NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 11

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1 NATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD MATHEMATICS P/WISKUNDE V NOVEMBER 05 MEMORANDUM MARKS/PUNTE: 50 This memorandum consists of 7 pages. Hierdie memorandum bestaan uit 7 bladse.

2 Mathematics/P/Wiskunde V DBE/November 05 CAPS/KABV Grade/Graad Memorandum NOTE: If a candidate answered a question TWICE, mark onl the FIRST attempt. If a candidate crossed out an answer and did not redo it, mark the crossed-out answer. Consistent accurac applies to ALL aspects of the marking memorandum. Assuming values/answers in order to solve a problem is unacceptable. LET WEL: As 'n kandidaat 'n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na. As 'n kandidaat 'n antwoord deurgehaal en nie oorgedoen het nie, sien die deurgehaalde antwoord na. Volgehoue akkuraatheid is op ALLE aspekte van die memorandum van toepassing. Dit is onaanvaarbaar om waardes/antwoorde aan te neem om 'n probleem op te los. QUESTION/VRAAG. Range/Omvang kg ma min (). Mode/Modus 7 kg (). Median/Mediaan T 4 9 kg ().4 Q T 7 8 Q T 7 IQR Q Q kg Q 8 Q bo/mond whiskers/snor () ().6 SD 5,88 5,84 kg ().7 98,59 + σ 98,59 + 5,84 4,4 kg 7 > 4,4 I agree with this person/ek stem met die persoon saam. 98,59 4,4 conclusion/ gevolgtrekking () [4]

3 Mathematics/P/Wiskunde V DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG WEIGHT LOSS OVER 4 WEEKS GEWIGSVERLIES IN 4 WEKE (IN GRAMS/GRAM) FREQUENCY FREKWENSIE f CUMULATIVE KUMULATIEWE f 000 < < < < < < < < Average/Gemiddelde ,59 009,6 g Cumulative Frequenc/Kumulatiewe frekwensie OGIVE/OGIEF Weight loss (in grams) over 4 weeks/ Gewigsverlies (in gram) in 4 weke. (00 ; 4) 7 4 participants/deelnemers (accept/aanvaar: 4) 8 50 () grounded upper limits cumulative frequenc smooth curve geanker boonste limiete kumulatiewe frekwensie gladde kurwe 4 () [8]

4 Mathematics/P/Wiskunde V 4 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG C(0 ; ) A( ; ) F α G O D(5 ; ) E... m AC 0 8 ( ) m m [DE CA] DE AC ( ) m m + c ( ) ( 5) ( 5) + c OR/OF c tan FĜO m AC F ĜO,69 α 90 +, 69 [et/buite of ], 69 subst into/in gradient form/ gradiëntvorm gradients equal/ gradiënte gelk subst m & (5 ; ) into eq of straight line/ in vgl v rt ln equation/vgl tan FĜO,69 m AC () () ()

5 Mathematics/P/Wiskunde V 5 DBE/November 05 CAPS/KABV Grade/Graad Memorandum.4. midpoint of BE midpoint of AD [diagonals of rectangle] midpt v BE midpt v AD [hoeklne van reghoek] ( ) M ; M ;.4. BE AD [diagonals of rect /hoeklne van regh] BE ( 5) + ( ( )) units/eenh R -value/waarde -value/waarde R () subst into distance formula/subst in afstandsformule () [4]

6 Mathematics/P/Wiskunde V 6 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 4 P O R S T 0 ; a a a a 0 P(0 ; ) + a a 0 + a P(0 ; ) 4. OP unit/eenh SP units/eenh S( ; 0) + a(0) a 0 a m PS PO OS + a a a OR/OF OR/OF 0 0 S( ; 0) m PS () () () ()

