O level Maths guiges and Notes ::

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  • 8/6/2019 O level Maths guiges and Notes :: www.O-Alevel.com

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    Aipmlaipkos KCO_L gepls

    Kg`l}

    9' @lokaihs ig` spig`iv` neva

    6' Ioo|vio{ ig` Lvvev

    ?' Zelvs ig` veepsohkod eg i pezko pe

    ~kskp pml gepls0' Vipke . zvezevpkeg

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    9' @lokaihs ig` spig`iv` neva pez

    -i+ a|hpkzh{kgc ig` `k~k`kgc

    -k+ Ae~l pml `lokaih zekgps pe pml vkcmp |gpkh liom ks i mehl

    g|aflv( gepkgc pml pepih g|aflv en ae~ls( zlvneva pml a|hpkzhkoipkeg( pmlg

    ae~l pml `lokaih zekgp fiod f{ pml zvl~ke|s pepih2

    6'< 9'?>

    ( se pml igslv ks6< 9?> ?0:: 1 ?'0tGepl kg pml zvl~ke|s l}iazhl( pmip pvigsnlvvkgc i niopev en 6( ev l~lg flpplv(

    0( nvea pml 9?> pe pml 6< aidls kp lisklv2

    q6< 9?> 6< -0 ?0+ -6< 0+ ?0 9:: ?0 ?0::1 1 1 1

    -kk+ Ae~l fepm `lokaih zekgps peclpmlv pe pml vkcmp |gpkh pml:'::93< :':06`k~ksev ks i mehl g|aflv( zlvneva pml oiho|hipkeg( ig` pmip ks pml igslv'9'3< 06 ( f|p skazhkn{ pml oiho|hipkeg f{ oigolhhkgc `eg ig{ niopevs nkvsp'

    Kg pmks oisl( fepm g|aflvs smivl i 3( se `k~k`l pmks e|p2 ( ig`:'6< >:':09>

    > :'63= ?':9? pe ? `'z'

    -k~+ skcgknkoigp nkc|vls

    Pe ve|g` i g|aflv pe g s'n'( oe|gp `kckps nvea pml hlnp spivpkgc kpm pml nkvsp

    geg!rlve `kckp( pmlg zveoll` is nev `lokaih zhiols'

    l'c' ve|g` ?9:;'=< pe ? s'n'( ?9:;'=< se?9:x;'=< ?99: pe ? s'n'

    l'c' ve|g` :'::?:9>6 pe ? s'n'( :'::?:9>6 ( se:'::?:9x>6 :'::?:6 pe ? s'n'

    -f+ spig`iv` neva

    -kkk+ Oeg~lvp pml nehhekgc pe spig`iv` neva2 -i+ 6< ::: -f+ :'::::96?

    Ae~l pml `lokaih zekgp |gpkh {e| mi~l i g|aflv} mlvl 9 9:} 8 ( ig` pmlg|aflv en zhiols {e| ae~l` pml zekgp khh kg`koipl pml g|alvkoih ~ih|l en pml

    zelv en 9:' _e 06

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    -~+ `k~k`kgc kg spig`iv` neva296

    ?

    ?'6 9:

    6'< 9:

    Icikg( vlivvigcl pml oiho|hipkeg pe

    96 ? ;-?'6 6' 3-6'< 9: + -?'3< 9: +$ > ev 9:3( pmlg i``'

    3 3-:'6< 9: + -?'3< 9: + 0 9: $ 1 3

    Y|lspkegs

    -i+ 6' 6+ -9: 9: + 9'? 9:

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    6' Ioo|vio{ ig` Lvvev pez

    ?a

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    ?' Zelvs ig` veeps pez

    9+ i f i f} } } $ 1 6+ i f i f} } } 1 ?+ - +i f if} }

    0+9i

    i}

    }

    1

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    Y|lspkegs

    _kazhkn{ pml nehhekgc is niv is zesskfhl2

    -i+ < ?} }

    -f+ ?

    -o+0 3

    ?

    6 0

    = 0

    Igslvs

    -i+ < ? < ? =} } } } 1 1 -f+ ? < > ? < >i i i i i$ 1 1 0

    -o+0 3 0 3 99

    99 >

    ? ? ? ?? ?

    ? ? ? ?

    $ $

    1 1 1 1

    -`+< 9: < 6 9: < 6: 6 ? ? > 6 ? 9= > 96

    6 0 6 -6 + 6 6 66

    = 0 -6 + -6 + 6 6 6

    1 1 1 1

    -f+ nviopkegih zelvs

    >+9

    gg} }

    3+ - +

    z

    y yz zy} } }1

    >+ l'c'9

    ??} } (9

    6; ; 1 ? 3+

    6

    6 6??63 - 63+ -?+ ;1 1Gepl2 kn {e| oig nkg` pml ypm veep en} liskh{ pmlg kps flpplv pe |sl pml - +y z} ~lvskeg'

    >

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    Y' _kazhkn{ pml nehhekgc is niv is zesskfhl2

    -i+

    9

    6

    9>

    -f+9

    ?>0

    -o+?

