# Mathematics Grade 11 P2 Eastern Cape November 2020 Memo > Grade 11 Mathematics Paper 2 memorandum from the Eastern Cape November 2020 (Afrikaans), 48 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/math-p2-g11-qp-ansbk-memo-nov2020-afr-d/71d12d6c-7fe0-4163-9708-d8b1e9c2ebc4 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Document type: Memorandum - Year: 2020 - Exam period: Eastern Cape November - Paper: 2 - Curriculum: CAPS - Pages: 48 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 11](https://www.hlayiso.com/library/grade-11) › [Mathematics](https://www.hlayiso.com/library/grade-11/mathematics) › [Mathematics Grade 11 P2 Eastern Cape November 2020 Memo](https://www.hlayiso.com/library/math-p2-g11-qp-ansbk-memo-nov2020-afr-d/71d12d6c-7fe0-4163-9708-d8b1e9c2ebc4) ## About this document Mathematics · Grade 11 · Eastern Cape November · 2020. Memorandum, 48 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com NASIONALE SENIOR SERTIFIKAAT GRAAD 11 NOVEMBER 2020 WISKUNDE V2 EKSEMPLAAR PUNTE: 150 TYD: 3 uur *Iwis2* Hierdie vraestel bestaan uit 10 bladsye en ’n antwoordeboek van 20 bladsye. ### Page 2 Downloaded from hlayiso.com 2 WISKUNDE V2 (EC/NOVEMBER 2020) INSTRUKSIES EN INLIGTING Lees die volgende instruksies aandagtig deur voordat die vrae beantwoord word. 1. Hierdie vraestel bestaan uit 9 vrae. 2. Beantwoord AL die vrae in die SPESIALE ANTWOORDEBOEK wat verskaf word. 3. Dui ALLE berekeninge, diagramme, grafieke, ensovoorts wat jy gebruik in die beantwoording van die vrae, duidelik aan. 4. Slegs antwoorde sal NIE noodwendig volpunte verdien NIE. 5. Jy mag ’n goedgekeurde wetenskaplike sakrekenaar gebruik, (nieprogrammeerbaar en niegrafies) tensy anders vermeld. 6. Indien nodig, rond antwoorde tot TWEE desimale plekke af, tensy anders vermeld. 7. Diagramme is NIE noodwendig volgens skaal geteken NIE. 8. Skryf netjies en leesbaar. Kopiereg voorbehou Blaai om asseblief ### Page 3 Downloaded from hlayiso.com (EC/NOVEMBER 2020) WISKUNDE V2 3 VRAAG 1 In die diagram hieronder, word reguitlyn PS deur 3 y  2x 6 gedefinieer, en sny die x-as by Q(3; 0). MQR is ’n reguitlyn wat PR by R(10; 4) ontmoet. N(6; -2) is ’n punt op PS en ˆ =T. RN is getrek. PQR 1.1 Bepaal die gradiënt van PS. (2) 1.2 Bereken die inklinasiehoek van MR. (4) 1.3 Bepaal die waarde van T . (3) 1.4 Bewys dat RN A PS . (3) 1.5 Bereken die oppervlakte van ' RQN . (6) 1.6 Bereken die y-afsnit van MR. (4) [22] Kopiereg voorbehou Blaai om asseblief ### Page 4 Downloaded from hlayiso.com 4 WISKUNDE V2 (EC/NOVEMBER 2020) VRAAG 2 ABCD is ’n parallelogram met A(-2; -6), B(4; 0), C(– 1; 0) en D(x ; y) soos hieronder aangetoon. 