Mathematics Grade 12 Paper 2 North West Mock 2020 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 MATHEMATICS P2/WISKUNDE V2 SEPTEMBER 2020 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 150 These marking guidelines consist of 20 pages./ Hierdie nasienriglyne bestaan uit 20 bladsye. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 2 NW/September 2020 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 has 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. NOTA: • As ‘n kandidaat ‘n vraag TWEE KEER beantwoord, merk slegs die EERSTE poging. • As ‘n kandidaat ‘n antwoord van ‘n vraag doodtrek en nie oordoen nie, merk die doodgetrekte poging. • Volgehoue akkuraatheid word in ALLE aspekte van die nasienriglyne toegepas. Hou op nasien by die tweede berekeningsfout. • Aanvaar van antwoorde of waardes om ‘n probleem op te los, word NIE toegelaat nie. QUESTION/VRAAG 1 1.1 k + 19 + 2k + 32 + 49 + 57 + 66 ✓ method/metode = 37, 43 7 3k + 223 = 37, 43 7 3k = 39, 01 ✓ 3k = 39,01  k = 13 (2) 1.2  x = 18, 63 Answer only: Full Marks ✓✓18,63 (2) 1.3 x + p x = 57 ✓method/metode 37, 43 + p (18, 63) = 57 ✓ subst./vervang 37,43 p = 1, 05 and/en 18,63 ✓answer/antwoord (3) 1.4.1 38 ✓answer/antwoord (1) 1.4.2 19 + y = 30 y = 11 ✓answer/antwoord (1) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 3 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 2.1 yˆ = a + bx ✓ a = –106,95 a = − 106,95 and / en b = 14, 76 ✓ b = 14,76 ✓ equation/  yˆ = − 106,95 + 14, 76 x vergelyking (3) 2.2 r = 0,94 ✓ r = 0,94 (1) 2.3 yˆ = − 106,95 + 14, 76(32) ✓substitute 32 into eq. yˆ = 365,37 visitors / besoe ker s OR /OF 32 yˆ = 365, 22 / vervang 32 in vgl. ✓365,37 / 365,22  365 people are predicted / mense word voorspel ✓ Yes/Ja  Yes, accept the prediction / Ja, aanvaar die voorspelling. (3) 2.4 The Madiba swimming pool. The daily maximum ✓Madiba temperatures (independent variable) remained the same. The ✓slope less steaper/ slope of yˆ = k + 12,85 x is less steaper, which means the helling minder steiler y-values for the Cronje swimming pool are smaller. This result ✓y-values for Cronje in less visitors for the Cronje swimming pool/ swimming pool are Die Madiba-swembad. Die daaglikse maksimum temperature smaller/y-waardes vir (onafhanklike veranderlike) bly dieselfde. Die helling van Cronje-swembad is yˆ = k + 12,85 x is minder steiler, wat beteken dat die y-waardes kleiner vir die Cronje-swembad kleiner is. Dit het tot gevolg dat die Cronje-swembad minder besoekers het. (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 4 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 y A(–20 ; 64)  x' B D(–12 ; p) E(9 ; 26) K C x 3.1 x = –20 ✓ x = –20 (1) 3.2 –20 + 16 = – 4 ✓ C ( −4;0 )  C ( −4;0 ) (1) 3.3 AC = (64) + (16) OR / OF d AC = (−20 + 4) + (64 − 0) 2 2 2 2 2 ✓method/metode = 4352 = 65,97 units / eenhede ✓65,97 (2) 3.4 64 + 0 64 + 0 =p ✓ 2 2  p = 32 (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 5 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 3.5 26 − 32 ✓method mDE = gradient/metode 9 + 12 gradiënt 2 =− ✓ mDE = − 2 7 7 2 mAB = m DE = − [DE || AB midpt.th / middelpuntstelling ] 7 2 ✓ mAB = − Through the point / Deur die punt ( −20;64 ) 7 2 y − 64 = − ( x + 20 ) ✓Subst./Vervang 