ZU

fx-991ZA PLUSIsiqondiso kumsebenzisi

Iwebhsayithi yakwa CASIO yezemfundo umhlaba wonke

http://edu.casio.com

OkuqukethweUlwazi olubalulekile ................................................................. 2Amasampula okusetshenziswa kwesibali ..............................2Ukuqala ukusebenzisa isibali ................................................. 2Amanyathelo okuvikela ingozi ............................................... 2Indlela yokuphatha ephephile ................................................ 2Ukususa ikhava yangaphandle .............................................. 3Ukukhanyisa nokucima ........................................................... 3Ukulungisa ukwahlukana ebusweni besibali .........................3Iziphawulo zezinkinobho ........................................................ 4Ukufunda umbukiso ................................................................ 4Ukusetshenziswa kohlu lwezinhlelo zengcinalwazi ..............5Ukubalula isimo sokubala ...................................................... 6Ukulungisa, ucuphe isethaphu yesibali .................................6Ukufaka izimeli namanani ....................................................... 8Ukubheka izimo ezahlukene zemiphumela ..........................11Izibalo eziyisisekelo .............................................................. 12Ukufekthorayiza ngezinombolo ezingahlukaniseki ngokuphelele ..........................................................................16Izibalo zamaFanshini ............................................................. 17Izibalo zezinombolo eziphicayo (CMPLX) ........................... 22Ukusebenzisa u CALC .......................................................... 23Ukusebenzisa uxazulula (SOLVE) ........................................ 24Izibalo zeStathistiksi (STAT) ................................................. 26Izibalo ezinesisekelo sokubala esingu n (BASE-N).............30Ukubalwa kwezibalo ezilingana nezinye (EQN) ..................33Izibalo zeMetriksi (MATRIX) .................................................. 35Ukwakha iThebula Lezinombolo lisuselwa kumafanshini amabili (TABLE) ......................................................................38Izibalo zamavektha (VECTOR) .............................................. 39Izibalo zokwaba (DIST) .......................................................... 42Abangaguquki besayensi ..................................................... 45Ukushintsha kweMetrikhi ..................................................... 46Uhlu lokuBala, INombolo yamaDijithi, kanye nokuCophelela ........................................................................47Amaphutha ............................................................................. 49Ngaphambi Kokuthatha Ngokuthi Isibali Asisebenzi Kahle… ...................................................................................51Ukushintsha iBhetri .............................................................. 52Incasiselo Enemininingwane ................................................ 52Imibuzo eBuzwa Njalo ........................................................... 52

ZU-1

ZU-2

Ulwazi olubalulekile• Imiboniso nemifanekiso (njengezimpawu zezinkinobho) ekhonjisiwe

kulesisiqondiso kumsebenzisi ngeyokufanekisa kuphela, ingahluka kancane kulezozinto ezimele.

• Okuqukethwe kulelibhukwana kungashintsha ngaphandle kokunikeza isaziso.

• Inkampani yakwa CASIO Computer Co., Ltd. ayizukuba nasibophezelo kunanoma ngubani mayelana nokuthengwa kumbe ukusetshenziswa kwalomkhiqizo nazozonke izinto ezihambisana nawo. Ngaphezukwalokho, I CASIO Computer Co., Ltd. ayizuba nasibophezelo sokukhokha izindleko zananoma yiluphi uhlobo ezingafunwa ngunanoma ngubani, ezakheke ngenxa yokusebenzisa lomkhiqizo nazozonke izinto ohambisana nazo.

• Yiba nesiqiniseko sokuthi ugcina wonke amabhukwana omsebenzisi kahle ukuze ukwazi ukuwasebenzisa nangesikhathi esizayo.

Amasampula okusetshenziswa kwesibali

Amasampula okusetshenziswa kwesibalinzulu asetshenziswe kulelibhukwana akhonjiswe ngaloluphawu, . Ngaphandle uma kubaluliwe, wonke amasampula athatha ngokuthi isibalinzulu sinjengoba sasisethiwe ekuqaleni. Landela inqubo ngaphansi kwesihloko “Ukuqala ukusebenzisa isibali” ukubuyisela isibalinzulu ekusethweni kwaso kwasekuqaleni.

Ukuthola ulwazi ngalezizimpawu B , b , v , kanye no V ezikhonjiswe kumasampula okusetshenziswa kwesibalinzulu, bheka isihloko “Ukulungisa, ucuphe isethaphu yesibali”.

Ukuqala ukusebenzisa isibaliYenza lenqubo uma ufuna ukuqala ukusebenzisa isibalinzulu futhi ufuna ukubuyisela isibalinzulu esimweni esasisethelwe kuso embonini. Qaphela ukuthi lenqubo icisha yonke imininingwane ekwisikhumbuzi sesibalinzulu.

!9(CLR)3(All)=(Yes)

Amanyathelo okuvikela ingozi

IBhetri

• Abantwana abancane bangafinyeleli lapho ugcine khona amabhetri.• Sebenzisa kuphela uhlobo lwebhetri olubalulelwe lesisibalinzulu,

kulelibhukwana.

Indlela yokuphatha ephephile• Noma ngabe isibalinzulu sisebenza ngendlela elindelekile, lishintshe

ibhetri okungenani kanye eminyakeni emibili (LR44 (GPA76)). Ibhetri eselonakele lingavuza, lidale umonakalo nokungasebenzi kahle

kwisibalinzulu. Ungalishiyi ibhetri elingasasebenzi kwisibalinzulu.• Ibhetri elifika nesibalinzulu liyavuza kancane ngesikhathin lithunyelwa

ngezithuthi nangesikhathi ligciniwe. Ngenxa yalokhu, lingadinga ukushintshwa ngokushesha kunokulindelekile.

ZU-3

• Ungalisebenzisi ibhetri le Oxyride* noma ngabe yiluphi uhlobo lwebhetri ene nickel kulomkhiqizo. Ukungahambelani kwalamabhetri kanye nalomkhiqizo kungadala ukuthi amabhetri ahlale isikhathi esincane futhi nalomkhiqizo ube nezinkinga ekusebenzeni kahle.

• Gwema ukusebenzisa nokugcina lomkhiqizo endaweni enamazinga okushisa nokubanda aphansi kakhulu noma phezulu kakhulu, nasezindaweni ezinomswakama kanye nezintuli eziningi.

• Isibalinzulu masingashayeki kanzima, singacindezeleki kanzima futhi singagotshiswa.

• Ungazami ukuqaqa isibalinzulu.• Sebenzisa indwangu ethambile, eyomile ukuhlanza ingaphandle

lesibalinzulu.• Uma usulahla isibalinzulu kumbe amabhetri, yiba nesiqiniseko sokuthi

lokho ukwenza ngokulandela imigomo nemithetho yasendaweni yakho.

* Amagama ezinkampani nemikhiqizo asetshenziswe kulelibhukwana kungaba amagama okuhweba ezinkampani arejistiwe kumbe awabanikazi bazo izinkampani arejistiwe.

Ukususa ikhava yangaphandleNgaphambi kokusebenzisa isibalinzulu, s h i s h i l i z e l i s e l a n g e z a n s i i k h a v a yangaphandle ukuze isuke, ebese uyixhuma ngemuva kwesibal inzulu n jengoba kukhonjisiwe emifanekisweni.

Ukukhanyisa nokucimaCindezela u O ukukhanyisa isibalinzulu.Cindezela u 1A(OFF) ukucima isibalinzulu.

Ukuzicima ngokwawoIsibali futhi sizozicimela ngokwaso ngemuva kwemizuzu cishe eli 10 noma imizuzu cishe engama 60 singasetshenziswa. Bheka “Ukulungisa, ucuphe isethaphu yesibali” ukuze uthole imininingwane. Uma lokhu kwenzeka cindezela inkinobho u O ukukhanyisa isibalinzulu.

Ukulungisa ukwahlukana ebusweni besibali

Khombisa isibuko sokwahlukana (contrast) ngokwenza lokhu okulandelayo: 1N(SETUP)c8(]CONT'). Sebenzisa u d no e ukulungisa ukwahlukana. Uma usulungise ngendlela oyifunayo cindezela u A.

Kubalulekile: Uma ukulungisa ukwahlukana kungenzingcono ukufundeka kokukhonjisiwe, kusho ukuthi amandla ebhetri aphansi. Lishintshe ibhetri.

ZU-4

Iziphawulo zezinkinobhoUkucindezela inkinobho u 1 noma u S kulandelwa inkinobho yesibili, yenza umsebenzi omunye wenkinobho yesibili. Umsebenzi omunye wenkinobho yesibili ukhonjiswa ngombhalo, obhalwa ngaphezu kwenkinobho. Okulandelayo kukhombisa ukuthi imibala ehlukene ngaphezu kwenkinobho isho ukuthini:

Uma umbhalo womaka wenkinobho unalombala: Kusho lokhu:

OphuzuCindezela u 1 bese ucindezela inkinobho yokufinyelela kwinsizakusebenza efanele.

ObomvuCindezela u S bese ucindezela inkinobho yokufaka oguquguqukayo, ongaguquguquki noma uphawu olufanelekile.

Obende (noma ophakathi kwabakaki ababubende) Faka i CMPLX Modi ukuthola ifanshini.

Oluhlaza okotshani (noma ophakathi kwabakaki abaluhlaza okotshani)

Faka i BASE-N Modi ukuthola ifanshini.

Ukufunda umbukisoUbuso besibali buveza lezozinhlamvu ozifakile, imiphumela yokubaliwe, kanye nezinkomba ezahlukahlukene.

Isimeli esifakiwe Izinkomba

Umphumela wokubaliwe

• Uma kuvela lenkomba ' ngakwesokudla komphumela wokubala, kusho ukuthi umphumela wesibalo oveziwe uyaqhubeka ngakwesokudla. Sebenzisa u e no d ukunyakazisa umbukiso womphumela wokubaliwe.

• Uma kuvela lenkomba g ngakwesokudla kwesimeli esiphathelene nezibalo, kusho ukuthi isibalo esiveziwe siyaqhubeka ngakwesokudla. Sebenzisa u e no d ukunyakazisa isimeli esifakiwe sehle, senyuke noma siye emaceleni ebusweni besibali. Qaphela ukuthi uma ufuna ukunyakazisa isimeli esifakiwe, sehle, senyuke noma siye emaceleni ebusweni besibali, ngesikhathi zivele zombili lezizimpawu u ' no g, udinga ukucindezela u A kuqala, bese usebenzisa u e no d ukunyakazisa.

Izinkomba zobuso

Lenkomba: Isho lokhu:Ibhodi lezinkinobho ligudluziwe ngokucindezela inkinobho u 1. Ibhodi lezinkinobho lizobuyela bese lenkomba inyamalala uma ucindezela inkinobho.

sin–1 D

s

Ifanshini enye

Ifanshini esenkinobhweni

sin–1 D

s

Ifanshini enye

Ifanshini esenkinobhweni

Math MathMath Math

ZU-5

Kufakwe isimo sika ALPHA ngokucindezela inkinobho u S. Isimo sika ALPHA kuzophumeka kusona futhi nalenkomba izonyamalala uma ucindezela inkinobho.

M Kunenani eligcinwe kwisikhumbuzi esizimeleyo.

STOIsibali silindele igama loguquguqukayo ukuze sinike lowo oguquguqukayo inani. Lenkomba ivela ngemuva kokucindezela lokhu 1t(STO).

RCLIsibali silindele igama loguquguqukayo ukuze sikhumbule inani loguquguqukayo. Lenkomba ivela ngemuva kokucindezela lokhu u t.

STAT Isibali sisesimweni esingu STAT.

CMPLX Isibali sisesimweni esingu CMPLX.

MAT Isibali sisesimweni esingu MATRIX.

VCT Isibali sisesimweni esingu VECTOR.

7 Isilinganiso esisetshenziselwa ama-engele (amagumbi), uphawu lokukala igumbi.

8 Isilinganiso esisetshenziselwa ama-engele (amagumbi), iradiyeni.

9 Isilinganiso esisetshenziselwa ama-engele (amagumbi), igradiyeni.

FIX Kusebenza inombolo emile (engashintshi) yamadijithi, ngemuva kwakhefana weqhezu lokweshumi.

SCI Kusebenza inombolo emile (engashintshi) yamadijithi abalulekile.

Math Kukhethwe isimo sobuso semvelo.

$`Umlando wokubaliwe uyatholakala futhi ungaphinda udlalwe, noma kuneminye imininingwane ngaphezulu/ngaphansi kwalokho okuveziwe.

Disp Ubuso besibalinzulu njengamanje bukhombisa umphumela omaphakathi wesibalo esinxakanxaka.

Kubalulekile: Kwezinye izinhlobo zezibalo okuthatha isikhathi eside ukuzenza, ubuso besibali bungaveza kuphela lezizinkomba ezingenhla (ngaphandle kwamanani) isibali sibe sisaqhubeka nokubala ngaphakathi.

Ukusetshenziswa kohlu lwezinhlelo zengcinalwazi

Okunye ukubala ngesibali kwenziwa kusetshenziswa uhlu lwezinhlelo zengcinalwazi. Ukucindezela u N noma u w kuzoveza uhlu lwezinhlelo zengcinalwazi enezinsizakusebenza ezifanelekile.Okulandelayo okufanele ukusebenzise ukunavigetha phakathi kwezinhla zezinhlelo zesigcinalwazi.• Ungakhetha into esohleni lwezinhlelo zesigcinalwazi ngokucindezela

inombolo yenkinobho ehambisana nenombolo ekwesobunxele kwi iskrini semenu.

• Lenkomba $ ekhoneni eliphezulu ngakwesokudla isho ukuthi kukhona enye imenu ngezansi kwaleyo evelile. Inkomba ` isho ukuthi kunenye imenu ngenhla. Sebenzisa u c no f ukusuka kumenu uya kwenye.

• Ukuvala imenu ngaphandle kokukhetha utho, cindezela u A.

ZU-6

Ukubalula isimo sokubala

Uma ufuna ukwenza loluhlobo lokubala: Cindezela lezinkinobho kanje:

Ukubala okwejwayelekile N1(COMP)

Ukubala okuphicayo N2(CMPLX)

Ukubala okuphathelene nestathistiksi kanye nobudlelwano phakathi kwama variyebhuli (oguquguqukayo).

N3(STAT)

Izibalo ezimbandakanya izinhlelo zezinombolo ezibaluliwe (ziqumbili, okthali, desimali, hekzadesimali)

N4(BASE-N)

Ukuxazulula i-ikhweyishini. N5(EQN)

Izibalo zematrix. N6(MATRIX)

Ukwakha itafula nombolo lisuselwa kwi fanshini eyodwa noma ezimbili. N7(TABLE)

Izibalo zamavektha. N8(VECTOR)

Izibalo zokwaba Nc1(DIST)

Qaphela: sicushelwe ukubala nge COMP modi.

Ukulungisa, ucuphe isethaphu yesibali

Kuqala yenza lokhu okulandelayo, okusemqoka ukuze uveze I menu yokucupha: 1N(SETUP). Okulandelayo, sebenzisa u c no f kanye nezinkinobho zezinombolo ukusetha isibali ngendlela oyifunayo.Ama sethingi adwetshelwe ( ___ ) angama opshini asethwe phambilini.

Laba 1MthIO 2LineIO babalula isimo sesibonisa. Isiboniso semvelo (MthIO) sakha amaqhezu, izinombolo ezi-irrashinali kanye nezinye izimeli ukuba zivele njengoba zibhalwa ephepheni.

MthIO: Ikhetha u MathO noma u LineO. U MathO uveza okufakiwe kanye nemiphumela esebenzisa isimo esifanayo naleso esisetshenziswa uma kubhalwa ephepheni. U LineO uveza okufakiwe ngendlela efanayo no MathO, kodwa imiphumela ivela iyisimo somudwa. Umbukiso Ongumugqa (LineIO): Yenza amaqhezu kanye nezinye izimeli ukuba zivele emgqeni owodwa.

Qaphela: • Isibali sizishintshela ekuvezeni izinto emgqeni owodwa njalo uma ufaka u STAT, BASE-N, MATRIX noma u VECTOR modi. • Kulelibhukwana, uphawu B eduze kwesampula yokubala, ikhombisa I Isiboniso semvelo MathO, ngesikhathi uphawu b lukhombisa I Umbukiso Ongumugqa.

O 3Deg 4Rad 5Gra babalula (cacisa) isilinganiso esisetshenziselwa ama-engela, amaradiyeni noma amagradi njenge unit ye-engela yenani lalokho okufakiwe kanye nomboniso ongumphumela wokubala.

MathMath

ZU-7

Qaphela: Kulelibhukwana, uphawu v eduze kwesampula yokubala, lukhombisa amadigrizi, kanti uphawu u V lukhombisa amaradiyeni.

