Mathematics Grade 12 Paper 2 NSC November 2020 Memo

Downloaded from hlayiso.com SENIOR CERTIFICATE/SENIOR SERTIFIKAAT NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 MATHEMATICS P2/WISKUNDE V2 NOVEMBER 2020 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 150 These marking guidelines consist of 27 pages. Hierdie nasienriglyne bestaan uit 27 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 2 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne NOTE:  If a candidate answers a question TWICE, only mark the FIRST attempt.  If a candidate has crossed out an attempt of a question and not redone the question, 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:  As 'n kandidaat 'n vraag TWEE KEER beantwoord, sien slegs die EERSTE poging na.  As 'n kandidaat 'n antwoord van 'n vraag doodtrek en nie oordoen nie, sien die doodgetrekte poging na.  Volgehoue akkuraatheid word in ALLE aspekte van die memorandum toegepas. Hou op nasien by die tweede berekeningsfout.  Aanvaar van antwoorde/waardes om 'n probleem op te los, word NIE toegelaat nie. GEOMETRY A mark for a correct statement (A statement mark is independent of a reason) S 'n Punt vir 'n korrekte bewering ('n Punt vir 'n bewering is onafhanklik van die rede) A mark for the correct reason (A reason mark may only be awarded if the statement is correct) R 'n Punt vir 'n korrekte rede ('n Punt word slegs vir die rede toegeken as die bewering korrek is) Award a mark if statement AND reason are both correct S/R Ken 'n punt toe as die bewering EN rede beide korrek is Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 3 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 1 1.1 a  9,5  a  9,5 b  0,909..  0,91  b  0,91 yˆ  9,5  0,91x  equation (3) 1.2 100 90  correct 80 slope going PHYSICAL SCIENCES (% ) 70 through 2 points: 60 (50 ; 55) or 50 (40 ; 46) or (60 ; 64) or 40 (0 ; 9,5) or 30 (45 ; 50) 20 9,5 10 0 0 10 20 30 40 50 60 70 80 90 MATHEMATICS (% ) (2) 1.3 Final exam mark  72,22% (calculator)  answer (2) OR yˆ  9,5  0,9169  substitution  72,29%  answer (2) 1.4 r = 0,95  answer(A) (1) 1.5 There is a very strong positive correlation between the Mathematics and  strong/ sterk Physical Sciences mark. Daar is ‘n baie sterk positiewe korrelasie tussen die Wiskunde en Fisiese Wetenskappunte. (1) 1.6 The teacher concludes that the higher the learners' Mathematics marks, the  answer higher the learners' Physical Sciences marks. Die onderwyser het waargeneem dat hoe hoër die wiskunde punte is, hoe hoër is die Fisiese Wetenskappunte. (1) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 4 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2 018 2 175 2 182 2 215 2 254 2 263 2 267 2 271 2 293 2 323 2 334 2 346 2.1 July / Julie  answer (1) 2.2 26 941  26 941 x Answer only: Full marks 12 = 2 245,083..  