7 ( −20;64 ) 2 40 y − 64 = − x − 7 7 2 408 2 408 y = − x + ✓y = − x + 7 7 7 7 (5) 3.6 mAB = tan  see / sien diagram −2 tan  = − 2 ✓ tan  = 7 7  2 tan −1  −  =   7   = − 15,95 + 180 ✓–15,95°  = 164, 05 ✓164,05° ˆ + 90 164, 05 = KAB ✓method/metode  KABˆ = 74, 05 ✓answer/antwoord (5) 3.7 ˆ = 74, 05 − 38, 67 CAB ˆ = 35,38 ✓ CAB = 35,38 coordinates of / koör di nate van B (22;52) ✓x = 22 ✓y = 52 d AB = ( 22 + 20 ) + ( 52 − 64 ) 2 2 = 6 53 ✓ 6 53 1 ˆ ✓correct use of area Area ABC = AC.ABsin CAB 2 rule/korrekte gebruik 1 ( ) = ( 65,97 ) . 6 53 sin 35,38 2 van oppv.reël = 834, 22 units 2 / eenhede 2 ✓answer/antwoord (6) [21] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 6 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 y N M J x F L K(9 ; –10) 4.1 r=5 ✓r = 5 (1) 4.2 x − 6 x + (−3) + y + 4 y + (2) = 87 + 9 + 4 2 2 2 2 ✓method/metode ( x − 3) + ( y + 2 ) = 100 2 2 ✓x = 3  F(3; − 2) ✓y = –2 Answer only: Full Marks (3) 4.3 r = 87 + (−3) + (2) = 100 2 2 2 ✓r = 100 (can also be shown in 2  r = 10 4.2/ kan ook in 4.2 gewys word) ✓r = 10 (2) 4.4 FM = 15 units/eenhede ✓FM = 15 ✓subst. into distance formulae d FM = (14 − 3) + ( h + 2 ) = 15 2 2 /vervang in afstandsformule 112 + ( h + 2 ) = 225 ✓square both sides /kwadreer 2 beide kante ( h + 2 ) = 104 2 ✓ ( h + 2) = 104 2 h =  104 − 2  h = 104 − 2 ( see / sien diagram ) (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 7 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 6 + 10 4 4.5 mJK = ✓ mJK = − −3 − 9 3 4 =− 3 3 3 mJN =  mJN = [rad ⊥ tangent / rad ⊥ raaklyn] ✓ 4 4 3 y−6= ( x + 3) ✓correct subst. into eq. / 4 korrekte vervanging in vgl. 3 9 y−6= x+ 4 4 3 33 y= x+ 4 4 (3) 4.6 Eq. of / vgl. van NL y− ( 104 − 2 ) = − 43 ( x − 14 ) ✓Correct subst into eq. / korrekte vervanging in vgl. 4 56 y − 104 + 2 = − x+ 3 3 4 50  y =− x + + 104 ✓ eq. of / vgl. van NL 3 3 Min. x − value of intersection will be at N / Min. x − waarde van snyding is by N 4 50 3 33 ✓ equate eqs. / stel vgls. gelyk − x+ + 104 = x + 3 3 4 4 4 3 33 50 ✓ simplify / vereenvoudig − x− x = − − 104 3 4 4 3 25 x − = − 18, 614705... 12 x = 8,94 ✓ 8,94 min.x -value of point of contact is p / min. x − waarde vir raakpunt is p  p = 8,94 ✓ conclude /lei af p = 8,94 (6) [19] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 8 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 y P(k ; 1) x O T ( 10 ) 2 5.1.1 k 2 + 12 = ✓Pythagoras k2 = 9 k = 3 k = − 3 (according to / vo lg ens diagram) ✓k = –3 (2) 5.1.2 − cos  (a)  −3  = −   10  3 3 3 10 = ✓ or / of 10 10 10 (1) 5.1.2 1 − sin(180 +  ).sin(360 −  ) ✓ sin (180 +  ) = − sin  (b) = 1 − (− sin  ).( − sin  ) OR/OF  1  1  ✓ sin ( 360 −  ) = − sin  1− −  −  = 1 − sin 2   10  10  = cos 2  = 1− 1 ✓ 1 − sin 2  = cos 2  10 = cos  OR/OF 9 1 −3 −3 10 = sin  = = or / of 10 10 10 10 −3 −3 10 −3 −3 10 = or / of ✓ or / of 10 10 10 10 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 9 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 5.1.3 1      ✓manipulation /   2sin  − 15  .cos  − 15   manipulasie 2  2  2  = 1 sin ( − 30 ) ✓ sin( − 30) 2 1 ✓expansion of identity/ = sin  .cos 30 − sin 30.cos   2 uitbreiding van identiteit 1 1 3 1 −3  ✓ sin  .cos 30 = 1 3 =  . − .  . 