Mathematics Grade 10 Paper 2 Gauteng November 2021 Memo

Downloaded from hlayiso.com PROVINCIAL EXAMINATION/ PROVINSIALE EKSAMEN NOVEMBER 2021 GRADE 10/GRAAD 10 MARKING GUIDELINES/NASIENRIGLYNE MATHEMATICS/WISKUNDE (PAPER/VRAESTEL 2) 10 pages/bladsye

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 1. SUGGESTED SOLUTIONS/VOORGESTELDE EXPLANATION MARKS OPLOSSINGS VERDUIDELIKING PUNTE 1.1 30 ✓ Answer/Antwoord (1) 1.2 1.2.1 35 ✓ Answer/Antwoord (1) 1.2.2 30 ✓ Answer/Antwoord (1) 1.2.3 38,5 Answer/Antwoord ✓ Accept 38 or 39/Aanvaar 38 of 39 (1) 1.3 Range = Max. – Min./ Omvang = Maks. – Min. ✓ Method/Metode = 44 – 24 ✓ Answer/Antwoord = 20 (2) 1.4 No. of packets of sweets above upper quartile/ ✓ Method/Metode Aantal pakkies lekkers bo die boonste kwartiel ✓ Answer/Antwoord 6 =  100% 25 = 24% (2) [8] 2

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 2. 2.1 200 < x ≤ 250 ✓ Answer/ Antwoord (1) 2.2 HISTOGRAM Histogram Amount spent by 120 motorists at KG petrol garage Bedrag gespandeer deur 120 motoriste by KG vulstasie ✓ 1st & 2nd columns/ 1ste en 2de Number of Motorists/ kolomme ✓ Last three Aantal motoriste columns/ Laaste drie kolomme Amount spent in Rands Bedrag gespandeer in Rand (2) 2.3 30 ✓ 36  120 = 36th value/36ste waarde 100 ∴ interval is/interval is 50 < x ≤ 100 ✓ Answer/ Antwoord (2) 2.4 42 ✓ 42  360 = 126 ✓ Answer/ 120 Antwoord (2) [7] 3

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 3. 𝑥 +𝑥 𝑦 +𝑦 Wrong Formula 3.1 ( 1 2 2 ; 1 2 2) NO Marks/ −7+1 1+(−7) Verkeerde Formule 𝑆( 2 ; 2 ) GEEN punte nie ∴ 𝑆(−3 ; −3) ✓ Formula/Formule ✓ x = –3; ✓ y = –3 (3) 𝑦 −𝑦 3.2 𝑚𝐴𝐶 = 𝑥2−𝑥1 Wrong Formula 2 1 NO Marks/ 5−(−7) Verkeerde Fomule = GEEN punte nie 5−1 = 3 ✓ Formula/Formule ✓ Answer/Antwoord (2) 3.3 BC = ( x1 − x2 ) 2 + ( y1 − y2 ) 2 ✓ Formula/Formule ✓ Correct BC = (−7 − 1) 2 + (1 − (−7)) 2 substitution/Korrekte vervanging BC = 8 2 AS = (5 − (−3) 2 + (5 − (−3)) 2 ✓ BC AS = 8 2 (3) 4

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 3.4 BC = 8 2 ✓ BC AS = (5 − (−3) 2 + (5 − (−3)) 2 ✓ Formula/Formule AS = 8 2 ✓ AS ✓ Method/Metode 1 Area of/area ∆ABC = 2 ∙base height/ ✓ Answer/Antwoord 1 Area van/Area ∆𝐴𝐵𝐶 = 2 basis hoogte 1 = 2 ∙ 8√2 ∙ 8√2 AS = 64 unit /eenheid2 2 OR/OF BS = ( x1 − x2 ) 2 + ( y1 − y2 ) 2 ✓ Formula/Formule ✓ BS BS = (−7 + 3) 2 + (1 + 3) 2 ✓ AS BS = 4 2 ✓ Method/Metode AS = (5 − (−3) 2 + (5 − (−3)) 2 ✓ Answer/Antwoord AS = 8 2 1 Area of ∆ABC = 2 × 2 ∙ base height/ 1 Area van ∆𝐴𝐵𝐶 = 2 × 2 ∙ basis hoogte 1 = 2 4 2 8 2 2 AS = 64 unit2/eenheid2 (5) [13] 5