2 245,08 aircraft landings  answer (2) 2.3 Standard deviation for landings at the King Shaka International airport:  answer   86,30 (2) 2.4 ( x   ; x   ) = (2 245,08 – 86,30 ; 2 245,08 + 86,30)  x  limit = (2 158,78 ; 2 331,38)  x  There were 9 months when the aircraft arrivals at the King Shaka International airport were within one standard deviation of the mean.  answer (3) 2.5 The standard deviation of the number of landings at the Port Elizabeth Airport will be higher than the standard deviation of the number of arrivals at the King Shaka International Airport OR C.  answer (1) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 5 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 y T W(–4 ; 4) N M V O x P(0; –4) S R K 3.1 4  (4) 8 m WP    substitution of W and P 40 4 mWP  2  mWP (2) 3.2 1 mST  (given) 2  mWP mST  mWP mST    2 1   mWP mST  = –1 2  1 (2) ST  WP 3.3 5 y  2 x  60  0 2  y   x  12 5 2 1  x  12  x  6  equating 5 2  4 x  120  5x  60 9 x  180  x value x  20  y    20  12 2  substitution 5  y  4  y value  S(–20; –4) (4) OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 6 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne y T W(–4 ; 4) N M V O x P(0; –4) S R K 5 y  2 x  60  0 1   substitution 5 x  6   2 x  60  0 2  5 x  30  2 x  60  0 2 9 x  90  x  20  x value 2  y    20  12 2  substitution 5  y  4  y value  S(–20; –4) (4) OR 5 y  2 x  60 ........(1) 2 y  x  12 ........(2) (1)  2(2) : 9 y  36  adding y  4  y value 2(–4) – x = 12  substitution x = –20  x value (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 7 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 3.4 y 2  4  12 OR 5 y  2(4)  60  0  substitution 5 52 y  y value 5  52   R   4;   OR R(–4 ; –10,4)  5  52   52   method or subst into  WR  4     OR WR = ( 4  ( 4)) 2  (4    ) 2 distance formula  5  5 72 2  answer  WR  units or WR  14 units 5 5 (4) OR WR  ST  SK 1  2   x  6    x  12   substitution 2  5  9  simplification  x  18 10 9  ( 4)  18 10  subst x = –4  14,4 units  answer (4) 3.5 2 mSK    mSK 5   158,19... (Ref.  =21, 801…°)  size of  MN̂S  21,80... 1 mST  2 NM̂S  26,56...  size of NM̂S   21,80...  26,56... [ext  of ]  method  answer   48,366... = 48,37° (5) 3.6 In SRW:  h = –4 – (–20)  h = 16units  h Area SRW   h WR  1 2  72   16  1  substitution 2  5  115,2 square units  area  Area SWRL = 2Area SRW =2(115,2) = 230,4square units  answer (4) OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 8 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne In SRW:  h = –4 – (–20)  h = 16units  h 72 Area SWRL = 16   substitution 5 = 230,40 square units  answer (4) OR SW = 8 5 SW   20  42   4  42  8 5  17,89 2  2 SR   20  4    4  10   16 29 16 29  17,23 2 SR=  5 5 5 Area SWRL = 2  Area SRW 1   2 SW  SR sin   2  1 16 29   2 8 5  sin 48,37  substitution 2 5  =230,41square units answer (4) [21] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 9 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 y T M(–3 ; 4) O x N(–11 ; p) S 4.1 x2  y2  r 2  substitution  r 2   3  4  25 2 2 x 2  y 2  25  answer (2) 4.2 TM  TN [tangent  radius] T(–11 ; 4) r = –3 – (–11) = 8  xT  11 x  32   y  42  64  LHS  RHS (3) 4.3 O (0 ; 0 ) and M(–3; 4) 40 4 04 4 4 mOM   OR   mOM   30 3 0  ( 3) 3 3 3 3 m NM   m NM  4 4 3 3 y  4  ( x  (3)) OR y xc  substitution of m and M 4 4 3 9 3 y 4  x 4  (3)  c 4 4 4 3 25 25 y x c 4 4 4  equation 3 25 y  x (4) 4 4 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 10 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 