2016 2014 CAPS Stats Memo

Western Cape Education Department Examination Preparation Learning Resource 2016 STATISTIC MEMO MATHEMATICS Grade 12 Razzia Ebrahim Senior Curriculum Planner for Mathematics E-mail: Razzia.Ebrahim@wced.info / Razzia.Ebrahim@westerncape.gov.za Website: http://www.wcedcurriculum.westerncape.gov.za/index.php/component/jdownloads/category/1835- grade-12?Itemid=-1 Website: http://wcedeportal.co.za

Index Page 1. 2016 June Paper 2 3–4 2. 2016 Feb-March Paper 2 5–6 3. 2015 November Paper 2 7–8 4. 2015 June Paper 2 9 5. 2015 Feb-March Paper 2 10 – 11 6. 2014 November Paper 2 12 – 13 7. 2014 Exemplar Paper 2 14 – 15 2

Mathematics P2/Wiskunde V2 DBE/2016 SCE/SSE — Memorandum NOTE: If a candidate answered a question TWICE, mark only the FIRST attempt. If a candidate has crossed out an attempt to answer a question and did not redo it, 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 het, sien slegs die EERSTE poging na. As 'n kandidaat ‘n poging om ‘'n vraag te beantwoord, doodgetrek en nie oorgedoen het nie, sien die doodgetrekte poging na. Volgehoue akkuraatheid is op ALLE aspekte van die memorandum van toepassing. Staak nasien by die tweede berekeningsfout. Om antwoorde/waardes om 'n probleem op te los, te veronderstel, word NIE toegelaat NIE. QUESTION/VRAAG 1 | . 189 ¥189 Mean/Genitddelde: = TL Answer only: Full marks = 17,18 Slegs antwoord: Volpunte v answer 2) 1.2 | Min = 8, max = 26 Y min, max Median/Mediaan = 19 ¥ median Qi = 10, Qs = 24 YQAEQ “. (8:10:19; 24 ; 26) (3) 1.3 | ° ¥ box/boks/mond eT TT et 1a w whiskers/sor 6 10 14 18 22 26 (2) 1.4. | The data is skewed to the left/Die data is skeef na links. v answer OR/OF a) Negatively skewed/Negatief skeef Y answer qd) 1.5 | SD/SA = 6,46 vv answer (2) 1.6 | 17,18 + 6,46 = 23,64 Y interval .. 3 destinations/bestemmings ¥ answer (2) [12] Copyright reserved/Kopiereg voorbehou

Mathematics P2/Wiskunde V2 SCE/SSE — Memorandum DBE/2016 QUESTION/VRAAG 2 Temperature at midday (in °C) Middaguur- 18 | 21 | 19 | 26 | 32 | 35 | 36 | 40 | 38 | 30 | 25 temperatuur (in °C) | Number of bottles of ae eam n= | 12 | 15] 13 | 31 | 46 | st | 57 | 70 | 63 | 53 | 23 (500 mv) | 2.1 | 30; 53) v answer Q) 2.2 | a=- 38,51 Y value a b = 2,68 Y value b P= 2,68x — 38,51 Y equation @) 2.3 | -. § ~ 36,53 bottles vv answer (2) OR/OF . } ~2,68(28) — 38,51 ¥ substitution = 36,53 bottles answer (2) 2.4 | Strong/Sterk ¥ strong/sterk The majority of the points lie close to the regression line./Die meerderheid | V reason/rede punte lé naby die regressielyn. (2) OR/OF Strong/Sterk Y strong/sierk r=0,98 v reason/rede _ (2) 2.5 | Temperature cannot rise beyond a certain point as this would be life v reason/rede | threatening OR there is only so much water one can consume before it (I) becomes a risk to your health (hyponatremia)./Temperatuur kan nie hoér | as 'n sekere punt styg nie, anders raak dit lewensgevaarlik. OF ‘n persoon kan net ‘n sekere hoeveelheid water inneem, anders raak dit ‘n gesondheidsrisiko [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblie}

Mathematics/P2/Wiskunde V2 DBE/ Feb.–Mar./Feb.–Mrt. 2016 NSC/NSC – Memorandum QUESTION/VRAAG 1 32 62 20 30 40 50 60 70 75 80 1.1 The data is skewed to the left/Die data is skeef na links. answ/antw OR/OF The data is negatively skewed/Die data is negatief skeef. answ/antw (1) 1.2 Range/Omvang = 80 – 20  max. – min. = 60 answ/antw (2) 1.3 25% of the learners failed/van die leerders het gedruip  answ/antw (2) 1.4 445 + T4 54 = 9  20 T4 = 41  41  62 20 28 36 41 62 69 75 75 80  75  80 (6) [11] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 5

