NATIONAL SENIOR CERTIFICATE GRADE 12/GRAAD 12
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1 NATIONAL SENIOR CERTIFICATE GRADE /GRAAD MATHEMATICS P/WISKUNDE V MARCH 7 MEMORANDUM MARKS: PUNTE: Tis memndum consists o pges. Hierdie memndum bestn uit bldse. Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
2 Mtemtics P/Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 NOTE: I cndidte nswers question TWICE, onl mrk te FIRST ttempt. Consistent Accurc pplies in ll spects o te mrking memndum. LET WEL: Indien n kndidt n vrg TWEE keer bentwod, merk slegs die EERSTE poging. Volgeoue kkurteid is DEURGAANS op ALLE spekte vn die memndum vn toepssing. QUESTION/VRAAG.. nswer nswer.. OR nswer squring bot sides.. nswer OR / OF + + OR / OF ; criticl vlues inequlit intervl Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
3 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie.. 7 =, =, OR =, =, subst crect mul nswer nswer 7 nswer nswer c c c c c b c c stndrd m c b substitution nswer. substitution simpliiction stndrd m cts ; -vlues c on bot -vlues
4 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 OR / OF. S F S to be mimum te denomint needs to be t minimum. Vir S om n mksimum wrde te ê, moet die deler n minimum wrde Minimum o is substitution simpliiction stndrd m cts ; -vlues c on bot -vlues Minimum o is Mimum o S [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
5 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 QUESTION/VRAAG.. F geometric: ; b ; ;... b b b b OR b b ; ; ;... r T 9 r OR / OF T r 9 b b b b b b b r = subst. into crect mul / r = subst. into crect mul / Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
6 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7. Te series is: ; ; ; ; ; ;... Te new positive term series: ; ; ; ; ; r n n OR/OF 9 p p etc.. No, te series is not convergent / Nee, die reeks konvergeer nie r = nd convergence < r < r = en vir konvergering < r < r n 9 p crect mul no reson [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
7 Mtemtics P/ Wiskunde V 7 DBE/Feb. Mr./Feb. Mrt. 7 QUESTION/VRAAG Tn n OR/OF 9 n 9 9 n 9 b n 9 n 9 b n n d Tn T n d n n n n n n n 9 n n 9 9 n 9n 9 n 9n n n n n sin sin 9 n ; sin sin sin ; ;... b c c 9 9 b c 9 9 Tn n n 9 mul substitution simpliing 9 Tn n n 9 equting generl term to 9 stndrd m cts n n sin sin sin 9 [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
8 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 QUESTION/VRAAG. U ; ;.. = T. ; log : log cnge nd. = nswer. V ; V,;, OR / OF OR / OF.7 ; V ; subs into crect mul V ; T / [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
9 Mtemtics P/ Wiskunde V 9 DBE/Feb. Mr./Feb. Mrt. 7 QUESTION.. C ; C ;.... AB = AB units D ;.. C ; D ; cts -vlue oter -vlue nswer vlue Averge grdient / Gemiddelde grdient.. OC = OB = O ĈB= isosceles rigt ngled tringle Gelkbenige regoekige drieoek OR / OF equl lengts tn mg tn OBˆ C tn OĈB.. k OR ; nottion..7 / //.. Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
10 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7. ; TP = = O ; ; intercepts -intercept ; spe [] QUESTION/VRAAG.. A,.. n = R9, n 9 n, nlog, log n Te mcine will need to be replced t te beginning o / Msjien moet n die begin vn vervng wd OR / OF, n 9 n, n log, n Te mcine will need to be replced t te beginning o / Msjien moet n die begin vn vervng wd in crect mul 9 n, 9 n log, n log n, 9 n log, n Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
11 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7.. R R9 =R. P v,, R9, n [ i ] i, 9, R79 7, R, i = =, nd n = subs into crect mul R 9,, i = n = substitution crect mul R 79 7, Lerto quliies lon o R 79 under te given conditions / Lerto kwliiseer vir n lening vn R 79 gegewe die kondisies R79 [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
12 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie QUESTION/VRAAG 7 PENALISE ONLY ONCE increct nottion in tis question. 7. lim lim lim lim OR/OF lim lim lim lim lim simpliing mul subst. into mul ctistion nswer mul subst. into mul simpliing ctistion nswer 7. / g g
13 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie 7. :, / / / [] QUESTION/VRAAG. 7 / Turning points re ; nd 7 ; derivtive derivtive = cts -vlues -vlues
14 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt No rel roots / Geen reële wtels = 7 OR / OF b c 7 No rel roots / Geen reële wtels = b c. ; 7 ; ; turning points spe Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
15 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7. / // // OR Point o inlection: b Te unction is concve up since OR Point o inlection: Te unction is concve up since // nswer // // [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
16 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 QUESTION/VRAAG 9 9. Lengt o one side o tesqure / lengte vn s vn vierknt Lengt o te rectngle / lengte vn l l A A F minimum re / Vir da d. min imum die regoek : da oppervlktte d da d 7 [7] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
17 Mtemtics P/ Wiskunde V 7 DBE/Feb. Mr./Feb. Mrt. 7 QUESTION/VRAAG.. PS nd T PS PT P T P T.. PS T PS PT PS nd T..! = PS nd T PS PT P T!... E ns n!!!! 7!!!!!!!!! PE 7! 7! [] Coprigt reserved/kopieregvobeou Plese turn over/bli om sseblie
18 Mtemtics P/ Wiskunde V DBE/Feb. Mr./Feb. Mrt. 7 QUESTION/VRAAG, W PF nd W =,9,7 F, L PF nd L =,, not F, W Pnot F nd W =,,, L Pnot F nd L = PWin = PF nd W + Pnot F nd W =,7, +,, =,9 +, =,7 = 7% 9 = PF nd W =,7, =,9 Pnot F nd W =,, =,,9 +, 9,7 / 7% / TOTAL/TOTAAL: [] Coprigt reserved/kopieregvobeou
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