7 Mathematics/P/Wiskunde V 7 DBE/November 05 CAPS/KABV Grade/Graad Memorandum PO mps OS m m PS TR (RT PS) m TR 5 + and/en 5 m PS m TR equation/vgl () ( 5 ) () 5 R( ; ) Area of/ Opp van ΔPRT 6 PT h (6 )() sq units/ vk eenh 4.6 PT is the diameter of the circle passing through P, R and T. [PT subtends 90 at circumference] PT is die middelln vd sirkel wat deur P, R en T gaan. [PT onderspan 90 op omtrek] r 6 subst of eq of TR into/subst v vgl v TR in + simplif/vereenv 6 h S/R () () [6]

8 Mathematics/P/Wiskunde V 8 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 5 5. P( ; 4) T 5 β O R (a) 5..(b) 5..(c) r sin β 5 cos(80 cos β 7 ( ) β ) tan( β ) tan β 4 ( ) sin β T T 5 7 cos β T T 5 T( 4 ; 4 ) 5 5 subst () () reduction/reduksie () reduction/reduksie equating ratios/ stel verh's gelk T equating ratios/ stel verh's gelk T ()

9 Mathematics/P/Wiskunde V 9 DBE/November 05 CAPS/KABV Grade/Graad Memorandum sin sin.cos.( + ) cos sin cos cos + sin sin.cos.( cos cos ( ) cos sin sin.cos.( + cos sin cos sin sin.cos.( + cos sin cos ( + ) cos (cos + sin ) cos A 4( sina) sin A 4sinA sina 4 sin 0, 4 sin 0,84 ref/verw 57.4 ) cos ) sin OR/OF cos ) sin 7,4 + k.60 or 0,86 + k.60 8,57 + k.80 or 5,4 + k.80 ; k Z tan sin cos identit/identiteit simplif/vereenv tan sin cos simplif/vereenv identit/identiteit sin A identit/identiteit correct equation/ korrekte vgl 0,84 () ref/verw 57,4 7,4 & 0,86 8,57 & 5,4 k.80 ; k Z (6) [4]

10 Mathematics/P/Wiskunde V 0 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 6 f f f b < 67,5 OR/OF (45 ; 67,5 ] etreme values/ grenswaardes notation/notasie 6.. The graph of f has to shift 55 to the left to form the graph of h. Die grafiek f het 55 na links geskuif om grafiek h te vorm. 0 and/en k g 0 80 TP( 90 ; ) TP(90 ; -) () () () ( 50 ; ) and/en (0 ; 0,87) -intercept/afsnit

11 Mathematics/P/Wiskunde V DBE/November 05 CAPS/KABV Grade/Graad Memorandum 6.. min value/waarde cos( + 60 ) sin cos(90 + ) + 60 (90 + ) 50 + k k or/of 05 or no solution cos( + 60 ) sin cos(90 ) (90 ) or (90 ) k k.60 no solution/geen oplossing 05 + k or 05 () co-ratio/ko-verh correct equations korrekte vgls 75 + k (6) co-ratio/ko-verh correct equations korrekte vgls 05 + k (6) OR/OF cos( + 60 ) sin co-ratio/ko-verh sin[90 ( + 60 )] sin correct equations or korrekte vgls 0 + k.60 no solution/geen oplossing 5 k.80 5 k or (6) < < 05 OR/OF ( 75 ; 05 ) etreme values/ grenswaardes notation/notasie () 6..5 cos( + 60 ) sin[90 ( + 60 )] co-ratio/ko-verh sin(0 ) sin( 0 ) θ 0 OR/OF B inspections/deur inspeksie: θ 0 () () []

12 Mathematics/P/Wiskunde V DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 7 P θ Q T R 7. PQ QR () cosθ ()() PR + () QR.PR.cosθ ()().cosθ 7. PT QR [ in semi-circle/halfsirkel] PT PT sin θ PR PT sin θ OR/OF subst into cosine rule/in cos-reël cos θ as subject/ as onderwerp simplif/vereenv R correct ratio/ korrekte verh () PT QR [ in semi-circle/halfsirkel] R Qˆ 90 θ [ s opposite sides/ e to se] θ sin(90 ) PT PT θ.cos correct ratio/ korrekte verh ( [7]

