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 uit bladsye.
Mathematics/P/Wiskunde/V DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) NOTE: If a candidate answers a question TWICE, mark only the FIRST attempt. If a candidate crossed out an attempt of a question and did not redo the question, mark the crossed-out version. Consistent accuracy applies in ALL aspects of the marking memorandum. Stop marking at the second calculation error. Assuming answers/values in order to solve a problem is NOT acceptable. LET WEL: Indien 'n kandidaat 'n vraag TWEE KEER beantwoord, sien slegs die EERSTE poging na. Indien 'n kandidaat 'n antwoord doodgetrek het en nie oorgedoen het nie, sien die doodgetrekte poging na. Volgehoue akkuraatheid word in ALLE aspekte van die memorandum toegepas. Hou op nasien by die tweede berekeningsfout. Om antwoorde/waardes om 'n probleem op te los, te veronderstel, word NIE toegelaat NIE. QUESTION/VRAAG 4 5 6 6 7 7 8 8 9 9 9 0 4 4 9. Median/Mediaan 9 seconds/sekondes. Lower quartile/onderste kwartiel (Q ) 7 Upper quartile/boonste kwartiel (Q ). 4 7 9 9 6 0 4 8.4. IQR/IKO 6 9 7.4. 75% of the boys took at least 9 seconds to complete the puzzle./ 75% van die seuns het ten minste 9 sekondes geneem om die legkaart te voltooi..5 About 50% but not more than 75% of the boys completed the puzzle in less than seconds./ongeveer 50% maar nie meer as 75% van die seuns het die legkaart in minder as sekondes voltooi. More than 75% of the girls completed the puzzle in less than seconds./meer as 75% van die dogters het die legkaart in minder as sekondes voltooi. Therefore more girls completed the puzzle in less than seconds./meer dogters het dus die legkaart in minder as sekondes voltooi. () Q Q () box/mond whiskers/snor Q Q 75% () () () relevant/relevante explanation/verduideliking girls/dogters () [0]
Mathematics/P/Wiskunde/V DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG NUMBER OF HOURS GETAL UUR (h) FREQUENCY FREKWENSIE 0 < h 0 < h 4 5 4 < h 6 0 6 < h 8 5 8 < h 0 5 0 < h 5. The modal class is/die modale klas is 6 < h 8 6 < h 8. 0 + 5 +... + 5 Average/Gemiddelde 0 70 Estimated mean/geskatte gemiddelde ( x ) 0 midpts/midpte 70 () 6,08 hours/uur [4]
Mathematics/P/Wiskunde/V 4 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG y A(0 ; 4) D( 4 ; ) L x K 0 ; 4 B(4 ; 4) C... DB ( x x ) + ( y y ) ( 4 4) + ( ( 4)) 64 + 6 00 0 x + x y + y M ; 4 + 4 4 M ; M(0 ; ) mad y y x x 4 0 ( 4) 4 correct formula/ korrekte formule subst correct formula/ korrekte formule x-value/waarde y-value/waarde correct formula/ korrekte formule subst into/in gradient form/ gradiëntvorm
Mathematics/P/Wiskunde/V 5 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum).4 y y m AB x x 4 ( 4) 0 4 8 4 m m AD AB AD AB.5 parallelogram with one internal angle 90 parallelogram met een binnehoek 90.6 m KL mad [KL AD] y x 4.7 AC DB 0 units [diag of rectangle /hkle v regh ] 4 yc 0 yc 6 C(0 ; 6) OR/OF m BC mad [sides of rectangle /sye v regh ] 4 yc 4 0 8 yc 4 yc 6 C(0 ; 6) subst gradient of AB/ gradiënt van AB m AD m AB R () gradient of KL gradiënt van KL equation/vgl R equation/vgl R equation/vgl () [8]
Mathematics/P/Wiskunde/V 6 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG 4 P 6 4 S 8 6 Q 0 θ R 4.. 4.. 4.. 4..4 4. tan Pˆ 0 5 Accept answers as unsimplified 4 fractions. 6 sin S Qˆ R 0 5 cos θ 0 5 Aanvaar antwoorde as nievereenvoudigde breuke. 6 answer/antw 0 5 sec S Rˆ Q 6 cot θ cosec QRˆ S 0 0 4 8 0 0 4 8 () () () () [7]