Mathematics/P2/Wiskunde V2 DBE/ Feb.–Mar./Feb.–Mrt. 2016 NSC/NSC – Memorandum QUESTION/VRAAG 2 2.1 2(15) + 8(25) + ...2(85) 3080  3 080 Mean/Gemiddelde = = 60 60 3080  = 51,33 messages per day/boodskappe per dag 60 answ/antw (3) 2.2 OGIVE/OGIEF grounding at 70 (10 ; 0) 65 plotting at upper 60 limits Cumulative Frequency/Kumulatiewe Frekwensie plotting. 55 cumulative f 50 smooth shape of curve 45 40 geanker by (10 ; 0) 35 stip by boonste 30 limiete 25 plot kumulatiewe f 20 gladde vorm 15 van kurwe 10 (4) 5 0 0 10 20 30 40 50 60 70 80 90 100 Number of messages/Getal boodskappe – 2.3 Number of days/Getal dae = 60 – 46 (see on graph above/sien op grafiek hierbo) 46 (accept 45 – 49) = 14 days/dae answ/antw (accept 11 – 15) OR/OF (2) 1 add correct Number of days/Getal dae = 2 + 3 + × 18 = 14 days/dae values/tel 2 korrekte waardes by answ/antw (2) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 6

Mathematics/P2/Wiskunde/V2 DBE/November 2015 NSC/NSS – Memorandum QUESTION/VRAAG 1 Fat/Vet (in g) 9 14 25 8 12 31 28 14 29 20 Energy/Energie 1 100 1 300 2 100 300 1 200 2 400 2 200 1 400 2 600 1 600 (in kJ) 1.1 1.1  Scatter plot/Spreidiagram plotting 3 points correctly  2600 plotting 6 2500 points 2400 correctly 2300  2200 plotting all points 2100 correctly Energy/Energie (in kJ) 2000 1900  1800 stip 3 punte 1700 korrek 1600 •  1500 stip 6 punte korrek 1400  1300 stip alle 1200 punte korrek 1100 1000 • (3) 900 800 700 600 500 400 1.2.2 300 1.2.2 200  100 any 2 of/ 0 enige 2 van 0 5 10 15 20 25 30 35 ±(11;1000) ±(19;1620) Fat/Vet (in g) ±(18;1543) (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 7

Mathematics/P2/Wiskunde/V2 DBE/November 2015 NSC/NSS – Memorandum 1.2.1 ŷ = 154,60 + 77,13(18)  subst = 1 542,94 ≈ 1 500 kJ  answ/antw (2) 1.3 (8 ; 300)  answ/antw (1) 1.4 r = 0,9520... ≈ 0,95  answ/antw (2) 1.5 very strong positive relationship/  very strong/ baie sterk positiewe verband baie sterk (1) [11] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 8

Mathematics/P2/Wiskunde V2 DBE/2015 NSCNSS – Memorandum QUESTION/VRAAG 1 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 9

Mathematics P2/Wiskunde V2 DBE/Feb.–Mrt. 2015 NSC/NSS – Memorandum QUESTION/VRAAG 1 1.1 3310 3310 x=  21 Answer only: Full marks 21 = 157,62 slegs antw: volpunte 157,62 (2) 1.2 (131 ; 142,5 ; 151 ; 173 ; 189)  131 and/ en 189  142,5  173  151 (4) 1.3 box/mond  whiskers/ 131 142,5 151 173 189 snor 120 130 140 150 160 170 180 190 200 (2) 1.4 positively skewed/positief skeef OR/OF skewed to the right/skeef na regs  answer/ antwoord (1) 1.5 σ = 17,27 answer/ antwoord (2) 1.6.1 x = 157,62 + p  answer (1) 1.6.2 σ = 17,27  answer/ antwoord (1) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 10

Mathematics P2/Wiskunde V2 DBE/Feb.–Mrt. 2015 NSC/NSS – Memorandum QUESTION/VRAAG 2 2.1 As the temperature increases, the sales of ice-creams increase/Soos  reason/rede die temperatuur styg, neem die verkope toe. (1) OR/OF As the temperature decreases, the sales of ice-creams decrease/Soos  reason/rede die temperatuur daal, neem die verkope af. (1) 2.2 The liveable temperature cannot keep on increasing/Die leefbare  reason/rede temperatuur kan nie aanhou styg nie. (1) 2.3 a = – 460,35  –460,35 b = 30,09  30,09 yˆ = 30,09 x − 460,35 OR/OF yˆ = −460,35 + 30,09 x  equation/vgl Answer only: Full marks (4) slegs antw: volpunte 2.4 r = 0,96  0,96 (1) 2.5 There is a very strong positive relationship (correlation)/Daar is 'n  very strong/baie baie sterk positiewe verband (korrelasie). sterk (1) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 11