2  10 2 2 10  10 2 1 −3 1 3 3  ✓ sin 30.cos  = . =  +  2 10 2  2 10 2 10  1  3 + 3 =   2  2 10  3+3 = 4 10 (5) 5.2.1 d  [−1;1] or / of − 1 d  1 ✓critical values/kritiese waardes ✓notation/notasie (2) 3 5.2.2 sin ( + 60 ) = sin  .cos 60 + 8 3 ✓LHS expansion / LK sin  .cos 60 + sin 60.cos  = sin  .cos 60 + uitbreiding 8 3 3 ✓ sin 60.cos  = sin 60.cos  = 8 8 3 3 3 sin 60 = .cos  = ✓ 2 2 2 2 1 cos  = 1 2 cos  = ✓ 2  =  45 + n.360 ✓m = 45° (5) 5.3 sin(m − m) = sin 0 = 0 ✓sin 0  A = 20 ✓ 20 ✓1 =1 (3) [22] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 10 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 y g P(90° ; 3) f h B(154.69 ; 1,28) x A 1 6.1 a = 3 and/en b = ✓a = 3 3 1 ✓b = 3 (2) 6.2 540° ✓540° (1) 6.3 A(–154,69° ; –1,28) ✓ –154,69° ✓ –1,28 (2) 1 3 6.4 tan x = ✓ g(x) = h(x) 3 2 1 ✓ 56,3099° x = 56,3099... 3 x = 168,93 ✓ 168,93° vertical dist./vertikale afst. = tan56,31°– 3sin168,93° t +5 t+5 vertical distance / vertikale afs tan d = ✓ 2 2 (4) [9] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 11 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 A x F x B C y D G E 7.1 BC2 = AB2 + AC 2 − 2AB.AC.cos  ✓correct use of cosine- BC = x + x − 2 x.x.cos  2 2 2 rule/korrekte gebruik van cos-reël BC2 = 2 x 2 − 2 x 2 cos  ✓subst/vervanging BC2 = 2 x 2 (1 − cos  ) ✓factorisation/ faktorisering BC = x 2(1 − cos  ) (3) 7.2 ˆ = 90 BDG ✓answer/antwoord (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 12 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 1 1 1 7.3 DG = DE = BC ✓ DG = BC 2 2 2 BG = BD + DG 2 2 2 2  x 2 (1 − cos  )  = y2 +   ✓subst./vervanging  2    x .2.(1 − cos  ) 2 = y2 + 4 x 2 (1 − cos  ) x (1 − cos  ) 2 y2 + = y2 + ✓ 2 2 2 y + x (1 − cos  ) 2 2 = 2 2 y 2 + x 2 (1 − cos  )  BG = 2 (3) 7.4 Max. length of BG is where 1 − cos  is a max / Maks. lengte van BG is waar 1 − cos ' n maks is max value of / maks. waarde van 1 − cos  = 2 ✓ 1 − cos  = 2 2 y 2 + x 2 (1 − cos  ) BG max/ maks = 2 2 2 8  15  2   +   (2) = 3  2 ✓subst./vervanging 2 2281 = 36 = 7,96 units / eenhede ✓answer/antwoord (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 13 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne GEOMETRY/MEETKUNDE Please read carefully through the following table before marking QUESTION 8 – 10 / Lees asseblief sorgvuldig deur die volgende tabel alvorens VRAAG 8 –10 nagesien word. The order in which the candidate answer a geometry question must follow logically/ Die volgorde waarin ‘n kandidaat ‘n meetkundevraag beantwoord moet logies volg. Example/Voorbeeld ˆ = 115 Given/Gegee AB || CD and/en EFD A D 65° F E y x B C The candidate first need to calculate x BEFORE he/she can calculate y/Die kandidaat moet eerste vir x bereken VOORDAT hy/sy vir y kan bereken. 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 the statement AND reason are both correct (Both MUST be correct to get one mark) S/R Ken ‘n punt toe as die bewering EN rede beide korrek is (Beide MOET korrek wees om een punt te kry) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 14 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 A B 1 2 3 D 2 1 O 2 2 E 1 1 G 20° 2 3 4 1 C N F 8.1.1 Ô1 = 20  alt s / verwiss e ;OF || BC  ✓S/R (1) 8.1.2 D̂1 = 10   at centre = 2  circumference / midtpt = 2  omtrek   ✓S✓R (2) 8.1.3 Ĉ2 = 10  opps of cyclic quad / teenoorst.e