Mathematics Grade 12 Paper 2 North West Prelim 2024 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 MATHEMATICS P2/WISKUNDE V2 SEPTEMBER 2024 MARKING GUIDELINES/NASIENRIGLYNE MARKS/PUNTE: 150 These marking guidelines consist of 19 pages and 3 pages containing the cognitive grid./ Hierdie nasienriglyne bestaan uit 19 bladsye en 3 bladsye wat die kognitiewe tabel bevat. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 2 NW/September 2024 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 Guidelines. 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, sien slegs die EERSTE poging na.  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/waardes om ‘n probleem op te los, word NIE toegelaat nie. QUESTION/VRAAG 1 1.1 33 players/spelers  33 (1) 1.2 x   2  22    8  26   15  30    6  34    2  38   33 982  982  33  29, 76 Answer only: full marks  answer/antwoord (CA if/as  33) (2) 1.3.1  Cumulative  Age class Frequency frequency  Ouderdomklas Frekwensie Kumulatiewe  frekwensie   20  x  24 2 2   24  x  28 8 10 2 & 10 28  x  32 15 25 32  x  36 6 31 36  x  40 2 33 33 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 3 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne 1.3.2  Ogive/Ogief  35 grounding/anker (20 ; 0) 30 plotting ogive at upper limits correctly/korrekte Cumulative frequency/ 25 plot van ogief by boonste limiete 20 shape (smooth)/ vorm (vryhand) 15 Kumulatiewe frekwensie 10 5 0 16 20 24 28 32 36 40 44 Age (in years)/ Ouderdom (in jare) (3) 1.4 On graph the y-value at 16,5 / y-waarde van 16,5 op die graph/grafiek grafiek.   median / mediaan  29,8 years / jare  29,8 (accept values/aanvaar waardes: 29, 4  x  30 ) (2)   1.5 The affected intervals are/ die geaffekteerde intervalle is: identify affected intervals/ 24  x  28 and / en 32  x  36 . identifiseer geaffekteerde intervalle If the frequency of both intervals are increased to 9 players, increase frequency to 9 the data will be symmetrical/as die frekwensie van beide players/verhoog intervalle tot 9 spelers verhoog word, is die data simmetries. frekwensie na 9 spelers  k  4 Answer only: full marks k=4 (3) [13] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 4 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 2 Preparatory examination (x)/ 38 65 78 23 67 93 39 83 51 66 Voorbereidende eksamen (x) Final examination (y)/ 57 72 81 27 59 94 41 85 54 79 Finale eksamen (y) 2.1 a  10,85 Answer only: full marks, but if a a  b  0,90 and b are swopped only 1/3 marks/  b  yˆ  10,85  0,9 x maar as a en b omgeruil is, slegs equation/ 1/3 punte. vergelyking (3) 2.2.1 yˆ  10,85  0,9(46) substitute 46 into eq. /  52, 25% vervang 46 in vgl.  Answer only: full marks answer/antwoord OR /OF (2) 46 yˆ  52, 08% (calculator / sakrekenaar )  52,08 % (2) 2.2.2 r = 0,94   Yes, because there is a very strong correlation between the data/ yes/ja Ja, want die korrelasie tussen die data is baie sterk. very strong/baie sterk (2) 2.3 B B (1) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 5 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 3 y B(3 ; 6) F A(–3 ; 4) E S P O R Q x  3  3 4  6   3.1.1 F ;  x-value/waarde  2 2  y-value/waarde  F  0 ; 5 (2) 50  3.1.2 mDF  subst./vervang  5 0     2 2 Answer only: full marks answer/antwoord (2) 