6Fix 7Sci 8Norm Ubalula inani yamadijithi angavela ebusweni besibali uma sekuphuma umphumela wokubala.Fix: Inani olibalulayo (kusuka ku 0 kuya ku 9) lilawula inombolo yamadijithi emva kukakhefu weqhezu lokubalwa ngokweshumi emiphumeleni yokubala ezovela ebusweni besibali. Imiphumela yokubaliwe iyasondezelwa kuleyodijithi ebaluliwe ngaphambi kokuba ivezwe.Isibonelo: b 100 ÷ 7 = 14.286 (Fix 3)

14.29 (Fix 2)Sci: Inani olibalulayo (kusuka ku 1 kuya ku 10) lilawula inombolo yamadijithi abalulekile emiphumeleni yokubaliwe eveziwe. Imiphumela yokubaliwe iyasondezelwa kuleyodijithi ebaluliwe ngaphambi kokuba ivezwe.Isibonelo: b 1 ÷ 7 = 1.4286 × 10–1 (Sci 5)

1.429 × 10–1 (Sci 4)Norm: Ukukhetha enye yezindlela ezimbili zokusetha (Norm 1, Norm 2) inquma uhla okuzovezwa kulo imiphumela ngesimo esingesiye umphindwa. Ngaphandle kohlu olubaluliwe, imiphumela ivezwe kusetshenziswa isimo esingumphindwa. Norm 1: 10–2 � |x|, |x| � 1010 Norm 2: 10–9 � |x|, |x| � 1010

Isibonelo: b 1 ÷ 200 = 5 × 10–3 (Norm 1) 0.005 (Norm 2)

c1ab/c c2 d/c Ibalula iqhezungxube (ab/c) kumbe iqhezu mbumbulu (d/c) ekuvezweni kwamaqhezu emiphumeleni yokubala.

c3CMPLX 1a+bi ; 2r∠� Ibalula ukuvumelana okusanxande (a+bi) noma ukuvumelana okusaphola (r∠�) ezixazululweni za EQN Modi.

c4STAT 1ON ; 2OFF Ibalula ukuba luvezwe noma lungavezwa uhlu lweFREQ (ukuphindaphinda) kwi STAT Modi Stat Editha.

c5TABLE 1f(x) ; 2f(x),g(x) Ibalula ukuthi ungasebenzisa ifanshini f(x) kuphela noma amafanshini u f(x) no g(x) kwi TABLE Modi.

c6Disp 1Dot ; 2Comma Ibalula ukuthi ungasebenzisa yini icashazi kumbe ukhefana ukumela icashazi leqhezu lokweshumi emphumeleni wokubala. Icashazi liyilokhu livezwa ngesikhathi kusafakwa imininingwane.Qaphela: Uma kukhethwe icashazi njengecashazi leqhezu lokweshumi, umhlukanisi wemiphumela eminingi kuba ukhefana (,). Uma kukhethwe ukhefana, umhlukanisi kuba ikhefana-ngqi (;).

c7APO 1 10 Min. ; 2 60 Min. Ungazicuphela isikhathi esingangemizuzu eli 10 noma ama 60 okuthi isibali sizicishe ngokwaso.

c8]CONT' Ihlela ukwahlukana kobuso. Bheka isihloko “Ukulungisa ukwahlukana ebusweni besibal” ukuthola imininingwane.

Ukulungisa isibali ukuze sikwazi ukuqala ukusebenzaYenza lenqubo to ukulungisa isibali, ebuyisela isimo sokubala ku COMP, ibuyisele wonke amanye amasethingi, okubandakanya nemenu yokusetha, esimweni ayecushelwe kusona embonini.

19(CLR)1(Setup)=(Yes)

ZU-8

Ukufaka izimeli namananiImithetho yokufaka imininingwane eyisisekeloIzibalo zingabhalwa kwisibali ngendlela efanayo naleyo ezibhalwa ngayo ephepheni. Uma ucindezela u = isibali sihlola ngokushesha okubaluleke ukuba sikwenze kuqala, sikwenze ngokulandelana kokubaluleka bese sikhipha umphumela ebusweni baso.

4 × sin30 × (30 + 10 × 3) = 120

4 *s 30 )*( 30 + 10 * 3 )=

*1

*2 *3

*1 Imininingwane yabakaki bokuvala iyadingeka ku sin, sinh, namanye ama fanshini anama anabakaki.

*2 Lezimpawu zokuphindaphinda (×) zingeqiwa. Uphawu lokuphindaphinda lungeqiwa uma lulandelwa abakaki bokuvula, lulandelwa u sin noma enye ifanshini enabakaki, lulandelwa I fanshini kaRan# (inombolo engahleliwe), noma lulandelwa oguquguqukayo (A, B, C, D, E, F, M, X, Y), izimeli zesayensi ezingaguqukiyo, π noma u e.

*3 Amaparenthesisi okuvala alandelwa u = angeqiwa.

Isibonelo lapho kweqiwa khona u **2 no )*3 esibonelweni esingenhla.

4 s 30 )( 30 + 10 * 3 =

Kubalulekile: Uma wenza isibalo esimbandakanya ukuhlukanisa nokuphindaphinda, lapho uphawu lokuphindaphinda lweqiwe khona, abakaki bazozingenela ngokwabo njengoba kukhonjisiwe ezibonelweni ngezansi.• Uma uphawu lokuphindaphinda lweqiwe ngaphambi komkaki wokuvula

noma ngemuva komkaki wokuvala.

6 ÷ 2 (1 + 2) � 6 ÷ (2 (1 + 2)) 6 ÷ A (1 + 2) � 6 ÷ (A (1 + 2)) 1 ÷ (2 + 3) sin(30) � 1 ÷ ((2 + 3) sin(30))

• Uma uphawu lokuphindaphinda lweqiwe ngaphambi koguquguqukayo, ongaguquki, njll.

6 ÷ 2π � 6 ÷ (2π) 2 ÷ 2'2 � 2 ÷ (2'2) 4π ÷ 2π � 4π ÷ (2π)

• Uma ufaka ifanshini (njengo Pol, Rec, no RanInt#), qinisekisa ukuthi ufaka abakaki bokuvala abadingwa isimeli. Uma ungabafakanga abakaki bokuvala, abakaki kungenzeka bangazingeneli ngokwabo njengoba kuchaziwe ngenhla.

Kubalulekile: Uma wenza isibalo esinophawu lokuphindaphinda olweqiwe ngaphambi kweqhezu (kumbandakanya namaqhezungxube), abakaki bazozingenela ngokwabo njengoba kukhonjisiwe ezibonelweni ngezansi.

12 × 3

: B ' 1 c 3 dddd 2

=

MathMath

MathMath

MathMath

MathMath

ZU-9

4sin(30) × 5

: B

' 4 c 5 dddds 30 )

=

Qaphela: • Uma isibalo siba side kunobuso besibali ngesikhathi kusafakwa imininingwane yesibalo, isibuko sizozihambela ngokwaso siye ngakwesokudla bese kuvela inkomba u ]. Ngesikhathi kwenzeka lokhu, ungabuyela ngakwesobunxele ngokusebenzisa u d no e ukuhambisa inkomba. • Uma kukhethwe umboniso oveza imininingwane emqgeni owodwa, ukucindezela f kwenza inkomba ijombele ekuqaleni kwesibalo, kanti ukucindezela u c kuyenza ijombele ekugcinen I kwesibalo. • Uma kukhethwe umboniso wemvelo, ukucindezela u e ngesikhathi inkomba isekugcineni kwemininingwane yesibalo efakiwe, kuzokwenza inkomba ijombele ekuqaleni, kanti ukucindezele u d inkomba isekuqaleni kuzoyenza ijombele ekugcineni. • Ungafaka amabytes angama 99 esibalo. Inombolo ngayinye, uphawu, kumbe I function ngokujwayelekile isebenzisa I byte eyodwa. Amanye ama functions adinga amabytes amathathu kuya kwayi 13. • Inkomba izoshintsha isimo ibe nje k uma sekusele ama bytes ali 10 noma ngaphansi asengasetshenziswa. Uma lokhu kwenzeka, yeka ukufaka imininingwane, ucindezele u =.

Ukubala ngokulandelanisa ngokubalulekaUkulandelana ngokubheka okwenziwa kuqala ezibalweni, kuhlolwa ngokulandela imithetho engezansi. Uma ukubaluleka kwezimeli ezimbili kulingana, isibalo senziwa kusuka kwesobunxele kuya kwesokudla.

Okokuqala: Izimeli eziphathelene nabakaki

Okwesibili: Amafunshini adinga i-agumenti ngakwesokudla nabakaki bokuvala “)” belandela i-agumenti.

Okwesithathu: Amafunshini eza emva kwenani elifakiwe (x2, x3, x–1, x!, °’ ”, °, r, g, %, 't), Abaphindaphindi (x^), imisuka (")

Okwesine: Amaqhezu

Okwesihlanu: Uphawu lokususa (–), Izimpawu zesisekelo sokubala u-n (d, h, b, o)

Qaphela: Uma uphindaphinda inani, elinophawu lokususa, ngalo (njengo –2), inani eliphindaphindwayo kumele livalelwe kubakaki ((- 2 )w=). Njengoba u x2 ephambili kunophawu lokususa, ukufaka u - 2 w= kungenza ukuthi kuphindaphindeke u 2 bese kufakwa uphawu lokususa emphumeleni. Njalo nje gcina ukulandelana ngokuphambili emqondweni, bese uvalela amanani anophawu lokususa kuma parenthesisi uma kunesidingo.

Okwesithupha: Imiyalelo yokuguqula yemetrikhi (cm'in, njll).STAT Modi ubungako obuhlawunjiselwe (m, n, m1, m2)

Okwesikhombisa: Ukuphindaphinda lapho uphawu lokuphindaphinda lweqiwe

Okwesishiyagalombili: Phemutheshini (nPr), ukuhlanganiswa (nCr), uphawu lwenombolo yokuvumelana okusaphola, okuphicayo (∠)

MathMath

MathMath

ZU-10

Okwesishiyagalolunye: Umphumela wokuphindaphinda, wechashazi (·)

Okweshumi: Ukuphindaphinda (×), ukuhlukanisa (÷)

Okweshumi nanye: Ukuhlanganisa, ukususa (+, –)

Okweshumi nambili: AND (and) enelojiki

Okweshumi nantathu: OR, XOR, XNOR (or, xor, xnor) abanelojiki

Ukufaka Ngombukiso WemveloUkukhetha umboniso wemvelo kwenza ukuthi ukwazi ukufaka futhi ubonise amaqhezu nezinye izinhlobo zamafanshini (log, x2, x3, x^, ), #, ", x−1, 10^, e^, ∫, d/dx, Σ, Abs) zinjengoba zibhaliwe encwadini yakho.

2 + '21 + '2

B

' 2 +! 2 ee 1 +! 2 =

Kubalulekile: • Ezinye izinhlobo zezimeli zingenza ubude bomklamo wokubala bube bukhulu kunomugqa womboniso owodwa. Ubude obuphezulu obuvumelekile kumklamo wokubala, izibuko zokubonisa ezimbili (31 amachashazi × 2). Futhi ukufaka imininingwane kungangenzeki uma ubude besibalo osifakayo budlula umkhawulo. • Ukuhlanganisa ndawonye amafanshini nama pharenthesisi kuvumelekile. Angeke ukwazi ukufaka imininingwane uma uhlanganise ndawonye ama functions nama pharenthesisi amaningi kakhulu. Uma lokhu kwenzeka, hlukanisa isibalo izingxenye eziningu bese ubala ingxenye ngayinye.Qaphela: Uma ucindezela u = bese uthola umphumela wokubala usebenzisa umbukiso wokwemvelo, ingxenye yesimeli osifakile ingasikeka. Uma udinga ukubuka futhi isimeli osifakile Sisonke, cindezela u A bese usebenzisa u d no e ukunyakazisa isimeli esifakiwe.

Ukusebenzisa amanani nezimeli njengama agumenti (Umbukiso wokwemvelo kuphela)

Inani noma isimeli osususifakile singasetshenziswa njenge agumenti ye

function. Emva kokuba usufake u 76 , ungamenza abe yiagumenti ye ',

umphumela kube u 76' .

Ukufaka u 1 + 76 bese umshintshela ku 1 + 7

6' B

1 + 7 ' 6

dddd1Y(INS)

!

Njengoba kukhonjisiwe ngenhla, inani kumbe isimeli esingakwesokudla senkomba emva kokucindezela laba 1Y(INS) siba yi agumenti yefanshini ebalulwayo esinyathelweni esilandelayo. Uhla olufakwe phakathi njenge

MathMath

MathMath

MathMath

MathMath

ZU-11

agumenti, yiyoyonke into kuze kuyofika kwi parenthesisi yokuqala evulekile ngakwesokudla, uma ikhona, noma yonke into kuze kuyofika kwi function yokuqala, uma uya ngakwesokudla (sin(30), log2(4), njalo njalo).Lokhu kungasetshenziswa nama fanshini alandelayo: ' , & , 7 , 17(F), 1&(8), 16("), 1l($), 1i(%), !, 6, 1!(#), 1w(Abs).

Ukushintsha isimo sokufaka (Umboniso Ongumugqa kuphela)Ungakhetha u insert noma u overwrite njengesimo sokufaka, kodwa kuphela uma kukhethwe umboniso ongumugqa. Esimweni sokushintsha, umbhalo owufakayo uthatha indawo yombhalo endaweni lapho inkomba imi khona. Ungasuka kwimodi yokufaka uye kumamodi okuovarayitha ubuye uphinde emuva ngokucindezela laba: 1Y(INS). Inkomba ivela kanje “I” kwimodi yokufaka bese ivela kanje “ ” kwimodi yokuovarayitha. Qaphela: Umboniso wemvelo njalo usebenzisa Imodi yokufaka, ngakho ukushintsha indlela yombukiso, usuka kweyomugqa uya kweyemvelo kuzofaka Imodi yokufaka ngokuzenzekela.

Ukulungisa nokucisha isimeliUkucisha uhlamvu olulodwa noma I fanshini: Hambisa inkomba iye ngakwesokudla kohlamvu noma I fanshini ofuna ukuyicisha, bese ucindezela u Y. Kwimodi yokuovarayitha, hambisa inkomba ibe ngaphansi kohlamvu noma I fanshini ofuna ukuyicisha, bese ucindezela u Y. Ukufaka uhlamvu noma I fanshini esibalweni: Sebenzisa u d no e ukuhambisa inkomba iye endaweni lapho ufuna ukufaka khona uhlamvu noma I fanshini, bese uyalufaka. Qiniseka ukuthi njalo usebenzisa Imodi yokufaka uma ukhethe umboniso owumugqa. Ukucisha konke ukubala okufakile: Cindezela u A.

Ukubheka izimo ezahlukene zemiphumela

Ngesikhathi ukhethe umbukiso wemvelo, lokho nayilokho kucindezelwa kwa f kwenza lowomphumela oveziwe ngalesosikhathi ushintshe isimo, ungaba isimo seqhezu noma isimo seqhezu lokweshumi, isimo se ' noma isimo seqhezu lokweshumi, isimo sika π noma isimo seqhezu lokweshumi. Lenkinobho yenza ukwazi ukushintshashintsha phakathi kwalezizimo.

π ÷ 6 = 16

π = 0.5235987756 B

15(π)/ 6 = 16 π f 0.5235987756

('2 + 2) × '3 = '6 + 2'3 = 5.913591358 B

(! 2 e+ 2 )*! 3 = ''6 + 2'3 f 5.913591358

Ngesikhathi kukhethwe umbukiso womugqa, yilokho nayilokho kucindezelwa kwa f kuzogcogcomisa umphumela wokubala, oveziwe ngalesosikhathi, phakathi kwesimo sawo sobuqhezu lokweshumi nesokweqhezu.

1 ÷ 5 = 0.2 = 15

b

1 / 5 = 0.2 f 1{5

ZU-12

1 – 4545

= 15

= 0.2 b

1 - 4 ' 5 = 1{5 f 0.2

Kubalulekile: • Kuyoncika ohlotsheni lomphumela wokubaliwe oliveziwe, kodwa uma ucindezela inkinobho u f uhlelo lokushintsha lungathatha isikhathi ukwenzeka. • Kweminye imiphumela yokubaliwe, ukucindezela inkinobho u f akuzukusishintsha isimo senani eliveziwe. • Awukwazi ukusuka eqhezwini lokweshumi, ushintshele kwiqhezungxube uma isamba samadijithi esewonke asetshenzisiwe kwiqhezungxube (kubandakanya izimpawu zezinombolo eziphelele, inombolo engenhla eqhezwini, inombolophansi eqhezwini nomhlukanisi) singaphezulu kwe 10.Qaphela: Kwisiboniso semvelo (MathO), ukucindezela u 1= endaweni ka = emuva kokufaka isibalokuzoveza umphumela wokubala osesimweni seqhezu lokweshumi. Ukucindezela u f ngemuva kwalokho, kuzoshintsha umphumela lowo ube isimo seqhezu noma isimo sa π. Isimo sika ' asizukuvela kulokhu.

Izibalo eziyisisekeloIzibalo ezingamaqhezuQaphela ukuthi indlela yokufaka amaqhezu ihlukile, kuncike ekutheni usebenzisa isiboniso semvelo noma isiboniso esiwumugqa.

2 + 1 = 73 2 6

B 2 ' 3 e+ 1 ' 2 = 76

Noma ' 2 c 3 e+' 1 c 2 = 76

b 2 ' 3 + 1 ' 2 = 7{6

1 = 12 2

4 − 3 B 4 -1'(() 3 e 1 c 2 = 12

b 4 - 3 ' 1 ' 2 = 1{2

Qaphela: • Ukuxuba amaqhezu kanye namanani amqhezu okweshumi esibalweni ube usebenzisa isiboniso esiwumugqa kuzokwenza ukuthi umphumela uvele uliqhezu lokweshumi. • Amaqhezu emiphumeleni yokubala avezwa esencishiselwe kuma themu aphansi.