Mathematics/P/Wiskunde/V 7 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG 5 y β r O R x P(x ; y) 5.. x 5 r 7 x + y r ( 5) + y 7 y 64 y 8 5..(a) 8 sin β 7 5..(b) cos 0.tan β 8. 5 8 4 5 5 5.. R ÔP 80 + 8,07 08,07 5.. tan x, x 65,75 5.. sec( x + 0 ) 5, 759 5.. cos( x + 0 ) 0,7... OR/OF x +0 80,0 x 70, 0 sin x,4 0, sin x,4 0, sin x 0,648 x 40,9 cos( x + 0 ) 5,759 x-value/waarde r-value/waarde using/gebruik Pyth y-value/waarde (4) () 8 5 ref /verw () cos( x 0 ) + ref/verw addition/optelling () 5,759 multipl/vermenigv [8]
Mathematics/P/Wiskunde/V 8 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG 6 6. amplitude 6. min value/waarde + 6. y g f 0 90 80 70 x 60 () () y-intercept/afsnit (90 ; ) (70 ; 0) 6.4. f ( 80 ) g(80 ) correct values/ korrekte waardes () 6.4. x (90 ; 70 ) OR/OF 90 < x < 70 correct values/ korrekte waardes notation/notasie () 6.5. f (x) cos x () 6.5. y [ 5 ; ] OR/OF 5 y () []
Mathematics/P/Wiskunde/V 9 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG 7 8 cm 50 cm 0 cm 0 cm 7. Vol of post vol of rectangle + vol of pyramid area of base h + area of base h Vol van pilaar vol v reghoek + vol v piramide oppervl v basis h + oppervl v basis h sum of formulae/ som v formules Volume ( 0 0 50) + ( 0 0 8) 7 400 cm 7. Slant height of pyramid/skuinshoogte van piramide 8 7 + 5 subst into/in both/beide formulae 7 Total surface area of pyramid area of base + (perimeter of base slant height) Surface area of pyramid section 4 0 7 00 cm Totale buite-oppervlakte van 'n piramide oppervl v basis + (omtrek v die basis skuinshoogte) Surface area of pyramid section/ Buite-opp van piramide gedeelte 4 0 7 00 cm subst into/in correct/korrekte form
Mathematics/P/Wiskunde/V 0 DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) 7. Volume (new) 4 450 cm ( 7400) Number of smaller posts that can be made Volume (nuwe) 4 450 cm ( 7 400) G etal kleiner pilare wat gemaak kan word 4 7 400 450 7 400 450 4 50 4 () 4 OR/OF Volume (nuwe) ( 5 5 50) + ( 5 5 8) 4 50 cm G etal kleiner pilare wat gemaak kan word 7 400 450 4 50 Volume (new) 4 + 5 5 8 ( 5 5 50) ( ) 450 cm G etal kleiner pilare wat gemaak kan word 7 400 450 4 () 4 [8]
Mathematics/P/Wiskunde/V DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG 8 A B O 6,87 8 cm D C 8.. C Dˆ O 6,87 () 8.. A ÔD 90 () 8. AO AO tan 6,87 tan 6,87 8 8 AO 8 tan 6,87 6 cm () 8. AD 8 + 6 [Theorem of Pythagoras/se 00 stelling] AD 0 with AD 0 reason/met rede AE EB [converse midpoint theorem/omgekeerde midptst] OE AD 5 cm [midpoint theorem/midptst] S R 5 cm (4) [8]
Mathematics/P/Wiskunde/V DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) QUESTION/VRAAG 9 9. 9.. Two sides and an included angle/twee sye en 'n ingeslote hoek R 9.. one pr of sides and R een pr sye en 9.. S DE DF [DE EF] DF BC [opp sides of parm/tos sye v parm ] S DE BC () () ()
Mathematics/P/Wiskunde/V DBE/November 05 CAPS/KABV Grade/Graad 0 (Memorandum) 9. S R M C P B Q A 9.. In SAR, SB BA [given/gegee] QR QA [converse midpoint th/omgekeerde midptst] But/maar QR SP [opp sides of parm /tos sye v parm] SP QA 9.. SP QA [proven/bewys] SP QA [opp sides of parm /tos sye v parm ] SPAQ is a parm [one pr of sides and /een pr sye en ] 9.. M midpoint of/midpt van PR and/en B midpoint of/midpt van PQ [diag bisect of parm/hkle halveer parm] S R S R (4) both statements/ beide bewerings R () S MB QR MB AR 4MB AR [midpoint theorem/midptst] S R QR AR (4) [4] TOTAL/TOTAL: 00