Mathematics Grade 12 P2 Eastern Cape Mock 2021 QP

Downloaded from hlayiso.com SENIOR CERTIFICATE/ NATIONAL SENIOR CERTIFICATE IBANGA 12 MATHEMATIKA P2 SEPTEMBA 2021(2) AMANQAKU: 150 IXESHA: 3 iiyure Eliphepha lemibuzo linamaphepha ayi15 kudibene nephepha eli1 lolwazi. *MATXHO2* Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 2. DBE/Septemba 2021(2) SC/NSC IMIYALELO NOLWAZI Funda imiyalelo elandelayo ngocoselelo phambi kokuphendula imibuzo. 1. Eliphepha lemibuzo linemibuzo eyi 10. 2. Phendula YONKE imibuzo kwiNCWADI EKHETHIWEYO YOKUPHENDULELA enikiweyo. 3. Bonisa ngokucacileyo ZONKE iikhaltyhuleyshini, iidayagram, iigrafu, njl. ozisebenzisileyo ukubonisa iimpendulo zakho. 4. Iimpendulo kuphela azinyanzelekanga UKUNIKWA amanqaku apheleleyo. 5. Ungayisebenzisa ikhaltyhuleytha esayentifikhi evunyiweyo (engaprogranywanga nengenagrafikhi), ngaphandle kokuba uxelelwe ngeny’indlela. 6. Ukuba kunyanzelekile, sondeza iimpendulo kwiindawo EZIMBINI zedesimal, ngaphandle kokuba uxelelwe ngeny’indlela. 7. Iidayagram AZI zotywanga ngokwesikeyile (scale). 8. Iphepha lolwazi elineefomyula lifakiwe ekugqibeleni kwiphepha lemibuzo. 9. Bhala ngokucocekileyo nangokucacileyo. Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 3. DBE/Septemba 2021(2) SC/NSC UMBUZO 1 Umnyhadala wonyaka wezemidlalo ubanjwe iintsuku eziyi11. Ivenkile ithengisa iziselo ezishushu kulo mnyhadala. Ngosuku ngalunye kwiintsuku eziyi10 zokuqala, umnikazi wevenkile urekhode amaqondo obushushu ngo13:00 namanani eekomityi zesiselo esishushu ezithengisiweyo. Olu lwazi luboniswe kwitheybhile nakwi skatha ploti esingezantsi. Amaqondo 14 24 26 18 20 28 22 15 12 19 obushushu (nge °C) Inani leziselo ezishushu 410 258 192 324 328 156 280 384 230 280 ezithengisiweyo 450 SKATHA PLOT 400 Inani leziselo ezishushu ezithengisiweyo 350 300 250 200 150 10 15 20 25 30 Amaqondo obushushu (nge °C) 1.1 Chaza ithrend yedatha. (1) 1.2 Fumana i-ikhweyzhini yezona zikwere zincinci zomgca werhigreshin zedatha. (3) 1.3 Umnikazi uqaphele okokuba usebenzise ilitha enye yobisi kwiikomityi eziyi8 zeziselo ezishushu ezithengisiweyo. Ukuba amaqondo obushushu ngo13:00 kusuku lwe11 ebelindeleke ukuba abe ngu17 °C, qikelela inani lebhokisi ze1- litha yobisi umnikazi afanele ukuzithenga ndosuku lwe11 . (3) 1.4 Chonga iawthlaya kwidatha. (1) [8] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 4. DBE/Septemba 2021(2) SC/NSC UMBUZO 2 2.1 Abafundi abasuka kwizikolo ezohlukileyo babhale uvavanyo olukhawulezileyo ukuze balungele ukufumana ibhasari. Amanqaku wabo (ngokwepesenti) aboniswe kwiogive (tyhumulethiv frikhwensi