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

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1 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 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 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) [3]

2 QUESTION/ VRAAG Q SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/. a =, a- value/waarde b = 0, b-value/waarde y =,7 + 0,0x Equation/Vergelyking (3). r = = 0,85 r ().3 y =,7 + 0,0(350) Substitute/Instel y = 47,9 = 47 Ans/Antw ().4 a positive strong correlation/ sterk positief Ans/Antw () [7] QUESTION/ VRAAG 3 Q3 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ 3. AB = (4 + ) + (9 ) Subst in correct formula/instel in korrekte = formule = 00 Ans/Antw = 0 () 3. AB = BC = 0 x value/waarde y value = BC y axis y value/waarde () C(4; 9) K ( x + x K ( 4 K( ; 0) ; y + y ; 9 + ) m = y y = 9 x x 4 + = 8 6 = 3 y y = m(x x ) y = 3(x + ) y = 3x y = 3x m AC = 3 Angle of inclination = tan (3) = 7,57 θ = 90 7,57 = 8,43 OR In the right-angled triangle: 3.6 tan θ = 6 8 θ = 8.43 Area ABC =. BC. h ) = (0)(6) = 30 sq units ubst in correct formula/ Instel in korrekte formule Ans/ Antw m ubst A or C point into correct formula/ Stel A of C in korrekte formule Ans/Antw tan = m of 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 () (3) [7]

3 QUESTION/ VRAAG4 Q4 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ 4. OC tangent [r tangent] both/ beide S s CE tangent [r tangent] O, C and E straight line [adjacent s = 80 ] R 4. m OC = 0 0 = Substitute/ Vervang C Ans/ Antw 4.3 m CD = y y = x x 6 + t = (t ) = 4 t = t = m tangent = AC: y y = m(x x ) y + = (x ) y = x y = x D is the midpoint of circle x coordinate: + x = 3 + x = 6 x = 5 y coordinate: y 6 y = y = 0 E(5; 0) 4.6 AC D = 90 [radius tangent] AE is the diameter ACE AE = (5 5) + (0 + 0) AE = AE = 0 radius = (0) = 5 Midpnt AE ( ; 0 ) Centre ofcircle (5;-5) Equation of circle ACE: (x 5) + (y + 5) = Circle centre O: x + y = 5 Diameter = 5 0 < r < < r < 4 5 m tangent/raaklyn Substitute( any point) correct equation/ Vervang enige punt m tangent/raaklyn Substitute( any point) correct equation/ Vervang enige punt Answer/ Antw x value/ waarde y value/ waarde AE diameter/ middellyn AE = 0 Radius = 5 Midpnt Equation of Circle/Vegel van sirkel Point/ Punt r (6) r = 5 Diameter / Middellyn Endpoints/ Eindpunte () () () (3) () []

4 QUESTION/ VRAAG 5 Q5 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ () = p + (opp) () (p) = x x = p 5.. sin 4 = sin( ) = sin 34 = p sin 34 Ans/ Antw () 5.. cos 34.cos (- ) + sin 34.sin 338 = cos 34. cos + sin 34 ( sin ) = cos 34. cos sin 34. sin = cos (34 + ) = cos 56 = p reduction/ reduksie compound angles/ saamgestelde hoeke p 5..3 cos 68 = cos (34 ) = cos 34 = ( p ) = ( p ) = p 5.. cos(90ᵒ θ). sin(θ). sin (80ᵒ + θ) cos(70 + θ). = = sin θ. (sin θ) ( sinθ). (cosθ) sinθ cosθ. sin θ sin θ. cosθ. = 5.. sin x tan x = sin x cos x sin x = cos x sin x = sin x sin x = Double angle/ dubbele hoek Ans/ Antw () sinθ ( sin θ) sin θ cos θ sinθ cosθ (6) cos x sin x cos x sin x sin x 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/ (3) (80 ; -0,5) (-90 ; -0,87) - 6. sin x = cos (x 60 ) sin x = sin (90 (x 60 )) sin x = sin(50 x) sin(80 + x) = sin (50 x) 80 + x = 50 x + n(360 ), nε Z 3x = 30 + n(360), n Z x = 0 + n(0 ) equate the equations / vergelyking co-functions/ kofunksies sin(80 + x) Ans/ Antw (5) 6.4 Inequality/ (3) 0 x 0 Ongelykheid Ans/ Antw 6.4 y = sin (x + 30 ) Ans/ Antw () 6.5 g must shift 30 right 30 right/regs () [5]

