I (2006)
P'
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Q.(c): Transf ormation I (2008)Q.(c): Transf ormation I (2008)
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PART BPART B
TRANSLATIONS&
ROTATIONS
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Q.(1): Transf ormation I (2005)Q.(1): Transf ormation I (2005)
(a) (i) The Direction of therotation is ClockwiseClockwise
(ii) The coordinates of the
centre of the rotation is(2,4)
(b) M is a translationtranslation of ¹¹ º
¸©©ª
¨
2
7
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Q.(2): Transf ormation I (2006)Q.(2): Transf ormation I (2006)
Transformation L is a translationtranslation of ¹¹ º
¸©©ª
¨
2
7
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Q.3: Transf ormation 1 (2008)Q.3: Transf ormation 1 (2008)
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STATISTICS I (Charts)STATISTICS I (Charts)
7
2 marks / [ 1 + 2 =3 marks]2 marks / [ 1 + 2 =3 marks]YearYear TopicTopic
20052005 --
20062006 Line GraphLine Graph20072007 Vertical Bar ChartVertical Bar Chart
20082008 --
20092009 Horizontal Bar ChartHorizontal Bar Chart
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Q.1: Statistics I (2006)Q.1: Statistics I (2006)
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Q.2: Statistics 1 (2007)Q.2: Statistics 1 (2007)
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SOLID GEOMETRY I & II (Net)SOLID GEOMETRY I & II (Net)
8
[3 marks][3 marks]YearYear TopicTopic
20052005 --
20062006 --20072007 Net of a prismNet of a prism
20082008 --
20092009 --
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Q.1: Solid Geometry I & II (2004)Q.1: Solid Geometry I & II (2004)
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Q.2: Solid Geometry I & II (2007)Q.2: Solid Geometry I & II (2007)
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LOCI IN T WO DIMENSIONSLOCI IN T WO DIMENSIONS
9
[5 marks][5 marks]
(2005 (2005 -- 2009) 2009) YearYear
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Q.1: Loci in Two Dimensions (2007)Q.1: Loci in Two Dimensions (2007)
(a) Locus of X is the diagonal PN
(b) (i), (ii)
(c)
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GEOMETRICAL CONSTRUCTIONSGEOMETRICAL CONSTRUCTIONS
10
[5 marks][5 marks]
(2005 (2005 -- 2009) 2009) YearYear
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Q.1: Geometrical Constructions (2007)Q.1: Geometrical Constructions (2007)
(a) r! 60 JKL
(b) (i)
(b) (ii)
cmcm PQ 2.01.6 s!
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SESI SOAL JAW ABSESI SOAL JAW AB
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Sekian, Terima KasihSekian, Terima Kasih
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