Mathematics P2/Wiskunde V2 DBE/November 2014 NSC/NSS – Memorandum QUESTION/VRAAG 1 1.1 816 816 x= = 68  12 12  68 (2) 1.2 σ = 18,42  answer/antw (1) 1.3 (68 – 18,42 ; 68 + 18,42) = (49,58 ; 86,42)  interval ∴ 6 candidates had a mark within one standard deviation of the  answer/antw mean/6 kandidate het 'n punt binne een standaardafwyking vanaf (3) die gemiddelde. 1.4 a = 22,828... = 22,83  value of a/ waarde van a b = 0,66429... = 0,66  value of b/ waarde van b ∴ yˆ = 0,66 x + 22,83 OR/OF yˆ = 22,83 + 0,66 x  equation/vgl (3) 1.5 yˆ = 0,66 x + 22,83 y = 0,66(60) + 22,83  subs of 60 into 62,43...% ≈ 62% equation  answer/antw OR/OF (2) 62,69% ≈ 63%  answer/antw (2) 1.6 (82 ; 62)  answer/antw (1) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 12

Mathematics P2/Wiskunde V2 DBE/November 2014 NSC/NSS – Memorandum QUESTION/VRAAG 2 2.1 50 < x ≤ 60 OR/OF 50 ≤ x < 60 OR/OF  answer/antw between 50 and 60/tussen 50 en 60 (1) 2.2.1 Class Frequency Cumulative frequency Klas Frekwensie Kumulatiewe frekwensie 20 < x ≤ 30 1 1 30 < x ≤ 40 7 8 8 40 < x ≤ 50 13 21 50 < x ≤ 60 17 38 60 < x ≤ 70 9 47 70 < x ≤ 80 5 52 80 < x ≤ 90 2 54 90 < x ≤ 100 1 55  55 (2) 2.2.2 60  grounding at (20 ; 0)/ anker by (20 ; 0)  plotting at 50 upper limits/ plot by boonste limiete 40  smooth shape of curve/gladde kurwe Cumulative Frequency/ 30 20 Kumulatiewe frekwensie 10 0 0 10 20 30 40 50 60 70 80 90 100 Speed in km per hour/ Spoed in km per uur (3) 2.3 55 – 44 (accept/aanvaar 43 – 45)  44 ≈ 11 motorists/motoriste  11 (accept/aanvaar 10 – 12 motorists/motoriste) (2) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief 13

Wiskunde/V2 DBE/2014 NSS – Graad 12 Model – Memorandum VRAAG 1 1.1 Indien die aantal dae wat ‘n atleet oefen toeneem, neem die tyd  verduideliking 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. (1) 1.2 (60 ; 18,1)  (1) 1.3 a = 17,81931464…  a b = – 0,070685358...  b ∴ ŷ = – 0,07x + 17,82  vergelyking (4) 1.4 ∴ ŷ ≈ – 0,07(45) + 17,82  substitusie ≈ 14,67 sekondes  antwoord (2) 1.5 r = – 0,74 (–0,740772594...)  r (2) 1.6 Daar is ‘n redelike sterk verwantskap tussen die veranderlikes.  redelik sterk (1) [11] Kopiereg voorbehou Blaai om asseblief 14

Wiskunde/V2 DBE/2014 NSS – Graad 12 Model – Memorandum VRAAG 2 2.1 anker by 0 170 plot by boonste 160 limiete 150  gladde kurwe 140 130 120 110 100 Kumulatiewe frekwensie 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 110 120 Tyd (in uur) (3) 2.2 40 ≤ t < 60  klas (1) 2.3 (96 ; 164) 164 ∴ 172 – 164 = 8 leerders 8 (2) 2.4 Frekwensie: 25; 44; 60; 28; 9; 6 frekwensie  middelpunte 25 × 10 + 44 × 30 + 60 × 50 + 28 × 70 + 9 × 90 + 6 × 110 gemiddelde = 172 8000  8000 172 =  antwoord 172 = 46,51 uur (4) [10] Kopiereg voorbehou Blaai om asseblief 15