NATIONAL SENIOR CERTIFICATE GRADE/GRAAD 12
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1 NATIONAL SENIOR CERTIFICATE GRADE/GRAAD MATHEMATICS P/WISKUNDE V NOVEMBER 4 MEMORANDUM MARKS: 5 PUNTE: 5 Tis memoradum cosists of pages. Hierdie memoradum bestaa uit bladsye. Copyrigt reserved/kopiereg voorbeou
2 Matematics P/Wiskude V DBE/November 4 NOTE: If a cadidate aswers a questio TWICE, oly mark te FIRST attempt. Cosistet accuracy applies i all aspects of te markig memoradum. LET WEL: Idie kadidaat vraag TWEE keer beatwoord, merk slegs die EERSTE pogig. Volgeoue akkuraateid is DEURGAANS op ALLE aspekte va die memoradum va toepassig. QUESTION/VRAAG or 4 4 b ± b 4ac a ± 4 4 ± 7 6,5 or/ of,85 4 stadard form/stadaardvorm substitutio ito correct formula/ substitusie i korrekte formule aswers/ atwoorde ± ± 4,5 or/ of,85 for addig 9 o bot sides/tel 9 by aa beide kate ± 4 aswers 4 Copyrigt reserved/kopiereg voorbeou
3 Matematics P/Wiskude V DBE/November commo factor/gemee. faktor simplificatio/ vereevoudigig aswer/atwoord commo factor/gemee. faktor simplificatio/ vereevoudigig aswer/atwoord y aswer/atwoord 5y 4 6y... i : y 5 y y 4 6y 4 y y 9 y 5y 4 6y y 6y 7 y 5y 4 6y y 5y y y y or y or or ; ; substitutio/substitusie simplificatio/ vereevoudigig stadard form/ stadaardvorm factorisatio/faktoriserig y-values/y-waardes -values/-waardes 6 Copyrigt reserved/kopiereg voorbeou
4 Matematics P/Wiskude V 4 DBE/November 4 y : or y or y substitutio/substitusie simplificatio/ vereevoudigig stadard form / stadard vorm factors/faktore - values/- waardes y-values/y-waardes 6. < 6 < 6 4 < 4 < stadard form/ stadaardvorm factorisatio/faktoriserig 4 OR/ OF < < 4 or ; 4 4 critical values i te cotet of iequality / kritiese waardes i die koteks va die ogelykeid otatio/otasie 4.4 k 4 k 4 k 4 aswer/atwoord [] Copyrigt reserved/kopiereg voorbeou
5 Matematics P/Wiskude V 5 DBE/November 4 QUESTION/VRAAG. T 4. T5 a d a ad d 7 57 subst. ito correct formula /subt. i 75 korrekte formule geeral term/ 7 5 algemee term complete aswer /volledige atwoord p p S S 5 7 [ a l] [ 75] geeral term/ algemee term complete aswer / volledige atwoord substitutio/substitusie 7 S [ a d] 5 [ 57] 7.5 Te ew series/die uwe reeks is T is divisible by /is deelbaar deur 4 Te T 7, T, T5,..., T5 are divisible by 4, tus eac 4 t term is divisible by 4. Daara is T 7, T, T5,..., T5 deelbaar deur 4, d.w.s. elke 4 de term is deelbaar deur 4. 5 umber of terms divisible by 4 will be aatal terme deelbaar deur 4 sal wees 6 4 Copyrigt reserved/kopiereg voorbeou substitutio/substitusie 7 geeratig ew series divisible by 4/ vormig va uwe reeks deelbaar deur 4 T T is divisible by 4/ is deelbaar deur 4 idetifyig terms divisible by 4/ idetifiseer terme deelbaar deur 4 reasoig/redeerig 6 4
6 Matematics P/Wiskude V 6 DBE/November 4 Positio of terms divisible by 4: ; 7 ; ; ; 47; T geeratig sequece ivolvig positio of terms/vormig va reeks i.t.v. posisie va terme T [] Copyrigt reserved/kopiereg voorbeou
7 Matematics P/Wiskude V 7 DBE/November 4 QUESTION/VRAAG.. ; 7 ; ; p ; p p 4 p 5 p p 5 p ; 7 ; ; p ; p first differeces/ eerste verskille.. p p a a p a a b 6 b 6 b 9 b 9 a b c 9 c c 7 T 9 7 c 7 aswer/atwoord 4 T T d d formula/formule substitutio of first ad secod differeces/substitusie va eerste e tweede verskille simplificatio/vereevoudigig aswer/atwoord 4 Copyrigt reserved/kopiereg voorbeou
8 Matematics P/Wiskude V 8 DBE/November 4 7; ; 7 ; ; p ; p T 7 c a a a b 6 b 9 T 9 7 a T b c T b c... T 7 4 b c 7... : b 6 b 9 sub i : c 7 T 9 7 c-value/c-waarde a-value/a-waarde b-value/b-waarde aswer/atwoord a-value/a-waarde b-value/b-waarde c-value/c-waarde aswer/atwoord 4 4 Copyrigt reserved/kopiereg voorbeou
9 Matematics P/Wiskude V 9 DBE/November 4.. Te sequece of first differeces is/die reeks va eerste verskille is: 6 ; 4 ; ; ; two terms are/twee terme is: T T Te sequece of first differeces is/die reeks va eerste verskille is: 6 ; 4 ; ; ;... Te formula for te sequece of first differeces/die formule vir die reeks va eerste verskille is T 8 st differece/ ste verskil: two terms are/twee terme is: T T T T [ 7] T 5 T T 96 T [ 9 7] [ 9 7] T T 96 T T T T Copyrigt reserved/kopiereg voorbeou
10 Matematics P/Wiskude V DBE/November T 6 a 6 ad r 4 4 or S 4, S 4, or or T 4 T 5 5 T 4 4 5,,... is a aritmetic sequece wit T a ad d subst. ito correct formula/ subt i korrekte formule aswer/atwoord substitutio ito correct formula /substitusie i korrekte formule aswer/atwoord substitutio ito correct formula /substitusie i korrekte formule aswer/atwoord improper fractios/ oegte breuke or aswer/atwoord 4 99 givig te first tree terms / gee die eerste drie terme aswer /atwoord 4 [9] Copyrigt reserved/kopiereg voorbeou
11 Matematics P/Wiskude V DBE/November 4 QUESTION/VRAAG p q Reflect ; across y to get T ; Reflekteer ; om y om T ; te kry p value /waarde q value /waarde reflect across/reflekteer om y 4. Siftig g five uits to te left sifts ; five uits to te left. 6 aswer/atwoord 4.4 equatig bot graps/stel grafieke gelyk y OS OS sice at S, >,7... y 6 6,45 uits/ eeede ad y OS 6 aswer/atwoord 5 Copyrigt reserved/kopiereg voorbeou
12 Matematics P/Wiskude V DBE/November 4 Traslate g oe uit dow ad oe uit to te rigt/trasleer g ee eeeid af e ee eeeid a regs Te ew equatio/die uwe vergelykig : p S / ; / Terefore te image of S is Daarom is die beeld va S ou S ; / Now traslate p back to g/trasleer p terug a g: S ; OS OS 6,45 uits/eeede 4.5 k < will give roots wit opposite sigs/ k < sal wortels met teeoorgestelde tekes gee p coord. of/koörd. va coord. of/koörd. va S / S aswer/atwoord 5 k < [] Copyrigt reserved/kopiereg voorbeou
13 Matematics P/Wiskude V DBE/November 4 QUESTION y loga log subt. ; a a a or a a a log y swop ad y/ruil e y : y g log aswer/atwoord aswer/atwoord OR/ OF g log aswer/atwoord OR/ OF g log aswer/atwoord 5.4 > y y aswer/atwoord aswer/atwoord aswer/atwoord 5.5 ; log 7 7 aswer/atwoord epoetial form/ ekspoesiële vorm simplificatio/vereevoudigig aswer/atwoord [9] Copyrigt reserved/kopiereg voorbeou
14 Matematics P/Wiskude V 4 DBE/November 4 QUESTION/VRAAG y, - coordiate of S is positive, 6. ; QT f g 4 QT 4 6 Deravitive of QT 8 or or,5 4 6 or Ma/ Maks QT 4 6 6,75uits/eeede correct formula/ korrekte formule substitutio/substitusie derivative/afgeleide derivative equal to / afgeleide gelyk aa 8 -value/-waarde substitutio/substitusie aswer/atwoord 6 [] Copyrigt reserved/kopiereg voorbeou
15 Matematics P/Wiskude V 5 DBE/November 4 QUESTION/VRAAG 7 7. A P i i 5 75 i 5 45,94... Rate of iterest/retekoers is,94 % p.a./p.j. substitutio/substitusie writig i terms of i erskryf i terme va i aswer/atwoord i 5 5 i i,94 Rate of iterest/retekoers is,94 % p.a./p.j. [ i ] P i 7.., 5,, 5 4, R555,4 4 substitutio/substitusie writig i.t.o i aswer, i 4 substitutio ito correct formula aswer/atwoord 4 Copyrigt reserved/kopiereg voorbeou
16 Matematics P/Wiskude V 6 DBE/November 4 [ ] 7.. i P i, 6 5, 5,, 6 5, 6 log 6 log, 8,7 Melissa settles te loa i 8 mots 7.. Samuel He is payig off is loa over a loger period tus more iterest will be paid./hy betaal sy leig oor ' lager tydperk af, dus sal y meer rete betaal. 6 substitute ito correct formula/substitusie i korrekte formule use of logs/gebruik va logs aswer/atwoord 4 Samuel reaso/rede Samuel He will pay/hy betaal R555,4 4 R5 R8, Se will pay betwee/sy sal tusse R58 ad/e R586, betaal. Samuel reaso/rede [] Copyrigt reserved/kopiereg voorbeou