Ukushintsha umphumela wokubala, uwususa eqhezwinimbumbulu uya kwi qhezungxube: Cindezela lezizinkinobho ezilandelayo: 1f(<)

Ukushintsha umphumela wokubala uwususa esimweni seqhezu uya esimweni seqhezu lokweshumi: Cindezela u f.

Izibalo zamaPhesentiUkufaka inani ucindezele lezizinkinobho 1((%) kwenza lelonani olifakile libe iphesenti.

150 × 20% = 30 150 * 20 1((%)= 30

Bala ukuthi ama 660 ayiliphi iphesenti lika 880. (75%)

660 / 880 1((%)= 75

ZU-13

Khulisa u 2 500 ngo 15%. (2875)

2500 + 2500 * 15 1((%)= 2875

Yehlisa u 3 500 ngo 25%. (2625)

3500 - 3500 * 25 1((%)= 2625

Izibalo zamaDigri, IMizuzu neMizuzwana (Sexagesimal)Ukuhlanganisa nokususa phakathi kwamanani angama sexagesimali, noma ukuphindaphinda, noma ukuhlukanisa phakathi kwenani eliyi sexagesimali nenani eliyiqhezu lokweshumi izokwenza umphumela ukuba uvezwe uyinani eliyisexagesimali. Uyakwazi futhi ukushintsha phakathi sexagesimali neqhezu lokweshumi. Lokhu okulandelayo indlela okufakwa ngayo inani eliyisexagesimali: {Amadigri}, $, {Imizuzu}, $, {Imizuzuwana}, $.

Qaphela: Kufanele njalo ufake into kumadigrizi, nemizuzu, noma ngabe inani lakhona kuliqanda.

2°20´30˝ + 39´30˝ = 3°00´00˝

2 $ 20 $ 30 $+ 0 $ 39 $ 30 $= 3°0´0˝

Shintsha u 2°15´18˝ abe liqhezu lokubalwa ngokweshumi elilingana naye.

2 $ 15 $ 18 $= 2°15´18˝(Ishintsha ama sexagemali abe amqhezu okubalwa ngokweshumi) $ 2.255(Ishintsha amaqhezu okubalwa ngokweshumi abe amasexagemali) $ 2°15´18˝

Izitatimende ezixhantileUngalusebenzisa uhlamvu lwekholoni (;) ukuhlanganisa izimeli ezimbili noma ngaphezulu bese uwarana ngokulandelana kusuka nkwesobunxele kuya kwesokudla uma ucindezela u =.

3 + 3 : 3 × 3 3 + 3 S7(:) 3 * 3 = 6 = 9

Ukusebenzisa izimpawu zobunjiniyelaUkucindezela inkinobho ethize kushintsha inani eliveziwe likhonjiswe ngezimpawu zobunjiniyela.

Shintshela inani u 1234 livele ngezimpawu zobunjiniyela, ugudluzela icashazi leqhezu lokweshumi ngakwesokudla.

1234 = 1234 W 1.234×103

W 1234×100

Shintshela inani u 123 livele ngezimpawu zobunjiniyela, ugudluzela icashazi leqhezu lokweshumi ngakwesokunxele.

123 = 123 1W(←) 0.123×103

1W(←) 0.000123×106

ZU-14

Umlando WokubalaKwi Modi engu COMP, CMPLX, noma BASE-N, uyakwazi ukwehla wenyuka ubheka okuqukethwe umlando wokubaliwe usebenzisa f no c.

1 + 1 = 2 1 + 1 = 2 2 + 2 = 4 2 + 2 = 4 3 + 3 = 6 3 + 3 = 6 (Uphindela emuva) f 4 (Uphindela emuva futhi) f 2

Qaphela: Umlando wokubala uyacisheka njalo uma ucindezela u O, noma ushintshela kwimodi yokubala eyahlukile, noma ushintsha isimo sombukiso, noma wenza noma iyiphi inqubo yokusetha isibali.

Ukudlala futhiNgesikhathi umphumela wokubala usabinisiwe, ungacindezela u d noma u e ukuhlela isimeli osisebenzise esibalweni esidlule.

4 × 3 + 2.5 = 14.5 b 4 * 3 + 2.5 = 14.5 4 × 3 − 7.1 = 4.9 (Okuqhubekayo) dYYYY- 7.1 = 4.9

Qaphela: Uma ufuna ukulungisa isibalo, lenkomba ' ingakwesokudla kwomphumela wesibalo (bheka “Ukufunda umbukiso”), cindezela u A, bese usebenzisa u d no e ukwehla wenyuka nesibalo.

IMemori Yomphumela (Ans)/IMemori Yomphumela Owedlule (PreAns)Umphumela otholakele wesibalo sakamuva ugcinwa kwimemori u Ans (impendulo). Umphumela wesibalo otholakale ngaphambi kowokugcina ugcinwa kwimemori u PreAns (impendulo edlule). Ukuveza umphumela wesibalo esisha, kususa okuqukethwe kwimemori yamanje (Ans) kuye kwi PreAns bese kugcinwa imiphumela yesibalo esisha kwi memori yamanje (Ans). I memori ye PreAns ingasetshenziswa kuphela kwi COMP Modi. Okuqukethwe ku PreAns memori kuyacisha njalo uma isibali singena kwenye imodi, sisuka ku COMP Mode.

Ukuhlukanisa umphumela ka 3 × 4 ngama 30 b

3 * 4 =

(Uqhubeka) / 30 =

123 + 456 = 579 B 123 + 456 =

789 – 579 = 210 (Uqhubeka) 789 -G=

ZU-15

Thola uhlu lokulandelana kusuka ku T1 kuya ku T5, lwalokhu kulandelana kukaFibonacci Tk+2 = Tk+1 + Tk. Qaphela nokho ukuthi u T1 = 1 no T2 = 1. B

T1 = 1 1 =

(Ans = T1 = 1)

T2 = 1 1 =

(Ans = T2 = 1, PreAns = T1 = 1)

T3 = T2 + T1 = 1 + 1

G+SG(PreAns)=

(Ans = T3 = 2, PreAns = T2 = 1)

T4 = T3 + T2 = 2 + 1 =

(Ans = T4 = 3, PreAns = T3 = 2)

T5 = T4 + T3 = 3 + 2 =

Umphumela: Ukulandelana kunje {1, 1, 2, 3, 5}

Abaguquguqukayo (A, B, C, D, E, F, X, Y)Isibali sakho sinabaguquguqukayo abayisishiyagalombili asebevele besethiwe, ababizwa kanje A, B, C, D, E, F, X no Y. Unganikeza amanani kulaba abaguquguqukayo futhi ungabasebenzisa ezibalweni.

Ukunikeza umphumela ka 3 + 5 koguquguqukayo u A 3 + 5 1t(STO)y(A) 8

Ukuphindaphinda okuqukethwe oguquguqukayo u A nge 10 (Uqhubeka) Sy(A)* 10 = 80

Ukukhumbula okuqukethwe oguquguqukayo u A (Uqhubeka) ty(A) 8

Ukucisha okuqukethwe oguquguqukayo u A

0 1t(STO)y(A) 0

Imemori Ezimele (M)Ungangeza imiphumela yokubala noma uyisuse kwimemori ezimele. U “M” uvela ebusweni uma kukhona nanoma yiliphi inani, ngaphandle kweqanda, eligcinwe kwimemori ezimele.

ZU-16

Ukucisha okuqukethwe ngu M 0 1t(STO)l(M) 0

Ukwengeza umphumela ka 10 × 5 ku M (Uqhubeka) 10 * 5 l 50

Ukususa umphumela ka 10 + 5 ku M (Uqhubeka) 10 + 5 1l(M–) 15

Ukukhumbula okuqukethwe ngu M (Uqhubeka) tl(M) 35

Qaphela: Oguquguqukayo u M usetshenziswa kwimemory ezimele.

Ukucisha okuqukethwe kuwowonke amamemoriI-Ans memori, imemori ezimele, kanye nokuqukethwe oguquguqukayo kuyagcinwa noma ngabe ucindezela u A, ushintsha imodi yokubala, noma ucisha isibali. Okuqukethwe kwi PreAns memori kuyagcinwa noma ngabe ucindezela u A bese usicisha isibali ngaphandle kokuphuma kuCOMP Modi. Yenza lokhu okulandelayo uma ufuna ukucisha okuqukethwe yiwo wonke amamemori.

!9(CLR)2(Memory)=(Yes)

Ukufekthorayiza ngezinombolo ezingahlukaniseki ngokuphelele

Kwi COMP Modi, ungafektha inombolo ephelele kuze kube enamadijithi ali 10, ibe iziphindi ezingahlukaniseki ngokuphelele kuze kube ezinamadijithi amathathu.

Ukufekthorayiza i 1 014 usebenzisa iziphindi ezingahlukaniseki ngokuphelele

1014 =

!e(FACT)

Uma ufek thoray iza usebenz isa iz iph ind i ez ingah lukan isek i ngokuphelele,enanini elibandakanya isiphindi (ifektha) esiyinombolo engahlukaniseki ngokuphelele, enamadijithi angaphezulu kwamathathu, ingxenye engafekthorayizeki izoba phakathi kwabakaki embukisweni.

Ukufekthorayiza i 4 104 676 usebenzisa iziphindi ezingahlukaniseki ngokuphelele (= 22 × 10132)

4104676 =!e(FACT)

Noma yikuphi kwalokhu okulandelayo kuzokukhipha embukisweni womphumela wokufekthorayiza ngezinombolo ezingahlukaniseki ngokuphelele: • Ukucindezela u !e(FACT), noma =.• Ukucindezela noma eyiphi yalezinkinibho: . noma e.• Ukusebenzisa imenu yokuhlela ukushintsha uhlelo lwesilinganisi sama

engela (Deg, Rad, Gra) noma uhlelo lombukiso wamadijithi (Fix, Sci, Norm).

ZU-17

Qaphela: • Angeke ukwazi ukufekthorayiza ngezinombolo ezingahlukaniseki ngokuphelele ngesikhathi kusavezwe umphumela wokubala oyinani eliyi qhezu lokubalwa ngokweshumi, iqhezu, noma inani elinophawu lokususa. Ukuzama ukwenza lokho iphutha lezibalo (Math ERROR). • Angeke ukwazi ukufekthorayiza ngezinombolo ezingahlukaniseki ngokuphelele ngesikhathi kuvezwe umphumela wokubala osebenzisa u Pol noma u Rec.

Izibalo zamaFanshiniUkubona ukwenza kwangempela usebenzisa I fanshini ngayinye, bheka ingxenye “Izibonelo” elandela loluhla olungezansi.

ππ : U π uvezwa njengo 3.141592654, kodwa u π = 3.14159265358980 osetshenziselwa izibalo zangaphakathi.

e : U e uvezwe njengo 2.718281828, kodwa u e = 2.71828182845904 osetshenziselwa izibalo zangaphakathi.

sin, cos, tan, sin−1, cos−1, tan−1 : Amafanshini aphathelene netrigonometri. Cacisa isilinganisi se engela ngaphambi kokuqala ukubala. Bheka u 1.

sinh, cosh, tanh, sinh−1, cosh−1, tanh−1 : Amafanshini ahayphabholikhi. Faka ifunshini ekwimenu evela uma ucindezela u w. Uhlelo lokuhlela isilinganisi sama-engela aluzichaphazeli izibalo. Bheka u 2.

°, r, g : Lamafanshini abalula isilinganisi se-engela. U ° balula amadigri, u r amaradiyeni, bese u g amagradi. Faka ifunshini ekwimenu evela uma wenza lokhu okusemqoka okulandelayo: 1G(DRG'). Bheka u 3.

$, % : Amafanshini angumphindwa. Qaphela ukuthi indlela yokufaka iyehluka, kuncike ekutheni usebenzisa umbukiso oyimvelo noma umbukiso owumugqa. Bheka u 4.

log : Ifanshini emayelana nenombolo eyisibambiso. Sebenzisa inkinobho u l ukufaka u logab njengo log (a, b). Umsuka wokubala, i 10, iwona esicushelwe ukumsebenzisa isibali, uma ungafakanga lutho endaweni ka a. Ukhiye u &, naye angasetshenziswa ukufaka imininingwane, kodwa kuphela uma kukhethwe isiboniso semvelo. Kulesisimo kumele unikeze umsuka wokubala inani. Bheka u 5.

ln : Inombolo yesibambiso yemvelo kumsuka wokubala u e. Bheka u 6.

x2, x3, x^, ), #, ", x−1 : Abaphindaphindi, Imisuka yomphindaphindi, kanye nezinombolo othi uma uziphindaphinda zikukhiphele umuvo (1). Qaphela ukuthi izindlela zokufaka u x^, ), #, no " zahlukene, kuncike ekutheni usebenzisa isiboniso semvelo noma isiboniso esingumugqa. Bheka u 7.

: Ifanshini yokwenza i-intagrashini yezinombolo usebenzisa indlela

ka Gauss-kronrod. Kufakwa kanjena kwisiboniso semvelo ∫ab f(x)dx,

embonisweni ongumugqa kufakwa kanje ∫ ( f(x), a, b, tol). U tol ukhomba

ukubekezela, okuba ngu 1 × 10–5 uma kungafakwanga lutho ku tol. Bheka futhi “Okumele ukuqaphele eziBalweni ze-Intagreshini neDifarentiyeshini” kanye “Amathiphu okwenza izibalo ze-intagreshini eziyimpumelelo” ukuthola olunye ulwazi. Bheka u 8.

F: Ifanshini yokusondezela yedirivathivu encike endleleni yomahluko

omaphakathi. Kufakwa kanje kwisiboniso semvelo dxd

( f (x)) � x=a , kanti

kwisiboniso esiwumugqa kufakwa kanje dxd ( f (x), a, tol). U tol ukhomba

ZU-18

ukubekezela, okuba ngu 1 × 10–10 uma kungafakwanga lutho ku tol. Bheka

futhi “Okumele ukuqaphele eziBalweni ze-Intagreshini neDifarentiyeshini”

ukuthola olunye ulwazi. Bheka u 9.

8: Ifanshini esebenza uma unikeze uhla oluthize f(x), ikunikeze

umphumela wokuhlanganisa Σ ( f (x))x=a

b

= f(a) + f(a+1) + f(a+2) + ...+

f(b). Kufakwa kanje kwisiboniso semvelo Σ ( f (x))x=a

b

, kanti kwisiboniso

esiwumugqa kufakwa kanje Σ( f(x), a, b). U a no b izinombolo eziphelele

ezingabalulwa kuloluhla –1 × 1010 � a � b � 1 × 1010. Bheka u 10.

Qaphela: Lokhu okulandelayo akusebenziseki ku f(x): Pol, Rec. Lokhu okulandelayo akusebenziseki ku f(x), a, noma b: ∫, d/dx, Σ.

Pol, Rec : U Pol ushintsha ukuvumelana okungunxande kube ukuvumelana okungu phola, u Rec yena ushintsha ukuvumelana okungu phola kube ukuvumelana okungunxande. Bheka u 11.

Pol(x, y) = (r, �) Rec(r, �) = (x, y) Balula isilinganisi sama-engele, ngaphambi Kokwenza izibalo. Umphumela wesibalo ka r no � kanye no x no y, ngamunye banikezelwe Kwabaguquguqukayo o X no Y. Umphumela wesibalo u � uvezwa kuloluhla: −180° � θ � 180°

Amakho-odinethi Angunxande (REC)

Amakho-odinethi Ayiphola (POL)

x ! : Ifanshini efekthoriyali. Bheka u 12.

Abs : Ifanshini enenani loqobo. Qaphela ukuthi indlela yokufaka ihlukile, kuncike ekutheni usebenzisa umbukiso wemvelo noma owomugqa. Bheka u 13.

Ran# : Wenza inombolo enamadijithi ama 3 ehlanganisa izinombolo ezakheke kwisikhwensi engenakho ukulandelana. Umphumela uvezwa njengeqhezu uma kukhethwe umboniso wemvelo. Bheka u 14.

RanInt# : Uma ufaka imininingwane ye fanshini enjengo RanInt#(a, b), eyenza inombolo ephelele evela kwisikhwensi engenakho ukulandelana, ohlwini a kuyaku b. Bheka u 15.

nPr, nCr : Amafanshini iPhemutheshini (nPr) nekhombineshini (nCr). Bheka u 16.

Rnd : I-agumenti yalefanshini yenziwa inani leqhezu lokubalwa ngokweshumi bese lisondezelwa ngokomyalelo wangalesosikhathi wenombolo yamadijithi angavezwa (Norm, Fix, noma Sci). Ngo Norm 1 noma u Norm 2, i-agumenti isondezelwa kumadijithi ali 10. Ngo Fix no Sci, i-agumenti isondezelwa kumadijithi abaluliwe. Uma u Fix 3 kunguye osetshenziswayo, umphumela ka 10 ÷ 3 uvezwa engu 3.333, isibali sona sigcina inani elingu 3.33333333333333 (amadijithi ali 15) ngaphakathi ukulisebenzisa ekubaleni. Ku Rnd(10÷3) = 3.333 (ngo Fix 3), Womabili amanani, eveziwe negcinwe ngaphakathi kwisibali aba ngu 3.333. Ngenxa yalokhu uchungechunge lwezibalo lungakhipha imiphumela engafani kuncike ekutheni kusetshenziswe u Rnd (Rnd(10÷3) × 3 = 9.999) noma cha (10 ÷ 3 × 3 = 10.000). Bheka u 17.