4.4 N(–11 ; p) 3 25 y x 4 4 4 p p   11  3 25 3 OR   subst x = –11 into eq or 4 4  3  ( 11) 4 gradient p2  p2  N 11;  2  3  xS 4  yS 0 and 0 2 2 S3;  4  xS  yS SN   11  32   2  (4)2  10 2 units or 14,14 units  answer (CA) (5) 4.5 B 2 ; 5 BM  2 units  2 Radius of circle centred at M = 8 units k 8 2 or k 8 2 = 6,59 units = 9,41 units = 6,6 units = 9,4 units  k  6,6  k  9,4 (5) [19] y 6,6 (–2 ; 5) 9,4 x Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 11 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 y g A(130,9° ; 0,33) x 0° 90° 150° 180° f 5.1 Period of g = 360  answer (1) 5.2 1  answer (A) Amplitude of f = (1) 2 5.3 f (180) – g(180) 1  1     2  2  1 =1 (1) 5.4.1 x  140,9  x  140,9 (1) 5.4.2 3 sin x  cos x  1 3 1 1 sin x  cos x   dividing by 2 2 2 2 sin x cos 30  cos x sin 30  1  cos 30; sin 30 2 1 1 sin( x  30)   sin( x  30)  2 2 1 sin( x  30)  at x  0 or x  120 2  x [0 ;120] OR 0  x  120  interval (4) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 12 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 y P(5 ; 12) <  x  T 6.1.1 12 2 tan    or  2 answer 5 5 (1) 2 2 2 6.1.2 (OP) = (–5) + (12)  Pythagoras OP = 13  OP 5 cos     answer 13 (3) 6.1.3 b sin(  90)   sin(  90)  b 6,5 y 6,5 b P(–5 ; 12) cos    cos  6,5 5 b 13  13 6,5  5 b   5 13 6,5 b x  value of b 2 O (4) OR 6,5 S(a ; b) a cos(90   )  a  cos(  90)  6,5 6,5 a   sin   sin   6,5 12 a  value of a    a  6 13 6,5 5 b  (6,5) 2  ( 6) 2    value of b 2 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 13 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 6.2 sin 2 x. cos( x)  cos 2 x. sin(360  x) sin(180  x) sin 2 x cos x  cos 2 x  sin x    cos( x)  cos x  sin x  sin(360  x)   sin x sin(2 x  x)   sin(180  x)   sin x  sin x sin x   numerator = sin x  sin x  1  answer (5) 6.3 2 6 sin x  7 cos x  3  0  identity 6(1  cos 2 x )  7 cos x  3  0 6  6 cos 2 x  7 cos x  3  0  standard form 6 cos 2 x  7 cos x  3  0  factors (3 cos x  1)( 2 cos x  3)  0 1 3  both solutions of cos x cos x   or cos x  (N/A) 3 2  x  109,47  k.360; k  Z or  x  109,47 & 250,53 x  250,53  k.360; k  Z  + k.360; k  Z (6) 6.4 1 x  3 cos A x 2 3 cos A 2   x  1  squaring both sides  x 1 1 9 cos 2 A  x 2  2  2  9 cos 2 A  x 2  2 x x2 9 cos A  2  2 2 4 cos 2 A  4 9  cos 2 A  9 cos 2A  2 cos 2 A  1  cos 2A  2 cos 2 A 1 4  2   1 9 1  9  answer OR (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 14 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 1 x2  2  0 x2 2  1 x    0  x x2  1 x  1 3cosA  2 or 3cosA  2 2 2 cosA  or cosA   3 3 cos2A  2cos 2 A  1  x  1 2 2  2  cos A   2    1 3  3 2 1  cos A    3 9 double angle identity  answer (5) [24] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 15 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 P r Q 2x 30° R S 7.1 3r tan 30  OR  trig ratio QS 3r  QS subject QS  tan 30 3r 3r  or 1 3 3 3  3r (3) 7.2 Area of flower garden   3r   r 2  substitution into 2 difference of areas  9r 2  r 2  8r 2  answer (2) 7.3 2 2 2 RS  r  (3r )  2( r )(3r ) cos 2 x substitution into cosine rule correctly  r 2  9r 2  6r 2 cos 2 x  10r 2  6r 2 cos 2 x  10r 2  6r 2 cos 2 x  r 2 (10  6 cos 2 x )  r 2 (10  6 cos 2 x ) (3) RS  r 10  6 cos 2 x 7.4 RS  10 10  6 cos 2(56) substitution  34,9966...  