    60

    -`+?

    0=9

    -l+

    6

    > ?- +}

    Igslvs'

    -i+9

    69> 9> 01 -f+

    9

    ??>0 >0 01 -o+

    ?? ?60 - 0+ -6+ =1 1

    -`+?

    ? ?00=9 - =9+ -?+ 631 1

    -l+ lisklv pe |sl zelv hi -?+ ife~l2

    6 6>

    > 0? ?- +} } }1 1

    3

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    0' Vipke ig` Zvezevpkeg

    -i+ \skgc vipkes

    Pmks ks vlihh{ i szlokih oisl en zvezevpkeg' Kn y|igpkpkls ivl hkglivh{ vlhipl`(

    lkpmlv `kvloph{ ev kg~lvslh{( -hkdl g|aflv en evdlvs ig` pkal pidlg pe `e i bef+(

    oiho|hipl f{ a|hpkzh{kgc f{ i vipke2

    l'c' Kn = evdlvs oig peclpmlv `e i bef kg > i{s( me hegc e|h` pml sial bef pidl

    kpm 96 evdlvs5

    igs2 kp khh pidl hlss pkal( se l a|hpkzh{ f{ pml vipke =96

    ' _e kp pidls

    =96

    > 0 1 `i{s'

    l'c' Kn i evdnevol en 6: oig zve`|ol 96 oivs kg 9< `i{s( me aig{ evdlvs

    sme|h` fl |sl` kn 9< oivs ivl gll`l` kg 9: `i{s5

    igs2 ge' en evdlvs 1 9< 9'6{ }

    Vlvkpl is ( ig` s|fspkp|pl pml ck~lg ~ih|ls pe nkg` d26{ d}163'6 >d1 ( se

    :'6d1 ' Pml vlhipkegsmkz oig ge fl vkpplg is6:'6{ }1 ( ig` ig{ zvefhlas seh~l`'

    -kk+ Kg~lvsl zvezevpkeg

    Pmks ks mlg ig kgovlisl kg egl y|igpkp{ oi|sls ig `lovlisl kg pml epmlv'

    l'c' Kn{ ks kg~lvslh{ zvezevpkegih pe pml o|fl en}(

    pmlg?

    9{

    }

    Vlvkpl is?

    d{

    }1 ( ig` zveoll` is |s|ih'

    -kkk+ A|hpkzhklv alpme`

    Nev pml o|ggkgc( kp ks zesskfhl -f|p miv`lv+ pe seh~l i zvefhla kpme|p oiho|hipkgc d'

    l'c' Vi`kipkeg ~ivkls kg~lvslh{ is pml sy|ivl en pml `kspigol ii{ nvea pml se|vol' Kg

    s|kpifhl |gkps( pml vi`kipkeg ip 9:a ii{ nvea pml se|vol ks 3

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    Y|lspkegs'

    -i+ Siplv gll`s pe fl vlae~l` nvea ig |g`lvcve|g` omiaflv flnevl evd oig

    oeaalgol' Smlg pml iplv is ip i `lzpm en ?a( nk~l s|opkeg zkzls lvl |sl` ig`

    lazpkl` pml omiaflv kg 0 me|vs' Kn pml iplv ks ge ip i `lzpm en 0

    -o+ Pml pkal psloeg`s pidlg nev ig efblop pe pvi~lh i olvpikg `kspigol nvea vlsp ks

    kg~lvslh{ zvezevpkegih pe pml sy|ivl veep en pml ioolhlvipkeg i' Smlg i ks 0a%s6( p ks

    6s'

    Smip ks pml ~ih|l eni kn pml pkal pidlg ks < sloeg`s5

    Igslvs

    -i+ Ge' en zkzls 1< 0

    < 1? 9:

    9?

    ? ( se kp e|h` fl glolssiv{ pe |sl 0 zkzls pe fl s|vl

    en lazp{kgc kpmkg 9: me|vs'

    -f+ ig` l dge mlg} ks ( se

    6

    6

    { }

    { d}

    1

    ( se6> d1 < >6

    60 ( se}1

    6 6< ='>0

    >}

    1 ge( `egp vliom nev pml oiho|hipev {lp)

    6 6< 9'00} 1 ( se '< 9'6 >} 1 1

    -o+

    9p (

    i

    _ed

    pi

    1 ' _|fspkp|pkgc ck~lg ~ih|ls2

    60

    d1 ( se ( kl0d1

    0p

    i1 '

    Smlg p 1

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    ? (

    pmlg nkg` pml helsp oeaaeg `lgeakgipev( kg pmks oisl >' Pmlg

    9; < 9; 6 < ; 99

    > ? > > 6

    1 1 1 '

    -kk+ A|hpkzh{kgc%`k~k`kgc2 l'c'9 3