Mathematics Grade 10 P2 Gauteng November 2022 Memo (Afr)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION/ PROVINSIALE EKSAMEN NOVEMBER 2022 GRADE 10/GRAAD 10 MARKING GUIDELINES/ NASIENRIGLYNE MATHEMATICS (PAPER 2)/WISKUNDE (VRAESTEL 2) 10 pages/bladsye

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 1 QUESTION/ Suggested solution/ Explanation/ Marks/ VRAAG Voorgestelde oplossing Verduideliking Punte 1.1 ✓ Ist and 2nd leaf 1ste en 2de tak should be in order eg. 0139 ✓ 3rd and 4th leaf moet in volgorde wees bv.0139 3de en 4de tak ✓ 5th and 6th leaf Should be in order eg. 237 5de en 6de tak moet in volgorde wees bv.0139 ✓ key/sleutel (4) 1.2 1.2.1 139 + 142 ✓ method/metode Q2 = 2 ✓ = 140,5 (2) answer/antwoord 1.2.2 129 and/en 162 ✓ both values (1) beide waardes 1.2.3 Lower Quartile/onderste kwartiel = 129 ✓ answer/antwoord Upper Quartile/ boonste kwartiel = 152 ✓ answer/antwoord (2) 1.2.4 − x x = ✓ 2 531 n Answer ONLY: FULL marks 2 531 SLEGS antwoord : VOLPUNTE = 18 = 140,61 ✓ 140,61 (2) [11] 2

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 2 QUESTION/ Suggested solution/ Explanation/ Marks/ VRAAG Voorgestelde oplossing Verduideliking Punte 2.1 AGE INTERVALS TALLY/ FREQUENCY/ OUDERDOMS- TELLING FREKWENSIE ✓ tallies and f =10/ INTERVALLE telling en f =10 25  x < 33 //// //// 10 ✓ tallies and f =13/ 33  x < 41 //// //// /// 13 telling en f =13 ✓ tallies and f = 4 / 41  x < 49 //// 4 telling en f =4 49  x < 57 /// 3 ✓ tallies and f = 3 / telling en f =3 (4) 2.2 ✓ 1st and 2nd column/ frequency/ 1ste en 2de kolomme frekwensie ✓ 3rd and 4th column/ 3rde en 4de kolomme Age/Ouderdomme (2) 2.3 ✓ shape/vorm frequency/ ✓ (29;10) frekwensie (28;13) (45;4) (53; 3) ✓ grounding both sides/begronding beide kante At/By (21;0) and/en (61;0) Age/Ouderdomme (3) [9] 3

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 3 QUESTION/ Suggested solution/ Explanation/ Marks/ VRAAG Voorgestelde oplossing Verduideliking Punte 3.1 y2 − y1 mBC = x2 − x1 6−2 ✓ substitution/vervanging = 4+8 1 = ✓ answer/answer 4 (2) 3.2 BC = ( x1 − x2 ) + ( y1 − y2 ) 2 2 BC = ( 4 + 8) 2 + (6 − 2) 2 ✓ substitution/vervanging BC = 12,65 OR 4 10 ✓ answer/answer (2) 3.3 6+2 ✓ correct substitution/ k= korrekte vervanging 2 =4 ✓ answer/antwoord (2) 3.4 For AD ✓ deduction/afleiding mBC  mAD = –1 7−4 ✓ substitution/vervanging mAD = 3+ 2 ✓ answer/antwoord mAD = –3 1   –3  –1 4 AD not ⊥ BC AD nie ⊥ op BC (3) [9] 4

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 4 QUESTION/ Suggested solution/ Explanation/ Punte/ VRAAG Voorgestelde oplossing Verduideliking Marks 4.1 4.1.1 cos (x + y) = cos (66,4°+ 114,7°) ✓ substitution/vervanging = cos (181,1°) = –1,00 ✓ answer/antwoord (2) 4.1.2 2sin x = 2sin (66,4°) ✓ substitution/vervanging = 1,83 ✓ answer/antwoord (2) 4.1.3 cosec x 1 sin (66,4  ) ✓ correct substitution/ korrekte vervanging = 1,09 ✓ answer/antwoord (2) 4.2 4.2.1 sin  + 0,38 = 1 Penalise 1 mark for sin  = 0,62 incorrect rounding off/ ✓ 0,62  = 38,3° Penaliseer 1 punt vir ✓answer/antwoord verkeerde afronding (2) 4.2.2 2 cot 2 = 3 2 cot 2 = 3 ✓ 3 2 2 2 = tan –1( 2 ) ✓ tan –1( 2 ) 3 OR/OF 3 2 = 33,69 …° 2 = 33,69 …°  = 16,8° ✓ answer/antwoord (3) 4.2.3 2 cos(3 – 60°) = 1,71 cos(3 – 60°) = 0,855 ✓ 0,855 3 – 60° = 31,24 …° ✓ 3 – 60° = 31,24° 3 = 91,24 …° ✓ 3 = 91,24°  = 30,4° ✓ answer/antwoord (4) [15] 5

