Mathematics Grade 11 Paper 3 Eastern Cape November 2012 Memo

Downloaded from hlayiso.com Province of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE/ GRAAD 11 NOVEMBER 2012 MATHEMATICS P3/ WISKUNDE V3 MEMORANDUM MARKS: 100 PUNTE: This memorandum consists of 6 pages./ Hierdie memorandum bestaan uit 6 bladsye.

Downloaded from hlayiso.com 2 MATHEMATICS P3 (Memo) (NOVEMBER 2012) QUESTION/ VRAAG 1 1.1 1.1.1 P(A and/en B) = P(A) × P(B) √ P(A) × P(B) (1) 1.1.2 P(A or/of B) = P (A) + P(B) √ P(A) + P(B) (1) 1.2 1.2.1 (a) 30 √ (b) 150 √ (c) 40 √ (d) 150 √ (e) 160 √ (f) 140 √ (6) 1.2.2 P(M passed and S passed./ √ 0,40 (1) (W slaag en S slaag) = = 0,40 1.2.3 P(M passed and S failed/ √ 0,10 (1) (W slaag en S druip) = = 0,10 1.2.4 P(M passed and S passed/ (W slaag en S slaag) = = 0,40 P(M passed/ W slaag) = = 0,50 P(S passed/ S slaag) = = 0,53  P(M passed/ W slaag) × (5) P(S passed/ S slaag) = 0,50 × 0,53 = 0,267  P(M passed and S passed/W slaag en S slaag)  P(M passed/W slaag) × P(S passed/S slaag)  Events M and S are dependent/ Gebeurtenisse W en S is afhanklik [15] QUESTION/ VRAAG 2 2.1 31+10+23+15+x+18 +48+5 = 160 √ equation/vergelyking (2) x = 10 √ answer/antwoord 2.2 = = 0,03125 √ answer/antwoord (1) 2.3 P(B) = √ addition/optelling = √ 160 (3) √ answer/antwoord = 0,381 2.4 P(at least TWO candidates/ Ten minste TWEE kandidate) = √ addition/optelling = √ 160 (3) √ answer/antwoord = 0,331 = 33% [9]

Downloaded from hlayiso.com (NOVEMBER 2012) WISKUNDE V3 (Memo) 3 QUESTION/ VRAAG 3 3.1 The statement is correct as far as the sample is concerned/ Die stelling is korrek sover dit die steekproef aangaan. This does not imply that the total voter population will have the same result/ Dit impliseer nie dat die totale stemgeregtigde bevolking dieselfde resultaat gaan hê nie. It is a small sample to consider when you look at a presidential race, as is far less than 10%/ (4) Dit is ʼn klein steekproef om in ag te neem as jy kyk na ʼn presidensiële wedloop, wetende dat ver kleiner as 10%. This could swing the broader public’s vote unfairly in the actual voting as they might believe it is not worthwhile voting for the other candidate(s) in the race./ Dit kan die breër publiek se stem onregverdig in die werklike stemming swaai, omdat hulle mag dink dit sal nie die moeite werd wees om vir die ander kandidaat/kandidate in die wedloop te stem nie. 3.2 3.2.1 2 M ×7= = (MM) 7 3 M 5 8 7 W ×7= (MW) (7) 5 3 M ×7= (WM) 8 W 7 4 7 W ×7= = (WW) 3.2.2 P(W,W) = = 0,36 (2) 3.2.3 P(M,W any order/ enige orde) = + = (3) = 53,4% [16]

Downloaded from hlayiso.com 4 MATHEMATICS P3 (Memo) (NOVEMBER 2012) QUESTION/ VRAAG 4 4.1 P(HIV+) = 7 √ fraction / breuk = 0,245 (2) √ percentage / persentasie = 24,5% 4.2 7 7 P(25 – 29) = 7 √ fraction / breuk = 0,057 (2) √ percentage / persentasie = 5,7% 4.3 P(15 – 19, not infected/nie-geïnfekteer nie) = 7 √ fraction / breuk = 0,168 (2) √ percentage / persentasie = 16,8% 4.4 Total population/Totale bevolking (HIV+)= x100 √ fraction / breuk 7 (2) = 24,5% √ percentage / persentasie 4.5 Age group/Ouderdomsgroep: 25 – 29 = 35,4% √ age group / ouderdom √ comparing / vergelyking (3) √ percentage / persentasie 4.6 More education on HIV/Aids issues, knowing your status, single partner, faithful to partner, use of √√√ Any THREE logical condoms, etc./ reasons/ (3) Meer opvoeding oor HIV/Vigs, ken jou status, enkel genoot, Enige DRIE logiese redes getrou aan genoot, gebruik van kondome, ens. [14] QUESTION/ VRAAG 5 5.1 GRAPH A. The scale on the vertical axis is causing the  GRAPH A / effect./ GRAFIEK A (2) GRAFIEK A. Die skaal op die vertikale as veroorsaak die  reason / rede effek. 5.2 GRAPH B. It is clear from the graph that the illegal GRAPH B / immigrant influx shows a slight increase for a three GRAFIEK B month period, which show that the minister is in control of the problem./  reason / rede (2) GRAFIEK B. Dit is duidelik vanaf die grafiek dat die instroming van onwettige immigrante ʼn matige toename wys vir ʼn drie-maande periode, wat toon dat die minister in beheer van die probleem is 5.3 GRAPH A. It is clear from the graph that the illegal  GRAPH A / immigrant influx shows a steep increase for the three GRAFIEK A month period, which the opposition could use to show the  reason / rede lack of control by government over the problem./ (2) GRAFIEK A. Dit is duidelik vanaf die grafiek dat die instroming van onwettige immigrante ʼn skerp toename wys vir die drie–maande periode, wat die opposisie kan gebruik om te wys dat die regering in gebreke bly om die probleem te beheer. [6]