van kvh  ✓S✓R (2) 8.1.4 Ĉ 4 = 70  rad ⊥ tangent / rad ⊥ raaklyn  ✓S✓R ˆ = 70  tan − chord.th / raaklyn − koordst. Dˆ 2 = C 4 ✓S✓R (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 15 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 8.2 OE ⊥ BC  midpt. , midpt. chord / midpt. , midpt. koord  ✓S✓R  OE is the perpendicular height of trapezium OECF / OE is die loodregte hoogte van trapesium OECF 1 3 ✓area ( OF + EC )  OE = y 2 − x 2 2 4 formulae ( ) 1 3 trapezium/ 3 y + 2 x  OE = y 2 − x 2 oppv. 2 4 formule  3  3  y + x   OE = y 2 − x 2 trapesium  2  4 ✓factors  3  3   y − x y + x RHS / OE =  2  2  faktore RK  3   y + x  2  3 ✓answer/  OE = y−x 2 antwoord (5) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 16 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 B F 1 2 A O E 2 1 C D 9.1 Construction: Draw diameter CF and connect F with B/  constr/ Konstruksie: Trek middellyn CF en verbind F met B konstr ˆ = 90  rad ⊥ tangent / rad ⊥ raaklyn  ˆ +C C1 2  S/R ˆ +B B ˆ = 90  in 1  1 2  2   S/R C ˆ +C ˆ =B ˆ +B ˆ = 90  S/R 1 2 1 2 ˆ ˆ =C but / maar B1 2 s in the same seg. / e in dies. seg.  S/R ˆC1 = ˆB2 ˆ = ABC  ACD ˆ (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 17 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 9.2 K O1 1 R S P 2 2 3 P/ 3 2 N N/ 1 N// L M M/ M// 9.2.1 OR = 6 6 (1) 9.2.2 OR = 36 2  KR 2 − KO 2 = OR 2 S  OR ⊥ KL converse Pythagoras / omgekeerde Pythagoras  R (2)  1  9.2.3 N̂ 2 = 90  in  S R  2  ORNL is a cyclic quad / is ' n kvh converse opp. s of cyclic quad / omgekeerde teenoorst.e kvh  R OR/OF converse ext. cyclic quad / omgekeerde buite kvh (3) // // / 9.2.4 If / As M N P touches the circle / die sirkel raak : M / / N / / P / ⊥ OP /  rad ⊥ tangent / rad ⊥ raaklyn S/R If M / N / P / ||MNP and P / coincide with S, then LSMˆ /  90 / S ˆ /  90 As M / N / P / || MNP en P / val saam met S , dan is LSM Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 18 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne ˆ = 90  from / uit 9.2.2  LOS ˆ  ˆ  LOS LSM S M N P is not a tangent to circle through L,O and S / / / S/R converse tan-chord th. not true  M / N / P / is nie ' n raaklyn aan sirkel deur L, O en S nie omgekeerde raaklyn − koordst. nie waar nie  (4) [15] QUESTION/VRAAG 10 G H A D 1 2 34 1 2 B O 3 4 2 1E C F 10.1.1 alt s / verwiss e ; HC || GF R (1) 10.1.2 tan-chord.th/raaklyn-koordst. R (1) 10.2.1 In  DBE and / en  DBC ˆ =B B ˆ  common / gemeenskaplik  S/R ˆ =C D ˆ  both / beide = B ˆ  S/R 4  4 Eˆ 2 = CDB ˆ [sum of s of  / som van e van ] S/R   BDE |||  BCD     OR/OF Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 19 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne In  DBE and / en  DBC ˆ =B B ˆ  common / gemeenskaplik  S/R ˆ =C D ˆ  both / beide = B ˆ  S/R 4  4   BDE |||  BCD     R (3) AH AD 1 10.2.2 = =  prop.th/eweredigheidst. HC||GF S R AG AB 2  AD = DB S OR/OF OB ⊥ FG  rad ⊥ tangent / rad ⊥ raaklyn   OB is the diameter of the smaller circle / OB is die middellyn van die kleiner sirkel  converse tan ⊥ rad / omgekeerde rad ⊥ raaklyn  S/R ˆ = 90  in 1 ODB  S/R  2   AD = DB  midpt. , midpt.chord / midpt. , midpt.koord  S/R (3) BD DE BE 10.2.3 = = from / vanuit |||   S/R BC CD BD  BD 2 = BC.BE S AB but / maar BD = from / vanuit 10.2.2 S 2 2  AB   = BD 2  squaring/  2  kwadrering AB2  = BD 2 = BC.BE 4 (4) 10.2.4 AB = 2DB = 2(3) = 6 units / eenhede 62 = BC  2  from / vanuit 10.2.3  subst. / 4 vervanging BC = 4,5 units / eenhede  4,5 but / maar CE = BC − BE = 4,5 − 2 = 2,5 units / eenhede  2,5  CE : BC = 2,5 : 4,5 = 5 : 9 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 20 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne 1 ˆ .AH.HD.sin AHD area  AHD 2 10.3 =  given/gegee AH = HG  area rule area  HGB 1 .HG.GB.sin G /oppv.-reël 2 ˆ HD.sin AHD = GB.sin G ˆ  corresp.s / ooreenk .e HC||GF ˆ =G AHD S/R area  AHD HD  = S area  HGB GB 1 but / maar HD = GB  midpt.th s / midpt.st e  S R 2 area  AHD 1  = S area  HGB 2 (6) TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Mathematics P2/Wiskunde V2 Downloaded from hlayiso.com 21 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne GRID-Analysis (According to BLOOMS TAXONOMY) KNOWLEDGE ROUTINE COMPLEXED PROBLEM PROCEDURES PROCEDURES SOLVING Question Description Low Mod High Low Mod High Low Mod High Low Mod High Statistics(Gr.11) [9] 1.1 Mean average 2 1.2 Standard deviation 2 1.3 Within standard deviation 3 1.4.1 Adjusted range 1 1.4.2 Adjusted lower quartile 1 2 Regression(Gr.12) [10] 2.1 Regression line 3 2.2 Correlation Coefficient 1 2.3 Application reg. line 3 2.4 Application slope 3 3 Analytical (Gr.11) [21] 3.1 Equation vertical line 1 3.2 Translation 1 3.3 Distance 2 3.4 Midpoint 1 3.5 Equation of str line 5 3.6 Angle + integr. geometry 5 3.7 Area 6 4 Analytical(Gr.12) [19] 4.1 Length of radius 1 4.2. Centre of circle 3 4.3 Radius from equation 2 4.4 Integrating concepts 4 4.5 Eq. of tangent 3 4.6 Min.value of intersection 6 Copyright reserved / Kopiereg voorbehou Please turn over/Blaai om asseblief

Mathematics P2/Wiskunde V2 Downloaded from hlayiso.com 22 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne ROUTINE COMPLEX KNOWLEDGE PROCEDURES PROCEDURES PROBLEM SOLVING Question Description Low Mod High Low Mod High Low Mod High Low Mod High 5 Trigonometry [22] 5.1.1 Pythagoras 2 5.1.2 (a) Ratio 1 5.1.2 (b) Reduction + ratio 4 5.1.3 Double angle 5 5.2.1 Range 2 5.2.2 General solution 5 5.3 Problem 3 6 Trig Graphs [9] 6.1 Parameters 2 6.2 Period 1 6.3 Symmetry 2 6.4 Vertical distance 4 7 2D/3D Trig [10] 7.1 cos-rule 3 7.2. Basic geometry 1 7.3 Pythagoras 3 7.4 Maxima 3 8 Geometry [14] 8.1.1 Alternating angles 1 8.1.2 Angle at centre 2 8.1.3 Opp. Angle Cyclic quads 2 8.1.4 Tangents 4 8.2 Integrating concepts 5 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Mathematics P2/Wiskunde V2 Downloaded from hlayiso.com 23 NW/September 2020 NSC/NSS – Marking Guidelines/Nasienriglyne ROUTINE COMPLEX PROBLEM KNOWLEDGE PROCEDURES PROCEDURES SOLVING Question Description Low Mod High Low Mod High Low Mod High Low Mod High 9 Geometry [15] 9.1 Tan-chord theorem 5 9.2.1 Ratios 1 9.2.2 Converse Pythagoras 2 9.2.3 Prove cyclic quad 3 9.2.4 Problem 4 10 Geometry 10.1.1 Theory 1 10.1.2. Theory 1 10.2.1 Similarity 3 10.2.2 Proportionality 3 10.2.3 Ratios 4 10.2.4 Ratios 3 10.3 Area ratio 6 7 10 13 18 14 23 26 20 0 19 0 0 % Breakdown of cognitive 30 20% 55 36,7% 46 30,7% 19 12,7% levels Expected % 20% 35% 30% 15% Copyright reserved / Kopiereg voorbehou