A/CA Cum frequency values/ Kum.frek. waardes

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1 SEPTEMBER P/ V 06 MARKING/ NASIEN MEMORANDUM NOTE: If a candidate answers a question TWICE, only mark the FIRST attempt. If a candidate has crossed out an attempt of a question and not redone the question, mark the crossed out version. Consistent accuracy applies in ALL aspects of the marking memorandum. Assuming answers/values in order to solve a problem is NOT acceptable.. NOTA: As 'n kandidaat 'n vraag TWEEKEER beantwoord, merk slegs die EERSTE poging. As 'n kandidaat 'n poging om die vraagte beantwoord, doodgetrek het en nie dit oorgedoen het nie, merk die doodgetrekte poging. Volgehoue akkuraatheid word in ALLE aspekte van die Nasienmemorandum toegepas. Aanvaarding van antwoorde/waardes om 'n probleem op te los, is ONaanvaarbaar. QUESTION/ VRAAG Q DESCRIPTORS/ BESKRYWERS MARK/. Aantal leerders Kum f Tyd in minute Number of Cum f Time in minutes learners < t < t < t < t < t < t A/CA Cum frequency values/ Kum.frek. waardes anchor point (5;0)/ Begin punt Kummulatiewe frekwensie use cum freq/ gebruik kum frek use upper limits/ boonste limiete smooth curve/ gladde kurwe Tyd in minute.3 average time = 4,95 min ans/ antw.4 SD = 6,89 ans/ antw.5 > 4,95 + 6,89 =, = 98 learners,84 accept/ aanvaar accept/aanvaar [3]

2 QUESTION/ VRAAG Q SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/. a =, b = 0, ,70,0 a- value/waarde b-value/waarde Equation/Vergelyking. r = = 0,85 ().3,70,0350 y = 47,9 = 47 Substitute/Instel Ans/Antw.4 a strong positive correlation/ sterk positief Ans/Antw () [7] QUESTION/ VRAAG 3 Q3 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ Subst in correct 6 8 formula/instel in korrekte formule 00 Ans/Antw BC 4; ; ; 9 ; tan 3 7, ,57 8,43 OR In the right-angled triangle: tan Area ABC =. BC. h = (0)(6) = 30 sq units value/waarde value/waarde ubst in correct formula/ Instel in korrekte formule Ans/ Antw ubst A or C point into correct formula/ Stel A of C in korrekte formule Ans/Antw tan = m in inclination/ Inklinasie Comple s/ Kompl Ants/Antw OR correct trig ratio/ korrekte trig verhouding correct values /korrekte waardes Ans/ Antw correct formula/ korrekte formule base/basis = 0 height/hoogte = 6 ans/ antw [7]

3 QUESTION/ VRAAG4 Q4 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ 4. OC tangent [r tangent] CE tangent [r tangent] O, C and E straight line [adjacent s = 80 ] : D is the midpoint of circle : : 6 0 5; : ACE ; 0 (5;-5) Equation of circle ACE: both/ beide S s R Substitute/ Vervang C Ans/ Antw / Substitute( any point) correct equation/ Vervang enige punt / Substitute( any point) correct equation/ Vervang enige punt Answer/ Antw value/ waarde value/ waarde 5 Diameter / Middellyn Endpoints/ Eindpunte AE diameter/ middellyn AE = 0 Radius = 5 Midpnt Equation of Circle/Vegel van sirkel Point/ Punt (6) []

4 QUESTION/ VRAAG 5 Q5 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ 5.. p sin4 sin80 34 sin cos 34.cos (- + sin 34.sin 338 cos34. sin34 cos34.cos sin34.sin = cos (34 + ) = cos 56 sin34 Ans/ Antw reduction/ reduksie compound angles/ saamgestelde hoeke 5..3 cos68 cos34 cos 34 = p 5.. cos90ᵒ.sin. 80ᵒcos70. sin.sin. sinθ Double angle/ dubbele hoek Ans/ Antw sin cos sinθ (6) sin Ans/ Antw [8]

