954 mathematics t [ppu] semester 1 topics

7/31/2019 954 Mathematics T [PPU] Semester 1 Topics

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GAZT] ]EZN? CFLEJZC CIM LEBNE]ZQ

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Pezabm Fecziail Bu}dbne

3 Guid}abit :8 Dcimamc}et thbufm je cjfe }b?

3)3 Guid}abit 7 (c! t}c}e }he mbncai cim zcile bg c guid}abi& cim

gaim dbnpbta}e guid}abit;

(j! me}eznaie |he}hez c guid}abi at bie.}b.bie&

cim gaim }he aiwezte bg c bie.}b.bie guid}abi;

(d! tke}dh }he lzcpht bg tanpfe guid}abit&

aidfumail paede|ate.megaiem guid}abit;

3): Pbfqibnacf cim

zc}abicf guid}abit

8 (m ! ute }he gcd}bz }hebzen cim }he zencaimez

}hebzen;

(e! tbfwe pbfqibnacf cim zc}abicf esuc}abit cim

aiesucfa}aet;

( g ! tbfwe esuc}abit cim aiesucfa}aet aiwbfwail

nbmufut talit ai tanpfe dctet;

(l! medbnpbte c zc}abicf expzettabi ai}b pcz}acf

gzcd}abit ai dctet |heze }he meibnaic}bz hct

}|b mat}aid} faiecz gcd}bzt& bz c faiecz gcd}bz

cim c pzane sucmzc}ad gcd}bz;

3)4 Expbiei}acf cim

fblcza}hnad guid}abit

7 (h! zefc}e expbiei}acf cim fblcza}hnad guid}abit&

cflejzcadcffq cim lzcphadcffq;

(a! ute }he pzbpez}aet bg expbiei}t cim fblcza}hnt;

( o! tbfwe esuc}abit cim aiesucfa}aet aiwbfwail

expbiei}acf bz fblcza}hnad expzettabit;

3)= ]zalbibne}zad

guid}abit

8 (k ! zefc}e }he pezabmada}q cim tqnne}zaet bg }he

taie& dbtaie cim }cilei} guid}abit }b }heaz

lzcpht& cim amei}agq }he aiwezte taie& aiwezte

dbtaie cim aiwezte }cilei} guid}abit cim }heaz

lzcpht;

(f! ute jctad }zalbibne}zad amei}a}aet cim }hegbznufce gbz tai ( C ³ J!& dbt ( C ³ J! cim

}ci ( C ³ J!& aidfumail tai : C& dbt : C cim

}ci : C;

(n! expzett c tai + j dbt ai }he gbznt

z tai ( ³γ! cim z dbt ( ³γ!;

(i! gaim }he tbfu}abit& |a}hai tpedagaem ai}ezwcft&

bg }zalbibne}zad esuc}abit cim aiesucfa}aet)



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: Tesueidet cim Tezaet 38 Dcimamc}et thbufm je cjfe }b?

:)3 Tesueidet = (c! ute ci expfada} gbznufc cim c zeduztawe gbznufcgbz c tesueide;

(j! gaim }he fana} bg c dbiwezlei} tesueide;

:): Tezaet 8 (d! ute }he gbznufce gbz }he i}h }ezn cim gbz }he

tun bg }he gazt} i }eznt bg ci cza}hne}ad tezaet

cim bg c lebne}zad tezaet;

(m ! amei}agq }he dbima}abi gbz }he dbiwezleide bg c

lebne}zad tezaet& cim ute }he gbznufc gbz }he

tun bg c dbiwezlei} lebne}zad tezaet;

(e! ute }he ne}hbm bg maggezeidet }b gaim }he i}hpcz}acf tun bg c tezaet& cim memude }he tun bg

}he tezaet ai }he dcte |hei a} at dbiwezlei};

:)4 Jaibnacf expcitabit 7 ( g ! expcim (c + j!i

& |heze i ;

(l! expcim (3 + x!i

& |heze i & cim amei}agq }he

dbima}abi x 6 3 gbz }he wcfama}q bg }hat

expcitabi;

(h! ute jaibnacf expcitabit ai cppzbxanc}abit)

4 Nc}zadet 37 Dcimamc}et thbufm je cjfe }b?

4)3 Nc}zadet 30 (c! amei}agq iuff& amei}a}q& maclbicf& }zacilufcz cim

tqnne}zad nc}zadet;

(j! ute }he dbima}abit gbz }he esucfa}q bg }|b

nc}zadet;

(d! pezgbzn tdcfcz nuf}apfadc}abi& cmma}abi&

tuj}zcd}abi cim nuf}apfadc}abi bg nc}zadet |a}h

c} nbt} }hzee zb|t cim }hzee dbfunit;

(m ! ute }he pzbpez}aet bg nc}zax bpezc}abit;

(e! gaim }he aiwezte bg c ibi.tailufcz nc}zax utail

efenei}czq zb| bpezc}abit;

( g ! ewcfuc}e }he me}eznaici} bg c nc}zax;

(l! ute }he pzbpez}aet bg me}eznaici}t;



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4): Tqt}ent bg faiecz

esuc}abit

7 (h! zemude ci culnei}em nc}zax }b zb|.edhefbi

gbzn& cim me}eznaie |he}hez c tqt}en bg faiecz

esuc}abit hct c uiasue tbfu}abi& aigaia}efqnciq tbfu}abit bz ib tbfu}abi;

(a! cppfq }he Lcuttaci efanaic}abi }b tbfwe c

tqt}en bg faiecz esuc}abit;

( o! gaim }he uiasue tbfu}abi bg c tqt}en bg faiecz

esuc}abit utail }he aiwezte bg c nc}zax)

= Dbnpfex Iunjezt 3: Dcimamc}et thbufm je cjfe }b?

(c! amei}agq }he zecf cim anclaiczq pcz}t bg c

dbnpfex iunjez;

(j! ute }he dbima}abit gbz }he esucfa}q bg }|bdbnpfex iunjezt;

(d! gaim }he nbmufut cim czlunei} bg c dbnpfex

iunjez ai dcz}etaci gbzn cim expzett }he

dbnpfex iunjez ai pbfcz gbzn;

(m ! zepzetei} c dbnpfex iunjez lebne}zadcffq jq

necit bg ci Czlcim maclzcn;

(e! gaim }he dbnpfex zbb}t bg c pbfqibnacf

esuc}abi |a}h zecf dbeggadaei}t;

( g ! pezgbzn efenei}czq bpezc}abit bi }|b

dbnpfex iunjezt expzettem ai dcz}etaci gbzn;

(l! pezgbzn nuf}apfadc}abi cim mawatabi bg }|b

dbnpfex iunjezt expzettem ai pbfcz gbzn;

(h! ute me Nbawze‑t }hebzen }b gaim }he pb|ezt

cim zbb}t bg c dbnpfex iunjez)

5 Cicfq}ad Lebne}zq 3= Dcimamc}et thbufm je cjfe }b?

(c! }zcitgbzn c lawei esuc}abi bg c dbiad ai}b }he

t}cimczm gbzn;

(j! gaim }he wez}ex& gbdut cim mazed}zax bg c

pczcjbfc;

(d! gaim }he wez}adet& dei}ze cim gbda bg ci effapte;

(m ! gaim }he wez}adet& dei}ze& gbda cim ctqnp}b}et

bg c hqpezjbfc;

(e! gaim }he esuc}abit bg pczcjbfct& effaptet cim

hqpezjbfct tc}atgqail pzetdzajem dbima}abit

(exdfumail eddei}zada}q!;



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( g ! tke}dh dbiadt;

(l! gaim }he dcz}etaci esuc}abi bg c dbiad megaiem

jq pczcne}zad esuc}abit;

(h! ute }he pczcne}zad esuc}abit bg dbiadt)

7 Wed}bzt :0 Dcimamc}et thbufm je cjfe }b?

7)3 Wed}bzt ai }|b cim

}hzee maneitabit

8 (c! ute uia} wed}bzt cim pbta}abi wed}bzt;

(j! pezgbzn tdcfcz nuf}apfadc}abi& cmma}abi cim

tuj}zcd}abi bg wed}bzt;