3.1.3 tan   2  tan  = mDF    63, 43 answer/antwoord (2) 3.2 y = 2x answer/antwoord (1) 3.3 mDF = mOB  2  Lines have the same gradient/lyne het dieselfde gradiënte answer/antwoord (1) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 6 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne 3.4 QR  PQ  3 x QR = PQ = 3x  R  3  3x ; 0  coordinates of/ QP  3 x koördinate van R  S  3  3x ; 3x  coordinates of/ koördinate van S Equation / vergelyking : OB   y  2x  3x  2  3  3x    3x  6  6 x  2 value of/ x 3 waarde van x Substitute/vervang   2   2  S 3  3  ; 3     3   3   xs -value/waarde  S 1 ; 2   ys -value/waarde (6) OR/OF SR  3x SR = 3x ˆ  tan 63, 43  SR tan SOR OR 3x OR = OR 2 OQ  3 units / eenhede RQ  3 x 3x   3x  3 2 2  x value of/ 3 waarde van x S  3  3x ; 3x  coordinates of/ koördinate van S   2   2   S 3  3  ; 3     3   3   xs -value/waarde S 1 ; 2   ys -value/waarde (6) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 7 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne  converse midpt.theorem /  3.5 E is midpt. of / van || AO   S  omgekeerde midpt .  stelling    3  coordinates of E/ E ; 2  2  koördinate van E ES || DO (same y  coordinates / dieselfde y  koördinate) S/R EDOS is ||m [both pairs opp. sides || / reason/rede beide pare teenoorst . sye ||] (4) OR/OF converse midpt.theorem /  E is midpt. of / van || AO   S omgekeerde midpt.  stelling    3  coordinates of E/ E ; 2  2   koördinate van E  3   3   3  Midpt. EO   ; 1 & Midpt. DS   ; 1  ; 1  4   4   4  EDOS is || [converse diag. of/omgekeerde hoeklyne van ||m ] m reason/rede (4) [18] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 8 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 4 y Q(10 ; 10) P S x R(10 ; t) x 2  4 x   2   y 2  8 y   4   80   2    4  2 2 2 2 4.1   x  2    y  4   100 2 2 LHS/LK RHS/RK (2) 4.2.1 P(2 ; 4) x = 2 y = 4 (2)  4.2.2 x  10 equation/vergelyking (1) 10  4 subst./vervanging 4.3 mQP   10  2  3  3  mQP  4 4 4 4  mQS   [rad  tangent / rad  raaklyn]  mQS   3 3 4 4 10   10   c OR / OF y  10    x  10  subst./vervang m & (10 ; 10)  3 3 70 c 3  4 70 equation/vergelyking y x 3 3 (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 9 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne 4 4.4 tan QSˆ x    3 QSˆ x  126,87 ˆ  QSx ˆ  90  ext  of  / buite van   126,87  RQS method/metode ˆ  36,87 RQS answer/antwoord (3) 4.5 ˆ = 53,13°  radius  tangent / raaklyn  PQR ˆ  PQR ˆ  53,13  s opp.  radii/e teenoor = radiusse  ˆ = QRP PQR ˆ = 73, 74  s of  / e van   QPR ˆ   QPR 1 area  PQR =  PQ  PR  sin QPR ˆ subst. in area rule 2 correctly/vervang korrek 1 = 10 10  sin 73, 74 in oppv.-reël 2  48 units 2 / eenhede2 answer/antwoord (4) OR/OF PQR = 53,13°  radius  tangent / raaklyn  ˆ ˆ  PQR Q and R are symmetrical about the line y = 4/ Q en R is simmetries rondom die lyn y = 4  t =  2 & QR  12  QR 1 area  PQR =  PQ  QR  sin PQR ˆ subst. in area rule 2 correctly/vervang korrek 1 = 10 12  sin 53,13 in oppv.