17 Matematics P/Wiskude V 7 DBE/November 4 Copyrigt reserved/kopiereg voorbeou QUESTION/VRAAG 8 8. lim lim lim lim f f f f f f f f f lim lim lim lim lim lim lim OR simplifyig/vereevoudig formula/formule subst. ito formula/subst. i formule factorizatio/faktoriserig aswer/atwoord 5 formula/formule subst. ito formula/subst. i formule simplifyig/vereevoudigig factorizatio/faktoriserig aswer/atwoord 5
18 Matematics P/Wiskude V 8 DBE/November 4 f f f lim lim lim lim lim formula/formule subst. ito formula/subst. i formule factorizatio/faktoriserig simplifyig/vereevoudigig aswer/atwoord 5 8. f y 6 simplificatio/vereevoudigig dy 5 derivative/afgeleide d 5 6 factors/faktore 5 y 8.4 f 4 / first derivative/eerste afgeleide f secod derivative/tweede // f 4 afgeleide // // f is cocave up we/is kokaaf op as f > f > 4 > > 4 > > 4 [4] Copyrigt reserved/kopiereg voorbeou
19 Matematics P/Wiskude V 9 DBE/November 4 QUESTION/VRAAG 9 9. f / 8 or 5 4 y or y 8 or 8, y 5 Turig poits are/draaipute is ; ad ; 7 9. derivative/afgeleide derivative/ afgeleide factors/faktore -values/waardes eac y- values/elke y-waarde 6 y ;8, 5 8 ; O ; -itercepts/afsitte y-itercept/afsit turig poits/ draaipute sape/vorm 9. < or < < OR ; ; < 4 bot critical poits/ beide kritieke-pute otatio/otasie Copyrigt reserved/kopiereg voorbeou
20 Matematics P/Wiskude V DBE/November 4 QUESTION/VRAAG. l 4 l 4. b b 5 V lb V 4 5. V 5 4 V V ± ,86 or 8,8 for a bo as large as possible, 8,8cm vir die grootste mootlike boks 8,8 cm aswer b b 5 volume formula simplifyig/vereevoudig derivative / afgeleide -values i ay form / -waardes i eige vorm aswer/atwoord 5 [9] QUESTION/VRAAG.. 8 Pmale/malik or,46 or 46,% 8 aswer/atwoord.. Pot game park/ie wildreservaat Pgame park/wildreservaat or,66 or 65,56% aswer/atwoord Pot game park/ie wildreservaat or,66 or 65,56% aswer/atwoord Copyrigt reserved/kopiereg voorbeou
21 Matematics P/Wiskude V DBE/November 4. Evets are idepedet if /Gebeure is oafaklike idie Pmale Pome Pmale ad ome Pmalik Puis Pmalik e uis 8 Pmale/malik 8 ad/e Pome/uis 8 or, or,% Pm P ad teir values/e ulle waardes aswer of product Pmale/malik Pome/uis ,5 or 5,% Pmale ad ome/malik e uis 8 Pm ad/e value/waarde,7 or 7,% Terefore Pmale Pome Pmale ad ome Dus Pmalik Puis Pmalik e uis Tus te evets are ot idepedet./dus is die gebeure ie oafaklik ie coclusio/afleidig 4 Home/Huis Not Home/ Nie uis M 7 8 F Pfemale/vroulik Pot ome/ie uis ,47945 or 47,9% Pfemale ad ot ome/vroulik e ie-uis 9 8,5 or 5% Terefore Pfemale Pot ome Pfemale ad ot ome Tus te evets are ot idepedet. Dus Pvroulik Pie-uis Pvroulik e ie-uis Dus is die gebeure ie oafaklik ie. Copyrigt reserved/kopiereg voorbeou Pf Pot ad teir values/e ulle waardes aswer of product Pf ad/e ot value/waarde coclusio/afleidig 4 [7]
22 Matematics P/Wiskude V DBE/November 4 QUESTION/VRAAG ! 6! P !! formula/formule aswer/atwoord 4 44 product/produk Te five 'uits' ca be parked i 5 4 ways./die vyf 'eeede' ka op 5 4 maiere geparkeer word. Te tree silver cars ca be parked i ways./die drie silwer motors ka op maiere parkeer word. So tere are ways to park te cars./dus is daar maiere om die motors te parkeer. Suppose for te momet te silver cars are at oe ed./veroderstel die drie silwer motors is op die put. Te cars ca be arraged i 6 ways./die motors ka op 6 maiere geragskik word. For eac of tem te remaiig four cars ca be arraged i 4 4 ways./die 4 oorblywede motors ka op 4 4 maiere ragskik word. So ways if all cars at oe ed./dus is daar maiere as die motors op die put is Togeter, te silver cars ca oly occupy 5 differet positios amogst te 7 positios../saam ka die silwer motors slegs 5 verskillede posisies ê tusse die 7 mootlike posisies. Total ways/totale getal maiere [9] TOTAL/TOTAAL: 5 Copyrigt reserved/kopiereg voorbeou
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