Gr10 MATH P1 (ENG _ AFR) June 2022 Possible Answers_hlayiso.com_.pdf

Downloaded from hlayiso.com PROVINCIAL EXAMINATION/ PROVINSIALE EKSAMEN JUNE/JUNIE 2022 GRADE/GRAAD 10 MARKING GUIDELINES/NASIENRIGLYNE MATHEMATICS/WISKUNDE (PAPER/VRAESTEL 1) 5 pages/bladsye NOTE/LET WEL • If a candidate answers a question TWICE, mark only the FIRST attempt./As 'n kandidaat 'n vraag TWEE KEER beantwoord het, merk slegs die EERSTE poging. • If a candidate crossed out an answer and did not redo it, mark the crossed-out answer./As 'n kandidaat 'n antwoord deurgehaal het en dit nie oorgedoen het nie, merk die deurgehaalde antwoord. • Consistent accuracy applies to ALL aspects of the marking guidelines./Konsekwente akkuraatheid is van toepassing op ALLE aspekte van die nasienriglyne. • Assuming values/answers in order to solve a problem is unacceptable./Om waardes/antwoorde te aanvaar om 'n probleem op te los, is onaanvaarbaar. 1

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 1) GRADE/GRAAD 10 QUESTION/VRAAG 1 Q./VR. Suggested solution/voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 1.1 x=1 ✓1 (1) 1.2 1.2.1 2 x 2 − 32 = 2( x 2 − 16) ✓factorise/faktoriseer ✓factorise/faktoriseer = 2( x + 4)( x − 4) (2) 1.2.2 6a 2 − b + a ( 2 − 3b ) ✓simplify/vereenvoudig = 6a 2 − b + 2a − 3ab ✓grouping/groepering = 2a(3a + 1) − b(3a + 1) OR/OF ✓factorise/faktoriseer = (3a + 1)(2a − b) = 3a(2a − b) + (2a − b) = (2a − b)(3a + 1) (3) 1.3 1.3.1 ( x − 1)( x 2 + x + 1) If they multiply everything out and ✓𝑥 3 answer is incorrect then no marks. ✓–1 = x3 − 1 As hulle alles vermenigvuldig en antwoord is verkeerd, dan geen punte nie. (2) 1.3.2 x+7 3 2 − + x − x − 6 x − 3 2x + 4 2 x+7 3 2 ✓factorise trinomial and/ = − + faktoriseer drieterm en ( x − 3)( x + 2) x − 3 2( x + 2) 2x + 4 x+7 3 1 = − + ( x − 3)( x + 2) x − 3 x + 2 x + 7 − 3( x + 2) + x − 3 = ✓common denominator ( x − 3)( x + 2) gemeenskaplike noemer x + 7 − 3x − 6 + x − 3 = ( x − 3)( x + 2) ✓numerator/teller −x − 2 = ( x − 3)( x + 2) −( x + 2) ✓simplify numerator/ = ( x − 3)( x + 2) vereenvoudig die teller −1 = x−3 ✓factorise and simplify faktoriseer en vereenvoudig (5) 2

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 1) GRADE/GRAAD 10 1.3.3 4 x +1.9 x 62 x −1 22( x +1).32 x = (3.2) 2 x −1 22 x + 2.32 x ✓numerator/teller = 32 x −1.22 x −1 ✓denominator/noemer = 23.3 ✓answer/antwoord = 24 (3) 1.4 −2 x , 2− x , 2 x ,2 x , 2 x 0 2 ✓✓ all correct/alles reg ✓one error/een fout (2) [18] QUESTION/VRAAG 2 Q./VR. Suggested solution/Voorgestelde oplossing Explanation/ Marks/ Verduideliking Punte 2.1 2.1.1 ax = b 𝑎𝑥 = 𝑏 2 ✓square/vierkant 𝑏2 ✓divide/deel 𝑥 = 𝑎 ; a≠0 (2) 2.1.2 3x + 3x−1 = 36 3x (1 + 3−1 ) = 36 ✓factorise/faktoriseer 4 3x   = 36 3 3 = 27 x ✓simplify isolate/ vereenvoudig isoleer 3𝑥 3x = 33 x=3 ✓answer/antwoord (3) 2.2 2.2.1 x x  +1 3 2 2 x  3x + 6 ✓LCD/KGV −x  6 ✓answer/antwoord x  −6 (2) 2.2.2 x = −10 ✓answer/antwoord (1) 3