-reël 2  48 units 2 / eenhede 2 answer/antwoord (4) 2 12 4.6 2 12  h  x   h  x  k x  8 x2   h  x   h  x  k  x  8 x2  h  2   14 h  2   14 12 12  h  x    h  x   h  2 x 3 x2  12 12  h  x    h  x   h  2 x 3 x2 12   h  x   k  14 answer/antwoord x 3 (4) [21] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 10 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 5 y 1 f Q g x – 90° – 45° 0° 45° 90° P(– 68,53 ; – 0,68) –1 5.1.1 a 1 answer/antwoord (1) 5.1.2 Q  68,53 ; 0, 68  x-value/waarde  y-value/waarde (2) 5.1.3 x   75 or / of x  15  –75°  15° (2) 5.1.4 x    68,53 ; 90 OR / OF  68,53  x  90  – 68,53° & 90°  notation/notasie (2) 5.1.5 f  x  45   f  x  45  m   45  – 45° (2) 1 1 5.1.6 b  2 2 (1) 5.2 x   68,53 ; 90 OR / OF 68,53  x  90 accuracy/akkuraatheid (2) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 11 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 6 6.1.1 x 2  242  252 y  x2  y 2  r 2 x 2  49 P(–7 ; 24) x  7 x  7 25 x O T (2) 6.1.2 tan  360      tan    tan    24       7   24 Answer only: full marks answer/antwoord  7 (2) 24  6.1.3 tan    7    73, 74 size of/grootte van  ˆ  180  73, 74 POT  106, 26 answer/antwoord (2) 6.2.1 sin 20  cos120. tan 405  cos110   sin 20  cos 180  60  .tan  360  45   cos  90  20    sin 20  cos 60.tan 45  sin 20   cos 60  tan 45 1   sin 20   answer/antwoord 2 (4) 6.2.2  2 cos15  1 2 cos15  1 sin   2 x    4sin x cos x    2 cos 15  1 .   sin 2 x  2   2 cos 2 15  1  4sin x cos x  2sin x cos x   cos 30  .  2sin x cos x  4sin x cos x  cos 30 3  answer/antwoord 4 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 12 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne 4 cos  90  2 y  .cos 2 x  4sin 2 x.cos  360  2 y   6.3  4sin 2 y .cos 2 x  4sin 2 x .cos 2 y  sin 2 y  cos 2 y    4 sin  2 y  2 x   compound angle/ saamgestelde hoek  4 sin 2  y  x     4.2sin  y  x  .cos  y  x  double angle/dubbelhoek  8t answer/antwoord (5)  6.4.1 LHS / LK  sin 2 x  cos 2 x  tan 2 x    1  tan x 2  sin 2 x  cos 2 x  1 sin 2 x sin 2 x 1  cos 2 x  cos 2 x cos 2 x  sin 2 x cos 2 x  sin 2 x    cos 2 x cos 2 x 1  cos 2 x (3) 6.4.2 If/as x  180 ; 270  , then/dan is cos x  0   sin 2 x  cos 2 x  tan 2 x  negative / negatief statement/bewering  Attie is correct / korrek answer/antwoord (2) 6.5 2 2sin 2 x  5.2 cos 2 x  3   2 2sin 2 x  5.2 1  2sin 2 x  3  1  2sin 2 x  22sin x  5.2.22sin x   3 2 2  10 10 22sin x  30 2 2sin 2 x  2sin 2 x 2 2  22sin x .22sin x  3.22sin x 10  0 2 2 2 standard form/standaardvorm 2     5 22sin x  2  0 2 2 2sin x factors/faktore 22sin x   5 or / of 22sin x  21 2 2  22sin x   5 2 2sin 2 x  1   1 1 sin 2 x   sin 2 x   2 2 1  sin x    2 (6) [30] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 13 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 7 A 30° h B D C h 7.1 tan 30   correct trig ratio/ BC korrekte trig verhouding h  BC as the subject/ BC  tan 30 as die onderwerp h   3h 1 3 (2) 7.2 ˆ  2 DBC answer/antwoord (1) 7.3 DC BC correct use of sine-rule/ korrekte  sin B sin D gebruik van sinus-reël DC  BC correct substitution into the sin 2  sin  90    formula/korrekte vervanging in die formule DC.cos   BC.2sin  cos   sin 2   2sin  cos  3h .2sin  cos  co-ratio/ko-verhouding DC  cos   2 3 h sin   2 3h sin   12h sin  (5) [8] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 14 NW/September 2024 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 VRAE 8–10 nagesien word. The order in which the candidate answers a geometry question must follow logically/ Die volgorde waarin ‘n kandidaat ‘n meetkundevraag beantwoord moet logies volg. Example/Voorbeeld Given/Gegee