grafu) engezantsi. OGIVE 190 180 170 160 150 140 Tyhumulayithivi frikhwensi 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 110 Amanqaku (ngokwe %) 2.1.1 Bangaphi abafundi ababhale uvavanyo? (1) 2.1.2 Bhala imodal klasi yedata. (1) 2.1.3 Iminimam makh ebalungeleyo ukufumana ibhasari ngu75%. Bangaphi abafundi abalungele ukufumana ibhasari? (2) Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 5. DBE/Septemba 2021(2) SC/NSC 2.2 Itheybhile engezantsi ibonisa amanqaku wabafundi abayi15 abasuka kwisikolo esithile afumaneke kuvavanyo. Amanqaku 62 58 78 85 74 48 74 84 100 46 80 92 60 90 92 (ngokwe%) Khaltyhuleytha: 2.2.1 Imean mark efunyenwe ngabafundi (2) 2.2.2 IStandad deviyeyshin yamanqaku abafundi (1) 2.2.3 Amanani wabafundi abanamanqaku afumaneka ngaphezulu kwe standad deviyeyshin esinye ngaphezu kwe mean (2) 2.3 Amanqaku okugqibela webanga 11 (ngokwe pesenteyji) afunyenwe liqela labafundi elianalayziweyo. I-intavali yestandard deviyeyshin esinye nge mean ikhaltyhuleythiwe njengo (82,7; 94,1). Khaltyhuleytha istandad deviyeyshin samanqaku okugqibela webanga 11. (3) [12] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 6. DBE/Septemba 2021(2) SC/NSC UMBUZO 3 Kwidayagram engezantsi, umgca uBF uzotywe esuka k u B(8 ; –2) wanqumla i x-ekhziz ku P ne y- ekhziz ku F. Iinklineyshini ka BF ne β ne ikhweyzhin ka BF ngu 1 y  x  2 . Ukusuka ku A(4 ; k), omnye umgca uzotywe w a pharalel ku BF waze 2 wanqumla i y-ekhziz ku E. U mgca odlula ku A no B ine inklineyshin ka 45° ize inqumle i x-ekhziz ku C. AB̂F T . y F β 45° O P C x T B(8 ; –2) E A(4 ; k) 3.1 Khaltyhuleytha igradiyent kaAB. (1) 3.2 Bonisa ivelyu ka k ukuba ngu –6. (2) 3.3 Fumana i-ikhweyzhin ka EA ngokwefom y mx  c . (3) 3.4 Khaltyhuleytha: 3.4.1 Isayzi ka T (3) 3.4.2 Ubude buka BF (3) 3.4.3 Ieriya ka 'ABF (4) 3.5 Yenza G abe yipoynti kwi khwadrent yesine ukuze u APBG abe yipharalelogram. Khaltyhuleytha isayzi ka PAG. (4) [20] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 7. DBE/Septemba 2021(2) SC/NSC UMBUZO 4 Kwidayagram engezantsi, u S yipoynti kwi x-ekhziz. Isekile enombindi ku S ne sekile enombindi ku M zizotyiwe. Zombini iisekile zingqubana ngaphandle kuE. FE yithanjenti ekhomon kwiisekile ku E. Isekile enombindi ku M, eno ER njengedayametha, ikwreca i x-ekhziz ku P. y F R M E x S P O 4.1 I-ikhweyzhin yesekile enombindi ku S ngu ( x  8) 2  y 2 4. 