6 QUESTION/VRAAG 7 Q7 SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS MARK/ 7. cosθ = DC p p. cosθ = DC BD sin (90 θ) = BD cos θ = DC sin θ DC sin θ. cos θ BD = DC.cos θ butp cosθ = DC sin θ.cos θ BD = pcos θ. cos θ sin θ. cos θ BD = pcosθ sinθ sin 30 = AC p 3 sin 30 = AC AC =,5 m BD = 3 cos 30 sin 30 = 3 ( 3 ) = 3 AB = AD + BD AD. BDcos ADB = 3 + ( 3 ) = cos 70 4 = 7.97 AB =.8 metres (3) ( 3 ) cos 70 DC Subst in Sine Rule/ Sinus reël implification/ Vereenvoudig ubst/ vervang DC Simplification/ Vereenvoudig (5) ubstitution /Instel Ans/Antw 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.. B ÂE = 90 in semi circle/ in halwesirkel S R () MARK/ 8.. Ê = 80 opp angles cyclic quad/ teenoorst e koordevierhoek S R () 8..3 D =45 ext of FED/ buite van FED S R () 8. ˆB = 35 Interior of F = 35 given AB CF 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/Trek GH Proof/ Bewys: A = D given/gegee AG = DE AH = DF Constr./ konstr Constr./ konstr GAH EDF (s; ; S) G = E But / maar B = E given/gegee G =B GHll BC corresp s = / ooreenk. e = AG AB AH AC DE DF AG = DE ; AH = DF AB AC constr/ konstr. R G =B &R &R (7)

9 9. C F B E D A 9.. ) B = E tan-chord thm/ raakl- koordstelling E = E equal chords; equal s /gelyke koorde gelyke e E = B &R (3) 9.. In BDA and / en EFB : BD A = F ext of cyclic quad/ buite van koordevierhoek E = B Proven BDAlll EFB ( ; ; ) In BDA and / en EFB : OR ) BD A = F ext of cyclic quad/ buite van koordevierhoek ) B = E tan-chord thm/ raakl- koordstelling E = E equal chords; equal s /gelyke koorde gelyke e E = B A = B 3 BDAlll EFB sum of s in / e van &R &R &R &R &R &R 9.. BD EF = DA FB BD. FB = EF. DA BD² = DA.EF BD = FB &R () [6]

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 BE = BS Prop. Thm; EF ll PS/ Ewer.

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 BE = BS Prop. Thm; EF ll PS/ Ewer. Stelling; EF ll PS BF BP. BF BS R () 0.. In ΔBGP and/ en ΔBEG: ) Ĝ = ˆP Tan chord thm/ Raaklyn koordstelling ) B B common / gemene BGPlll BEG ( ; ; ) 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 &R &R S&R &R BGPlll BE 0..3 BG = BP BE BG BG² = BP.BE BP. BF BS BG = BP. BG = BP. BF BS BG BP = BF BS BGPlll BEG Subst (3) [0]

11 QUESTION/ VRAAG Q SUGGESTED ANSWER/ VOORGESTELDE ANTWOORD DESCRIPTORS/ BESKRYWERS.... FC FC= DB 5 DB= 45 EF llad DE llab 0 cm &R MARK/ answer/antw (3) DC = 36 &R answer/antw. Area ECF Area ABC = Area ECF Area ABC = 3 8.4k. 8. sin C. 9k. 8. sin C ½. 4k. 8. sinc ½. 9k sinc Answer TOTAL / TOTAAL: [50] []

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

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