ZU-19

Qaphela: Ukusebensisa amafanshini kunganciphisa ukushesha kokubala, okungalibazisa ukuvezwa komphumela. Ungenzi lutho olunye ngesikhathi usalinde umphumela wesibalo ukuba uvele. Ukuphazamisa ukubala okuqhubekayo ngaphambi kokuba umphumela wako uvele, cindezela u A.

Okumele ukuqaphele eziBalweni ze-Intagreshini neDifarentiyeshini• Izibalo ze-intagreshini kanye nedifarentiyeshini zingenziwa kuphela kwi

Modi engu COMP (,1). • Lokhu okulandelayo akusebenziseki ku f(x): Pol, Rec. Lokhu okulandelayo

akusebenziseki ku f(x), a, b, noma tol: ∫, d/dx, Σ.• Uma usebenzisa ifanshini yetrigonometri ku f(x), kumele ubalule u Rad

njengesilinganisi sama-engela.• Inani elincane lika tol, likhuphula izinga lokucophelela khonamanjalo landisa

isikhathi sokubala. Uma ubalula u tol, sebenzisa inani elingu 1 × 10–14 noma elingaphezulu.

Okumele ukuqaphele ezibalweni ze-Intagreshini kuphela• I-intagreshini ngokujwayelekile ithatha isikhashana ukuyenza.• Kungenzeka kwakheke iphutha lokubala elizodlula izinga lokubekezela,

okungadala ukuba isibala siveze umyalezookhombisa iphutha. Lokhu kuncika kulokho okuqukethwe ngu f(x) kanye nerijini ye-intagreshini.

Okumele ukuqaphele ezibalweni zeDifarentiyeshini kuphela• Uma ingatholakali ikhonvegensi yesixazululo kweqiwe ukufaka u tol, inani

lika tol lizolungiswa ngokuzenzakalela ukuze kutholakale isixazululo.• Amachashazi angalandelani, ukwahlukahluka okuphuthumayo

okungalindelekile, amacashazi amancane kumbe amakhulu kakhulu, amacashaza lapho ushintsho lwenzeka khona kwinsongo, nokufakwa kwamacashaza angadifarentishiyeki, noma icashazi lokudifarentishiyetha, noma umphumela wesibalo sokudifarentishiyetha osondela eqandeni, kungadala ukungacopheleli kumbe iphutha.

Amathiphu okwenza izibalo ze-intagreshini eziyimpumeleloUma ifanshini enenani eliphindaphindekayo kumbe i-inthavali ye-intagreshini ikunikeza imiphumile engaphezu kweqanda kanye nengaphansi kweqandaYenza ama-intagreshini ahlukene, umjikelezo ngamunye, kumbe wenzele ingxenye engaphezu kweqanda, ingxenye engaphansi kweqanda yodwa, bese uyayihlanganisa imiphumela.

Uma amnani e-intagreshini ehlukahluka kakhulu ngenxa yokugudluka kancane kwi inthavali ye-intagreshiniYehlukanise i-inthavali izingxenye eziningi (ngendlela ehlukanisa izindawo ezinokwahlukahluka okukhulu zibe izingxenye ezincane), yenza i-intagreshini engxenyeni ngayinye, bese uyayihlanganisa imiphumela.

S Ongaphezulu Kweqanda

S Ongaphansi Kweqanda

S Ongaphezulu Kweqanda

S Ongaphansi Kweqanda

∫ ∫a

b f(x)dx =

a

c f(x)dx + ∫c

b f(x)dx

Ingxenye Engaphezulu Kweqanda

(S Ongaphezulu kweqanda)

Ingxenye Engaphansi Kweqanda

(S Ongaphansi kweqanda)

∫ ∫a

b f(x)dx =

a

c f(x)dx + ∫c

b f(x)dx

Ingxenye Engaphezulu Kweqanda

(S Ongaphezulu kweqanda)

Ingxenye Engaphansi Kweqanda

(S Ongaphansi kweqanda)

ZU-20

Izibonelo

sin 30°= 0.5 bv s 30 )= 0.5 sin−10.5 = 30° bv 1s(sin−1) 0.5 )= 30

sinh 1 = 1.175201194 wb(sinh) 1 )= 1.175201194 cosh–1 1 = 0 wf(cosh−1) 1 )= 0

π /2 radiyeni = 90°, 50 gradi = 45° v

(15(π)/ 2 )1G(DRG')c(r)= 90 50 1G(DRG')d(g)= 45

Ukubala u e5 × 2 umphumela ube namadijithi abalulekile amathathu (Sci 3)

1N(SETUP)7(Sci)3

B 1i(%) 5 e* 2 = 2.97×102

b 1i(%) 5 )* 2 = 2.97×102

log101000 = log 1000 = 3 l 1000 )= 3 log216 = 4 l 2 1)(,) 16 )= 4 B & 2 e 16 = 4

Ukubala u 90 (= loge 90) umphumela ube namadijithi abalulekile amathathu (Sci 3)

1N(SETUP)7(Sci)3 i 90 )= 4.50×100

1.2 × 103 = 1200 B 1.2 * 10 6 3 = 1200 (1+1)2+2 = 16 B ( 1 + 1 )6 2 + 2 = 16 (52)3 = 15625 ( 5 x)1w(x3)= 15625 32

5 = 2 B 16(") 5 e 32 = 2 b 516(") 32 )= 2

Ukubala u '2 × 3(= 3'2 = 4.242640687...) umphumela ube namadijithi amathathu ngemuva kwekhoma (Fix 3).

1N(SETUP)6(Fix)3 B ! 2 e* 3 = 3'2 1= 4.243 b ! 2 )* 3 = 4.243

∫1

eln(x)dx = 1

B 7iS)(X))e 1 eS5(e)= 1 b 7iS)(X))1)(,)

1 1)(,)S5(e))= 1

ba x1 x2 x3 x4

x0

f (x)

ba x1 x2 x3 x4

x0

f (x)

a

b f(x)dx =

a

x1

f(x)dx + x1

x 2

f(x)dx + .....∫ ∫ ∫x4

b f(x)dx∫+

a

b f(x)dx =

a

x1

f(x)dx + x1

x 2

f(x)dx + .....∫ ∫ ∫x4

b f(x)dx∫+

11

22

33

44

55

66

77

88

ZU-21

Ukuthola i-dirivathivu ecashazini u x = π/2 lefanshini u y = sin(x) V

B 17(F)sS)(X))

e'15(π)e 2 = 0 b 17(F)sS)(X))

1)(,)15(π)' 2 )= 0

Σx = 1

5

(x + 1) = 20

B 1&(8)S)(X)+ 1 e 1 e 5 = 20 b 1&(8)S)(X)+ 1 1)(,) 1 1)(,) 5 )= 20

Ukushintsha ukuvumelana okusanxande ('2 , '2 ) kube okuvumelana okuyiphola. v

B 1+(Pol)! 2 e1)(,)! 2 e)= r=2,�=45 b 1+(Pol)! 2 )1)(,)! 2 ))= r= 2 �= 45 Ukushintsha ukuvumelana okuyiphola ('2 , 45°) kube okuvumelana

okusanxande. v

B 1-(Rec)! 2 e1)(,) 45 )= X=1, Y=1

(5 + 3) ! = 40320 ( 5 + 3 )1E(x!)= 40320

|2 – 7| × 2 = 10 B 1w(Abs) 2 - 7 e* 2 = 10 b 1w(Abs) 2 - 7 )* 2 = 10

Ukuthola izinombolo eziphelele ezivela kwisikhwensi engenayo iphethini, ezinamadijithi amathathu, zibe ntathu.

1000 1.(Ran#)= 459 = 48 = 117

(Imiphumela ekhonjiswe lapha eyokufanekisa kuphela. Imiphumela yangempela izohluka).

Ukwakha izinombolo eziphelele ezivela kwisikhwensi engenayo iphethini ohlwini olusuka ko 1 kuya kokuyi 6.

S.(RanInt) 1 1)(,) 6 )= 2 = 6 = 1

(Imiphumela ekhonjiswe lapha eyokufanekisa kuphela. Imiphumela yangempela izohluka).

Ukuthola inani lama phemutheshini nama khombinashini angenzeka uma ukhetha abantu abane eqenjini labali 10.

Amaphemutheshini: 10 1*(nPr) 4 = 5040 Amakhombinashini: 10 1/(nCr) 4 = 210

99

1010

1111

1212

1313

1414

1515

1616

ZU-22

Ukwenza lezibalo ezilandelayo ngesikhathi kukhethwe u Fix 3 wamadijithi azovezwa ebusweni: 10 ÷ 3 × 3 no Rnd(10 ÷ 3) × 3 b

1N(SETUP)6(Fix)3 10 / 3 * 3 = 10.000 10(Rnd) 10 / 3 )* 3 = 9.999

Izibalo zezinombolo eziphicayo (CMPLX)Ukwenza izibalo zezinombolo eziphicayo, kuqala cindezela u N2(CMPLX) ukufaka imodi ka CMPLX. Ungasebenzisa noma ukuvumelana okusanxande (a+bi) noma okusaphola (r∠�) ukufaka izinombolo eziphicayo. Imiphumela yezibalo zezinombolo eziphicayo ivezwa ngokulandela isimo sokusethwa kwemenu yokuhlela.

(2 + 6i) ÷ (2i) = 3 – i (Isimo senombolo ephicayo: a + bi) ( 2 + 6 W(i))/( 2 W(i))= 3–i

2 ∠ 45 = '2 + '2 i Bv (Isimo senombolo ephicayo: a + bi) 2 1-(∠) 45 = '2 +'2 i

'2 + '2 i = 2 ∠ 45 Bv (Isimo senombolo ephicayo: r∠�)

! 2 e+! 2 eW(i)= 2∠45

Qaphela: • Uma uhlela ukufaka nokuveza umphumela wokubala esimweni esingukuvumelana okuyiphola, balula isilinganisi sama-engela ngaphambi kokuqala ukubala. • Inani lika � womphumela wokubala livezwa ohlwini –180° � � � 180°. • Ukuvezwa komphumela ngesikhathi kukhethwe umbukiso ongumugqa kuzoveza u a no bi (noma r no �) besemigqeni eyahlukene.

Izibonelo zokubala ku CMPLX Modi

(1 – i)–1 = 12

12

+ i B (Isimo senombolo ephicayo: a + bi) ( 1 -W(i))E= 1

212

+ i

(1 + i)4 + (1 – i)2 = – 4 – 2i B

( 1 +W(i))6 4 e+( 1 -W(i))w= –4–2i

Ukuthola inombolo ephicayo eyikhonjugethi ka 2 + 3i (Isimo senombolo ephicayo: a + bi)

12(CMPLX)2(Conjg) 2 + 3 W(i))= 2–3i

Ukuthola inombolo ngaphandle kokunaka uphawu lwayo (+ noma –) kanye ne-agumenti ka 1 + i Bv

Inani ngaphandle kokunaka uphawu: 1w(Abs) 1 +W(i)= '2 I-agumenti: 12(CMPLX)1(arg)1+W(i))= 45

1717

ZU-23

Ukusebenzisa umyalo ukubalula isimo somphumela wesibaloOmunye wemiyalo emibili ekhethekile ('r∠� noma 'a+bi) angafakwa ekugcineni kwesibalo ukubalula isimo okuzovezwa ngaso imiphumela yezibalo. Umyalo lona uyayiqgiba indlela obekusethwe ngayo isibali, sisethelwa izinombolo eziphicayo.

'2 + '2 i = 2 ∠ 45, 2 ∠ 45 = '2 + '2 i Bv

! 2 e+! 2 eW(i)12(CMPLX)3('r∠�)= 2∠45 2 1-(∠) 45 12(CMPLX)4('a+bi)= '2 +'2 i

Ukusebenzisa u CALCU CALC ukuvumela ukuba useyive iz imel i zemethamathiks i ezinabaguquguqukayo, ongabuya uzilande bese uzisebenzisa kwi COMP Modi (N1) naku CMPLX Modi (N2). Okulandelayo kuchaza izinhlobo zezimeli zemathamethiksi ezinabaguqugukayo ongaziseyiva ngo CALC:

• Izimeli o: 2X + 3Y, 2AX + 3BY + C, A + Bi• Izitatimende eziningi: X + Y : X (X + Y)• Isibalo esilingana nesinye ezinoguquguqukayo oyedwa ngakwesobunxele

kanye nesimeli esibandakanya abaguquguqukayo ngakwesokudla: A = B + C, Y = X2 + X + 3

(Sebenzisa Ss(=) ukufaka uphawu lokulinganisa.)

Ukugcina u 3A + B bese ubambelisa ngalamanani ukwenza isibalo: (A, B) = (5, 10), (7, 20)

3 S-(A)+Se(B)

s

Okukutshela ukuthi faka inani lika A Inani lika A lamanje

5 = 10 =

s (noma =)

7 = 20 =

Ukuphuma ku CALC: A

MathMath

MathMath

MathMath

MathMath

MathMath

ZU-24

Ukugcina u A + Bi bese uthola u '3 + i, 1 + '3 i usebenzisa ukuvumelana okuyiphola (r∠�) v

N2(CMPLX)

S-(A)+Se(B)W(i) 12(CMPLX)3('r∠�)

s! 3 )= 1 =

s (Noma =) 1 =! 3 )=

Ukuphuma ku CALC: A

Qaphela: Ngalesisikhathi kusukela ucindezela u s kuze kube uyaphuma ku CALC ngokucindezela u A, kumele usebenziseindlela yokufaka imininingwane yomboniso osamugqa.

Ukusebenzisa uxazulula (SOLVE)Uxazulula usebenzisa umthetho ka Newton ukusondezela isixazululo sesibalo esilingana nesinye. Qaphela ukuthi uxazulula angasetshenziswa kwi COMP Modi (N1) kuphela. Lokhu okulandelayo kuchaza izinhlobo zezibalo ezilingana nezinye izixazululo zazo ezingatholakala kusetshenziswa uxazulula (SOLVE).

• Izibalo ezilingana nezinye ezinoguquguqukayo u X: X2 + 2X – 2, Y = X + 5, X = sin(M), X + 3 = B + C

U SOLVE ukutholela inani lika X. Isimeli esinjengo X2 + 2X – 2 sithathwa njengo X2 + 2X – 2 = 0.

• Izibalo ezilingana nezinye ezimbandakanya okulandelayo: {Isibalo esilingana nesinye}, {Isixazululo oguquguqukayo}

U SOLVE ukutholela inani lika Y, isibonelo, uma isibalo esilingana nesinye sifakwe kanje: Y = X + 5, Y

Kubalulekile: • Uma isibalo esilingana nesinye sinamafanshini ambandakanya abakaki bokuvula (njengaku sin no log), ungabashiyi abakaki bokuvala. • Lamafanshini alandelayo awavumelekile maphakathi nesibalo esilingana nesinye: ∫, d/dx, Σ, Pol, Rec.

Ukuxazulula u y = ax2 + b ufuna u x uma u y = 0, a = 1, no b = –2

Sf(Y)Ss(=)S-(A)

S)(X)w+Se(B)

1s(SOLVE)

Okukutshela ukuthi faka inani lika Y Inani lika Y lamanje

MathCMPLX MathCMPLX

MathMath

MathMath

ZU-25

0 = 1 =- 2 =

Inani lika X lamanje

Faka inani lokuqala lika X (Lapha faka 1): 1 =

Ubuso obuveza isixazululo

Ukuphuma ku SOLVE: A

Qaphela: Ngalesisikhathi kusukela ucindezela u 1s(SOLVE) kuze kube uyaphuma ku SOLVE ngokucindezela u A, kufanele usebenzise inqubo yokufaka imininingwane yomboniso osamugqa. Kubalulekile: • Kungenzeka u SOLVE angakwazi ukuthola izixazululo, kuncike ekutheni ufake bani njengenani lokuqala lika X (oguquguqukayo wesixazululo). Uma lokhu kwenzeka, zama ukushintsha inani lokuqala ukuze asondele kwisixazululo. • U SOLVE kungenzeka angakwazi ukuthola isixazululo esiyiso, noma ngabe sikhona. • U SOLVE usebenzisa umthetho ka Newton, ngakho-ke noma ngabe izixazululo ziziningi, eyodwa kuphela kuzo ezobuyiswa. • Ngenxa yemikhawulo emthethweni ka Newton, izixazululo kubanzima ukuzithola ezibalweni ezilingana nezinye ezinjengalezi ezilandelayo: y = sin(x), y = ex, y = 'x .

Okuqukethwe Isibuko SesixazululoIzixazululo zivezwa ngesimo sedesimali.

Isibalo esilingana nesinye (leso osifakile)

Oguquguqukayo ofunwayo

Math

Isixazululo

(ohlangothi lwesinxele) – (uhlangothi lwesokudla) umphumela

“(ohlangothi lwesinxele) – (uhlangothi lwesokudla) umphumela” kukhombisa umphumela uma uhlangothi lwangakwesokudla lususwa ohlangothini lwangakwesobunxele, ngemuva kokunikeza inani koguquguqukayo okufunwa isixazululo sakhe. Ukusondela kwalomphumela eqandeni, kusho izinga eliphezulu lokucophelela esixazululweni.

Isibuko sokuqhubekaU SOLVE wenza iconvegensi kangangoba kubaluliwe. Uma ingasitholi isixazululo, iveza isibuko sesiqiniseko esikhombisa lokhu “Continue: [=]”, ikubuza ukuthi uyafuna ukuqhubeka na.Cindezela u = ukuqhubeka noma u A ukukhansela I ophareshini ka SOLVE.

