NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE 12/GRAAD 12
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1 NAIONAL ENIOR CERIFICAE NAIONALE ENIOR ERIFIKAA GRADE /GRAAD MAHEMAIC P/WIKUNDE V NOVEMBER 7 MARKING GUIDELINE/NAIENRIGLYNE MARK/PUNE: 5 is memodum cosists o pges. Hiedie memodum best uit bldsye. Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
2 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye NOE: I cdidte swes questio WICE, oly mk te FIR ttempt. Cosistet ccucy pplies i ALL spects o te mkig guidelies. LE WEL: Idie ' kdidt ' vg WEE KEER betwood, mek slegs die EERE pogig. Volgeoue kkuteid is op ALLE spekte v die sieiglye v toepssig. QUEION/VRAAG o ctos 7 b ± ± b c ± 8, o,5 substitutio simpliictio,, ± 8 8 ± 8, o,5 5 8 o ddig o 6 bot sides simpliictio,, o stdd om bot swes select 5 Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
3 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye... y 6 y 7 y 8 y y y 8 6 y 8y 6 6y y y 6 6 y y 8 6 > > y y y y y y y y y 7 y y y 8 y 6y 7 y o y 7 R, o ; o ; o < o > o o o 7 y 7 y y subject o omul substitutio coect stdd om ctos -vlues y-vlues subject o omul substitutio coect stdd om ctos y-vlues -vlues y oe o te solutios > > e uctio vlues emi positive R, y oe o te solutios Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
4 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye.. y ;6 y p Copyigt eseved/kopieeg voobeou - ; Fo two egtive uequl oots: < p < p 8 6 p < 6 p < 6 6 < p < < p < p p 8 ± 6 6 < 6 6 p < 6 < p < 6 < p < p Roots e el d uequl : p p 6 > p > p > 8 ± p Roots e : Fo bot oots to be egtive : p < 8 p < 6 p < 6 < p < 6 6 < p < 6 6 < p < 6 6 < p < < < p [] Plese tu ove/bli om sseblie
5 Mtemtics/P/Wiskude/V 5 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye QUEION/VRAAG ist dieeces: ; 5; secod dieece 6 b b b b c 5 c 5 c 8 b c secod dieece 8 ist dieeces 6 b c d d b c o e d tem s vlue o 5 86 swe Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
6 Mtemtics/P/Wiskude/V 6 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye.. k 7 ; k 8 d k k 8 k 5 k k k k 7; k 8 d k k 7 k k 8 7 ; ;... d equece is 7 ; ; ; 6 ; ;. Evey ltete tem o te sequece will be eve / Elke tweede tem v die y sl ewe wees 6... [ 6 ] 5[ 7] 6 k 7 k 8 k 8 k k 7 d d 6 subst ito coect omul swe d 6 swe [8] Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
7 Mtemtics/P/Wiskude/V 7 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie QUEION/VRAAG
8 Mtemtics/P/Wiskude/V 8 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie. 8 o o 8 N/A substitutio o ito te coect omul 6 substitutio o ito te coect omul
9 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie substitutio o 6 substitutio o 6 [8]
10 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye QUEION/VRAAG. / b 6 b b t b 7 7 b 6 b 7 b 5 b [ ] [ ] [ ] [ ] b b 7 b 6 solve simulteously 5. / b b b 7 - b 7 itecepts : ; 6 ; b b 7 6 solve simulteously 5 6 ; 6 ; Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
11 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye. 6 / o b. o 6 /. 6 / y 6 8 P ; 8 6 y 8..6 y ` P [ ] ; 8 8 ; 6 - ; - ; ; - y ; 8 g 6 ; ` 8 y 8.: : spe - itecepts y- itecept ; 8.6: g:.5 < < o ;.7 o 6 ; ] o [-; 6] - itecept y- itecept < < 6 [] Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
12 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye QUEION/VRAAG 5 5. y R ; y y < o y > swe y ; o y ; R {} 5. D ; D ; g 5. log. coect substitutio o A log t g t t t t t t 5. log y itecge d y y y 5.5 < < < < < < ; ; 5.6 Equtio o te is o symmety: y equtio o is o symmety -itecept o te is o symmety is t s -itecept t B ; wic is te sme s te -itecept o te is o symmety Poit o itesectio: B ; B o ; ice BE ED d D lies o te is o symmety d te gdiet o te is o symmety is, B will lso lie o te is o symmety. But B lso lies o. eeoe B ; is te poit o itesectio betwee d te is o symmety wit egtive gdiet./ Omdt BE ED e D op die simmetie-s lê e die simmetie-s se gdiët is, sl B ook op die simmetie-s lê. M B lê ook op. Dus is B ; die syput v e die simmetie-s met egtiewe gdiët. Copyigt eseved/kopieeg voobeou BE ED B o ; [] Plese tu ove/bli om sseblie
13 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye QUEION/VRAAG 6 6. A P i 6,7 6,67 6,67,56,56,65 6,5% [ ] 6.. i P i, 5, 5, R5 56,5 Copyigt eseved/kopieeg voobeou, 5 His motly istlmet is R 5 56,5 6.. Amout pid o te ye : 56,5, Blce 5 6, R 66,, 5 56,5, 5 56,5 5 6,7 Iteest 66, 7,57 7,8 6 coect substitutio ito omul 6, 67 6,5%, i 5 coect substitutio i P swe R 66, 5 Plese tu ove/bli om sseblie, 5, 5 56,5, R 6, 7 R 7,8 R 7,57
14 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye otl mout pid i ist ye R R66, Blce o lo te ye P o emiig istllmets [ i ] P i, 5 56,5, R 6, Amout pid o i te ist ye: R5 R 6, R 7,8 Amout o iteest R 66, R 7,8 R 7,6, 556,5 P, R 6 68, ,8 R7 5,8 Ate mots, moey owed o ouse is, 7 5,8 6,7 Amout pid te mots is 5 56,5 R 66, Amout o iteest pid: R 66, substitutio ito coect omul R 6, R 7,8 R 7,6 R6 68,8 R7 5,8 R 6, 7 R66, 6 R 66, 5 6,7 R 7, ,7 R 7,57 6 [5] Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
15 Mtemtics/P/Wiskude/V 5 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie QUEION/VRAAG 7 7. / / / subst. ito omul / subst. ito omul [ ] D D d dy y y π π 5 5 deivtive o π is []
16 Mtemtics/P/Wiskude/V 6 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye QUEION/VRAAG 8 8. / // // // Poit o ilectio t < > epltio 5 8. y O ; ; ; spe ; ; s P ; 8. cocve up o > y will be cocve dow o > > 8.. ;7 8.. Do ot gee wit Clie s e sttemet is icoect. Betwee d te gp o is decesig. eeoe t te gdiet will ve egtive vlue. tem ie sm met Clie ie, wt stellig i vekeed. Die giek v is dled/emed tusse e. By moet die gdiët dus ' egtiewe wde ê. 7 o justiictio / [5] Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
17 Mtemtics/P/Wiskude/V 7 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie QUEION/VRAAG PB B ; ; P y PB will be miimum i PB is miimum,87 PB PB o PB d d PB d d PB swe
18 Mtemtics/P/Wiskude/V 8 DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye Gdiet o tget to cuve Gdiet o lie joiig B d te cuve otest distce will be wee tget to cuve is pepedicul to te lie joiig P d te cuve. kk P ; d B; PB PB o,87 PB swe P kk ; BP tget pssig toug t P. y mtget t P k mbp k Equtio o BP: y k yp k,5 k k,5 d so k,5 d P,5;,5 BP,5,5,87 m tget t P k m BP k y k vlue o y t P vlue o k swe [7] Copyigt eseved/kopieeg voobeou Plese tu ove/bli om sseblie
19 Mtemtics/P/Wiskude/V DBE/Novembe 7 NC/N Mkig Guidelies/Nsieiglye QUEION/VRAAG. I 8 vlues eed to be plced i coect positio: W o coect: mk o 5 coect: mks 6 o 7 coect: mks 8 coect: mks P use oly oe pplictio QUEION/VRAAG o 7% settig up equtio swe 7 8 swe [8] No o digits Lettes Digits otl used Codes o two lettes d ive digits will esue uique umbes o 7 cliets ive digits [6] OAL/OAAL: 5 Copyigt eseved/kopieeg voobeou
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