answer  35 m (2) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 16 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 L K O 1 1 2 1 3 2 M 32° 2 26° N P 8.1.1(a) Ô 2  64 [ at centre = 2 × at circumference/ S R Middelpts  = 2 × omtreks] (2) 8.1.1(b) M̂ 2  90 [Line from centre to midpt of chord/lyn v midpt SR na midpt v koord] KÔN  90  26  116 [ext  of /buite  van ] S Ô1 116  64  52  answer OR (4) M̂ 2  90 [Line from centre to midpt of chord/lyn v midpt SR na midpt v koord] Ô3  64 [sum of s in ] S Ô1  52 [s on straight line/op ‘n reguitlyn]  answer (4) 8.1.2 PK̂O  P̂  128 [sum of s in ∆/som e van ∆] PK̂O  P̂ [s opp = sides/e teenoor = sye] S  64 S  K̂ 2  32 or K̂ 2  K̂1 S (3)  KN bisects/halveer OK̂P OR K̂ 2  KN̂O [s opp = sides/e teenoor = sye] S K̂ 2  KN̂O  64 [sum of s in ∆/som e van ∆] S  K̂ 2  32 or K̂ 2  K̂1 S  KN bisects/halveer OK̂P (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 17 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 8.2 A G 1 F 2 1 D 2 C B 8.2.1 F̂1  D̂1 [tan chord theorem/raaklyn koordst] S R D̂1  B̂ [Given/Gegee]  F̂1  B̂  F̂1  B̂  FG || BC [corresp s =/Ooreenkomstigee =]  R (4) 8.2.2 GC FB  [line || one side of /lyn || een sy v ] S R AC AB x9 5   substitution 2x  6 7 7 x  63  10 x  30 3x = 93 x = 31  answer (4) OR AG  2 x  6  x  9  x  15 AG AF S R  [line || one side of /lyn || een sy v ] GC FB x 15 2  substitution  x9 5 5x  75  2 x 18 3x = 93  answer x = 31 (4) OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 18 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne AF AG S R  [line || one side of  /lyn || een sy v ] AB AC 2 x  15  substitution  7 2x  6 7 x  105  4 x  12 3x  93  answer x  31 (4) [17] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 19 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 9.1 K R T O Q S 9.1 Construction: Draw diameter KS and draw KR  construction Konstruksie: Trek middellyn KS en verbind KR QŜT  90  TŜK [radius  tangent/raaklyn]  S/R SR̂K  90 [ in semi circle/halfsirkel]  S/R SR̂T  90  KR̂T S TŜK  TR̂K [s same segment/e dieselfde segment]  S/R (5) QŜT  R̂ OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 20 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne R T O Q S 9.1 Construction: Draw radii OS and OT  construction Konstruksie: Trek radii OS en OT QŜT  90  OŜT [radius  tangent/raaklyn]  S/R OŜT  ST̂O [s opp = sides/e teenoor = sye]  S/R  SÔT  180  2OŜT [s of /e van ] S R̂  90  OŜT [ at centre = 2× circumf/  S/R midpts = 2× omtreks]  QŜT  R̂ (5) OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 21 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne K R T O Q S 9.1 Construction: Draw diameter KS and join K to T.  construction Konstruksie: Trek middellyn KS en verbind K tot T K QŜT  90  TŜK [radius  tangent/raaklyn]  S/R ST̂K  90 [ in semi circle/halfsirkel]  S/R  K̂  90  TŜK S  QŜT  K̂ but R̂  K̂ [s same segment/e dieselfde segment]  S/R  QŜT  R̂ (5) OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 22 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne R y T y z x O x z Q S 9.1 Construction: Draw radii OT, OR and OS  construction Konstruksie: Trek radiuse OT, OR en OS OŜT  OT̂S [s opp = radii/e teenoor = radiuse]  S/R Also: OT̂R  OR̂T and OR̂S  OŜR 2 x  2 y  2 z  180 [s of ] x  y  z  90 y  z  90  x S OŜQ  90 [radius  tangent/raaklyn]  S/R  TŜQ  90  x S  TŜQ  y  z  R̂ (5) OR Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 23 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne R T O Q S 9.1 Construction: Draw radii OT and OS, tangent QT  construction Konstruksie: Trek radiuse OT en OS, raaklyn QT OŜQ  90 [radius  tangent/raaklyn]  S/R  TŜQ  90  TŜO  TŜO  ST̂O [s opp = radii/e teenoor = radiuse] S TÔS  180  2TŜO [s of ] S R̂  90  TŜO [ at centre = 2× circumf/ midpts = 2× omtreks]  S/R  TŜQ  R̂ (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 24 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 9.2 R N 1 3 2 M 2 1 S x 1 2 3 P 1 2 Q 9.2.1(a) N̂ 2  x [alt s; PR || NQ/verw. e; PR || NQ] SR (2) 9.2.1(b) Q̂ 2  x [tan chord theorem/raaklyn koordstelling] SR OR (2) M2  x [tan chord theorem/raaklyn koordstelling]  S/R Q̂ 2  x [s in same segment/e in dieselfde segm]  S/R (2) 9.2.2 MN MS S R  [QN || PR; Prop Th] NR SP N̂1  N̂ 2  x [given] S SR P̂3  x [s in same segment/e in dieselfde segm] P̂3  Q̂ 2 [= x] R SQ = PS [sides opp = /sye teenoor = e] MN MS  (6) NR SQ [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 25 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 10 C D M E 1 2 1 2 4 1 F 3 2 1 2 B 3 A 10.1.1 DB̂E  90 [ in semi-circle/ in halfsirkel] S R  DM̂A  90 [ AM  DE ]  FBDM is a cyclic quadrilateral/koordevh R [converse opp s cyclic quad/omgek teenoorst e kvh ] (3) OR DB̂E  90 [ in semi-circle/ in halfsirkel] S R M̂ 2  DB̂E  90  FBDM is a cyclic quadrilateral/koordevh [converse ext of cyclic quad/omgek buite van kvh ] R (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 26 DBE/November 2020 SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne 10.1.2 B̂3  D̂ 2 [tangent chord th/raaklyn koordst] S R F̂1  D̂ 2 [ext  cyc quad/buite  koordevh] S R  B̂3  F̂1 (4) OR B̂1  Ê  x [tangent chord th/raaklyn koordst] S R F̂1  90  x [ sum in / van ] F̂1  90  x  D̂ 2  90  x [ sum in / van ]  D̂ 2  F̂1  D 2 B̂3  D̂ 2 [tangent chord th/raaklyn koordst] R  B̂3  F̂1 (4) OR B̂1  Ê  x [tangent chord th/raaklyn koordst] S R B̂3  90  x [straight line/ reguitlyn ] S F̂1  90  x [sum of s  / som van e van ] S  B̂3  F̂1 (4) 10.1.3 In ∆CDB and ∆CBE Ĉ  Ĉ [common /gemeenskaplike  ] S  S/R CB̂D  CÊB [tangent chord th/raaklyn koordst] CD̂B  CB̂E [ sum in / van ] R ∆CDB ||| ∆CBE (3) OR In ∆CDB and ∆CBE CB̂D  CÊB [tangent chord th/raaklyn koordst]  S/R Ĉ  Ĉ [common /gemeenskaplike  ] S ∆CDB ||| ∆CBE [, , ] R (3) 10.2.1 BC DC  [||| s] EC BC  ratio BC 2  EC  DC  8 2  substitution  16 BC  4 answer (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics/P2/Wiskunde/V2 27 DBE/November 2020 SCE/SSE– Marking guidelines/Nasienriglyne 10.2.2 BC DB  [||| s] EC BE DB 4 1   BE 8 2 BE  2DB  BE = 2DB DB2  BE 2  DE2 [Pyth theorem]  substitution into DB2  (2DB)2  36 Pyth theorem 5DB2  36 36 DB2  36 5  DB2  5 6 answer DB   2,68 units 5 (4) [17] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou