# teknik menjawab 1

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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

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

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

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

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