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 1) GRADE/GRAAD 10 2.3 2 x + y = 4 and/en and 3x − y = 11 y = 4 − 2x ✓equation/vergelyking 1 2x + y = 4 ✓subs./vervang 3 x − (4 − 2 x) = 11 ✓x value/x-waarde 3 x − y = 11 3 x − 4 + 2 x = 11 ✓y value/y-waarde 5x = 15 5 x = 15 OR/OF x=3 x=3 y = −2 y = 4 − 2(3) y = −2 ALTERNATIVE/ALTERNATIEF Eq1 + Eq2 Adding the two equations: 5𝑥 = 15 Optel van 2 vergelykings: 𝑥=3 ✓5𝑥 ✓15 𝑦 = −2 ✓x value/x-waarde ✓y value/y-waarde (4) [12] QUESTION/VRAAG 3 Q./VR. Suggested solution/Voorgestelde oplossing Explanation/Verduideliking Marks/Punte 3.1 3; 5; 7; 9; 11 9✓ 11 ✓ (2) 3.2 2n + 1 ✓✓ correct answer/korrekte antwoord (2) 3.3 4(131) +1 ✓ substitute/vervang 131 524 +1 ✓ 525 525 (2) [6] 4

Downloaded from hlayiso.com MARKING GUIDELINES MATHEMATICS/WISKUNDE NASIENRIGLYNE (Paper/Vraestel 1) GRADE/GRAAD 10 QUESTION/VRAAG 4 Q.VR. Suggested solution/Voorgestelde oplossing Explanation/Verduideliking Marks/Punte 4.1 B(0;4) Answers must be in coordinate form (see ✓ B(0;4) D(0;2) question)./ Antwoorde moet in koördinaatvorm ✓ D(0;2) wees (sien vraag). (2) 4.2 𝑦≤4 ✓ OR/OF 𝑦𝜖(−∞; 4] (1) 4.3 −𝑥 2 + 4 = 0 ✓ equation/vergelyking = 0 (2 − 𝑥)(2 + 𝑥) = 0 ✓factors/faktore 𝑥=2 𝑥 = −2 ✓Both values of x/albei waardes van x AE = 2 – (-2) AE = 4 ✓Answer/Antwoord (4) 4.4 Using values for A/Gebruik waardes vir A ✓sub./vervang 0 = 𝑚(−2) + 2 ✓𝑚 = 1 2𝑚 = 2 𝑚=1 (2) 4.5 𝑓(𝑥) = 𝑔(𝑥) ✓𝑓(𝑥) = 𝑔(𝑥) −𝑥 2 + 4 = 𝑥 + 2 𝑥2 + 𝑥 − 2 = 0 (𝑥 + 2)(𝑥 − 1) ✓Correct x values/Korrekte 𝑥 = −2 𝑥 = +1 x-waardes A(-2;0) Sub/vervang 𝑥 = 1 into/in 𝑔(𝑥) 𝑦 = 1(1) + 2 y=3 ✓ C(1;3) C(1;3) (3) 4.6 Using the reflection of the points of intersection CA from 4.5/CA van 4.5 in Q.4.5/Gebruik die reflekse van die snypunte in Vr. 4.5. ✓correct x values/korrekte x- waardes −1 ≤ 𝑥 ≤ 2 ✓inequality/ongelykheid (2) [14] TOTAL/TOTAAL: 50 5