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 4. 4.1 4.1.1 ( ) y 2 = (2) 2 − 3 2 ✓ sub in Pythagoras/ vervang in =4–3 ∴ y=1 Pythagoras 1 ✓y=1  sin  = 2 ✓ 1/2 ✓ diagram/diagram 2 (3) 4.1.2 sin  . cos 1 √3 = (2) ( 2 ) ✓ Sub.into cos/ √3 = 4 Vervang in cos √3 ✓ 4 (2) 4.2 1 𝑥 ✓ Correct substitution/ 𝑠𝑖𝑛 2𝑦 −[2 𝑡𝑎𝑛2 ( )]cos 𝑥 2 2 Korrekte vervanging 1 60° sin 2(45°) −[2 𝑡𝑎𝑛2 ( 2 )]cos 60° 2 1 1 √3 1 ✓ 2 (1) = 2 (1) −[2( 2 )2 ](2 ) √3 3−2√3 ✓ [2( 2 )2 = 1 6 ✓2 3−2√3 ✓ (6) 6 6

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 4.3 4.3.1 sin(𝛽 − 17.8°) = 0.215 𝛽 − 17.8° = 12.4155° ✓ 12,4155° ✓ +17,8° 𝛽 = 12.4155° + 17.8° ✓Answer/Antwoord 𝛽 = 30.22° (3) 4.3.2 𝑡𝑎𝑛 3𝛽 = √3 3𝛽 = 60° ✓60° 𝛽 = 20° ✓ Answer/Antwoord (2) 4.3.3 𝛽 3𝑠𝑖𝑛 2 = 2.012 𝛽 𝛽 ✓ 𝑠𝑖𝑛 2 = 0,670666 𝑠𝑖𝑛 2 = 0.670666 𝛽 𝛽 ✓ = 41,11848° = 41.11848° 2 2 ✓ Answer/Antwoord 𝛽 = 84.24° (3) 4.4 tan 30𝑐𝑜𝑠𝑒𝑐 60° 𝑐𝑜𝑡45°𝑠𝑖𝑛45° √3 ✓ 3 √3 2 2 . ✓ = 3 √2 √3 √3 1. 2 ✓1 4 =3 ✓ Answer/Antwoord (4) [23] 5. 5.1 ✓ diagram/diagram y 7 4 𝑥 33 4 sin 𝑥 = 4 7 ✓ sin 𝑥 = 7 √33 tan 𝑦 = 4 √33 ✓ tan 𝑦 = 4 But/Maar: tan 𝑦 = 𝑡 ✓ tan 𝑦 = 𝑡 √33 √33 ∴ 𝑡 2 = ( 4 )2 ✓𝑡 2 = ( 4 ) 2 33 ✓ Answer/Antwoord 𝑡 = 16 (6) 7

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 5.2 5.2.1 1 − 𝑐𝑜𝑠 2 𝑥 − 𝑠𝑖𝑛2 𝑥 1 − (𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 ) ✓ −(𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 ) =1−1 ✓ Simplification/ = 0 Vereenvoudiging ✓ Answer/Antwoord (3) 5.2.2 𝑐𝑜𝑠 2 𝑥 +tan 𝑥. 𝑐𝑜𝑡𝑥 + 𝑠𝑖𝑛2 𝑥 ✓rearrangement and 2 2 𝑠𝑖𝑛𝑥 cos 𝑥 identity/ 𝑐𝑜𝑠 + 𝑠𝑖𝑛 𝑥 + 𝑐𝑜𝑠𝑥 . sin 𝑥 herrangskikking en =1+1 identiteit =2 ✓ Simplification/ Vereenvoudig ✓ Answer/Antwoord (3) 5.3 ∠𝑆𝑀𝐸 = 34.4° (𝑎𝑙𝑡./𝑣𝑒𝑟𝑤. 𝑏𝑖𝑛𝑛𝑒 . ∠𝑠) ✓ Deductions/ Aftrekkings ∠𝑆𝐻𝐸 = 26.2° (𝑎𝑙𝑡./𝑣𝑒𝑟𝑤. 𝑏𝑖𝑛𝑛𝑒 . ∠𝑠) 55 ✓ 𝑡𝑎𝑛34.4° = 𝑆𝑀 55 Disance/Afstand SM: 𝑡𝑎𝑛34.4° = 𝑆𝑀 ✓ 𝑆𝑀 = 80.3254 𝑚 𝑆𝑀 = 80.3254 𝑚 55 Distance/Afstand SH:tan 26.2 ° = 𝑆𝐻 ✓ 𝑆𝐻 = 111.77 𝑚 𝑆𝐻 = 111.77 𝑚 ✓ Answer/Antwoord ∴ 80.3254 𝑚 + 111.77𝑚 − 80.3254 𝑚 = 31.45 𝑚 (5) [17] 6. 6.1 a = −2 ✓ a = −2 b =1 ✓b =1 (2) 6.2 0  x  180 ✓Inequality signs/ OR/OF Ongelykheidstekens x  (0 ;180  ) ✓Critical points/Kritieke punte (2) 6.3 2 ✓2 (1) 8