(d! gaim }he tdcfcz pzbmud} bg }|b wed}bzt& cim

me}eznaie }he cilfe je}|eei }|b wed}bzt;

(m ! gaim }he wed}bz pzbmud} bg }|b wed}bzt& cim

me}eznaie }he czec c pczcffefblzcn cim bg c

}zacilfe;

7): Wed}bz lebne}zq 3: (e! gaim cim ute }he wed}bz cim dcz}etaci esuc}abit

bg faiet;

( g ! gaim cim ute }he wed}bz cim dcz}etaci esuc}abit

bg pfciet;

(l! dcfdufc}e }he cilfe je}|eei }|b faiet& je}|eei

c faie cim c pfcie& cim je}|eei }|b pfciet;

(h! gaim }he pbai} bg ai}ezted}abi bg }|b faiet& cimbg c faie cim c pfcie;

(a! gaim }he faie bg ai}ezted}abi bg }|b pfciet)



TEDBIM ]EZN? DCFDUFUT

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< Fana}t cim Dbi}aiua}q 3: Dcimamc}et thbufm je cjfe }b?

<)3 Fana}t 7 (c! me}eznaie }he exat}eide cim wcfuet bg }he feg}.

hcim fana}& zalh}.hcim fana} cim fana} bg c

guid}abi;

(j! ute }he pzbpez}aet bg fana}t;

<): Dbi}aiua}q 7 (d! me}eznaie }he dbi}aiua}q bg c guid}abi c} c

pbai} cim bi ci ai}ezwcf;

(m ! ute }he ai}eznemac}e wcfue }hebzen)

8 Maggezei}ac}abi :8 Dcimamc}et thbufm je cjfe }b?

8)3 Mezawc}awet 3: (c! amei}agq }he mezawc}awe bg c guid}abi ct c fana};

(j! gaim }he mezawc}awet bg xi

(i !& e x& fi x&

tai x& dbt x& }ci x& tai3 x& dbt

3 x& }ci

3 x& |a}h

dbit}ci} nuf}apfet& tunt& maggezeidet&

pzbmud}t& sub}aei}t cim dbnpbta}et;

(d! pezgbzn anpfada} maggezei}ac}abi;

(m ! gaim }he gazt} mezawc}awet bg guid}abit megaiem

pczcne}zadcffq;

8): Cppfadc}abit bg

maggezei}ac}abi

37 (e! me}eznaie |heze c guid}abi at aidzectail&

medzectail& dbidcwe up|czm cim dbidcwe

mb|i|czm;

( g ! me}eznaie }he t}c}abiczq pbai}t& ex}zenun

pbai}t cim pbai}t bg aigfexabi;

(l! tke}dh }he lzcpht bg guid}abit& aidfumail

ctqnp}b}et pczcffef }b }he dbbzmaic}e cxet;

(h! gaim }he esuc}abit bg }cilei}t cim ibzncft }b

duzwet& aidfumail pczcne}zad duzwet;

(a! tbfwe pzbjfent dbideziail zc}et bg dhcile&aidfumail zefc}em zc}et;

( o! tbfwe bp}anatc}abi pzbjfent)

1 Ai}elzc}abi :8 Dcimamc}et thbufm je cjfe }b?

1)3 Aimegaia}e ai}elzcft 3= (c! amei}agq ai}elzc}abi ct }he zewezte bg

maggezei}ac}abi;

(j! ai}elzc}e xi

(i !& e x& tai x& dbt x& ted

: x& |a}h

dbit}ci} nuf}apfet& tunt cim maggezeidet;



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(d! ai}elzc}e zc}abicf guid}abit jq necit bg

medbnpbta}abi ai}b pcz}acf gzcd}abit;

(m ! ute }zalbibne}zad amei}a}aet }b gcdafa}c}e }he

ai}elzc}abi bg }zalbibne}zad guid}abit;

(e! ute cflejzcad cim }zalbibne}zad tujt}a}u}abit

}b gaim ai}elzcft;

( g ! pezgbzn ai}elzc}abi jq pcz}t;

1): Megaia}e ai}elzcft 3= (l! amei}agq c megaia}e ai}elzcf ct }he czec uimez c

duzwe;

(h! ute }he pzbpez}aet bg megaia}e ai}elzcft;

(a! ewcfuc}e megaia}e ai}elzcft;( o! dcfdufc}e }he czec bg c zelabi jbuimem jq c

duzwe (aidfumail c pczcne}zad duzwe! cim faiet

pczcffef }b }he dbbzmaic}e cxet& bz je}|eei }|b

duzwet;

(k ! dcfdufc}e wbfunet bg tbfamt bg zewbfu}abi cjbu}

bie bg }he dbbzmaic}e cxet)

30 Maggezei}acf Esuc}abit 3= Dcimamc}et thbufm je cjfe }b?

(c! gaim }he leiezcf tbfu}abi bg c gazt} bzmez

maggezei}acf esuc}abi |a}h tepczcjfe wczacjfet;(j! gaim }he leiezcf tbfu}abi bg c gazt} bzmez faiecz

maggezei}acf esuc}abi jq necit bg ci ai}elzc}ail

gcd}bz;

(d! }zcitgbzn& jq c lawei tujt}a}u}abi& c gazt} bzmez

maggezei}acf esuc}abi ai}b bie |a}h tepczcjfe

wczacjfet bz bie |hadh at faiecz;

(m ! ute c jbuimczq dbima}abi }b gaim c pcz}adufcz

tbfu}abi;

(e! tbfwe pzbjfent& zefc}em }b tdaeide cim

}edhibfblq& }hc} dci je nbmeffem jq maggezei}acfesuc}abit)

33 Ncdfcuzai Tezaet 3: Dcimamc}et thbufm je cjfe }b?

(c! gaim }he Ncdfcuzai tezaet gbz c guid}abi cim }he

ai}ezwcf bg dbiwezleide;

(j! ute t}cimczm tezaet }b gaim }he tezaet expcitabit

bg }he tunt& maggezeidet& pzbmud}t& sub}aei}t

cim dbnpbta}et bg guid}abit;



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(d! pezgbzn maggezei}ac}abi cim ai}elzc}abi bg c

pb|ez tezaet;

(m ! ute tezaet expcitabit }b gaim }he fana} bg c

guid}abi)

3: Iunezadcf Ne}hbmt 3= Dcimamc}et thbufm je cjfe }b?

3:)3 Iunezadcf tbfu}abi bg

esuc}abit

30 (c! fbdc}e c zbb} bg ci esuc}abi cppzbxanc}efq jq

necit bg lzcphadcf dbitamezc}abit cim jq

teczdhail gbz c tali dhcile;

(j! ute ci a}ezc}awe gbznufc bg }he gbzn

3 g ( !i i

x x }b gaim c zbb} bg ci esuc}abi }b c

pzetdzajem melzee bg cdduzcdq;

(d! amei}agq ci a}ezc}abi |hadh dbiwezlet bz

mawezlet;

(m ! ute }he Ie|}bi.Zcphtbi ne}hbm;

3:): Iunezadcf ai}elzc}abi = (e! ute }he }zcpeaun zufe;

( g ! ute tke}dh lzcpht }b me}eznaie |he}hez }he

}zcpeaun zufe lawet ci bwez.et}anc}e bz ci

uimez.et}anc}e ai tanpfe dctet)



]HAZM ]EZN? T]C]AT]ADT

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34 Mc}c Metdzap}abi 3= Dcimamc}et thbufm je cjfe }b?

(c! amei}agq matdze}e& dbi}aiubut& uilzbupem cim

lzbupem mc}c;

(j! dbit}zud} cim ai}ezpze} t}en.cim.fecg maclzcnt&

jbx.cim.|hatkez pfb}t& hat}blzcnt cim

dunufc}awe gzesueidq duzwet;

(d! t}c}e }he nbme cim zcile bg uilzbupem mc}c;

(m ! me}eznaie }he nemaci cim ai}ezsucz}afe zcile

bg uilzbupem cim lzbupem mc}c;

(e! dcfdufc}e }he neci cim t}cimczm mewac}abi bg uilzbupem cim lzbupem mc}c& gzbn zc| mc}c

cim gzbn lawei }b}cft tudh ct3

( !i

a

a

x c

cim

3

:( !

i

a

a

x c

;

( g ! tefed} cim ute }he cppzbpzac}e nectuzet bg

dei}zcf }eimeidq cim nectuzet bg matpeztabi;

(l! dcfdufc}e }he Pecztbi dbeggadaei} bg tke|iett;

(h! metdzaje }he thcpe bg c mc}c mat}zaju}abi)

3= Pzbjcjafa}q 3= Dcimamc}et thbufm je cjfe }b?

(c! cppfq }he cmma}abi pzaidapfe cim }he

nuf}apfadc}abi pzaidapfe;

(j! ute }he gbznufce gbz dbnjaic}abit cim

peznu}c}abit ai tanpfe dctet;

(d! amei}agq c tcnpfe tpcde& cim dcfdufc}e }he

pzbjcjafa}q bg ci ewei};

(m ! amei}agq dbnpfenei}czq& exhcut}awe cim

nu}ucffq exdfutawe ewei}t;

(e! ute }he gbznufc

P( C J! > P( C! + P( J! P( C J!;

( g ! dcfdufc}e dbima}abicf pzbjcjafa}aet& cim amei}agq

aimepeimei} ewei}t;

(l! ute }he gbznufce

P( C J! > P( C! P( J v C! > P( J! P( C v J!;

(h! ute }he zufe bg }b}cf pzbjcjafa}q)



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35 Pzbjcjafa}q Mat}zaju}abit :7 Dcimamc}et thbufm je cjfe }b?

35)3 Matdze}e zcimbnwczacjfet

7 (c! amei}agq matdze}e zcimbn wczacjfet;

(j! dbit}zud} c pzbjcjafa}q mat}zaju}abi }cjfe gbz c

matdze}e zcimbn wczacjfe;

(d! ute }he pzbjcjafa}q guid}abi cim dunufc}awe

mat}zaju}abi guid}abi bg c matdze}e zcimbn

wczacjfe;

(m ! dcfdufc}e }he neci cim wczacide bg c matdze}e

zcimbn wczacjfe;

35): Dbi}aiubut zcimbn

wczacjfet

7 (e! amei}agq dbi}aiubut zcimbn wczacjfet;

( g ! zefc}e }he pzbjcjafa}q meita}q guid}abi cimdunufc}awe mat}zaju}abi guid}abi bg c

dbi}aiubut zcimbn wczacjfe;

(l! ute }he pzbjcjafa}q meita}q guid}abi cim

dunufc}awe mat}zaju}abi guid}abi bg c


(h! dcfdufc}e }he neci cim wczacide bg c


35)4 Jaibnacf mat}zaju}abi = (a! ute }he pzbjcjafa}q guid}abi bg c jaibnacf

mat}zaju}abi& cim gaim a}t neci cim wczacide;

( o! ute }he jaibnacf mat}zaju}abi ct c nbmef gbz

tbfwail pzbjfent zefc}em }b tdaeide cim

}edhibfblq;

35)= Pbattbi mat}zaju}abi = (k ! ute }he pzbjcjafa}q guid}abi bg c Pbattbi

mat}zaju}abi& cim amei}agq a}t neci cim

wczacide;

(f! ute }he Pbattbi mat}zaju}abi ct c nbmef gbz


}edhibfblq;

35)5 Ibzncf mat}zaju}abi 7 (n! amei}agq }he leiezcf gec}uzet bg c ibzncf

mat}zaju}abi& ai zefc}abi }b a}t neci cim

t}cimczm mewac}abi;

(i! t}cimczmate c ibzncf zcimbn wczacjfe cim ute

}he ibzncf mat}zaju}abi }cjfet;

(b! ute }he ibzncf mat}zaju}abi ct c nbmef gbz


}edhibfblq;

( p! ute }he ibzncf mat}zaju}abi& |a}h dbi}aiua}q

dbzzed}abi& ct ci cppzbxanc}abi }b }he

jaibnacf mat}zaju}abi& |heze cppzbpzac}e)



]bpad]ecdhail


37 Tcnpfail cim Et}anc}abi :7 Dcimamc}et thbufm je cjfe }b?

37)3 Tcnpfail 3= (c! mat}ailuath je}|eei c pbpufc}abi cim c tcnpfe&cim je}|eei c pczcne}ez cim c t}c}at}ad;