5 QUESTION/ VRAAG 6 Q6 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS 6. y g f x shape / vorm endpoints/ eindpunte intercepts with axes/ snypunte met asse MARK/ (80 ; -0,5) (-90 ; -0,87) - 6. sincos 60 sinsin sinsin50 sin80 sin , , 0 0 equate the equations / vergelyking co-functions/ kofunksies sin80 Ans/ Antw (5) 6.3 Inequality/ 0 0 Ongelykheid Ans/ Antw 6.4 sin 60 Ans/ Antw 6.5 must shift 30 right 30 right/regs [5]

6 QUESTION/VRAAG 7 Q7 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ 7. cosθ 7. p.cosθ sin 90 sin cos BD BD sin.cos...cos sin.cos sin30 3sin30,5 but DC Subst in Sine Rule/ Sinus reël implification/ Vereenvoudig ubst/ vervang DC Simplification/ Vereenvoudig (5) ubstitution /Instel Ans/Antw 7.3 3cos30 sin cos metres cos70 BD Cos rule/reël ubst / vervang AB AB (5) []

7 EUCLIDEAN GEOMETRY/ EUKLIDIESE MEETKUNDE Statement/ Bewering R Reason/ Rede /R Statement + Reason/ Bewering + Rede QUESTION/ VRAAG 8 8. Q8 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS 8.. BÂE 90 in semi circle/ in halwesirkel S R MARK/ 8.. Ê = 80 int angles cyclic quad/ binne koordevierhoek S R 8..3 D =45 ext of FED/ buite van FED S R 8. ˆB = 35 Interior of = 35 given Alternate angles = S R S R [0]

8 QUESTION/ VRAAG 9 Q9 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS 9. MARK/ G H Consider other proofs as well/ Oorweeg ander bewyse ook Constr./Konstr.: Measure/Meet AG=DE on/op AB and/en AH = DF on/op AC. Draw/TrekGH Proof/ Bewys: D given/gegee AG = DE AH = DF Constr./ konstr Constr./ konstr ;; = constr/ konstr. R But / maar given/gegee = GHll BC corresp = / ooreenk. = AG = AB AH AC DE DF = AG = DE ; AH = DF AB AC = &R &R 7

9 9. C F B E D A 9.. ) tan-chord thm/ raakl- koordstelling equal chords; equal s /gelykekoordegelyke e &R R 9.. In and / en : BDA = ext of cyclic quad/ buite van koordevierhoek Proven lll (<;<;<) In and / en : BDA = OR ext of cyclic quad/ buite van koordevierhoek R &R &R tan-chord thm/ raakl- koordstelling equal chords; equal s /gelykekoordegelyke e lll sum of s in / e van &R &R &R BD² = DA.EF BD = FB &R [6]

10 QUESTION/ VRAAG 0 P S D E F G A B C Q0 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS 0.. alt s / verwisselende e; YT RQ R () MARK/ 0.. BP BE = EF ll PS. R 0.. In ΔBGP and/ en ΔBEG: ) ˆP= x Tan chord ˆP= G ) PBG ˆ = EBˆ G common / gemene lll (<;<;<) OR In ΔBGP and/ enδbeg ) Ĝ = ˆP Tan chord ) Bˆ = Bˆ common / gemene 3) BGP ˆ = BEˆ G sum of s in / e van S&R S &R &R S&R &R lll 0..3 lll BG² = BP.BE... Substi [0]

11 QUESTION/ VRAAG Q SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS.... FC 4 0 = 5 FC= = DB 5 DB= 45 EF llad DE llab 0 cm &R MARK/ answer/antw DC = 36 &R answer/antw..4.6.sin.9.8.sin ½.4.6. ½ TOTAL / TOTAAL: [50] []

A/CA Cum frequency values/ Kum.frek. waardes

A/CA Cum frequency values/ Kum.frek. waardes Kummulatiewe frekwensie SEPTEMBER P/ V 06 MARKING/ NASIEN MEMORANDUM NOTE: If a candidate answers a question TWICE, only mark the FIRST attempt. If a candidate has crossed out an attempt of a question