4.1.1 Bhala iikho-odineythi zika S. (2) 4.1.2 Bonisa ukuba idayametha yesekile enombindi S ngu 4 yunithi. (1) § 8 24 · 4.2 Kuphindiwe kwanikwa ukuba uSR= 8 yunithi aze R¨  ; ¸ , khaltyhuleytha: © 5 5 ¹ 4.2.1 Ubude buka EM (2) 4.2.2 Igradiyenti yethanjent FE (3) 4.2.3 Iikho-odineythi zika M (4) 4.2.4 Iikho-odineythi zika E (2) 4.3 Isekile enombindi ku M(– 4 ; 3) ishiftiwe 1 yunithi ukuya ekhohlo ze yariflwekhthwa kwi x-ekhziz ukwenza isekile entsha enombindi ku K. Fumana ukuba ipoynti (– 8 ; 0) ifumaneka ngaphakathi okanye ngaphandle isekile enombindi ku K. Bonisa ZONKE iikhaltyhuleyshin. (5) [19] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 8. DBE/Septemba 2021(2) SC/NSC UMBUZO 5 5.1 Ipoyinti T(–1; –2) inikiwe kwidayagram engezantsi. uA yipoynti kwi x-ekhziz ukuze i r i f l e k h s i AÔT D . y A x O x T(–1; –2) D Fumana, ungasebenzisi khaltyhuleytha, ivelyu nganye kwezilandelayo: 5.1.1 tan D (1) 5.1.2 cos D (2) 5.1.3 cos(D  45q) ngefom elula (4) 5.2 Fumana, ungasebenzisi khaltyhuleytha, ivelyu ye-ekhsphreshin ezilandelayo : 2 sin( 20q). sin 160q  cos 40q (4) 5.3 Qaphela: 3 cos x. sin x  tan x. cos 2 (180 q  x) 5.3.1 Simplifaya iekhsphreshin iye kwi trigonometrikh reyshiyo enye. (4) 5.3.2 Ngoko, bhala ireynji ka: f ( x) 3 cos x. sin x  tan x. cos 2 (180 q  x) (2) cos 3x 5.4 Ngqina iayidentithi: 4 cos 2 x  3 (5) cos x 5.5 Fumana ijeneral solushini ka x kwi ikhweyzhin elandelayo: 32 tan x  3tan x1 54 (5) [27] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 9. DBE/Septemba 2021(2) SC/NSC UMBUZO 6 Kwidayagram, iigrafu zika f(x) = –cosx +1 no g(x) = 2sin(x + 30°) zizotywe kwiintaval ka x [180q; 90q] . y f –180° –150° –120° –90° –60° –30° 0° 30° 60° 90° x g 6.1 Zeziphi iivelyu zika x, x [180q ; 90q] , apho anokuba: 6.1.1 f ( x).g ( x) t 0 (2) 6.1.2 g ( x) 1 (2) 6.2 I y-ekhziz ihanjisiwe 90° ukuya ekunene. Fumana i-ikhweyzhin entsha yegrafu ebisakubizwa ngo f, ngefom yayo elula. (2) [6] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 10. DBE/Septemba 2021(2) SC/NSC UMBUZO 7 Kwidayagram, B, C no D bakwi pleyini ehorizontali enye. AD yipali evethikhal ebotshelelwe ngeekheybhile ezimbini, uAB no AC. Iengile ze eleveyshin ukusuka kuB no C ukuya kuA, imiphezulu yepali, ngu T and 2 T ngokulandelelana. AB = 5 yunithi no AC = x yunithi. A 5 x D B C 5 7.1 Bonisa ukuba x (5) 2 cos T Khaltyhuleytha ubude buka BC xa ngaba kunikwe ukuba BÂC 112q and 7.2 T 30q . (3) [8] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 11. DBE/Septemba 2021(2) SC/NSC UMBUZO 8 8.1 Kwidayagram, iikhodi uKL, LP no KP zizotywe kwisekile, enombindi ku O. SLR yithanjent kwisekile ku L. S L K O R P Ngqina ukuba ithiyorem echaza ukuba iengile phakathi kwethanjent SLR ne khodi KL ilingana neengile kwiolthaneyth segment, ngoko ngqina ukuba SL̂K P̂. (6) Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 12. DBE/Septemba 2021(2) SC/NSC 8.2 Kwidayagram engezantsi, PWRS yisayklikh khwadrilateral kwisekile, enombindi ongu 0. ∆PSW yiekhwilaieral trayengile. TW yithanjent kwisekile ku W. IiRadiyasi OR no OW Bazotyiwe. Ŵ5 25q . P O 1 2 1 2 3 S 1 4 W 5 25° 1 2 R T 8.2.1 Fumana, unika izizathu, isayzi ka: (a) Ŝ1 (2) (b) Ô 1 (2) (c) R̂ 1 (5) 8.2.2 Ngqina ukuba SP || TW. (3) Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 13. DBE/Septemba 2021(2) SC/NSC 8.3 Kwidayagram engezantsi, isekile enombindi kaO izotyiwe. H, J, G no L zipoynti kwisekile. ∆HJL lizotyiwe. HOG unqumla phakathi uJL ku M. HJ 12 5 yunithi no JM = 12 yunithi. H O J 12 M L G 8.3.1 Ukuba uMG= 6 unithi no OM= x, bhala HM ngethem zika x. (2) 8.3.2 Khaltyhuleytha, unika izizathu, ubude beradiyasi yesekile. (5) [25] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 14. DBE/Septemba 2021(2) SC/NSC UMBUZO 9 Kwi dayagram engezantsi, P, Q, R no S zipoyinti kwisekile. PS, PQ no PR batsaliwe ku V, T no W ngokulandelelana. VT || SQ no SR || VW. T Q 2 1 W R 1 2 P 2 1 3 S V Ngqina, unika izizathu, ukuba : TQ WR 9.1 (3) QP RP 9.2 TPVW yi sayklikh khwadrilatheral (5) [8] Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 15. DBE/Septemba 2021(2) SC/NSC UMBUZO 10 Kwidayagram engezantsi, B, C no D ziipoyinti kwisekile ukuze BC = CD. EC no ED zithanjent kwisekile C no D ngokulandelelana. BC utsaliwe wadibana nethanjent DE etsaliweyo ukuya ku F. B̂ x . B x 3 2 4 1 D 3 C 2 1 1 2 E F 10.1 Ngqina, unika izizathu, ukuba: 10.1.1 Ê 1 180q  2 x (5) 10.1.2 ∆ECD ||| ∆CBD (3) 10.2 Ngqina, unika izizathu, ukuba: 10.2.1 CD 2 CE.BD (3) CF 2 BD 10.2.2 EF 2 DE (6) [17] AMANQAKU EWONKE: 150 a Amalungelo akhuselekile Nceda tyhila

Downloaded from hlayiso.com Mathematika/P2 DBE/September 2021(2) SC/NSC IPHEPHA LOLWAZI  b r b 2  4ac x 2a A P(1  ni) A P(1  ni) A P(1  i) n A P(1  i) n n Tn a  (n  1)d Sn >2a  (n  1)d @ 2 a r n 1 a Tn ar n 1 Sn ; r z1 Sf ; 1  r  1 r 1 1 r F > x (1  i ) n  1 @ P > x 1  (1  i )  n @ i i f ( x  h)  f ( x ) f / ( x) lim h o0 h § x  x 2 y1  y 2 · d x2  x1 2  y2  y1 2 M¨ 1 ; ¸ © 2 2 ¹ y 2  y1 y mx  c y  y1 m x  x1 m m tan T x 2  x1 2 2 xa  y b r2 a b c In 'ABC: sin A sin B sin C a2 b 2  c 2  2bc. cos A 1 area 'ABC ab. sin C 2 sin( D  E ) sin D cos E  cosD sin E sin( D  E ) sin D cos E  cosD sin E cos(D  E ) cosD cos E  sin D sin E cos(D  E ) cosD cos E  sin D sin E ­cos 2 D  sin 2 D ° cos 2D ®1  2 sin D 2 sin 2D 2 sin D cos D °2 cos 2 D  1 ¯ n x ¦x ¦ x x i 2 n V2 i 1 n n( A ) P(A) P(A or B) P(A)  P(B)  P(A and B) n(S) yˆ a  bx b ¦ xx y y ¦ xx 2 Amalungelo akhuselekile