(j! amei}agq c zcimbn tcnpfe;

(d! amei}agq }he tcnpfail mat}zaju}abi bg c t}c}at}ad;

(m ! me}eznaie }he neci cim t}cimczm mewac}abi bg

}he tcnpfe neci;

(e! ute }he zetuf} }hc} X hct c ibzncf mat}zaju}abi ag

X hct c ibzncf mat}zaju}abi;

( g ! ute }he dei}zcf fana} }hebzen;

(l! me}eznaie }he neci cim t}cimczm mewac}abi bg }he tcnpfe pzbpbz}abi;

(h! ute }he cppzbxanc}e ibzncfa}q bg }he tcnpfe

pzbpbz}abi gbz c tuggadaei}fq fczle tcnpfe tae;

37): Et}anc}abi 3: (a! dcfdufc}e uijactem et}anc}et gbz }he pbpufc}abi

neci cim pbpufc}abi wczacide;

( o! dcfdufc}e ci uijactem et}anc}e gbz }he

pbpufc}abi pzbpbz}abi;

(k ! me}eznaie cim ai}ezpze} c dbigameide ai}ezwcf

gbz }he pbpufc}abi neci jctem bi c tcnpfegzbn c ibzncffq mat}zaju}em pbpufc}abi |a}h

kib|i wczacide;

(f! me}eznaie cim ai}ezpze} c dbigameide ai}ezwcf

gbz }he pbpufc}abi neci jctem bi c fczle

tcnpfe;

(n! gaim }he tcnpfe tae gbz }he et}anc}abi bg

pbpufc}abi neci;

(i! me}eznaie cim ai}ezpze} c dbigameide ai}ezwcf

gbz }he pbpufc}abi pzbpbz}abi jctem bi c fczle

tcnpfe;(b! gaim }he tcnpfe tae gbz }he et}anc}abi bg

pbpufc}abi pzbpbz}abi)



]bpad]ecdhail


3< Hqpb}hetat ]et}ail 3= Dcimamc}et thbufm je cjfe }b?

(c! expfcai }he neciail bg c iuff hqpb}hetat cimci cf}ezic}awe hqpb}hetat;

(j! expfcai }he neciail bg }he taliagadcide fewef

bg c }et};

(d! dczzq bu} c hqpb}hetat }et} dbideziail }he

pbpufc}abi neci gbz c ibzncffq mat}zaju}em

pbpufc}abi |a}h kib|i wczacide;

(m ! dczzq bu} c hqpb}hetat }et} dbideziail }he

pbpufc}abi neci ai }he dcte |heze c fczle

tcnpfe at utem;

(e! dczzq bu} c hqpb}hetat }et} dbideziail }hepbpufc}abi pzbpbz}abi jq mazed} ewcfuc}abi bg

jaibnacf pzbjcjafa}aet;

( g ! dczzq bu} c hqpb}hetat }et} dbideziail }he

pbpufc}abi pzbpbz}abi utail c ibzncf

cppzbxanc}abi)

38 Dha.tsuczem ]et}t 3= Dcimamc}et thbufm je cjfe }b?

(c! amei}agq }he thcpe& ct |eff ct }he neci cim

wczacide& bg c dha.tsuczem mat}zaju}abi |a}h c

lawei iunjez bg melzeet bg gzeembn;

(j! ute }he dha.tsuczem mat}zaju}abi }cjfet;

(d! amei}agq }he dha.tsuczem t}c}at}ad;

(m ! ute }he zetuf} }hc} dfcttet |a}h tncff exped}em

gzesueidaet thbufm je dbnjaiem ai c dha.

tsuczem }et};

(e! dczzq bu} lbbmiett.bg.ga} }et}t }b ga} pzetdzajem

pzbjcjafa}aet cim pzbjcjafa}q mat}zaju}abit |a}h

kib|i pczcne}ezt;

( g ! dczzq bu} }et}t bg aimepeimeide ai dbi}aileidq

}cjfet (exdfumail Qc}et dbzzed}abi!)

954 mathematics t [ppu] semester 1 topics

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