Mathematics Grade 10 Paper 2 Gauteng June 2022 Memo

Downloaded from hlayiso.com PROVINCIAL EXAMINATION/ PROVINSIALE EKSAMEN JUNE/JUNIE 2022 GRADE/GRAAD 10 MARKING GUIDELINES/ NASIENRIGLYNE MATHEMATICS/WISKUNDE (PAPER 2)/(VRAESTEL 2) 5 pages/bladsye 1

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 2) GRADE/GRAAD 10 Q./Vr. 1 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 1.1 𝑟 2 = (−3)2 + (−4)2  Using Pythagoras 𝑟 2 = 25 correctly/Gebruik 𝑟=5 Pythagoras korrek 3 ✓𝑟 = 5 ∴ sin 𝜃 = − ✓Answer/Antwoord (3) 5 5cos(90° − 𝜃) + 3 cot 𝜃 −3 1.2 5( 5 )✓ −4 −3 −4 3 (−3)✓ 5( 5 ) +3 (−3) = −3 + 4 Answer/Antwoord ✓ =1 (3) [6] Q./Vr. 2 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 2.1 sin( 𝛽 − 17.8°) = 0,215 𝛽 − 17,8° = 12,41554° ✓ 12,41554° 𝛽 = 30,22° ✓ 30,22° (2) 2.2 tan 3𝛽 = √3 3𝛽 =60° ✓ 3𝛽 =60° 𝛽 =20° ✓ Answer/Antwoord (2) 2.3 𝛽 3 sin = 2,012 2 ✓ 0,6706666 𝛽 sin = 0,6706666 2 𝛽 = 37,42097785° ✓ 37,4209778° 2 𝛽 = 74,84° ✓ 74,84° (3) Q./Vr. 3 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 3.1 𝑡𝑎𝑛 30°°. 𝑐𝑜𝑠𝑒𝑐 60° 𝑐𝑜𝑠 45°. 𝑠𝑖𝑛 45° ✓ 3 √3 √3 √2 √2 ✓ 3 × 3 3 √2 √2 √2 2 × 2 ✓ 2 √6 √2 = 2 3 ✓ Answer/Antwoord (4) [4] 2

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 2) GRADE/GRAAD 10 Q./Vr 4 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 4.1 𝑎 = −2 ; 𝑏 = 1 ✓𝑎 = −2 ✓𝑏=1 (2) 4.2 0° ≤ 𝑥 ≤ 180° ✓ IneQ /Ongelykhede ✓ critical values/ kritieke waardes (2) 4.3 2 ✓ Answer/Antwoord (1) 4.4 −1 ≤ 𝑦 ≤ 1 OR [-1;1] ✓Inequalities/ Ongelykhede ✓ critical values/kritieke waardes (2) 4.5 𝑥 = 270° ✓ Answer/Antwoord (1) [8] Q./Vr. 5 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 5.1 Square and Rhombus/Vierkant en Ruit ✓ Answer/ Antwoord (1) 5.2 Square and Rectangle/Vierkant en Reghoek ✓ Answer/ Antwoord (1) 5.3 Square; Rectangle; Parallelogram; Rhombus ✓✓ Answer/ Antwoord Vierkant; Reghoek; Parallelogram; Ruit (2) [4] 3

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 2) GRADE/GRAAD 10 Q./Vr. 6 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 6.1 M̂1 = x [alternate  s PS// QR] / [verwiss e ; PS // QR] ✓ S ✓R ✓ S ✓R Q̂1 = x [angles opp = sides] /[e teenoor gelyke sye ] (4) 6.2 Sˆ = Qˆ1 + Qˆ 2 [opp  s of //gm] /[oorst e van ||m ] ✓ S/R Sˆ = 2 x Mˆ 3 = 2 x [ s opp = sides] /[e teenoor gelyke sye ] ✓S/R OR/OF OR/OF Pˆ = 180  − (Qˆ1 + Qˆ 2 ) [co - interior  s PS//QR/ ko - binnee ; PS // QR] ✓ S/R Pˆ = 180  − 2 x Pˆ + Sˆ = 180 [co - interior  s SR//PQ / ✓ S/R ko - binnee ; SR // PQ] Sˆ = 2 x Mˆ = 2 x 3 [ s opp = sides / e teenoor gelyke sye ] (2) 6.3 ̂1 + M M ̂2 + M̂ 3 = 180° [sum of interior < s of Δ ✓ S/R som binnehoeke van ] 𝑥 + 90° + 2𝑥 = 180° 3𝑥 = 90° ✓ 𝑥 = 30° Answer/Antwoo rd (2) [8] Q./Vr. 7 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte BD = BD [common / gemeenskaplik ] ✓S ✓ S/R Dˆ = Bˆ [alternate  s AD// BC/ 1 2 ✓S verwissele nde binnee ; AD // BC ] Bˆ1 = Dˆ 2 [alternate  s AB // DC/ ✓S ✓R verwissele nde binnee ; B // DC ]  ABC  CBD [ AAS ] / S  AD = BC and / en AB = DC (5) [5] 4

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 2) GRADE/GRAAD 10 Q./Vr. 8 Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 8.1 AO = OC [diagonals of//gm bisect/ ✓S ✓R ✓S hoeklyne van ||m halveer ] ✓R DO = OB [diagonals of//gm bisect / hoeklyne van ||m halveer ]  BOAF is a / 'n // gm [opp sides of a quad equal/ oorst sye van vierhoek is gelyk ] (4) 8.2 EA // BC given / gegee ✓S BF // AC proven / bewys ✓S ✓R EBCA is a / 'n // gm [ two pairs of opp sides || / ✓S twee pare teenoorst sye ||] EA = BC EA = AD (4) [8] TOTAL/TOTAAL: 50 5