13 Mathematics/P/Wiskunde V DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 8 6,9 FIGURE FIGURE 8. Surface area(sa) πrh + πr + π r Buite-opp πrh + πr 8. π(,9)(6) + π(,9) 8,0π 70,80 cm 4 Volume of hemisphere/v hemisfeer πr 4 π(,9) 6,6π 80% of/van volume 0,8 6,6π 40,86 cm OR/OF Volume of hemisphere/v hemisfeer 80% of/van volume 0, ,8 40,86 cm πr π(,9) 4 πr SA of tin/oa v blik SA of hemisphere/ BO v hemisfeer SA of base/ BO v basis subst (5) V of hemisphere subst vol of hemisphere/ vol van hemisfeer subs () () [8]

14 Mathematics/P/Wiskunde V 4 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 9 L 58 K O N R 9. L Kˆ R 90 [ in semi-circle/halfsirkel] S R 9. Rˆ 80 ( ) [ s/e of/van ] S R 9. Nˆ [ s/e in same segment/dieselfde segment] S R () () () [6]

15 Mathematics/P/Wiskunde V 5 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG 0 0. C O A B 0.. AO and/en CO are radii/is radiusse Â Ĉ [ s opp equal sides/ e to gelke se] Â + Ĉ [et/buite of/van ] Ô 0.. Bˆ Ĉ [ s opp equal sides/ e to gelke se] Ô Bˆ + Ĉ [et/buite of/van ] AÔB + ( + ) (Ĉ AĈB + Ĉ ) S S R S S S () ()

16 Mathematics/P/Wiskunde V 6 DBE/November 05 CAPS/KABV Grade/Graad Memorandum 0. P S M R N Q 0.. et of cc quad/buite v koordevh R 0.. MP QM [radii] Qˆ [ s opp equal sides/ e to gelke se] S R 0.. Mˆ 80 [ s/e of/van ] Rˆ 90 [ at centre at circumference/ midpts omtreks ]] 0..4 In NSR: Rˆ 90 and Nˆ Ŝ 80 (90 + ) [ s/e of/van ] 90 PS SR [line from centre chord/ln v midpt kd] S S R S S R () () () () [5]

17 Mathematics/P/Wiskunde V 7 DBE/November 05 CAPS/KABV Grade/Graad Memorandum QUESTION/VRAAG B T F E A C. Bˆ Â [tangent-chord theorem/rkl-kdst] Â Tˆ [corresp s/ooeenk e ; TE AC] Bˆ Tˆ. BE CE [tangents from same point/rklne v dieselfde pt] Bˆ Ĉ [ s opp equal sides/ e to gelke se] Ĉ Tˆ [ Bˆ Tˆ ] TBEC a cclic quad [converse s in the same segment] TBEC is koordevh [omgekeerde e in dieselfde segment]..4.5 Bˆ Tˆ [ s in the same segment/ e in dieselfde segment] Bˆ Tˆ [proven/bews in.] Tˆ Tˆ ET bisects/halveer B Tˆ C Bˆ Ê [tangent-chord theorem/rkl-kdst] Ĉ Ê [ s in the same segment/ e in dieselfde segment] TB TC [sides opposite equal s/se to gelke e] Ĉ Tˆ [alternate/verwiss s/e ; TE AC] Ĉ Â AT TC [sides opposite equal s/se to gelke e] T is a point that is equidistant from A, B and C on the circle/ T is 'n punt wat ewever is vanaf A,B en C op die sirkel. T is the centre of the circle/t is die middelpunt van die sirkel. S R S R R S S R S R S R R R S S S () () [7] TOTAL/TOTAAL: 50

NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 10

NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 0 MATHEMATICS P/WISKUNDE V NOVEMBER 05 MEMORANDUM MARKS: 50 PUNTE: 50 This memorandum consists of pages./ Hierdie memorandum bestaan