Downloaded from hlayiso.com (NOVEMBER 2012) WISKUNDE V3 (Memo) 5 * FOR QUESTIONS 6 TO 9 FOLLOW CANDIDATES REASONING */ * VANAF VRAAG 6 TOT VRAAG 9 VOLG KANDIDATE SE REDENERING* QUESTION/ VRAAG 6 6.1 6.1.1 P(8;14) (1) 6.1.2 Q(8;1) (1) 6.1.3 R(2; 9) (1) 6.2 6.2.1 7 P(2; ) (1) 6.2.2 Q(2; ) (1) 6.2.3 R( ; ) (1) 6.3 Yes, the corresponding sides are equal in proportion/ Ja, die ooreenstemmende sye is eweredig gelyk. (2) = 2 or/of 6.4 Area ∆PQR = (2)2(16x) = 64x units2/ (2) Oppervlakte ∆P’Q’R’ = (2)2(16x) = 64x eenhede2 [10] QUESTION/ VRAAG 7 7.1 7.1.1 7 = answer / antwoord (2) 7.1.2 PM = 2PV (V is the midpoint of PM) = 22 PM = 2PV (V is die middelpunt van PM) = 22 = answer / antwoord (2) = 7.1.3 = answer / antwoord (2) 7.2 7.2.1 Q ̂ R = y (alternate angles, // lines/  statement / stelling (1) verwisselende hoeke, // lyne) 7.2.2 P ̂ T = 90° – y (angles on a straight line/  statement / stelling (1) hoeke op ʼn reguitlyn) 7.2.3 In ∆PSQ and/ en ∆STP ̂ 1 = ̂ 1 = 90° – y (alternate angles/ verwisselende hoeke : PQ // TR)  statement / stelling ̂ ̂ = = 90°  statement / stelling (3) ̂ 2 = ̂2 (3rd angle of ∆/3rde hoek van ∆)  statement / stelling  ∆PSQ /// ∆STP (AAA)/(HHH)/(, ,) 7.2.4 = = (similar triangles/ gelyksoortige driehoeke)  PS = ST × PQ 2  statement / stelling = ST × (RS + ST)  statement / stelling (3) (PQ = RT  answer / antwoord = RS + ST, opp. sides of rectangle equal/ teenoorst. sye van reghoek gelyk) [14]

Downloaded from hlayiso.com 6 MATHEMATICS P3 (Memo) (NOVEMBER 2012) QUESTION/ VRAAG 8 8.1 In ∆STP and/ en ∆SQT: ̂ is common/ is gemeen  statement / stelling S ̂ P = T ̂ S (given/ gegee)  statement / stelling (3) 3rd angle/3rde hoek  statement / stelling  ∆STP /// ∆SQT (AAA) 8.2 = (similar triangles/ gelyksoortige driehoeke)  statement / stelling =  substitution / (3) substitusie SQ =  answer / antwoord = 79,79 mm 8.3 = = QT =  statement / stelling = 45,37 mm  substitution / OR/OF (3) substitusie  answer / antwoord 79 79 29 5 45 37 [9] QUESTION/ VRAAG 9 9.1 = (similar triangles/ gelyksoortige driehoeke) =  statement / stelling  substitution/ EC = (3) substitusie = 2p units/ eenhede  answer / antwoord  OB = EC = 2p (opposite sides of a rectangle equal/ teenoorstaande sye van reghoek is gelyk) 9.2 OC = (10 – p) units/ eenhede  answer / antwoord (1) 9.3 / = =  statement/ stelling =  substitution/ (3) = substitusie  answer/ antwoord = [7] TOTAL/TOTAAL: 100