2.1 Bereken die lengte van BC. (2) 2.2 Bepaal die gradiënt van AB. (2) 2.3 Bepaal die vergelyking van CD. (3) 2.4 Bepaal die koördinate van M, die middelpunt van BD. (3) 2.5 Bepaal, vervolgens of andersins, die waardes van x en y. (3) [13] Kopiereg voorbehou Blaai om asseblief ### Page 5 Downloaded from hlayiso.com (EC/NOVEMBER 2020) WISKUNDE V2 5 VRAAG 3 3.1 As 12 tan B  5 0 en 90q d B d 360q , bepaal die waarde van sin B  cos B met behulp van ’n skets. (5) 3.2 As sin 43q p , bepaal die waardes van die volgende in terme van p, sonder ’n sakrekenaar. 3.2.1 cos133q (2) 3.2.2 tan(43q) (3) 3.3 Vereenvoudig elk van die volgende volledig, SONDER om ’n sakrekenaar te gebruik: 3.3.1 sin(360q  x) y tan( x  180q) sin(90q  x) (5) 3.3.2 sin 210q.cos150q.tan 25q tan 205q.cos315q.sin135q (7) [22] VRAAG 4 4.1 Bewys dat: sin T  cos T .sin T tan T cos T  (1  sin 2 T ) (4) 4.2 Bepaal die algemene oplossing van 2sin x cos x  cos2 x 0 (6) 4.3 Los op vir D as: 2. sin D 1, waar D  >0q;360q@ (3) § x y· 3 4.4 As x en y skerphoeke is sodat tan ¨ ¸ 1 en cos( x  y) , bepaal die © 2 ¹ 2 waardes van x en y. (5) [18] Kopiereg voorbehou Blaai om asseblief ### Page 6 Downloaded from hlayiso.com 6 WISKUNDE V2 (EC/NOVEMBER 2020) VRAAG 5 § x· Hieronder geskets is ’n grafiek van f ( x) cos ¨ ¸ , waar x  > 180q;180q@ . ©2¹ 5.1 Vir f ( x) , skryf neer die: 5.1.1 Waardeversameling (2) 5.1.2 Periode (1) 5.2 Teken ’n grafiek van g ( x) sin( x  30q) vir x  > 180q;180q@ op die assestelsel in die ANTWOORDEBOEK voorsien. Toon die draaipunt, begin en eindpunte, sowel as alle afsnitte met die asse, duidelik aan. (4) 5.3 Vir watter waardes van x  > 180q;180q@ is f ( x).g ( x) t 0 ? (3) [10] Kopiereg voorbehou Blaai om asseblief ### Page 7 Downloaded from hlayiso.com (EC/NOVEMBER 2020) WISKUNDE V2 7 VRAAG 6 ’n Paal, 8 m lank, word deur twee staalkabels van gelyke lengte in ’n vertikale posisie gehou. In die skets, stel PQ die paal, PS en PR die staalkabels voor. Die hoogtehoeke vanaf die ankerpunte R en S na die bopunt van die paal is in beide gevalle, 60q . P 8m Q 60q 60q R S 6.1 Bepaal die lengte van kabel PS. Laat jou antwoord in eenvoudigste wortelvorm. (3) 6.2 ˆ =100q . Gee jou antwoord korrek tot Bepaal die afstand tussen R en S, indien RQS TWEE desimale syfers. (7) [10] Kopiereg voorbehou Blaai om asseblief ### Page 8 Downloaded from hlayiso.com 8 WISKUNDE V2 (EC/NOVEMBER 2020) VRAAG 7 7.1 In die diagram hieronder is D die middelpunt van sirkel ABC met radius BD verleng na O. B D C O A ˆ = 2 u ABC Gebruik die diagram om die stelling wat meld dat ADC ˆ te bewys. (5) 7.2 In die figuur is O die middelpunt van sirkel ABCDE. DB = DF. AODF, BOE en ˆ = 10q . BCF is reguitlyne. CFD C F B 10q 3 1 2 1 2 3 2 1 D 2 1 3 O4 A E Bereken, met redes, die grootte van die volgende hoeke: 7.2.1 D̂ 2 (3) 7.2.2  (4) 7.2.3 Ô 2 (2) 7.2.4 Ĉ1 (2) 7.2.5 Ê (2) 7.2.6 Ĉ 2 (2) 7.2.7 Ô 3 (2) [22] Kopiereg voorbehou Blaai om asseblief ### Page 9 Downloaded from hlayiso.com (EC/NOVEMBER 2020) WISKUNDE V2 9 VRAAG 8 8.1 In die diagram hieronder is O die middelpunt van sirkel AEF met CFD ’n raaklyn by F. E A O C