Ukuxazulula y = x2 – x + 1 u x uma u y = 3, 7 no 13.

Sf(Y)Ss(=)

S)(X)w-S)(X)+ 1

MathMath

MathMath

MathMath

ZU-26

1s(SOLVE)

3 =

Faka inani lokuqala lika X (Lapha faka 1): 1 =

= 7 ==

= 13 ==

Izibalo zeStathistiksi (STAT)Ukuqala isibalo sestathistiksi, yenza lokhu okusemqoka N3(STAT) ukufaka imodi u STAT, bese usebenzisa iskrini esizovela ukukhetha uhlobo lwesibalo ofuna ukulenza.

Ukukhetha loluhlobo lwesibalo sestathistiksi:(Ifomula yerigreshini ikhonjiswe kubakaki)

Cindezela lenkinobho:

Oguquguqukayo oyedwa (X) 1(1-VAR)

Abaguquguqukayo abangababili (X,Y), irigreshini ewumugqa ( y = A + Bx) 2(A+BX)

Abaguquguqukayo abangababili (X,Y), irigreshini ekhwadrathikhi ( y = A + Bx + Cx2) 3( _+CX2)

Abaguquguqukayo abangababili (X,Y), irigreshini eyinombolo eyisibambiso ( y = A + Blnx) 4(ln X)

Abaguquguqukayo abangababili (X,Y), e irigreshini engumphindwa ( y = AeB x )

5(e^X)

Abaguquguqukayo abangababili (X,Y), ab irigreshini engumphindwa ( y = ABx)

6(A•B^X)

Abaguquguqukayo abangababili (X,Y), irigreshini engumphindaphindi ( y = AxB) 7(A•X^B)

Abaguquguqukayo abangababili (X,Y), irigreshini ehlanekezelwe ( y = A + B/x) 8(1/X)

Ukucindezela nanoma iyiphi yalezizinkinobho kusuka ko (1 kuya koku 8), kuveza okokuhlela u Stat.Qaphela: Uma ufuna ukushintsha uhlobo lwesibalo, emva kokufaka imodi ka STAT, yenza lokhu okulandelayo, ukuveza iskrini sokukhetha uhlobo lwesibalo: 11(STAT/DIST)1(Type).

MathMath

MathMath

MathMath

MathMath

MathMath

ZU-27

Ukufaka ImininingwaneSebenzisa okokuhlela u Stat ukufaka imininingwane. Yenza lokhu okulandelayo, okusemqoka, ukuveza okokuhlela uStat: 11(STAT/DIST)2(Data).Okokuhlela uStat kukunikeza imigqa engama 40 ukuze ufake imininingwane, lapho kukhona uhlu luka X kuphela, noma kukhona uhlu luka X no Y. Angama 20 lapho kukhona uhlu luka X noluka FREQ, noma imigqa engama 26 lapho kukhona uhlu luka X, Y, no FREQ.Qaphela: Sebenzisa uhlu luka FREQ (ukuphindaphinda) ukufaka inani lemininingwane yezinto ezifanayo. Umboniso wohlu lwe FREQ ungavezwa noma ucishwe ngokusebenzisa okokusetha u Stat okutholakala kwi menu yokusetha.

Ukukhetha irigreshini engumugqa nokufaka lemininingwane elandelayo: (170, 66), (173, 68), (179, 75)

N3(STAT)2(A+BX)

170 = 173 = 179 =ce

66 = 68 = 75 =

Kubalulekile: • Yonke imininingwane efakwe kwi Stat Editha ngalesosikhathi, iyasuleka njalo uma uphuma kwiModi yeStat, ushintsha phakathi kwesibalo sestathistiksi esinoguquguqukayo oyedwa nesinoguquguqukayo ngababili, noma ushintsha indlela okusethwe ngayo uStat kwi menu yokusetha. • Lokhu okulandelayo akusebenzelani no Stat Editha: m, 1m(M–), 1t(STO). UPol, uRec, kanye nezitatimende eziningi, angeke bakwazi ukufakeka nge Stat Editha.Ukushintsha imininingwane kwi seli: Kwi Stat Editha, hambisa inkomba iye kwi seli enemininingwane ofuna ukuyishintsha, Faka imininingwane emisha, bese ucindezela u =. Ukucisha umugqa: Kwi Stat Editha, hambisa inkomba iye kwi seli enemininingwane ofuna ukuyicisha, bese ucindezela u Y. Ukufaka umugqa: Kwi Stat Editha, hambisa inkomba iye endaweni lapho ufuna ukufaka khona umugqa bese wenza lokhu okulandelayo: 11(STAT/DIST)3(Edit)1(Ins). Ukucisha konke okuqukethwe kuStat Editha: Kwi Stat Editha, yenza lokhu okulandelayo: 11(STAT/DIST)3(Edit)2(Del-A).

Ukuthola amanani estathistiksi kwimininingwane efakiwe:Ukuthola imininingwane yestathistiksi, cindezela u A ngesikhathi uku Stat Editha bese ukhumbula oguquguqukayo westathistiksi (σx, Σx2, njalonjalo) omfunayo. Abaguquguqukayo bestathistiksi nezinkinobho okufanele uzicindezele ukubakhumbulu kuvezwe ngezansi. Kulezozibalo zestathistiksi

11

STATSTAT

STATSTAT

STATSTAT

ZU-28

ezinoguquguqukayo oyedwa, abaguquguqukayo abaphawulwe nge-asteriski (*) bakhona.

umphumela wokuhlanganisa: Σx2*, Σx*, Σy2, Σy, Σxy, Σx3, Σx2y, Σx4

11(STAT/DIST) 3(Sum) 1 kuya ku 8inani lezinto: n*, isilinganiso esiphakathi nendawo: o*, p, ukwahluka kokumisiwe kweqembu lonke labantu kumbe izinto: σx*, σy, ukwahluka kokumisiwe kweqenjana elikhethiwe: sx*, sy

11(STAT/DIST) 4(Var) 1 kuya ku 7Ikho-efishiyenti yerigreshini: A, B, ikho-efishiyenti yekhorileshini: r, amanani alinganiselwe: m, n11(STAT/DIST) 5(Reg) 1 kuya ku 5amakho-efishiyenti erigreshini ama regreshini akhwadrathikhi: A, B, C, amanani alinganiselwe: m1, m2, n 11(STAT/DIST) 5(Reg) 1 kuya ku 6

• Ukubona amafomula erigreshini,bheka ithebhula ekuqaleni kwalengxenye yemanuwali.

• m, m1, m2 no n ababona abaguquguqukayo. Bangamakhomandi ohlobo oluthatha i-agumenti efika kuqala ngaphambi kwabo. Bheka “Ukubala amaNani aLinganisiwe” ukuthola eminye imininingwane.

Inani eliphansi: minX*, minY, Inani eliphezulu: maxX*, maxY11(STAT/DIST) 6(MinMax) 1 kuya ku 2(Uma kukhethwe ukubala kwestathistiksi okusebenzisa oguquguqukayo oyedwa)11(STAT/DIST) 6(MinMax) 1 kuya ku 4(Uma kukhethwe ukubala kwestathistiksi okusebenzisa abaguquguqukayo abahamba ngababili)Ikwarthayli yokuqala: Q1, IMidiyeni: med, Ikwarthayili yesithathu: Q311(STAT/DIST) 6(MinMax) 3 kuya ku 5(Uma kukhethwe ukubala kwestathistiksi okusebenzisa oguquguqukayo oyedwa)Qaphela: Ngesikhathi kukhethwe ukubala kwestathistiksi okusebenzisa oguquguqukayo oyedwa, ungafaka amafanshini namiyalelo yokwenza izibalo zokwaba okwejwayelekile kwi menu evela uma wenza lokhu okulandelayo: 11 (STAT/DIST) 5 (Distr). Bheka “Ukwenza izibalo zokwaba okwejwayelekile” ukuthola eminye imininingwane.

Ukufaka imininingwane yoguquguqukayo oyedwa x = {1, 2, 2, 3, 3, 3, 4, 4, 5}, usebenzisa uhlu lwe FREQ ukubalula iphindwa kangaki into ngayinye ({xn; freqn} = {1;1, 2;2, 3;3, 4;2, 5;1}), bese ubala imean ne ukwahluka kokumisiwe kweqembu lonke labantu kumbe izinto.

1N(SETUP)c4(STAT)1(ON)

N3(STAT)1(1-VAR)

1 = 2 = 3 = 4 = 5 =ce

1 = 2 = 3 = 2 =

A11(STAT/DIST)4(Var)2(o)=

A11(STAT/DIST)4(Var)3(σx)=

Imiphumela: Isilinganiso esiphakathi nendawo: 3 ukwahluka kokumisiwe kweqembu lonke labantu kumbe izinto: 1.154700538

22

STATSTAT

ZU-29

Ukubala ama khoreleshini kho-efishiyenti e rigreshini engumungqa kanye neyenombolo eyisibambiso yemininingwane yabaguquguqukayo abangababili kanye nokuthola irigreshini fomula yekhorileshini enamandla kakhulu: (x, y) = (20, 3150), (110, 7310), (200, 8800), (290, 9310). Emiphumeleni balula u Fix: 3 (3 dp)

1N(SETUP)c4(STAT)2(OFF)

1N(SETUP)6(Fix)3

N3(STAT)2(A+BX)

20 = 110 = 200 = 290 =ce

3150 = 7310 =8800 = 9310=

A11(STAT/DIST)5(Reg)3(r)=

A11(STAT/DIST)1(Type)4(In X)

A11(STAT/DIST)5(Reg)3(r)=

A11(STAT/DIST)5(Reg)1(A)=

A11(STAT/DIST)5(Reg)2(B)=

Imiphumela: Ikhoreleshini Kho-efishiyenti yeRigreshini eNgumugqa: 0.923Ikhoreleshini Kho-efishiyenti yeRigreshini yenombolo eyisibambiso: 0.998Ifomula yeRigreshini yenombolo eyisibambiso: y = –3857.984 + 2357.532lnx

Ukubala amaNani aLinganisiweInani elilinganisiwe lika y lingabalelwa nanoma yiliphi inani elinikeziwe lika x, kuncikiswe kwi fomula yerigreshini etholakale ngesibalo sestathistiksi esinabaguquguqukayo abangababili. Inani lika x elihambisana nalo (amanani amabili, x1 no x2, uma kuyi rigreshini ekhwadrathikhi) nayo ingabalelwa nanoma yiliphi inani lika y kwifomula yerigreshini.

Ukuthola inani elilinganisiwe lika y uma u x = 160 kwi fomula yerigreshini eyakhiwe yirigreshini yenombolo eyisibambiso yemininingwane ku 3. Umphumela ubalulele u Fix 3. (Yenza lokhu okulandelayo emva kokuqeda ukwenza lokhu okuku 3.)

A 160 11(STAT/DIST)5(Reg)5(n)=

Umphumela: 8106.898

Kubalulekile: Irigreshini kho-efishiyenti, ikhorileshini kho-efishiyenti, kanye nezibalo zenani elilinganisiwe kungathatha isikhathi eside uma kunomthamo omkhulu wemininingwane.

Ukwenza izibalo zokwaba okwejwayelekile.Uma kukhethwe ukubala kwestathistiksi okusebenzisa oguquguqukayo oyedwa, ungenza isibalo sokwaba okwejwayekile usebenzisa amafanshini akhonjiswe ngezansi kwi menu evela uma wenza lokhu okulandelayo:11(STAT/DIST)5(Distr).

33

STAT FIXSTAT FIX

44

ZU-30

P, Q, R: Lamafanshini athatha i-agumenti t bese ethola okungenzeka kwokwabiwa okwejwayelekile okwamukelekile, njengoba kukhonjisiwe ngezansi.

't: Lefanshini ilandela i-agumenti u X, bese ithola ivariyethi eyenziwe yaba

ejwayelekile .

Kwimininingwane enoguquguqukayo oyedwa {xn ; freqn} = {0;1, 1;2, 2;1, 3;2, 4;2, 5;2, 6;3, 7;4, 9;2, 10;1}, ukuthola ivariyethi eyenziwe yaba eyejwayelekile e ('t) uma u x = 3, no P(t) kulelophoyinti kuze kuyofika kumadijithi amathathu ngemuva kwekhoma (Fix 3).

1N(SETUP)c4(STAT)1(ON)

1N(SETUP)6(Fix)3N3(STAT)1(1-VAR)

0 = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 9 =

10=ce1=2=1=2=2=2=3=

4 = 2 = 1 =

A 3 11(STAT/DIST)5(Distr)4('t)=

11(STAT/DIST)5(Distr)1(P()G)=

Imiphumela: Ivariyethi eyenziwe yaba ngejwayelekile ('t): –0.762 P(t): 0.223

Izibalo ezinesisekelo sokubala esingu n (BASE-N)

Cindezela u N4(BASE-N) ukufaka imodi enesisekelo sokubala esingu n, uma ufuna ukwenza izibalo usebenzisa amanani angamadesimali, amahekzadesimali, aziqumbili, kanye/noma amaokthali. Imodi yezinombolo okuyiyona esethelwe ukusebenza uma ufaka imodi enesisekelo sokubala esingu n idesimali, okusho ukuthi okufakwayo kanye nemiphumela kusebenzisa isimo samadesimali. Cindezela enye yalezizinkinibho ukushintshashintsha amamodi ezinombolo: w(DEC) uma ufuna idesimali, 6(HEX) uma ufuna ihekzadesimali, l(BIN) uma ufuna uziqumbili, noma i(OCT) uma ufuna i-okthali.

Ukufaka imodi enesisekelo sokubala esingu n, shintshela kwimodi kaziqumbili, bese ubala u 112 + 12

N4(BASE-N)

P (t) Q (t) R (t)

0 t 0 t 0 t

P (t) Q (t) R (t)

0 t 0 t 0 t

55

STAT FIXSTAT FIX

STAT FIXSTAT FIX

STAT FIXSTAT FIX

ZU-31

l(BIN)

11 + 1 =

Ukuqhubeka kokungenhla, shintshela ku hekzadesimali modi bese ubala u 1F16 + 116

A6(HEX) 1 t(F)+ 1 =

Ukuqhubeka kokungenhla, shintshela ku okthali modi bese ubala u 78 + 18

Ai(OCT) 7 + 1 =

Qaphela: • Sebenzisa lezizinkinobho ezilandelayo ukufaka izinhlamvu A kuya ku F kumanani ayihekzadesimali: -(A), $(B), w(C), s(D), c(E), t(F). • Kwi Modi enesisekelo sokubala esingu n, amanani okufakiwe okuyiqhezu (desimali) kanye nomphindaphindi awavumelekile. Uma umphumela unengxenye eyiqhezu, iyalahlwa. • Uhla lokufakiwe nokungumphumela lusukela kumabhithi ayi 16 kumanani ayiziqumbili, kuya kumabhithi angama 32 kwezinye izinhlobo zamanani. Okulandelayo kubonisa imininingwane ngohla lokufakiwe nokungumphumela.

IModi enesisekelo sokubala esingu n

Uhla lokufakiwe/okungumphumela

Ziqumbili

Uphawu lokuhlanganisa: 0000000000000000 � x � 0111111111111111Uphawu lokususa: 1000000000000000 � x � 1111111111111111

Okthali

Uphawu lokuhlanganisa: 00000000000 � x � 17777777777Uphawu lokususa: 20000000000 � x � 37777777777

Idesimali –2147483648 � x � 2147483647

Hekzadesimali Uphawu lokuhlanganisa: 00000000 � x � 7FFFFFFFUphawu lokususa: 80000000 � x � FFFFFFFF

Ukuveza ngokucacile imodi yenombolo yenani elifakwayoUngafaka ikhomandi eyisipesheli ngokushesha emva kwenani ukuveza ngokucacile imodi yenombolo yalelonani. Amakhomandi ayisipesheli yilawa: d (desimali), h (hekzadesimali), b (ziqumbili), kanye no o (okthali).

Ukubala u 1010 + 1016 + 102 + 108 bese umphumela uvezwa njengedesimali.

Aw(DEC) 13(BASE)c1(d) 10 +

13(BASE)c2(h) 10 +

ZU-32

13(BASE)c3(b) 10 +

13(BASE)c4(o) 10 = 36

Ukushintshela umphumela wesibalo kolunye uhlobo lwenaniUngasebenzisa nanoma yimuphi kulaba abalandelayo ukushintsha umphumela oveziwe, ube olunye uhlobo lwenani: x(DEC) (desimali), 6(HEX) (hekzadesimali), l(BIN) (ziqumbili), i(OCT) (okthali).

Ukubala u 1510 × 3710 kwidesimali modi, bese umphumela uwushintshela kwi hekzadesimali modi, imodi yoziqumbili, kanye ne okthali modi.

Ax(DEC) 15 * 37 = 555 6(HEX) 0000022B l(BIN) 0000001000101011 i(OCT) 00000001053

Ukubala okunelojiki nokunokususaIsibali sakho sikunikeza izinsizakubala ezinelojiki (and, or, xor, xnor) kanye namafanshini (Not, Neg) okwenza ukubala okunokususa kanye nelojiki kumanani aziqumbili. Sebenzisa imenu evela uma ucindezela u 13(BASE) ukufaka lezizinsizakubala ezinelojiki kanye namafanshini.

Zonke izibonelo ezilandelayo zenziwa kwimodi kaziqumbili (l(BIN)).

Ukuthola ilojikali AND ka 10102 no 11002 (10102 and 11002)

A 1010 13(BASE)1(and) 1100 = 0000000000001000

Ukuthola ilojikali OR ka 10112 no 110102 (10112 or 110102)

A 1011 13(BASE)2(or) 11010 = 0000000000011011

Ukuthola ilojikali XOR ka ka 10102 no 11002 (10102 xor 11002)

A 1010 13(BASE)3(xor) 1100 = 0000000000000110

Ukuthola ilojikali XNOR ka 11112 no 1012 (11112 xnor 1012)

A 1111 13(BASE)4(xnor) 101 = 1111111111110101

Ukuthola ibhithwayzi khomplimenti ka 10102 (Not(10102))

A13(BASE)5(Not) 1010 )= 1111111111110101

Ukususa (thatha ikhomplimenti yokubili) ka 1011012 (Neg(1011012))

A13(BASE)6(Neg) 101101 )= 1111111111010011

Qaphela: Esimweni lapho inani likaziqumbili, u-okthali, noma ihekzadesimali, linophawu lokususa, isibali sishintshela inani ku ziqumbili, sithathe ikhomplimenti yokubili, bese sishintshela emuva kwisisekelo sokubala sasekuqaleni. Kumanani angamadesimali (Isisekelo sokubala -10), isibali singafaka kuphela uphawu lokususa.

ZU-33

Ukubalwa kwezibalo ezilingana nezinye (EQN)

Ungasebenzisa lenqubo elandelayo kwi -EQN modi ukuxazulula izibalo eziwumugqa, ezilingana nezinye ngasikhathi sinye, ezinabaguquguqukayo ababili noma abathathu, izibalo ezilingana nezinye ezikhwadrathikhi, kanye nezibalo ezilingana nezinye ezikhubhikhi.

1. Cindezela N5(EQN) ukufaka i-EQN Modi2. Kwimenu ezovela, khetha uhlobo lwesibalo esilingana nesinye.

Ukukhetha loluhlobo lokubala: Cindezela lenkinobho:

Izibalo eziwumugqa, ezilingana nezinye ezixazululwa ngasikhathi sinye, ezinabaguquguqukayo ababili

1(anX + bnY = cn)

Izibalo eziwumugqa, ezilingana nezinye ezixazululwa ngasikhathi sinye, ezinabaguquguqukayo abathathu

2(anX + bnY + cnZ = dn)

Izibalo ezilingana nezinye ezikhwadrathikhi 3(aX2 + bX + c = 0)

Izibalo ezilingana nezinye ezikhubhikhi 4(aX3 + bX2 + cX + d = 0)

3. Sebenzisa i-editha yekho-efishiyenti evelayo ukufaka amanani ekho-efishiyenti. • Ukuxazulula u 2x2 + x – 3 = 0, cindezela u 3 iesinyathelweni sesi 2,

bese ufaka okulandelayo endaweni yamakho-efishiyenti (a = 2, b = 1, c = –3): 2=1=-3=.

• Ukushintsha inani lekho-efishiyenti osuvele ulifakile, yisa inkomba kwiseli efanelekile, faka inani elisha, bese ucindezela u =.

• Ukucindezela u A kuzosula wonke amakho-efishiyenti kuye eqandeni.

Kubalulekile: Lokhu okulandelayo akusebenzelani nekho-efishiyenti editha: m, 1m(M–), 1t(STO). Pol, Rec, futhi nezitatimende eziningiazifakeki ngekho-efishiyenti editha.

4. Uma onke amanani eseyileyondlela oyifunayo, cindezela u =.• Lokhu kuzoveza isixazululo (umphumela). Ngakunye ukucindezelwa

kuka = kuzoveza esinye isixazululo. Ukucindezela u = ngesikhathi kusavele isixazululo sokugcina, kukubuyisela kukho-efishiyenti editha.

• Ungagcogcoma phakathi kwezixazululo usebenzisa lezizinkinobho, c no f.

• Ukubuyela kwikho-efishiyenti editha ngesikhathi kusavezwe nanoma yisiphi isixazululo, cindezela u A.

Qaphela: • Nanoma ngabekukhethwe umboniso wemvelo, izixazululo zezibalo eziwumugqa, ezilingana nezinye ngasikhathi sinye azivezwa kusetshenziswa nanoma yisiphi isimo esinalokhu '. • Amanani awakwazi ukushintshelwa kumbhalo wobunjiniyela esibukweni sesixazululo. • Umyalezo uyavela ukukwazisa uma singekho isixazululo noma uma kunezixazululo ezingagcini. Ukucindezela u A noma u = kuzobuyisela kwikho-efishiyenti editha.

ZU-34

Ukushintsha ukuhlelwa kohlobo lwesibalo esilingana nesinye kwangalesosikhathiCindezela u N5(EQN), bese ukhetha uhlobo lwesibalo esilingana nesinye kwimenu evelayo. Ukushintsha uhlobo lwesibalo esilingana nesinye kwenza ukuthi amanani awowonke amakho-efishiyenti ekho-efishiyenti editha ashintshe abe iqanda.

Izibonelo zezibalo ku EQN Modi

x + 2y = 3, 2x + 3y = 4

N5(EQN)1(anX + bnY = cn)

1 = 2 = 3 =

2 = 3 = 4 =

= (X=) –1 c (Y=) 2

x – y + z = 2, x + y – z = 0, –x + y + z = 4

N5(EQN)2(anX + bnY + cnZ = dn)

1 =- 1 = 1 = 2 =

1 = 1 =- 1 =0 =

- 1 = 1 = 1 = 4 =

= (X=) 1 c (Y=) 2 c (Z=) 3

2x2 – 3x – 6 = 0 B

N5(EQN)3(aX2 + bX + c = 0)

2 =- 3 =- 6 == (X1=) 3 + 574

c (X2=) 43 – 57

c (X-Value Minimum=)* 34

c (Y-Value Minimum=)* 578

–

* Inani eliphansi livezwa uma u a � 0. Inani eliphezulu livezwa uma u a � 0.

x2 – 2'2x + 2 = 0 B

N5(EQN)3(aX2 + bX + c = 0)

1 =- 2 ! 2 )= 2 == (X=) '2

x3 – 2x2 – x + 2 = 0

N5(EQN)4(aX3 + bX2 + cX + d = 0)

1 =- 2 =- 1 = 2 == (X1=) –1 c (X2=) 2 c (X3=) 1

MathMath

MathMath

ZU-35

Izibalo zeMetriksi (MATRIX)Sebenzisa iMetriksi Modi ukwenza izibalo ezimbandakanya amametriksi afika emigqeni emi 3 namakholamu ama 3. Ukwenza isibalo sematrixi, uqala ngokunikeza imininingwane kwabaguquguqukayo abayisipesheli bemetriksi (MatA, MatB, MatC), ebese usebenzisa abaguquguqukayo esibalweni njengoba kukhonjisiwe esibonelweni ngezansi.

Ukunikeza 2 11 1

ku MatA no 2 –1–1 2

ku MatB, bese wenza lezibalo

ezilandelayo: ×2 11 1

2 –1–1 2

(MatA×MatB),

+2 11 1

2 –1–1 2

(MatA+MatB)

1. Cindezela u N6(MATRIX) ukufaka iMatrixi Modi.2. Cindezela u 1(MatA)5(2×2).

• Lokhu kuzoveza I Metriksi editha ukuze kufakwe amalungu ka 2×2 matrixi oyibalulele u MatA.

“A” umele “MatA”

3. Faka amalungu kaMatA: 2 = 1 = 1 = 1 =.4. Cindezela lezizinkinobho ezilandelayo: 14 (MATRIX)2 (Data) 2(MatB)5(2×2).• Lokhu kuzoveza I Matrixi editha ukuze kufakwe amalungu ka 2 × 2 matrixi

oyibalulele u MatB. 5. Faka amalungu ka MatB: 2 =- 1 =- 1 = 2 =.6. Cindezela u A, ukuqhubekela ebusweni bokubala, bese wenza isibalo

sokuqala (MatA×MatB): 14(MATRIX)3(MatA)*14(MATRIX) 4(MatB)=.• Lokhu kuzoveza ubuso be MatAns obunemiphumela.

“Ans” umele “MatAns”

Qaphela: “MatAns” umele “Matrix Answer memory”. Bheka u “IMemori yeMpendulo eyiMetriksi” ukuthola eminye imininingwane.

7. Yenza isibalo esilandelayo (MatA+MatB): A14(MATRIX)3(MatA)+14(MATRIX)4(MatB)=.

IMemori yeMpendulo eyiMetriksiNjalo uma umphumela wesibalo esenziwe kwi Matrixi modi uyi matrixi, ubuso be MatAns buzovela kanye nomphumela. Umphumela uzonikezwa oguquguqukayo u oqanjwe ngo “MatAns”.

11

MATMAT

→MATMAT

→MATMAT

→MATMAT

→MATMAT

ZU-36

Oguquguqukayo ka MatAns angasetshenziswa ezibalweni njengoba kuchazwe ngezansi.

• Ukufaka oguquguqukayo ka MatAns esibalweni, yenza lokhu okulandelayo: 14(MATRIX)6(MatAns).

• Ukucindezela nanoma iyiphi yalezizinkinobho ngesikhathi iskrini sika MatAns siveziwe kuzozishintshela ngokwako kuye kwiskrini sokubala: +, -, *, /, E, w, 1w(x3). Iskrini sokubala sizoveza oguquguqukayo weMatAns elandelwa insizakubala noma ifanshini yenkinobho oyicindezelile.

Ukunikeza Nokuhlela imininingwane yoguquguqukayo oyiMetriksiKubalulekile: Lokhu okulandelayo akusebenzelani ne Metrixi editha: m, 1m(M–), 1t(STO). Pol, Rec, nezitatimende eziningi nazo angeke zifakeke nge Metrixi editha.Ukunikeza imininingwane emisha koguquguqukayo oyimetrixi:1. Cindezela u 14(MATRIX)1(Dim), bese, kwimenu evelayo, ukhethe

oguquguqukayo oyimetrixi ofuna ukumhlela. 2. Kwimenu elandelayo evelayo khetha ubungako (m×n). 3. Sebenzisa imetrixi editha evelayo ukufaka amalungu emetriksi.

Ukufaka 1 0 –10 –1 1

ku MatC

14(MATRIX)

1(Dim)3(MatC)4(2×3)

1 = 0 =- 1 = 0 =- 1 = 1 =

Ukuhlela amlungu oguquguqukayo oyimetriksi:1. Cindezela u 14(MATRIX)2(Data), bese, kwimenu evelayo, ukhethe

oguquguqukayo oyimetrixi ofuna ukumhlela.2. Sebenzisa I metrixi editha evelayo ukuhlela amalungu emetrixi.

• Yisa inkomba kwiseli enelungu ofuna ukulishintsha, faka inani elisha, bese ucindezela u =.

Ukukopisha okuqukethwe oguquguqukayo oyimetriksi (noma MatAns):1. Sebenzisa I metrixi editha ukuveza imetriksi ofuna ukuyikopisha.

• Uma ukufan ukukopisha u MatA, yenza lokhu: 14 (MATRIX)2(Data)1(MatA).

• Uma ufuna ukukopisha okuqukethwe ngu MatAns, yenza lokhu ukuveza iskrini sika MatAns: A14(MATRIX)6(MatAns)=.

2. Cindezela u 1t(STO), bese wenza okukodwa kwalokhu okulandelayo, ukucacisa ukuthi ukopishela kuphi: - (MatA), $ (MatB), noma w(MatC). • Lokhu kuzoveza imetrixi editha kanye nokuqukethwe lapho kukopishelwa

khona.

Izibonelo zokubala imetriksi Lezibonelo ezilandelayo zisebenzisa u MatA = 2 1

1 1 no MatB = 2 –1–1 2

kusuka ku 1, kanye no MatC = 1 0 –10 –1 1 kusuka ku 2. Ungamfaka

oguquguqukayo oyimetrikisi ngokucindezela u 14(MATRIX) ebese ucindezela enye yalezizinkinobho zezinombolo: 3(MatA), 4(MatB), 5(MatC).

22MATMAT

ZU-37

3×MatA (Ukuphindaphinda kwemetriksi scala)

A 3 *MatA=

Thola idetheminenti ka MatA (det(MatA))

A14(MATRIX)7(det) MatA)= 1

Thola itranspozishini ka MatC (Trn(MatC))

A14(MATRIX)8(Trn) MatC)=

Thola imetrixi ehlanekezeliwe ka MatA (MatA–1).

Qaphela: Angeke ukwazi ukusebenzisa u 6 kulokhu. Sebenzisa lenkinobho E ukufaka u “ –1”.

AMatAE=

Thola inani langempela lalelo nalelo lungu lika MatB (Abs(MatB)).

A1w(Abs) MatB)=

Thola umphumela kamphindwa kanye nenombolo ephindwe kathathu ka MatA (MatA2, MatA3).

Qaphela: Angeke ukwazi ukusebenzisa u 6 kulokhu. Sebenzisa u w ukubalula umphumela kamphindwa, no ukubalula inombolo ephindwe kathathu 1w(x3).

AMatAw=

AMatA1w(x3)=

Thola u MatA= isimo somugqa oyi-ekheloni.

A!4(MATRIX)c1(Ref) MatA)=

Thola u MatA= isimo somugqa oyi-ekheloni encishisiwe.

A!4(MATRIX)c2(Rref) MatA)=

33

44

55

66

77

88

99

1010

ZU-38

Ukwakha iThebula Lezinombolo lisuselwa kumafanshini amabili (TABLE)

U TABLE wakha itafula lezinombolo elisusela kwifanshini eyodwa kumbe amabili. Ungasebenzisa I fanshin f(x) noma amafanshini amabili u f(x) no g(x). Bheka isihlokwana “Ukulungisa, ucuphe isethaphu yesibali” ukuthola eminye imininingwane.Thatha lezinyathelo ezilandelayo ukwakha itafula lezinombolo:

1. Cindezela u N7(TABLE) ukufaka u TABLE Modi.2. Sebenzisa oguquguqukayo u X uklufaka amafanshini amabili, eyodwa

esimweni esingu f(x) enye esimweni esingu g(x).• Yiba nesiqiniseko sokuthi ufaka oguquguqukayo u X (S)(X)) uma

wakha itafula lezinombolo. Omunye oguquguqukayo, ngaphandle kwa X uthathwa njengokungaguqukiyo.

• Uma usebenzisa ifanshini eyodwa, faka ifanshini eyisimo sika f(x) kuphela.

• U Pol, Rec, ∫, d/dx, Σ abafakeki kwifanshini.3. Ukuphendula izinkomba ezivelayo, faka amanani ofuna ukuwasebenzisa

ngokucindezela = njalo emva kwaleyo nayileyo.

Uma kunalenkomba: Faka lokhu:

Start? Faka umkhawulo ophansi ka X (i-opshini esethwe phambilini =1).

End? Faka umkhawulo ophezulu ka X (i-opshini esethwe phambilini =5). Qaphela: Qiniseka ukuthi inani lokuGcina njalo lihlala lilikhulu kunenani lokuqala.

Step? Faka isinyathelo sokwenyuka (i-opshini esethwe phambilini =1). Qaphela: Isinyathelo sicacisa ukuthi inani lokuqala lizokwenyuswa kanjani ngokulandelana ngesikhathi itafula lezinombolo lakheka. Uma ubalula u Start =1, no Step =1, u X uzonikezwa lamanani ngokulandelana 1, 2, 3, 4, kuqhubeka, ukwakha itafula lezinombolo kuze kufike enanini lokugcina.

• Ukufaka inani lesinyathelo bese ucindezela = kwacha futhi kuveze itafula lezinombolo ngokwemigomo oyibalulile.

• Ukucindezela u A ngesikhathi kusavele iskrini setafula lezinombolo, kuzokubuyisela kwiskrini sokufaka ifanshini esinyathelweni sesi 2.

Ukwakha ithebula lezinombolo lalamafanshini f(x) = x2 + 21 no g(x)

= x2 − 21 anohla –1 � x � 1, likhushulwa ngezinyathelu ezingu 0.5

B

N7(TABLE)

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ZU-39

1N(SETUP)c5(TABLE)2(f(x),g(x))

S)(X)x+ 1 ' 2

=

• Ukucindezela u = ngaphandle kokufaka lutho lwa g(x) kuzokwakha itafula lezinombolo kusetshenziswa u f(x) kuphela.

S)(X)x- 1 ' 2

=-1 =1 =0.5 =

Qaphela: • Inombolo ephezulu yemigqa kwi tafula lezinombolo elakhekile incika ku setup menu ukusetha itafula. Uhlelo luka “f(x)” lusebenzisa kufinyelele emigqeni engama 30, kanti oluka “f(x),g(x)” lusebenzisa kufinyelele emigqeni engama 20. • Ungasisebenzisa iskrini setafula lezinombolo ukubona amanani kuphela. Okuqukethwe ku Table akushintsheki. • Uhlelo lokwakha itafula lezinombolo lwenza ukuba okuqukethwe oguquguqukayo u X kushintshe. Kubalulekile: Ifanshini oyifakela ukwakha itafula lezinombolo iyacisheka njalo uma uveza isetup menu ku TABLE Modi bese ushintsha phakathi kombukiso wemvelo nowomugqa.