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 5 QUESTION/ Suggested solution/ Explanation/ Punte/ VRAAG Voorgestelde oplossing Verduideliking Marks 5.1 5.1.1 y 4 5 ✓ diagram  –3 y2 = (5)2 – = (4)2 Pythagoras; 90° ✓S y2 = 25 – 16 y=–3 ✓ y = –3 tan = – 4 ✓ answer/antwoord 3 (4) 5.1.2 2cos2 – 1 = 2 (– 3 )2 – 1 ✓ 2 (– 3 )2 – 1 5 5 7 =– 25 ✓ answer/antwoord (2) 5.2 cos 0° + sin2 60° + 2 . sec 45° 2 ✓  3 = 1 +   + 2  2. 2 .  3 2   2 ✓    2   3 3 OR/OF 15 4 4 ✓ 2. 2 2 ✓ answer/antwoord (4) 5.3 Distance/Afstand DB: tan21° = DB ✓ tan21° = DB 30 30 DB = 11,515 … m ✓ DB = 11,515 m Distance/Afstand BC: tan15° = BC ✓ tan15° = BC 30 30 BC = 8,038 … m ✓ BC = 8,038 m  DC = 11,515 m – 8,038 m ✓ DC = 11,515 m – 8,038 m  DC = 3,48 ✓ answer/antwoord (6) [16] 6

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 6 QUESTION/ Suggested solution/ Explanation/ Punte/ VRAAG Voorgestelde oplossing Verduideliking Marks 6.1 a=1 ✓1 (1) 6.2 y [0;2] NOTE/NOTA ✓ critical values/kritieke OR/OF waardes 0 y  2; y  R In this type of answers – ✓ notation/notasie look at values and give the mark. Then look at inequalities. If values are wrong, then ZERO marks In hierdie tipe antwoorde – kyk na waardes en gee die punt. Kyk dan na ongelykhede. As waardes verkeerd is, dan NUL (2) 6.3 1 ✓1 (1) 6.4 90°  x  180° ✓ values/waardes OR/OF See note above ✓ inequality signs/ Sien nota hierbo x [90°;180°] ongelykheidstekens (2) 6.5 x = 0° or/of x = 270° or/of x = 360° ✓ x = 0° ✓ x = 270° ✓ x = 360° (3) 6.6 h(x) = –sinx ✓answer/antwoord (1) [10] 7

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 7 QUESTION/ Suggested solution/ Explanation/ Punte/ VRAAG Voorgestelde oplossing Verduideliking Marks 7.1 7.1.1 AH2 = 0,82 + 1,52 ✓ AH2 = 0,82 + 1,52 AH2 = 2,89 AH = 1,7 m ✓ answer/antwoord (2) 7.1.2 Surface area of roof/Buite-oppv van dak 1 ✓4 (3  1,7) 1 2 = 4  (3  1,7) 2 ✓ answer/antwoord = 10,2 m2 (2) 7.1.3 Surface area of walls/Buite-oppv van mure ✓ = 25,2 m2 = 4  3  2,1 = 25,2 m2 ✓ answer/antwoord Total surface area/Totale oppv = 10,2 m2 + 25,2 m2 = 35,4 m2 (2) 8

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/ Suggested solution/ Explanation/ Punte/ VRAAG Voorgestelde oplossing Verduideliking Marks 7.2 7.2.1 4 3 Volume = r 3 4 ✓=   83 4 3 =   83 3 = 2 144,62 m3 ✓ answer/antwoord (2) 7.2.2 New volume/Nuwe volume : Orig volume/Oorspronklike ✓2 3 volume ✓answer/antwoord = 23 : 1 = 8:1 (2) Volume including silver/Volume met silwer ingesluit 4 7.2.3 ✓   93 4 3 =   93 = 3 053,66 mm3 3 Volume of silver/Volume van silwer ✓ answer/antwoord = 3 053,66 – 2 144,62 = 908, mm3 (2) [12] QUESTION/VRAAG 8 8.1 P̂1 = P̂2 = x [given/gegee] ✓S Ŝ1 = Ŝ 2 = y [given/gegee] ✓S x + x+ y + y = 180° [co-interior < s PQ // SR/ ✓S ✓R 2x+ 2y = 180° ko-binne <e ; PQ // SR] x+ y = 90° (4) 8.2 Ŵ1 + x + y = 180° [sum int < of / ✓ S/R som binne <e van ] ✓S Ŵ1 = 90° PWST is a parallelogram/ [both pairs of opp sides ✓S PWST is ʼn parallelogram parallel/albei pare ✓R teenoorstaande sye ewewydig]  PWST is a rectangle [ Ŵ1 = 90° and PWST is a parm PWST is ʼn reghoek Ŵ1 = 90° en PWST is ʼn parm] (4) [8] 9

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ (PAPER/VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 QUESTION/VRAAG 9 BD = BD [common/gemeenskaplik] ✓S D̂1 = B̂2 [alternate < s AD // BC/ ✓ S/R verw.binne <e ; AD // BC] B̂2 = D̂1 [alternate < s AB // DC ✓S verw.binne <e ; AB // DC] ABC  CBD [AAS/HHS] ✓S AD = BC, AB = DC 's/'e  ✓R (5) [5] QUESTION/VRAAG 10 DE // BC [midpoint theorem/middelpunt stelling] ✓S ✓R D̂2 = Â [corresponding < s DE // BC ✓ S/R ooreenkomstige <e ; DE // BC] B̂1 = Â [< s opp = sides /<e teenoor gelyke sye] ✓ S/R D̂2 = B̂1 DR = RB [sides opp equal s / ✓ S/R sye teenoor gelyke  e] RDB is isosceles [two equal angles/twee gelyke hoeke] RDB is gelykbenig (5) [5] TOTAL/TOTAAL: 100 10