D F ˆ te bewys. ˆ =A Gebruik die diagram om die stelling wat meld dat EFD (5) 8.2 In die diagram hieronder, is ADF ’n raaklyn aan die sirkel met punte E, B, C en D op die omtrek van die sirkel. AB || DC en EC = DC. A E 1 2 3 B O 1 2 D 2 x 1 C F 8.2.1 ˆ = x , noem met redes, VYF ander hoeke gelyk aan x. As CDF (10) 8.2.2 Bewys dat ABCD ’n parallelogram is. (4) [19] Kopiereg voorbehou Blaai om asseblief ### Page 10 Downloaded from hlayiso.com 10 WISKUNDE V2 (EC/NOVEMBER 2020) VRAAG 9 9.1 Voltooi die volgende stellings: 9.1.1 Die lynstuk vanaf die middelpunt van ’n sirkel na die middelpunt van ’n koord getrek is ... (1) 9.1.2 Die buitehoek van ’n koordevierhoek is gelyk aan die ... (1) 9.2 In die diagram is FH ’n middellyn van sirkel FCH met middelpunt O. FC is ’n koord en LCH is ’n snylyn. LF is ’n raaklyn aan die sirkel by F. E is ’n punt op CH sodat CE = HE. F 1 x O 1 2 3 1 2 L C E H 9.2.1 Bewys dat FC || OE. (5) 9.2.2 Bewys dat OFLE ’n koordevierhoek is. (3) 9.2.3 As F̂1 x , druk Ô1 , met redes, in terme van x uit. (4) [14] TOTAAL: 150 Kopiereg voorbehou Blaai om asseblief ### Page 11 Downloaded from hlayiso.com LEARNER’S NAME: LEERDERNAAM: GRADE 11: GRAAD 11: NATIONAL/NASIONALE SENIOR CERTIFICATE/SERTIFIKAAT GRADE 11/GRAAD 11 NOVEMBER 2020 MATHEMATICS P2/WISKUNDE V2 SPECIAL ANSWER BOOK/SPESIALE ANTWOORDEBOEK (EXEMPLAR/EKSEMPLAAR) Marker/Merker Moderator’s Initials / Moderator se paraaf Question Mark Initial Marks S Marks D Marks P Marks NM Vraag Punt Parafeer Punte M Punte M Punte M Punte 1 2 3 4 5 6 7 8 9 TOTAL TOTAAL *Iwisab2* This special answer book consists of 20 pages./ Hierdie spesiale antwoordeboek bestaan uit 20 bladsye. ### Page 12 Downloaded from hlayiso.com 2 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 1/VRAAG 1 1.1 (2) 1.2 (4) 1.3 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 13 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 3 1.4 (3) 1.5 (6) 1.6 (4) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 14 Downloaded from hlayiso.com 4 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 2/VRAAG 2 2.1 (2) 2.2 (2) 2.3 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 15 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 5 2.4 (3) 2.5 (3) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 16 Downloaded from hlayiso.com 6 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 3/VRAAG 3 Sketch here/Teken hier: 3.1 (5) 3.2.1 (2) 3.2.2 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 17 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 7 3.3.1 (5) 3.3.2 (7) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 18 Downloaded from hlayiso.com 8 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 4/VRAAG 4 4.1 (4) 4.2 (6) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 19 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 9 4.3 (3) 4.4 (5) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 20 Downloaded from hlayiso.com 10 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 5/VRAAG 5 5.1.1 (2) 5.1.2 (1) 5.2 (4) 5.3 (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 21 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 11 QUESTION 6/VRAAG 6 6.1 (3) 6.2 (7) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 22 Downloaded from hlayiso.com 12 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 7/VRAAG 7 B D C O A 7.1 (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 23 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 13 7.2 C F B 10q 3 1 2 1 2 3 2 1 D 2 1 3 O4 A E 7.2.1 (3) 7.2.2 (4) 7.2.3 (2) 7.2.4 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 24 Downloaded from hlayiso.com 14 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) 7.2.5 (2) 7.2.6 (2) 7.2.7 (2) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 25 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 15 QUESTION 8/VRAAG 8 E A O C D F 8.1 (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 26 Downloaded from hlayiso.com 16 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) A E 1 2 3 B O 1 2 D 2 x 1 C F 8.2.1 (10) 8.2.2 (4) [19] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 27 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 17 QUESTION 9/VRAAG 9 9.1.1 (1) 9.1.2 (1) F 1 x O 1 2 3 1 2 L C E H 9.2.1 (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 28 Downloaded from hlayiso.com 18 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) 9.2.2 (3) 9.2.3 (4) [14] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 29 Downloaded from hlayiso.com (EC/NOVEMBER 2020) MATHEMATICS P2/WISKUNDE V2 19 Additional Space/Addisionele ruimte Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 30 Downloaded from hlayiso.com 20 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) Additional Space/Addisionele ruimte Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 31 Downloaded from hlayiso.com  NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 11 NOVEMBER 2020 MATHEMATICS P2/WISKUNDE V2 MARKING GUIDELINE/NASIENRIGLYN EXEMPLAR/EKSEMPLAAR MARKS/PUNTE: 150 This marking guideline consists of 14 pages./ Hierdie nasienriglyn bestaan uit 14 bladsye.  ### Page 32 Downloaded from hlayiso.com 2 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 1/VRAAG 1 1.1 0  ( 2) 2 9 substitution / vervanging m PS  36 3 9 answer / antwoord OR/OF 3y  2x 6 OR/OF 3y 2 x  6 2 2 y  x2 9y  x2 3 3 2 m PS  3 9 answer / antwoord (2) ସି଴ 1.2 40 4 9 9gradient / gradiënt mMR ଵ଴ିଷ 10  3 7 ෡ X ൌ ݉ୖ୑ 9tan RQ ˆ 4 tan RQX= 7 9answer / antwoord ˆ RQX=29,74q (4) 1.3 ˆ =-2  tan PQX ෡X ൌ െ ଶ 3 9tan PQ ଷ ˆ =146, 31q PQX ෡ X ൌ 146,31° 9 PQ T 146,31q  29, 74q 9answer / antwoord T 116,57q (3) 1.4 3 9݉ୖ୒ mRN 2 3 2 9product / produk mRN u mPS u 1 2 3 9െ1 RN A PS (3) 1.5 2 2 NR= 10  6  4  2 9substitution / vervanging NR= 52 9answer / antwoord QN = 13 9length QN / lengte QN 1 Area = u QN u NR 2 9choosing correct sides / 1 kies korrekte sye Area = u 13 u 52 9substitution / vervanging 2 Area = 13 units 2 / eenhede 2 9answer / antwoord (6)    Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 33 Downloaded from hlayiso.com (EC/SEPTEMBER 2020)) MATHEMATICS P2/WISKUNDE V2 3  1.6 y0 4 9x = 0 x 3 7 9substitution / vervanging 7 y 12 9equation / vergelyking 12 9y-coordinate / y-koördinaat y  7 OR/OF OR/OF 4 y xc 9equation / vergelyking 7 Subst./vervang (3; 0) 4 0= 3 c 9substitution / vervanging 7 12 c  9value of c / waarde van c 7 12 y  9y-coordinate / y-koördinaat 7 (4) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 34 Downloaded from hlayiso.com 4 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 2/VRAAG 2  2.1 BC = 2 1  4  10  0 2 9substitution / vervanging BC = 25  100 9answer / antwoord BC = 125 5 5 (2) 2.2 6  0 mAB 9substitution / vervanging 2  6 3 mAB 9answer / antwoord 4 (2) 2.3 3 mCD mAB 9gradient / gradiënt 4 y mx  c 3 y xc 4 Sub C 1;10 9substitution / vervanging 3 10 1  c 4 43 c 4 3 43 y x 9answer / antwoord (3) 4 4   Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 35 Downloaded from hlayiso.com (EC/SEPTEMBER 2020)) MATHEMATICS P2/WISKUNDE V2 5 2.4 M is the midpoint of both BD and AC / is die middelpunt van beide BC en AC 9 statement / stelling Midpoint of AC and BD /Middelpunt van AC en BD § 1  2 10  6 · M¨ ; ¸ 9 substitution / vervanging © 2 2 ¹ § 3 · 9answer / antwoord M ¨ ;2¸ © 2 ¹ (3) 2.5 x  4 3 y  0 ; 2 9 substitution / vervanging 2 2 2 x  4 3; y  0 4 9x- value/waarde 9y-value/waarde x 7; y 4 Answer only: Full marks/ Slegs antwoord: Volpunte (3) [13]  Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 36 Downloaded from hlayiso.com 6 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 3 / VRAAG 3  3.1 y B x O (– 12; – 5) 9diagram / diagram Therefore/d.w.s: r = 13 9value of r / waarde van r sin B  cos B 5 12  99substitution / vervanging 13 13 17 9answer / antwoord 13 (5) 3.2 sin 43q p 3.2.1 cos133q  cos(90q  43q)  sin 43q 9  sin 43q 9answer / antwoord p (2) 3.2.2 tan( 43q)   tan 43q 9  tan 43q p  99answer / antwoord 1  p2 (3) 3.3.1 sin(360q  x ) y tan( x  180q)  sin(90q  x )  sin x 9  sin x y tan x 9 cos x cos x 9 tan x  tan x y tan x  9  tan x 1 9 answer / antwoord (5) 3.3.2 sin 210q.cos150q.tan 25q tan 205q.cos 315q.sin135q  sin 30q.  cos 30.tan 25q 9  sin 30q 9  cos30q tan 25q.cos 45q.sin 45q 9 tan 25q 1 3 9 cos 45q .  2 2 9 sin 45q 1 1 . 2 2 9special angles / spesiale hoeke 3 9answer / antwoord 2 (7)  [22]   Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 37 Downloaded from hlayiso.com (EC/SEPTEMBER 2020)) MATHEMATICS P2/WISKUNDE V2 7 QUESTION 4 / VRAAG 4 4.1 sin 8 —cos 6.sin@ ———- = tano cos 8 —(1—sin’ 0) LHS = sin 0(1 — cos @) ¥ factorising / faktorisering cos@—cos’@ ¥ cos’ @ _ sin@(1—cos@) ~ cos 8(1—cos 6) ¥ common factor / gemene faktor v answer / antwoord =tand (4) 4.2 2sin xcosx—cos’ x =0 y . factors / faktore 2sin x — =0 cos x(2 sin x —cos »): V cosx=0 cosx=0 or/of 2sinx=cosx 1 1 ¥ tanx=— cosx=0 or/of tanx= > 2 x =90°+360°.k or/of x =270°+360°.k ¥ x =90°+360°.4 . Y x =270° + 360°. / x = 26,57° +180°.4 ovlof x= 26, V x= 26,57° + 180°. (6) 4.3 2Nsina =1 vsina = L 2 . 1 1 sina =— sina =— 4 4 @=14,48° a@=14,48° or/of a=165,52° a =165,52° (3) 44 x+y tan 2) and/en cost v= ase ct ¥ x-—y=30° X*Y Lae and/en x-y=30° 5 ¥ setting up equations/ XA Y= 90? ccerereeeee (1) opstel van vergelykings X= V = 30? vee (2) 2x =120° x= 60° v x-value/waarde y =30° v y-value/waarde (5) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 38 Downloaded from hlayiso.com 8 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 5 / VRAAG 5 5.1.1 0 d y d1 or > 0;1@ 90 91 (2) 5.1.2 Period = 720q 9answer (1) 5.2 9 shape / vorm 9 x-intercept / x-afsnit 9 y-intercept / y-afsnit 9 turning points / draaipunte (4) 5.3 180q d x d 150 or/of 30q d x d 180q 99 180q d x d 150  9 30q d x d 180q  (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 39 Downloaded from hlayiso.com (EC/SEPTEMBER 2020)) MATHEMATICS P2/WISKUNDE V2 9 QUESTION 6 /VRAAG 6 6.1 PQ sin 60q PS 8 sin 60q 8 PS 9 sin 60q  PS 8 PS = 8 sin 60q 9 PS =  sin 60q 16 3 PS = 16 3 3 9 PS = 3 (3) 6.2 PQ In 'PQS: tan 60q QS 8 9 QS =  tan 60q 8 8 3 QS = m 8 3 tan 60q 3 9 QS = m 3 8 3 QR = m 8 3 3 9 QR = m 3 In 'RQS: RS2 QR 2  QS2  2.QR.QS.cos100q 9formula / 2 2 2 2 §8 3 · §8 3 · §8 3 · §8 3 · formule = ¨¨ ¸¸  ¨¨ ¸¸  2. ¨¨ ¸¸ . ¨¨ ¸¸ cos100q © 3 ¹ © 3 ¹ © 3 ¹ © 3 ¹ 9substitution / = 50,0756...... vervanging RS = 7,08 m 9simplification/ vereenvoudiging 9answer / antwoord (7) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 40 Downloaded from hlayiso.com 10 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 7 / VRAAG 7 B D C O A 7.1 ˆ =x Let/Laat A ˆ = x (angles opp = sides)/(hoeke teenoor BAD sye) 9S and/en R ˆ ADO = 2 x (angle at the centre)/(middelpuntshoek ) 99S and/en R Similarly, if you let / Net so, as jy: Cˆ = y; ˆ = 2y then/dan: CDO 9S ˆ = 2 x  2 y = 2( x  y ) ? ADC ˆ = 2 ABC 9S and conclusion en gevolgtrekking (5) 7.2.1 B̂3 10q (angles opp = sides; DB = DF) 9S 9R (hoeke teenoor sye; DB = DF) D̂ 2 20q (exterior angle of a 'BDF) 9S and/en R (buitehoek van 'BDF) (3) 7.2.2 ˆ ABD = 90q (angles in a semi-circle) 9S 9R (hoek in halwe sirkel )  = 70q (angles of a triangle) 9S 9R (hoeke van ' n driehoek ) (4) 7.2.3 Ô2 140q (angle at the centre) / (middelpuntshoek ) 9S 9R (2) 7.2.4 Ĉ1 110q (opposite angles of a c.q.)/(teenoorst. hoeke van k .v) 9S 9R OR  OF OR / OF ˆ O O ˆ O ˆ 220q (angles around a point/(omwenteling ) 1 4 3 9S and/en R Ĉ1 110q (angle at the centre)/(middelpuntshoek ) 9S and/en R (2)   Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 41 Downloaded from hlayiso.com (EC/SEPTEMBER 2020)) MATHEMATICS P2/WISKUNDE V2 11 7.2.5 Ê = 70q (angles in the same segment)/(hoeke in dieselfde segment ) 9S 9R OR/OF OR/OF Ê = 70q (opposite angles of a c.q.)/(teenoorst . hoeke van k .v ) 9S 9R (2) 7.2.6 Ĉ2 70q (ext. ‘ of a c.q.)/ (buitehoek van k .v) 9S 9R OR/OF OR/OF Ĉ2  110q 180q (‘s on a straight line)/(hoeke op ' n reguitlyn) 9S 9R Ĉ2 70q (2) 7.2.7 Oˆ Oˆ 140q (vertically opp. ‘s)/(regoorstaande ‘e) 9S 9R 4 2 (2) [22]   Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 42 Downloaded from hlayiso.com 12 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020) QUESTION 8 / VRAAG 8  P E A O C D F 8.1 ENG 9construction Draw diameter FP and join PA ˆ =x Let EFD 9S and R ˆ = 90q (tan A radius) OFD ˆ = 90q  x ? OFE 9S and R ˆ = 90q  x (angles in the same segment) ? PAE 9S and R ˆ = 90q (angles in a semi circle) PAF ˆ =x ? EAF 9conclusion ˆ =x ˆ =A ? EFD 8.1 AFR AFR Teken middellyn FP en verbind PA 9 konstruksie ˆ =x Laat EFD ˆ = 90q (raaklyn A radius ) OFD 9 S en R ˆ = 90q  x ? OFE ˆ = 90q  x (hoeke in dieselfde segment ) ? PAE 9 S en R 9 S en R ˆ = 90q (hoeke in ' n halwe sirkel ) PAF ˆ =x ? EAF 9 gevolgtrekking ˆ =x ˆ =A ? EFD (5)   Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 43 Downloaded from hlayiso.com (EC/SEPTEMBER 2020)) MATHEMATICS P2/WISKUNDE V2 13 A E 1 2 3 B O 1 2 D 2 x 1 C F ෡ = ‫ ݔ‬ሺcorresponding angles; AB 8.2.1 A 9S 9R ‫ צ‬DCሻ/ሺ‫ ;݁݇݁݋݄ ݁݃݅ݐݏ݉݋݇݊݁݁ݎ݋݋‬AB || DCሻ ෡ଶ ൌ ‫ ݔ‬ሺtan-chordሻ / ሺ‫݊ݕ݈݇ܽܽݎ‬-݇‫݀ݎ݋݋‬ሻ E 9S 9R D෡ ଶ ൌ ‫ ݔ‬ሺangles opposite = sidesሻ / ሺ݄‫ ݎ݋݋݊݁݁ݐ ݁݇݁݋‬ൌ syeሻ 9S 9R ෡ Eଵ ൌ ‫ ݔ‬ሺalternate angles, AB 9S 9R ‫ צ‬DCሻ/ሺ‫ ;݁݇݁݋݄ ݈݁݀݊݁݁ݏݏ݅ݓݎ݁ݒ‬AB || DCሻ ෠Cଵାଶ ൌ E ෡ଵ ൌ ‫ ݔ‬ሺexterior angle of a c.q.ሻ/ሺܾ‫ ݊ܽݒ ݇݁݋݄݁ݐ݅ݑ‬Ԣ݊ ݇. ‫ݒ‬ሻ 9S 9R (10) ෡ = 180° െ ‫ ݔ‬ሺopposite angles of a c.q.ሻ 8.2.2 B 9S 9R ሺ‫ݐݏݎ݋݋݊݁݁ݐ‬. ݄‫ ݊ܽݒ ݁݇݁݋‬Ԣ݊ ݇. ‫ݒ‬ሻ ෡ A+෡ B = ‫ ݔ‬൅ ሺ180° െ ‫ݔ‬ሻ ൌ 180° ‫ ׵‬AD ‫ צ‬BC ሺco-interior angles formed = ሻ ሺ݇‫݋‬-ܾ݅݊݊݁ ݄‫ = ݉ݎ݋ݒ݁݃ ݁݇݁݋‬180୭ ሻ 9R ‫ ׵‬ABCD is a parallelogram ሺopp. sides ‫צ‬ሻ ABCD is Ԣn parallelogram ሺ‫ݐݏݎ݋݋݊݁݁ݐ‬. ‫|| ݁ݕݏ‬ሻ 9R (4) [19]         Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief ### Page 44 Downloaded from hlayiso.com 14 MATHEMATICS P2/WISKUNDE V2 (EC/NOVEMBER 2020)  QUESTION 9 / VRAAG 9  9.1.1 perpendicular to the chord / loodreg op die koord 9answer/antwoord (1) 9.1.2 interior opposite angle / teenoorstaande binnehoek 9answer/antwoord (1) 9.2 F 1 x O 1 2 3 1 2 L C E H 9.2.1 ෡ଶ ൌ E E ෡ଵ ൌ 90° ሺline from centreሻ 9S 9R ሺ݈‫ݐ݊ݑ݌݈݁݀݀݅݉ ݁݅݀ ݂ܽ݊ܽݒ ݊ݕ‬ሻ ෠ FCH ൌ 90° ሺangles in a semi-circleሻ 9S 9R ሺ౹‫ ݊' ݊݅ ݁݇݁݋‬౹݈ܽ‫݈݁݇ݎ݅ݏ ݁ݓ‬ሻ ෠ ෡ ‫ ׵‬FCH ൌ Eଶ ‫ ׵‬FC ‫ צ‬OE ሺcorresponding angles formed are ൌሻ 9R ሺ‫ ݁݃݅ݐݏ݉݋݇݊݁݁ݎ݋݋‬౹‫ ݏ݅ ݀ݎ݋ݓ ݉ݎ݋ݒ݁݃ ݐܽݓ ݁݇݁݋‬ൌሻ (5) 9.2.2 ˆ LFO = 90q (tan A radius) / (raaklyn A radius ) 9S and/en R Ê 2 90q (proven) / (reeds bewys ) 9S and/en R ? OFLE is a c.q. 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