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    TEKNIK MENJAWABTEKNIK MENJAWAB

    MATEMATIKMATEMATIK

    KERTAS 2KERTAS 2

    OLEH :OLEH :

    SITI NOR RAYA BT ABDUL RAHIMSITI NOR RAYA BT ABDUL RAHIM

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    AGIHAN SOALANAGIHAN SOALAN

    KERTAS 1KERTAS 1 -- 1 jam 151 jam 15 minitminit

    -- 4040 soalansoalan objektifobjektif

    -- 4040 markahmarkah

    KERTAS 2KERTAS 21 jam 451 jam 45 minitminit

    -- 2020 soalansoalan subjektifsubjektif-- 6060 markahmarkah

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    TOPIK DALAM KERTAS 2TOPIK DALAM KERTAS 2

    Directed numbersDirected numbers

    Square, square roots, cubes, cubes rootsSquare, square roots, cubes, cubes roots

    Linear equationsLinear equations

    Linear InequalitiesLinear Inequalities Algebraic ExpressionsAlgebraic Expressions

    Algebraic FormulaeAlgebraic Formulae IndicesIndices

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    KERTAS 2KERTAS 2

    StatisticsStatistics

    TrigonometryTrigonometry

    Graph of FunctionsGraph of Functions

    Geometrical ConstructionsGeometrical Constructions Loci in Two DimensionsLoci in Two Dimensions

    TransformationsTransformations Scale DrawingsScale Drawings

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    KERTAS 1KERTAS 1 Whole numbersWhole numbers

    Number pattern andNumber pattern andsequencessequences

    FractionsFractions

    DecimalsDecimals

    PercentagesPercentages

    IntegersIntegers

    Lines and AnglesLines and Angles

    PolygonsPolygons CirclesCircles

    Algebraic expressionsAlgebraic expressions

    Perimeter and AreaPerimeter and Area

    Solid GeometrySolid Geometry Graph of FunctionsGraph of Functions

    Linear EquationsLinear Equations

    Ratios, rates andRatios, rates andProportionsProportions

    CoordinatesCoordinates

    Loci in two dimensionsLoci in two dimensions

    StatisticsStatistics TransformationsTransformations

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    Directed numbersDirected numbers

    BODMASBODMASselesaikanselesaikan kurungankurungan,, kuasakuasa

    duadua atauatau tigatiga, division, multiplication,, division, multiplication,additionaddition dandan subtractionsubtraction

    KuasaiKuasai pendarabanpendaraban,, pembahagianpembahagian,,pecahanpecahan dandan perpuluhanperpuluhan dengandengan baikbaik..

    MestiMesti hafalhafal sifirsifir

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    Examples 1:Examples 1:

    86865(32 + 565(32 + 56 7)7)

    Solution:Solution:

    = 86= 865( 32 + 8)5( 32 + 8)

    = 86= 865( 40)5( 40)= 86= 86200200

    == -- 114114

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    Examples 2:Examples 2:

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    Examples :Examples :

    1. 1001. 1004( 244( 24 4 + 9)4 + 9)2.2.0.60.6(( -- ++ 33//55))

    3. 5.64 x 0.23. 5.64 x 0.2((--11 ))4. ( 34. ( 322 11//88)) 0.050.05

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    Squares, square roots, cube andSquares, square roots, cube and

    cube rootscube roots

    Example 1 :Example 1 :

    Solve a)Solve a) 0.250.25

    b) (b) ( 6464 -- 33 125)125)22

    Solution:Solution:

    a) 0.5 N1a) 0.5 N1

    b) ( 8b) ( 85)5) 22 K1K1

    = (3)= (3)22

    = 9 N1= 9 N1

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    Example 2:Example 2:

    a)a) 33 0.2160.216

    b) (3.3b) (3.3 33 27)27)22

    Solution:Solution:

    a) 0.6 N1a) 0.6 N1 b) ( 3.3b) ( 3.3 3)3) 22

    = (1.1)= (1.1)

    22

    K1K1= 1.21 N1= 1.21 N1

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    Examples:Examples:

    1. a)1. a) 33 0.5120.512

    b) 4b) 422 x (x (33 --2727//88))

    2. a)2. a) 33 --0.0270.027b) 2b) 233 ((22//55))

    22

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    StatisticsStatistics

    Bar chartsBar charts

    Line graphsLine graphs

    PictogramsPictograms

    Pie chartsPie charts Mode, median, meanMode, median, mean

    Frequency tableFrequency table

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    Bar chartBar chart

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    Jan Feb March April

    Month

    Totalsales

    Month

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    Dual Bar chartDual Bar chart

    010

    20

    30

    4050

    60

    70

    80

    90

    3 Bijak 3 pintar 3 cerdas 3 Arif

    BoyGirl

    Number ofstudents

    Class

    Mesti tulis petunjuk

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    Line GraphLine Graph

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    3 Bijak 3 Cerdas 3 Arif 3 Pintar

    Class

    Jangan sambungkan point yg pertama dari sifar. Labelkankedua-dua axes.

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    Pie ChartPie Chart

    3a

    3b

    3c

    3d

    3e

    3c3c9003d

    1200

    3e800

    3b500

    3a200

    Mesti labelkan sudut dan nama sektor. Ukuran mesti tepat.

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    pictogramspictograms

    20052005 20042004 20032003

    20022002 20012001

    represent 50 studentsrepresent 50 students

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    Mode, median and meanMode, median and mean ModeModefrequencyfrequency tertinggitertinggi

    MedianMedianitem yangitem yang terdapatterdapat didi tengahtengah

    tengahtengah datadata

    MeanMeanpuratapurata/ average/ average

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    Determine the mode, median and mean forDetermine the mode, median and mean for

    data given : 3, 5, 5, 4, 5, 6, 7, 9, 4data given : 3, 5, 5, 4, 5, 6, 7, 9, 4

    Answer :Answer :

    Mode = 5Mode = 5 Median = 3, 4, 4, 5, 5, 5, 6, 7, 9Median = 3, 4, 4, 5, 5, 5, 6, 7, 9

    = 5 (= 5 ( susunsusun dahuludahulu datadata mengikutmengikut

    tertibtertib menaikmenaik))Mean =Mean = 3 + 4+ 4+ 5+ 5+ 5+ 6+ 7+ 93 + 4+ 4+ 5+ 5+ 5+ 6+ 7+ 9

    99

    == 484899

    = 5.33= 5.33

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    Determine mode, median and mean from theDetermine mode, median and mean from the

    frequency table belowfrequency table below

    44664455FrequencyFrequency

    33221100ScoreScore

    a) Mean = 2b) Median = (19 +1) 2 = 10 th

    = 2c) Mean = 0(5) + 1(4) + 2(6) + 3(4)

    19= 4 + 12 + 12

    19= 28 19= 1. 47

    Common mistake = 28 4 = 7

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    Construct a frequency table.Construct a frequency table. 4, 2, 1, 5, 3, 2, 2, 2, 4, 1, 1, 5, 5, 2, 2, 5, 24, 2, 1, 5, 3, 2, 2, 2, 4, 1, 1, 5, 5, 2, 2, 5, 2

    Answer :Answer :

    Determine the mode, median and meanDetermine the mode, median and mean

    Saving

    frequency

    1 2 3 4 5

    3 7 1 24

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    IndicesIndices Law of indicesLaw of indices

    aamm x ax ann = a= a m+nm+n

    aamm aann = a= a mm--nn

    ((aamm))nn == aamxnmxn aa1/n1/n == nnaa

    aa--nn == 11/a/ann

    aan/mn/m == nnaamm

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    Examples 1:Examples 1: kk22 x kx k44 kk--22

    = k= k 2+42+4((--2)2)

    = k= k 88

    Common mistakeCommon mistake::

    = k= k 2+42+422

    = k= k 44

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    Examples 2:Examples 2: Simplify : (2mSimplify : (2m33nn22))33 x mx m--44nn22 mm22nn--33

    Solution:Solution:

    = 2= 233mm99nn66 x mx m--44nn22 mm22nn--33 K1K1

    = 8m= 8m 9+(9+(--4)4)--22 nn 6+26+2--((--3)3) K1K1

    = 8m= 8m33nn1111 N1N1 Common mistakeCommon mistake

    =2=2

    33

    mm

    99

    nn

    66

    x mx m

    --44

    nn

    22

    mm

    22

    nn

    --33

    K1K1 == 66mm 9+(9+(--4)4)--22 nn 6+26+2--((--3)3) K0K0

    == 66mm33nn1111 N0N0

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    Examples 3:Examples 3:

    Evaluate :Evaluate : 88 1/31/3 x 27x 27 1/31/3

    22 --11

    Solution :Solution :== ( 2( 233))1/31/3 x ( (3x ( (333))1/31/3

    22--11

    = 2 x 3 x 2= 2 x 3 x 2

    = 12= 12

    Or 216Or 216 1/31/3 x 2x 2= ( 6= ( 633))1/31/3 x 2x 2

    = 6 x 2 = 12= 6 x 2 = 12

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    Examples 4:Examples 4: 33 --22 x 3x 3 nn = 81, find the value of n= 81, find the value of n

    Solution:Solution:

    33 --22 x 3x 3 nn = 3= 344 (( tukarkantukarkan kpdkpd basebase ygyg

    samasama iaituiaitu 33 ------ 81= 381= 344

    ))--2 + n = 4 (2 + n = 4 ( ambilambil indeksindeks sahajasahaja--abaikanabaikan

    base)base)

    n = 4 + 2 (n = 4 + 2 ( selesaikanselesaikan sptspt linear equation)linear equation)

    = 6= 6

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    Examples:Examples:1. m1. m33 mm22 x mx m--33

    2.2. kk22hh33 x (3x (322khkh22))22

    3k3k44hh66

    3. 163. 16 1/31/3 x 4x 41/31/3 88 --1/31/3

    4. 54. 5 --22 x 125 = 5x 125 = 5nn, find the value of n, find the value of n

    5. x5. x33 = 8, find the value of x= 8, find the value of x--11

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    SELAMAT MENCUBASELAMAT MENCUBA

    SEMOGA BERJAYA!!!SEMOGA BERJAYA!!!SASARKAN A UNTUK MATEMATIKSASARKAN A UNTUK MATEMATIK

    PMR 2010PMR 2010