Izibalo zamavektha (VECTOR)Sebenzisa IVEKTHA Modi ukwenza izibalo zamavektha ezingu 2-D no 3-D. Ukwenza isibalo samavektha, udinga kuqala ukunikezaimininingwane kwabaguquguqukayo bamavektha abayisipesheli (VctA, VctB, VctC), bese usebenzisa abguquguqukayo esibalweni njengoba kukhonjisiwe ezibonelweni ngezansi.

Ukunikeza (1, 2) ku VctA no (3, 4) ku VctB, bese wenza lesisibalo: (1, 2)+(3, 4)

1. Cindezela u N8(VECTOR) ukufaka iVEKTHA Modi.2. Cindezela u 1(VctA)2(2).

• Lokhu kuzoveza iVektha Editha ukuze kufakwe ivektha engu 2-D ka VctA.

“A” umele “VctA”

3. Faka amalungu ka VctA: 1 = 2 =.4. Yenza lokhu: 15(VECTOR)2(Data)2(VctB)2(2).

• Lokhu kuzoveza iVektha Editha ukuze kufakwe ivektha engu 2-D ka VctB.

5. Faka amalungu ka VctB: 3 = 4 =.

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11

VCTVCT

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6. Cindezela u A ukudlulela kwisibonisi sokubala, bese ubala (VctA +VctB): 15(VECTOR)3(VctA)+15(VECTOR)4(VctB)=.• Lokhu kuzoveza isiboniso sokubala siks VctAns kanye nemiphumela.

“Ans” umele “VctAns”.

Qaphela: “VctAns” umele “Vector Answer Memory”. Bheka “Imemori Yezimpendulo zamaVektha” ukutholwa ulwazi oluthe xaxa.

Imemori Yezimpendulo zamaVekthaNjalo nje uma isibalo esenziwe kwiVektha modi siyivektha, isibonisi seVctAns sizovela kanye nomphumela. Umphumela uzonikwa oguquguqukayo obizwa ngo “VctAns”.

Oguquguqukayo ka VctAns angasetshenziswa ezibalweni njengoba kuchaziwe ngezansi.• Ukufaka oguquguqukayo ka VctAns esibalweni, enza lokhu okulandelay: 15(VECTOR)6(VctAns).

• Ukucindezela enye yalezizinkinobho, ngenkathi isibonisi sikaVctAns sisaveziwe, kuzokwenza ukuthi kubuye isibonisi sokubala: +, -, *, /. Isibonisi sokubala sizokhombisa oguquguqukayo ka VctAns elandelwa insizakubala yenkinobhooyicindezelile.

Ukunikeza noku-editha imininingwane Oguquguqukayo oyiVekthaKubalulekile: Lokhu okulandelayo akusebenzelani ne Vektha Editha: m, 1m(M–), 1t(STO). Pol, Rec, futhi izitatimende eziningi nazo azikwazi ukufakeka ngeVektha Editha.Ukunikeza imininingwane emisha koguquguqukayo oyiVektha:1. Cindezela u 15(VECTOR)1(Dim), bese, kwimenu evelayo, ukhethe

oguquguqukayo oyiVektha ofuna ukumnikeza imininingwane. 2. Kwimenu elandelayo ukuvela, khetha ubungako (m). 3. Sebenzisa iVektha Editha evelayo ukufaka amalungu evektha.

Ukunikezela u (2, −1, 2) ku VctC

15(VECTOR)1(Dim)3(VctC)1(3)

2 =- 1 = 2 =

Uku-editha amalungu oguquguqukayo oyivektha:1. Cindezela u 15(VECTOR)2(Data), ebese, kwimenu evelayo, khetha

oguquguqukayo oyiVektha ofuna ukumeditha. 2. Sebenzisa iVektha Editha evelayo uku-editha amalungu evektha.

• Hambisa inkomba iye kwiseli enelungu ofuna ukulishintsha, faka inani Elisha, bese ucindezela =.

Ukukopisha okuqukethwe oguquguqukayo oyivektha (VctAns): 1. Sebenzisa iVektha Editha ukuveza ivektha ofuna ukulikopisha.

• Uma ufuna ukukopisha u VctA, yenza lokhu okulandelayo: 15(VECTOR)2(Data)1(VctA).

→VCTVCT

→VCTVCT

22VCTVCT

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• Uma ufuna ukukopisha okuqukethwe ku VctAns, yenza lokhu ukuveza isibonisi sika VctAns: A15(VECTOR)6(VctAns)=.

2. Cindezela u 1t(STO), bese wenze okukodwa kwalokhu okulandelayo ukubalula lapho kukopishelwa khona: - (VctA), $ (VctB), noma w(VctC).• Lokhu kuzoveza iVektha Editha kanye nokuqukethwe lapho kukopishelwa

khona.

Izibonela zezibalo zama VekthaLezizibonelo ezilandelayo zisebenzisa u VctA = (1, 2) no VctB = (3, 4) kusuka

ku 1, no VctC = (2, –1, 2) kusuka ku 2. Ungamufaka oguqugukayo

wevktha ngokucindezela u 15 (VECTOR) bese ucindezela enye

yalezizinkinobho zezinombolo:3(VctA), 4(VctB), 5(VctC).

3 × VctA (ukuphindaphinda okuyiskala kweVektha), 3 × VctA – VctB (isibonelo sokubala usebenzisa u VctAns)

A 3 *VctA=

-VctB=

VctA • VctB (Umphumela wokuphindaphinda ngecashaza iVektha)

AVctA15(VECTOR)7(Dot)VctB=

VctA × VctB (Umphumela wokuphindaphinda ngesiphambano ivektha)

AVctA*VctB=

Thola amanani angempela ka VctC.

A1w(Abs)VctC)=

Thola i-engela eyakhiwa ngu VctA kanye no VctB, usondezele kumadijithi amathathu ngemuva kwekhoma (Fix 3). v

(cos � = (A • B)�A��B�

, oba ngu � = cos–1 (A • B)�A��B�

)

1N(SETUP)6(Fix)3

A(VctA15(VECTOR)7(Dot)VctB)/

33

VCTVCT

VCTVCT

44VCTVCT

55

VCTVCT

66VCTVCT

77

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(1w(Abs)VctA)1w(Abs)

VctB))=

1c(cos–1)G)=

Izibalo zokwaba (DIST)Ungasebenzisa inqubo engezansi ukwenza izinhlobo eziyisikhombisa ezahlukene zezibalo zokwahlukanisa.

1. Cindezela Nc1(DIST) ukufaka I DIST Modi.2. Kwimenu evelayo, khetha uhlobo lwesibalo sokwaba.

Ukukhetha loluhlobo lwesibalo: Cindezela lenkinobho:

Ukuminyana okujwayelekile kokungenzeka 1(Normal PD)

Ukwaba okwejwayelekile okukhumulathivu 2(Normal CD)

Ukwaba okwejwayelekile okukhumulathivu okuhlanezelwe

3(Inverse Normal)

Okungenzeka okubhayinomiyali 4(Binomial PD)

Ukwaba okukhumulathivu okubhayinomiyali c1(Binomial CD)

Okungenzeka kuka Poisson c2(Poisson PD)

Ukwaba okukhumulathivu kuka Poisson c3(Poisson CD)

3. Faka amanani abaguquguqukayo• Nge Binomial PD, Binomial CD, Poisson PD, no Poisson CD ungafaka

isampula yemininingwane bese wenza isibalo.4. Emva kokufaka amanani abo bonke abaguquguqukayo, cindezela u =.• Lokhu kuveza imiphumela.• Ukucindezela u = noma u A ngesikhathi umphumela usaveziwe,

kuzobuyisela kwisibonisi sokufaka soguquguqukayo wokuqala.Qaphela: • Ukushintsha uhlobo lwesibalo sokwaba emva kokufaka I DIST Modi, cindezela u !1(STAT/DIST)1(Type) bese ukhetha uhlobo olufunayo. • Ukucophelela ezibalweni zokwaba kugcina kumadijithi amahlanu abalulekile.

Abaguquguqukayo abamukela okufakwayoLaba abalandelayo bangabaguquguqukayo bezibalo zokwaba abemukela amanani afakwayo.Normal PD ........................... x, σ, �Normal CD ........................... Lower, Upper, σ, �Inverse Normal .................... Area, σ, � (Ukuhlela uTail njalo kuyasala.)Binomial PD, Binomial CD ... x (noma List), N, pPoisson PD, Poisson CD ..... x (noma List), �x: imininingwane, σ: ukwahluka kokumisiwe (σ � 0), �: Isilinganiso esiphakathi nendawo, Lower: umncele ophansi, Upper: umncele ophezulu, Tail: incasiselo yobungako bokungenzeka enemininingwane ka Tail, Area: ubungako

VCT FIXVCT FIX

VCT FIXVCT FIX

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bokungenzeka (0 � Area � 1), List: isampula lohla lwemininingwane, N: Inombolo yemizamo, p: impumelelo yokungenzeka (0 � p � 1)

Isibonisi Sohla (Binomial PD, Binomial CD, Poisson PD, Poisson CD)Nge Binomial PD, Binomial CD, Poisson PD ne Poisson CD, sebenzisa isibonisi sohla ukufaka imininingwane eysampula. Ungafaka kuye kuma 25 amasampula emininingwane oguquguqukayo ngamunye. Imiphumela nayo ivezwa kwisibonisi sohla.

Uhlobo lwesibalo sokwaba

Inani lapho kumi khona inkomba

X: Imininingwane eyisampula

Ans: Imiphumela

Ukulungisa imininingwane eyisampula: Yisa inkomba kwiseli enemininingwane ofuna ukuyilungisa, Faka imininingwane eysampula emisha, bese ucindezela u =.Ukusula imininingwane eyisampula: Hambisa inkomba iye kuleyomininingwane eyisampula ofuna ukuyisul bese ucindezela u D.Ukufaka imininingwane eyisampula: Hambisa inkomba iye lapho ufuna ukufaka khona imininingwane eyisampula, cindezela !1(STAT/DIST)2(Edit)1(Ins), bese ufaka imininingwane eyisampula.Ukusula yonke imininingwane eyisampula: Cindezela !1(STAT/DIST)2(Edit)2(Del-A).

Izibonelo zezibalo ku DIST Modi

Ukubala iprobhabhilithi densithi eyejwayelekile uma x = 36, σ = 2, � =35

Nc1(DIST)

1(Normal PD)

36 =

2 =

35 =

Umphumela: 0.1760326634

• Ukucindezela = noma A kubuyisela kwisibonisi sokufaka u x.

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Ukubala ibinomiyali probhabhilithi yemininingwane eyisampula {10, 11, 12, 13, 14} uma N=15 no p=0.6

Nc1(DIST)4(Binomial PD)

Iveza isibonisi sohla 1(List)

• Ukubalula imininingwane usebenzisa isimo sampharametha, cindezela 2(Var).

10 = 11 = 12 = 13 = 14 =

=

15 =

0.6 =

ecccc

Imiphumela: x = Okungenzeka okuyibhayinomiyali kwe 10 � 0.18594 x = Okungenzeka okuyibhayinomiyali kwe 11 � 0.12678 x = Okungenzeka okuyibhayinomiyali kwe 12 � 0.063388 x = Okungenzeka okuyibhayinomiyali kwe 13 � 0.021942 x = Okungenzeka okuyibhayinomiyali kwe 14 � 4.7018 × 10−3

• Ukucindezela = kubuyisela kwisibonisi sokufaka u N. Ukucindezela A kubuyisela kwisibonisi sohla (Amasampula emininingwane efakiwe ayagcinwa).

Qaphela: • Lokhu okulandelayo angeke kwasetshenziswa ezibalweni zokwaba: Pol, Rec, ∫, d/dx. • Uma imininingwane ibaluliwe kusetshenziswa isimo sepharametha, imiphumela iyagcinwa kwi Ans memori. • Umyalezo wephutha uyavela uma inani elifakiwe lingaphandle kohlu oluvumelekile. “ERROR” uzovela ku Ans kholomu yesibonisi sohla uma inani elifakiwe lingaphandle kohlu oluvumelekile.

ZU-45

Abangaguquki besayensiIsibali sakho siza nabangama 40 abangaguquki besayensi abakhelwe ngaphakathi, abangasetshenziswa kunannoma iyiphi imodi ngaphandle kwa BASE-N. Ngamunye ongaguquki wesayensi uvezwa njengophawu olwahlukile (njengo π), olungasetshenziswa ngaphakathi ezibalweni.Ukufaka ongaguquki wesayensi esibalweni, cindezela 17(CONST) bese ufaka inombolo enamadijithi amabili ehambisana nalowo ongaguqukiyo omfunayo.

Ukufaka ongaguquki wesayensi C0 (ijubane lokukhanya kwivakhumu), bese uveza inani

A17(CONST)

28(C0)=

Ukubala C0 = 1ε0μ0

B

A' 1 c!17(CONST)32(ε0)

17(CONST)33(�0)=

Okulandelayo kukhombisa izinombolo ezinamadijithi amabili zalowo nalowo ongaguquki wesayensi.

01: (mp) ingqumbi yeprothoni 02: (mn) ingqumbi yenyuthroni

03: (me) ingqumbi ye elekthroni 04: (m�) ingqumbi yemuyoni

05: (a0) ingxenye yenkabamudwa ka Bohr

06: (h) okungaguquki kuka Planck

07: (�N) imagnethon yenuzi 08: (�B) imagnethoni ka Bohr

09: (h) okungaguquki kuka Planck, okwenziwe kwezwakala.

10: (α) okungaguquki kwesakhiwo esihle

11: (re) ingxenye yenkabamudwa ye elekthroni eklasiki

12: (λc) amaza kaCompton

13: (γp) ireyishiyo ejayiromaginethikhi yeprothoni

14: (λcp) amaza eprothoni ka Compton

15: (λcn) amaza enyuthroni ka Compton

16: (R∞) okungaguquki kuka Rydberg

17: (u) okungaguquki kwesisindo se-athomu

18: (�p) umzuzu wobuzibuthe kwi prothoni

19: (�e) umzuzu wobuzibuthe kwi elekthroni

20: (�n) umzuzu wobuzibuthe kwi nyuthroni

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21: (��) umzuzu wobuzibuthe kwi muyoni

22: (F) okungaguquki kuka Faraday

23: (e) ishaji engumsuka24: (NA) okungaguquki kuka Avogadro

25: (k) okungaguquki kuka Boltzmann

26: (Vm) umthamo wemola yagesi ofanele (273.15K, 100kPa)

27: (R) okungaguquki kwe mola yegesi

28: (C0) isivinini sokukhanya lapho amagesi engekho khona

29: (C1) okungaguquki kwe radiyeshini yokuqala

30: (C2) okungaguquki kwe radiyeshini yesibili

31: (σ) okungaguquki kuka Stefan- Boltzmann

32: (ε0) okungaguquki kwa elektriki

33: (�0) okungaguquki kokusazibuthe

34: (φ0) ikhwantumu yamandla enkundla yobuzibuthe

35: (g) ukusheshisa okungumgomo kwe gravithi

36: (G0) ikhwantumu yesilinganiso sokudlulisa umbani

37: (Z0) umumo we-impendensi yalapho amagesi engekho khona

38: (t) Celsius izinga lokushisa

39: (G) okungaguquki kwegravitheshini kuka Newton

40: (atm) itmosfera engumgomo

Amanani ancikiswe kumanani njengokwezincomo ze CODATA (2010).

Ukushintsha kweMetrikhiAmakhomandi okushintsha kwemetrikhi enza kube lula ukushintsha amanani ukusuka kwesinye isilinganisi kuya kwesinye. Ungasebenzisa amakhomandi okushintsha kwemetrikhi kunanoma iyiphi imodi yokubala, ngaphandle kwa BASE-N no TABLE. Ukufaka imakhomandi yokushintsha kwemetrikhi esibalweni, cindezela 18(CONV), bese ufaka inombolo enamadijithi amabili ehambisana nekhomandi oyifunayo.

Ukushintsha u 5cm abe ngama intshi b

A 5 18(CONV)

02(cm'in)=

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Ukushintsha u 100g abe ngama ounce b

A 100 18(CONV)22(g'oz)=

Ukushintsha –31°C abe ama Fahrenheit b

A- 31 18(CONV)38(°C'°F)=

Lokhu okulandelayo kubonisa izinombolo ezinamadijithi amabili zaleyo naleyo khomandi yokushintsha kwemetrikhi.

01: in ' cm 02: cm ' in 03: ft ' m 04: m ' ft

05: yd ' m 06: m ' yd 07: mile ' km 08: km ' mile

09: n mile ' m 10: m ' n mile 11: acre ' m2 12: m2 ' acre

13: gal (US) 'R 14: R' gal (US) 15: gal (UK) 'R 16: R' gal (UK)

17: pc ' km 18: km ' pc 19: km/h ' m/s 20: m/s ' km/h

21: oz ' g 22: g ' oz 23: lb ' kg 24: kg ' lb

25: atm ' Pa 26: Pa ' atm 27: mmHg ' Pa 28: Pa ' mmHg

29: hp ' kW 30: kW ' hp 31: kgf/cm2 ' Pa 32: Pa ' kgf/cm2

33: kgf • m ' J 34: J ' kgf • m 35: lbf/in2 ' kPa 36: kPa ' lbf/in2

37: °F ' °C 38: °C ' °F 39: J ' cal 40: cal ' J

Imininingwane yefomula yokushintsha incikiswe kwi “NIST Special Publication 811 (2008)”.Qaphela: I J'cal khomandi ishintsha amanani asezingeni lokushisa elingu 15°C.