AB || CD and/en ˆ EFD  115 A D 65° 115° F E y x B C The candidate first needs 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 15 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 8 E A O 1 1 B 2F 2 2 1 C x D 8.1 F̂2  90  line from centre to midpt.chord/midpt. sirkel , midpt. koord  SR (2) 8.2.1 Ĉ1  x  s opp. = radii/e teenoor  radiusse  S Ô 2  180  2 x sum of s of / som van e van  DOC  S (2) 8.2.2 ˆ = 90°  co  int . s / ko  binne e ; AC || ED  DOF  S/R Ô1  90  180  2 x   2 x  90 S ˆ  x  45   at centre  2   at circ. / midpts  2  omtreks CAB SR B̂ + x  45  90  180 sum of s of / som van e van  FAB  S/R B̂  135  x S (6) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 16 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne QUESTION/VRAAG 9 A k h D E B C 9.1 Construction: draw altitudes h and k; join B with E and D with C/ construction/ Konstruksie: trek hoogtelyne h en k; verbind B met E en D met C. konstruksie 1 AD  h area  ADE 2 AD S   area  DEB 1 DB  h DB 2 1 AE  k area  ADE 2 AE S   area  DEC 1 EC  k EC 2 area  DEB  area  DEC same base;same||; dieselfde basisse ; dieselfde || S/R area  ADE area  ADE S   area  DEB area  DEC AD AE   DB EC (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 17 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne 9.2 P y S T y–1 Q K R 3 3  y y 4  prop.th / eweredigheidst.;ST || QR  S/R 9.2.1  2 y 1 y 1 2  1 3 3 y  y     y  1  y    2 2 4 1 3 9 3 simplification/ y2  y  y2  y  2 2 4 4 vereenvoudiging 4y  2y  6y  9y  3 2 2 0  2 y2  7 y  3 standard form/ 0   y  3 2 y  1 standaardvorm factors/faktore 1 y  3 or / of y  only/slegs 2 y3 (5) 9.2.2 ˆ Q PST ˆ corresps/ooreenk .e ;ST || QR  S/R ˆ  ˆ PST ˆ PKT  Q P, S, K and/en T are / is consyclic/konsiklies converse s in same segment / omgekeerde e in dies. segment  R  PSKT is a / is ' n cyclic quadrilateral / koordevierhoek (2) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 18 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne A QUESTION/VRAAG 10 C 1 D 2 3E 1 2 F 2 3 1 B 10.1.1  in semi circle./ in halfsirkel  Ĉ  90 S R ˆ  90  radius  tangent / raaklyn  ABF S R ˆ  ABF C ˆ  90 (4) 10.1.2 In  DBF and / en  BCA Dˆ B ˆ  s opp. equal sides/e teenoor gelyke sye  S/R 2 2 C  from / vanuit 10.1.1 ˆ  ˆ DBF S  DFB |||  BAC     R DF DB   from / vanuit ||| s  S/R BA BC  DF.BC = AB.BD (4) OR / OF In  DBF and / en  BCA Dˆ B ˆ  s opp. equal sides/e teenoor gelyke sye  S/R 2 2 ˆ  from / vanuit 10.1.1 ˆ C DBF S ˆ F̂  A sum of s of  /binnee van   S  DFB |||  BAC     DF DB   from / vanuit ||| s  S/R BA BC  DF.BC = AB.BD (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

Downloaded from hlayiso.com Mathematics P2/Wiskunde V2 19 NW/September 2024 NSC/NSS – Marking Guidelines/Nasienriglyne 10.1.3 ˆ  tan chord theorem / raaklyn  koordst. B̂3  A S R ˆ ˆ  Fˆ  A B3 BE = EF sides opp.  s/sye teenoor  e  S/R  BE  EF  DE S  E is the midpt. of circle through D, B and F/ E is die midpt. van sirkel deur D, B en F (4) AC AB 10.2  from / vanuit ||| s  S BF DF 2AD  2EF AD S  EF 1 AC 1 AD 1     both sides/beide kante 3 AC BF AC EF 3 AC3 1 AD.BF S 2  AC EF.AC3 1 AD.BF Pythagoras  AB  BC 2 2 EF.AC3 1 AD.BF 1    BC  AB 2 2 EF.AC3 BC  AB2 2 1 AD.BF  BC  AB 2 2 EF.AC3 (6) [18] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief