MATHEMATICS Grade 12

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1 Western Cape Education Department Examination Preparation Learning Resource 2016 STATISTIC MEMO MATHEMATICS Grade 12 Razzia Ebrahim Senior Curriculum Planner for Mathematics / Website: grade-12?itemid=-1 Website:

2 Index Page June Paper Feb-March Paper November Paper June Paper Feb-March Paper November Paper Exemplar Paper

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5 Mathematics/P2/Wiskunde V2 DBE/ Feb. Mar./Feb. Mrt NSC/NSC Memorandum QUESTION/VRAAG The data is skewed to the left/die data is skeef na links. OR/OF The data is negatively skewed/die data is negatief skeef. 1.2 Range/Omvang = = 60 answ/antw answ/antw max. min. answ/antw % of the learners failed/van die leerders het gedruip answ/antw T 54 = 9 T = (6) [11] 5

6 Mathematics/P2/Wiskunde V2 DBE/ Feb. Mar./Feb. Mrt NSC/NSC Memorandum QUESTION/VRAAG (15) + 8(25) +...2(85) 3080 Mean/Gemiddelde = = = 51,33 messages per day/boodskappe per dag Cumulative Frequency/Kumulatiewe Frekwensie OGIVE/OGIEF answ/antw (3) grounding at (10 ; 0) plotting at upper limits plotting. cumulative f smooth shape of curve geanker by (10 ; 0) stip by boonste limiete plot kumulatiewe f gladde vorm van kurwe (4) Number of messages/getal boodskappe 2.3 Number of days/getal dae = (see on graph above/sien op grafiek hierbo) = 14 days/dae OR/OF 46 (accept 45 49) answ/antw (accept 11 15) 1 Number of days/getal dae = = 14 days/dae 2 add correct values/tel korrekte waardes by answ/antw [9] 6

7 Mathematics/P2/Wiskunde/V2 DBE/November 2015 NSC/NSS Memorandum QUESTION/VRAAG 1 Fat/Vet (in g) Energy/Energie (in kj) Energy/Energie (in kj) Scatter plot/spreidiagram Fat/Vet (in g) 1.1 plotting 3 points correctly plotting 6 points correctly plotting all points correctly stip 3 punte korrek stip 6 punte korrek stip alle punte korrek (3) any 2 of/ enige 2 van ±(11;1000) ±(19;1620) ±(18;1543) 7

8 Mathematics/P2/Wiskunde/V2 DBE/November 2015 NSC/NSS Memorandum ŷ = 154, ,13(18) = 1 542, kj subst answ/antw 1.3 (8 ; 300) answ/antw 1.4 r = 0, ,95 answ/antw 1.5 very strong positive relationship/ baie sterk positiewe verband very strong/ baie sterk [11] 8

9 Mathematics/P2/Wiskunde V2 QUESTION/VRAAG 1 NSCNSS Memorandum DBE/2015 9

10 Mathematics P2/Wiskunde V2 DBE/Feb. Mrt NSC/NSS Memorandum QUESTION/VRAAG x = 21 Answer only: Full marks 21 = 157,62 slegs antw: volpunte 157, (131 ; 142,5 ; 151 ; 173 ; 189) 131 and/ en , (4) , box/mond whiskers/ snor 1.4 positively skewed/positief skeef OR/OF skewed to the right/skeef na regs answer/ antwoord 1.5 σ = 17,27 answer/ antwoord x = 157, 62 + p answer σ = 17,27 answer/ antwoord [13] 10

11 Mathematics P2/Wiskunde V2 DBE/Feb. Mrt NSC/NSS Memorandum QUESTION/VRAAG As the temperature increases, the sales of ice-creams increase/soos die temperatuur styg, neem die verkope toe. reason/rede OR/OF As the temperature decreases, the sales of ice-creams decrease/soos die temperatuur daal, neem die verkope af. 2.2 The liveable temperature cannot keep on increasing/die leefbare temperatuur kan nie aanhou styg nie. 2.3 a = 460,35 b = 30,09 y ˆ = 30,09x 460,35 OR/OF yˆ = 460, , 09x Answer only: Full marks slegs antw: volpunte reason/rede reason/rede 460,35 30,09 equation/vgl (4) 2.4 r = 0,96 0, There is a very strong positive relationship (correlation)/daar is 'n baie sterk positiewe verband (korrelasie). very strong/baie sterk [8] 11

12 Mathematics P2/Wiskunde V2 DBE/November 2014 NSC/NSS Memorandum QUESTION/VRAAG x = = σ = 18,42 answer/antw 1.3 (68 18,42 ; ,42) = (49,58 ; 86,42) 6 candidates had a mark within one standard deviation of the mean/6 kandidate het 'n punt binne een standaardafwyking vanaf die gemiddelde. 1.4 a = 22, = 22,83 b = 0, = 0,66 y ˆ = 0,66x + 22, 83 OR/OF yˆ = 22,83+ 0, 66x 1.5 y ˆ = 0,66x + 22, 83 y = 0,66(60) + 22,83 62,43...% 62% 62,69% 63% OR/OF interval answer/antw (3) value of a/ waarde van a value of b/ waarde van b equation/vgl (3) subs of 60 into equation answer/antw answer/antw 1.6 (82 ; 62) answer/antw [12] 12

13 Mathematics P2/Wiskunde V2 DBE/November 2014 NSC/NSS Memorandum QUESTION/VRAAG < x 60 OR/OF 50 x < 60 OR/OF between 50 and 60/tussen 50 en Class Klas Frequency Frekwensie 20 < x < x < x < x < x < x < x < x Cumulative frequency Kumulatiewe frekwensie answer/antw 8 55 grounding at (20 ; 0)/ anker by (20 ; 0) plotting at upper limits/ plot by boonste limiete smooth shape of curve/gladde kurwe Cumulative Frequency/ Kumulatiewe frekwensie Speed in km per hour/ Spoed in km per uur (accept/aanvaar 43 45) 11 motorists/motoriste (accept/aanvaar motorists/motoriste) (3) [8] 13

14 Wiskunde/V2 NSS Graad 12 Model Memorandum DBE/2014 VRAAG Indien die aantal dae wat n atleet oefen toeneem, neem die tyd waarin die 100m naelloop afgelê word, af. OF Indien die aantal dae wat n atleet oefen afneem, neem die tyd waarin die 100m naelloop afgelê word, toe. OF Hoe meer dae n atleet oefen, hoe korter is die tyd wat hy die 100m naelloop aflê. verduideliking 1.2 (60 ; 18,1) 1.3 a = 17, b = 0, ŷ = 0,07x + 17, ŷ 0,07(45) + 17,82 14,67 sekondes a b vergelyking substitusie antwoord 1.5 r = 0,74 ( 0, ) r 1.6 Daar is n redelike sterk verwantskap tussen die veranderlikes. redelik sterk [11] (4) Kopiereg voorbehou Blaai om asseblief 14

15 Wiskunde/V2 VRAAG 2 NSS Graad 12 Model Memorandum DBE/ anker by plot by boonste 160 limiete gladde kurwe Kumulatiewe frekwensie t < 60 klas 2.3 (96 ; 164) = 8 leerders Frekwensie: 25; 44; 60; 28; 9; Tyd (in uur) gemiddelde = = 172 = 46,51 uur frekwensie middelpunte antwoord (3) (4) [10] Kopiereg voorbehou Blaai om asseblief 15

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