Uhlu lokuBala, INombolo yamaDijithi, kanye nokuCophelela

Uhlu lokubala, inombolo yamadijithi asetshenzisiwe ekubaleni kwangaphakathi, nokucophelela kokubala kuncibe ohlotsheni lwesibalo osenzayo.

Uhla Lokubala nokuCophelelaUhla lokubala ±1 × 10–99 kuya ku ±9.999999999 × 1099 noma 0

Inombolo yamadijithi okubala ngaphakathi

15 amadijithi

Ukucophelela Ngokujwayelekile, ±1 kwidijithi ye 10 esibalweni esisodwa. Ukucophelela embukisweni ongumphindwa kungu ±1 kwidijithi encane kunawowonke abalulekile. Amaphutha ayanda ezibalweni ezilandelanayo.

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Izibalo zamafanshini, Uhlu lokufakiwe, nokuCophelela

Ifanshini Uhlu olufakwayo

sinx

DEG 0 � |x| � 9 × 109

RAD 0 � |x| � 157079632.7

GRA 0 � |x| � 1 × 1010

cosx

DEG 0 � |x| � 9 × 109

RAD 0 � |x| � 157079632.7

GRA 0 � |x| � 1 × 1010

tanx

DEG Kuyafana naku sinx, ngaphandle uma |x| = (2n–1) × 90.

RAD Kuyafana naku sinx, ngaphandle uma |x| = (2n–1) × π/2.

GRA Kuyafana naku sinx, ngaphandle uma, ngaphandle uma |x| = (2n–1) × 100.

sin–1x0 � |x| � 1

cos–1x

tan–1x 0 � |x| � 9.999999999 × 1099

sinhx0 � |x| � 230.2585092

coshxsinh–1x 0 � |x| � 4.999999999 × 1099

cosh–1x 1 � x � 4.999999999 × 1099

tanhx 0 � |x| � 9.999999999 × 1099

tanh–1x 0 � |x| � 9.999999999 × 10–1

logx/lnx 0 � x � 9.999999999 × 1099

10x –9.999999999 × 1099 � x � 99.99999999

ex –9.999999999 × 1099 � x � 230.2585092

'x 0 � x � 1 × 10100

x2 |x| � 1 × 1050

x –1 |x| � 1 × 10100 ; x ≠ 03'x |x| � 1 × 10100

x! 0 � x � 69 (x − uyinombolo ephelele)

nPr0 � n � 1 × 1010, 0 � r � n (n, r bayizinombolo eziphelele)1 � {n!/(n–r)!} � 1 × 10100

nCr0 � n � 1 × 1010, 0 � r � n (n, r bayizinombolo eziphelele)1 � n!/r! � 1 × 10100 noma 1 � n!/(n–r)! � 1 × 10100

Pol(x, y)|x|, |y| � 9.999999999 × 1099

x2 + y2 � 9.999999999 × 1099

Rec(r, �)0 � r � 9.999999999 × 1099

�: Uyefana no sinx

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°’ ”|a|, b, c � 1 × 10100 ; 0 � b, cInani lemizuzwana linephutha elingu ±1 kwidijithi yesibili emva kwecashazi leqhezu lokweshumi.

|x| � 1 × 10100

Iqhezu lokubalwa ngokweshumi ↔ amakhonveshini esexagesimali0°0´0˝ � |x| � 9999999°59´59˝

xy

x � 0: –1 × 10100 � ylogx � 100x = 0: y � 0x � 0: y = n,

m2n+1 (m no n bayizinombolo eziphelele)

Uma u x eyinombolo eyindida: |y| � 1 × 1010 (u - y uyinombolo ephelele)Kodwa-ke: –1 × 10100 � ylog |x| � 100

x'y

y � 0: x ≠ 0, –1 × 10100 � 1/x logy � 100y = 0: x � 0y � 0: x = 2n+1, 2n+1

m (m ≠ 0; m, n bayizinombolo

eziphelele )Kodwa-ke: –1 × 10100 � 1/x log |y| � 100

a b/c

Isamba senombolo ephelele, inombolo engenhla eqhezwini, nenombolo engezansi eqhezwini kumele sibe amdijithi ali 10 noma ngaphansi (kubandakanya nezimpawu zokuhlukanisa)

RanInt#(a, b) a � b; |a|, |b| � 1 × 1010; b – a � 1 × 1010

• Ukucophelela kuyefana nalokho okuchazwe ngenhla ku “Uhla Lokubala nokuCophelela”.

• Amafanshini aloluhlobo xy, x'y , 3' , x!, nPr, nCr adinga ukubala

kwangaphakathi okulandelanayo, okungenza ukuthi amaphutha enzeka esibalweni ngasinye anqwabelane.

• Amaphutha ayanqwabelana bese eba into enkulu endaweni lapho kwenzeka khona i-inflekshini.

• Uhlu lwemiphumela yokubala engavezwa ngesimo sika π fuma usebsnzisa umbukiso wemvelo yilolu |x| � 106. Qaphela, nokho, ukuthi iphutha elenzeka kubalwa ngaphakathi lingenza ingaveli eminye imiphumela ngesimo sika π. Lingenza futhi ukuthi imiphumela yokubala okufanele ivele iyisakhiwo seqhezu lokweshumi, ibe isimo sika π.

AmaphuthaIsibali sizoveza umyalezo okhombisa ukuthi kunephutha njalo nje uma kwenzeka iphutha ngesikhathi kubalwa. Zimbili izindlela zokususa lomyalezo: Cindezela u d noma u e ukuveza lapho iphutha lenzeke khona, noma cindezela u A ukucisha umyalezo nesibalo.

Ukuveza indawo lapho iphutha lenzeke khonaNgalesisikhathi umyalezo okhombisa ukuthi kunephutha usaveziwe, cindezela u d noma u e ukubuyela kwiskrini sokubala. Inkomba izobe ikhombe endaweni lapho iphutha lenzeke khona, ilindele imininingwane efakwayo. Lungisa ngokufanele esibalweni, usenze futhi.

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Uma ufaka u 14 ÷ 0 × 2 = ngephutha esikhundleni sika14 ÷ 10 × 2 = B

14 / 0 * 2 =

e (noma d)

d 1 =

Ukucisha umyalezo obika iphutha Ngesikhathi omyalezo obika iphutha usaveziwe, cindezela u A ukubuyela kwiskrini sokubala. Qaphela ukuthi lokhu kucisha futhi isibalo leso esinephutha.

Imiyalezo yephutha

Iphutha lezibalo (Math ERROR)Imbangela: • Umphumela omaphakathi kumbe owokugcina esibalweni osenzayo udlula uhla lokubala oluwamukelekile. • Imininingwane oyifakile ungaphezulu kohlu olwamukelekile (ikakhulukazi uma usebenzisa amfanshini). • Isibalo osenzayo sinohlelo lokubala olungengo emthethweni (njengokuhlukanisa ngeqanda).Isinyathelo: • Hlola amanani okufakiwe, nciphisa inani lamadijithi, bese uzama futhi. • Uma usebenzisa imemori ezimele noma oguquguqukayo njenge agumenti yefanshini, qinisekisa ukuthi imemori noma inani loguquguqukayo lingena ngaphansi kohlu lwe fanshini.

Iphutha lestaki (Stack ERROR)Imbangela: • Isibalo osenzayo sense ukuba umthamo westaki sezinombolo noma istaki somyalo seqeke. • Isibalo osenzayo sesenze umthamo wemethriksi noma istaki sevektha seqeke.Isinyathelo: • Yenzalula isimeli sokubala ukuze singadluli umthamo wesitaki. • Zama ukwahlukanisa isibalo izingxenye ezimbili noma ngaphezulu.

Iphutha lesintaksi (Syntax ERROR)Imbangela: Kunenkinga ngendlela okumiswe ngayo isibalo osenzayo.Isinyathelo: Yenza izilungiso ezifaneleyo.

Iphutha le-Agumenti (Argument ERROR)Imbangela: Kufakwe i-agumenti engeyona inombolo ephelele kwifanshini yenombolo evela kwisikhwensi engenalo iphethini.Isinyathelo: Faka kuphela izinombolo eziphelele kwi-agumenti.

Iphutha lobungako (Dimension ERROR) (KumaModi e Matriksi neVektha kuphela) Imbangela: • Imatr iksi noma ivektha ozama ukuyisebenzisa esibalwenibeyingenabo ubungako obucacisiwe. • Uzama ukwenza isibalo ngama matriksi noma amavektha ubungako bawo obungaluvumeli lolohlobo lwesibalo.

MathMath

MathMath

MathMath

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Isinyathelo: • Cacisa ubungako bematriksi noma ivektha bese wenza isibalo futhi. • Bhekisisa ubungako obubaluliwe kuma matriksi noma kumavektha ukubona ukuthi buyahambisana yini nesibalo.

Iphutha loguquguqukayo (Variable ERROR) (SOLVE kuphela)Imbangela: • Awuzange umcacise oguquguqukayo wesixazululo, futhi akekho oguquguqukayo u X esibalweni sakho esilingana nesinye osifakile. • Oguquguqukayo wesixazululo ombalulile akayona ingxenye yesibalo esilingana nesinye osifakile.Isinyathelo: • Isibalo essilingana nesinye osifakayo kufanele sibe noguquguqukayo X uma ungambaluli oguquguqukayo wesixazululo. • Balula oguquguqukayo oyingxenye yesibalo esilingana nesinye osifakayo njengoguquguqukayo wesixazululo.

Iphutha lokungaxazululeki (Can’t Solve) (SOLVE kuphela)Imbangela: Isibali asikwazanga ukuthola isixazululoIsinyathelo: • Bheka ukuthi awekho na amaphutha esibalweni esilingan nesinye osifakile • Faka inani loguquguqukayo wesixazululo eliseduze nesixazululo esilindelekile bese uyazama futhi.

Iphutha le MEM engaphelele (Insufficient MEM)Imbangela: Umuzamo wokwenza itafula lezinombolo kwi TABLE Modi enezimo ezenza ukuthi idlule izinga eliphezulu lemigqa evumelekile. Izinga eliphezulu lemigqa ngama 30 uma kukhethwe u “f(x)” ku menu yokusetha ekusetheni itafula nama 20 uma kukhethwe u “f(x),g(x)”.Isinyathelo: Nciphisa uhlu lokubala lwetafula ngokushintsha amanani ka Start, End, no Step, bese uzama futhi.

Iphutha lokuphela kwesikhathi (Time Out)Imbangela: Isibalo samanje sedifarentiyali noma se intagreshini sigcina ngaphandle kokuba umbandela wokugcina ugcwaliseke. Isibalo sokwaba samanje sigcina ngaphandle kokuba umbandela wokugcina ugcwaliseke.Isinyathelo: Isibalo sedifarentiyali noma se intagreshini: Zama ukwandisa inani lika tol. Qaphela ukuthi lokhu futhi kunciphisa ukucophelela kwesixazululo.

Ngaphambi Kokuthatha Ngokuthi Isibali Asisebenzi Kahle…

Thatha lezizinyathelo ezilandelayo njalo uma kwenzeka iphutha ngesikhathi kubalwa noma uma imiphumela yokubala ingesiyo into oyilindele. Uma isinyathelo sokuqala singayilungisi inkinga, qhubekela kwesilandelayo.Qaphela ukuthi kufanele wenze amakhophi ahlukene emininingwane ebalulekile ngaphambi kokulandela lezizinyathelo.

1. Hlola isimeli sokubala ukuqiniseka ukuthi asinaphutha.2. Qiniseka ukuthi usebenzisa imodi efanele lolohlobo lwesibalo ozama

ukusenza.3. Uma lezizinyathelo ezingenhla zingayilungisi inkinga yakho, cindezela

inkinobho u O. Lokhu kuzokwenza ukuthi isibali sizihlilele ngokwaso ukuthi izinsiza zokubala zisebenza ngokuyikho na. Uma isibali sithola nanoma yikuphi okungalindelekile, izinishiyalezela ngokwayo imodi yokubala, bese icisha konke okuqukethwe kwi memori. Ukuthola imininingwane ngoku inishiyalayiza amasethingi, bheka isihlokwana “Ukulungisa, ucuphe isethaphu yesibali”.

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4. Inishiyalayiza wonke amamodi namasethingi ngokwenza lokhu okulandelayo: 19(CLR)1(Setup)=(Yes).

Ukushintsha iBhetri Ibhetri eliphansi likhonjiswa umbukiso ofiphele, noma ngabe ukwahlukana sekulungisiwe, noma ukwahluleka kwemifanekiso ukuvela esibukweni ngokushesha emva kokuba uvule isibali. Uma lokhu kwenzeka, shintsha ibhetri ufake elisha.Kubalulekile: Ukukhipha ibhetri kuzocisha konke okuqukethwe kwimemori yesibali.

1. Cindezela lokhu 1A(OFF) ukucisha isibali. • Ukuqinisekisa ukuthi awusikhanyisi isibali ngephutha

ngesikhathi ushintsha ibhetri, shishizelisa uqwembe oluqinile luye ngaphambili kwesibali.

2. Susa ikhava njengoba kukhonjisiwe emfanekisweni bese ushintsha ibhetri, ucophelela ukuthi uphawu lokuhlanganisa (+) nophawu lokususa (–) zibheke endaweni efanele.

3. Buyisela ikhava.4. Inishiyalayiza isibali:

O19(CLR)3(All)=(Yes)• Ungaseqi lesinyathelo esingenhla!

ibholidi

Incasiselo EnemininingwaneAmandla Adingekayo: Inebhetri lesola elakhelwe ngaphakathi; ibhetri LR44 (GPA76) × 1

Impilo yebhetri elinganiselwe: Iminyaka emithathu (uma lisetshenziswa ihora ngosuku)

Amazinga okushisa esebenza ngaphansi kwawo: 0°C kuya ku 40°C

Ubungako: 11.1 (ukuphakama) × 80 (ububanzi) × 162 (ubude) mm

Isisindo esilinganiselwe: 95 g kubalwa nebhetri.

Imibuzo eBuzwa Njalok Ngingayifaka kanjani imininingwane futhi ngiveze imiphumela

ngendlela engangenza ngayo kwimodeli engenayo I Natural Textbook Display?

Cindezela lezizinkinobho ezilandelayo: 1N(SETUP)2(LineIO). Bheka “Ukulungisa, ucuphe isethaphu yesibali”.

k Ngingasishintsha kanjani isimo somphumela oyiqhezu ube isimo seqhezu lokubalwa ngokweshumi?

Ngingasishintsha kanjani isimo somphumela oyiqhezu owakhiwe uphawu lokuhlukanisa ube isimo seqhezu lokubalwa ngokweshumi?

Bheka “Ukubheka izimo ezahlukene zemiphumela” ekhasini ZU-11, uthole inqubo.

ZU-53

k Yini umehluko phakathi kwe Ans memori, PreAns memori, imemori ezimele, nememori eguquguqukayo?

Ngayinye yalezinhlobo zamamemori isebenza “njengesitsha” esigcina inani elilodwa.

Ans Memori: Igcina umphumela wesibalo esenziwe kamuva. Sebenzisa lememori ukusebenzisa umphumela wesibalo esidlule kwesilandelayo.

PreAns Memori: Igcina umphumela wesibalo esenziwe ngaphambi kwesokugcina. I PreAns Memori ingasetshenziswa kuphela kwi COMP Modi.

Imemori Ezimele: Sebenzisa lememori ukuhlanganisa imiphumela yezibalo ezimagatshagatsha.

Onguqunguqu: Lememori iyasiza uma ufuna ukusebenzisa inani elilodwa izikhathi eziningi, esibalweni esisodwa noma eziningi.

k Yiziphi izinkinobho okumele ngizicindezele ukuze ngisuke ku STAT Modi noma TABLE Modi, ngiye kwimodi lapho ngingenza khona umunxa wezibalo?

Cindezela lokhu N1(COMP).k Ngingasibuyisela kanjani isibali kumasethingi aso ayesethwe

ngaphambili (ekuqaleni)? Yenza lokhu okulandelayo: 19(CLR)1(Setup)=(Yes)k Uma ngenza isibalo sefanshini, yini indaba ngithola umphumela

ohlukile kakhulu kunalowo okhishwa amamodeli eCASIO amadala? Kwimodeli ene Natural Textbook Display, i-argument yefanshini esebenzisa

abakaki, kumele ilandelwe abakaki abavalayo. Ukwahluleka ukucindezela u ) , emuva kwe-agumenti ukuvala abakaki kungenza amanani angadingeki noma izimeli ukuthi zifakwe njengenxenye ye-agumenti.

Isibonelo: (sin 30) + 15 v Imodeli endala (S-V.P.A.M.): s 30 + 15 = 15.5 iNatural Textbook Display Modeli: b s 30 )+ 15 = 15.5

Ukwahluleka ukucindezela u ) njengoba kukhonjisiwe ngezansi kuyobangela ukuthi kubalwe u sin 45.

s 30 + 15 = 0.7071067812

Manufacturer:CASIO COMPUTER CO., LTD.6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan

Responsible within the European Union:CASIO EUROPE GmbHCasio-Platz 122848 Norderstedt, Germany

Lomaka usebenza emazweni aseyurophu kuphela.

CASIO COMPUTER CO., LTD.

6-2, Hon-machi 1-chomeShibuya-ku, Tokyo 151-8543, Japan

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