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 6.4 −1  y  1 ✓ Inequality signs/ OR/OF Ongelykheidstekens y  [−1;1] ✓ Critical points/ Kritieke punte (2) 6.5 𝑥 = 270° ✓ Inequality signs/ Ongelykheidstekens ✓ Critical points/ Kritieke punte (2) [9] 7. 7.1 𝑅𝑄̂ 𝑇 + 𝑄𝑇̂𝑆 = 180° ̂ [ Cointerior < s ; RQ II ST ]/ ✓✓ S/R [ko-binnehoeke ; RQ || ST] 2𝑥 + 2𝑦 = 180° 𝑥 + 𝑦 = 90° ✓S 𝑉̂2 + 𝑄̂2 + 𝑇̂1 = 180° [sum of int/𝑠𝑜𝑚 𝑣𝑎𝑛 𝑏𝑖𝑛𝑛𝑒 ✓ S/R ✓S e van ]/ 𝑥 + 𝑦 + 𝑉̂2 = 180° 90° + 𝑉̂2 = 180° 𝑉̂2 = 90° (5) 7.2 𝑉̂1 = 𝑥 [Alt < s ; RS II QT//Verw binne e 𝑅𝑆 𝐼𝐼 𝑄𝑇] ✓S 𝑅𝑄 = 𝑅𝑉 [sides opp equal angles/sye teenoor gelyke ✓ S/R hoeke] 𝑅𝑄 = 𝑆𝑇 [opp sides of a parallelogram/teenoorst. sye ✓ S/R van ||m] 𝑉̂3 = 𝑇̂1 [Alt < s ; RS II QT/ ✓S Verw binne e 𝑅𝑆 𝐼𝐼 𝑄𝑇] ✓S 𝑉𝑆 = 𝑆𝑇 [sides opp equal angles/sye teenoor gelyke hoeke] ✓S 𝑅𝑄 = 𝑅𝑉 [sides opp equal angles/sye teenoor gelyke hoeke] 𝑉𝑆 = 𝑅𝑄 = 𝑅𝑉 𝑅𝑆 = 2𝑅𝑄 (6) [11] 9

Downloaded from hlayiso.com MATHEMATICS (PAPER 2)/ MARKING GUIDELINES/ WISKUNDE (VRAESTEL 2) NASIENRIGLYNE GRADE/GRAAD 10 8. 8.1 ✓ construction/ konstruksie / MN = NP {construction/konstruksie] ̂1 = 𝑁 𝑁 ̂2 Vertically opposite angles/ Regoorst e AN=AC given/gegee ∆𝑀𝑁𝐴 ≡ ∆𝑃𝑁𝐶 𝑆𝐴𝑆 / s  s ✓S MA = CP (≡ ∆𝑠) /e  ✓ S/R MP = BC and MB = PC ✓S ∴ MPCB is a parallelogram [both pairs of opp side =] ✓ S/R MPCB is ‘n ||m [beide pare teenoorst sye = ] ✓S MN // BC [opp sides of //gm/teenoorst sye van ||m ] ✓R (6) 8.2 TS // UR [midpoint theorem/middelpuntt stelling] ✓ S/R UR=2TS ✓S TS=2𝑥 [Converse midpoint theorem/omgekeerde midpt stelling] ✓ S/R UR=2TS=4𝑥 ✓S UR=UV+VR ✓S VR=3𝑥 (6) OR/OF given ✓S UT = TQ and QS = SR [ gegee ] 1 TS||UR and TS = UR [midpt theorem/midpt stelling] ✓ S/R 2 In ΔPTS TU = UP [given/gegee] TS||UV [proven/bewys] ✓S 1 PV = VS and UV = TS [converse; midpt theorem/ ✓ S/R 2 omgekeerde midpt stelling] TS = 2𝑥 UR = 4𝑥 ✓S VR = 3𝑥 ✓S [12] TOTAL/TOTAAL: 100 10