Mathematics Grade 9 P1 Gauteng November 2022 Memo (Afr)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION/ PROVINSIALE EKSAMEN NOVEMBER 2022 GRADE/GRAAD 9 MARKING GUIDELINES/ NASIENRIGLYNE MATHEMATICS/WISKUNDE (PAPER/VRAESTEL 1) 7 pages/bladsye

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 9 SECTION/AFDELING A QUESTION/VRAAG 1 1.1 1.2 1.3 1.4 1.5 B✓A B✓A D✓ A C✓A D✓A [5] SECTION/AFDELING B QUESTION/VRAAG 2 2.1 21 : 35 (÷ 7) 1 mark for 3./1 punt vir 3. = 3 : 5 ✓✓ A 1 mark for 5./ 1 punt vir 5. (2) 2.2.1 36 2 18 2 2 marks for prime factorisation using 9 3 ladder method./2 punte vir fatorisering 3 3 met die leertjie-metode. ✓✓M 1 mark for each prime factor in exponential form./1 punt vir elke priemfaktoor in eksponensiële vorm. 36 = 22 × 32 ✓ CA (3) 2.2.2 540 = 22 × 33 × 5 36 = 22 × 32 1 mark for the LCM./1 punt vir die LCM/KGV = 22 × 33 × 5 = 540 ✓ A KGV. HCF/GGF = 22 × 32 = 36 ✓ A 1 mark for the HCF./1 punt vir die GGF. (2) 2.3 Indirect Proportion/ Indirekte verhouding. 1 mark for setting up indirect proportion 4 × x = 7 × 12 ✓ M equation./1 punt vir opstel van indirekte 4x = 84 ✓ M verhouding vergelyking. x = 21 ✓ CA 1 mark for multiplication/1 punt vir 21 contractors will be needed to build the vermenigvuldiging. house in 4 days./21 kontrakteurs word 1 mark for answer./1 punt vir antwoord. benodig om die huis in 4 dae te bou. (3) [10] 2

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 9 QUESTION/VRAAG 3 3.1 Ascending order: Stygende volgorde: 1 mark for all numbers arranged correctly./1 punt vir –62; –55; –43; 0; 8; 25 ✓ A korrekte ranskikking van al die getalle. (1) 3.2 49 − 2 5 3 + ( −2 ) 3 7−2 ✓ M 5 1 mark for 7 in numerator./1 punt vir 7 in die teller. 3−8 ✓ M 1 mark for −8 in denominator./1 punt vir −8 in die 5 noemer. 5 ✓A −5 = –5 ✓ CA 1 mark for correct subtraction in both numerator and denominator./1 punt vir korrekte aftrekking in beide die teller en noemer. 1 mark for answer./1 punt vir antwoord. (4) [5] QUESTION/VRAAG 4 4.1 a–m ✓ A 1 mark for answer./ 1 punt vir antwoord. (1) 4.2 p 4 x + 4  p ( −2 x −2) ( p 2 ) x +1 1 mark for product law application./1 punt vir = p 4x + 4+(–2x – 2) – (2x + 2) ✓✓✓ M toepassing van die produkwet. 1 mark for quotient law application./1 punt vir = p 4x –2x – 2x + 4 – 2 – 2 toepassing van kwosiëntwet. 1 mark for multiplying a power with a power in = p0 ✓ CA denominator./1 punt vir vermenigvuldiging van magte in die noemer. = 1 ✓ CA 1 mark for simplifying by adding like terms./1 punt vir vereenvoudiging deur gelyksoortige terme bymekaar te tel. 1 mark for answer./1 punt vir antwoord. (5) [6] 3

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 9 QUESTION/VRAAG 5 5.1 5.1.1 2 marks for correct sixth Sixth/Sesde arrangement./2 punte vir die korrekte sesde ranskikking ✓✓A (2) 5.1.2 T1 : 3(1) + __________ = 2 T1 : 3(1) + (–1) = 2 T2 : 3(2) + __________ = 5 1 mark for 3n./1 punt vir 3n. T2 : 3(2) + (–1) = 5 1 mark for –1./1 punt vir −1. T3 : 3(3) + __________ = 8 T3 : 3(3) + (–1) = 8 ∴ Tn = 3n – 1 ✓✓ A (2) 5.1.3 Tn = 3n – 1 1 mark for correct substitution./ 101 = 3n –1 ✓ CA 1 punt vir korrekte vervanging. 102 = 3n 1 mark for correct answer./1 punt 34 = n ✓ CA vir korrekte antwoord. (2) 5.2 1 mark for each output value in the correct spot corresponding to the input value./1 punt vir elke uitvoergetal in die korrekte posisie in ooreenstemming met die invoergetal. ✓✓✓✓✓A (5) [11] 4

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 9 QUESTION/VRAAG 6 6.1 6.1.1 3y3 ✓ A 1 mark for answer./1 punt vir antwoord. (1) 6.1.2 2x3y + 5x2 + 3xy3 ✓ A 1 mark for answer./1 punt vir antwoord. (1) 6.2 6.2.1 (x + y)2 1 mark for 𝑥 2 ./1 punt vir 𝑥². = x2 + xy + xy + y2 1 mark for 2𝑥𝑦./1 punt vir 2𝑥𝑦. = x2 + 2xy + y2 ✓✓✓ CA 1 mark for 𝑦 2 ./1 punt vir 𝑦². (3) 6.2.2 ( x 3 + x 2 − 2 x) x2 −1 1 mark taking 𝑥 out as common factor./1 punt vir x ( x 2 + x − 2) ✓ A = uithaal van 𝑥 as gemene faktor ( x 2 − 1) 1 mark for each factor in numerator/1 punt vir x ( x + 2( x − 1)✓✓ A elke faktor in die teller. = ( x + 1)( x − 1) ✓✓ A (𝑥 + 2)(𝑥 − 1). 1 mark for each factor in denominator/1 punt vir x ( x + 2) elke faktor in die noemer. = ✓ CA (𝑥 + 1)(𝑥 − 1). x +1 1 mark for answer./ 1 punt vir antwoord. (6) [11] QUESTION/VRAAG 7 7.1 Gradient: 2 ✓ A 1 mark for correct gradient./1 punt vir korrekte y-intercept/y-afsnit: –5 ✓ A gradient of helling. 1 mark for correct y-intercept./ 1 punt vir regte y- afsnit. (2) 7.2 7.2.1 3y + 2x = –6 3(0) + 2x = –6 ✓ M 1 mark for substituting zero in the place of y./ 2x = –6 1 punt vir vervanging van 𝑦 met nul. x = –3 ✓ CA 1 mark for answer./1 punt vir antwoord. (2) 5

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 9 7.2.2 1 mark for plotting the x-intercept correctly./1 punt vir korrekte aanstip van x-afsnit. 1 mark for plotting the y-intercept correctly./1 punt vir korrekte aanstip van y-𝑎𝑓𝑠𝑛𝑖𝑡. 1 mark for correct shape./1 punt vir korrekte vorm. ✓✓✓CA (3) 7.3 2 1 𝐴(− 3 ; 1); 𝐵 (−2; 2) vertical change 𝑣𝑒𝑟𝑡𝑖𝑘𝑎𝑙𝑒 𝑣𝑒𝑟𝑎𝑛𝑑𝑒𝑟𝑖𝑛𝑔 Gradient = /𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = ℎ𝑜𝑟𝑖𝑠𝑜𝑛𝑡𝑎𝑙𝑒 𝑣𝑒𝑟𝑎𝑛𝑑𝑒𝑟𝑖𝑛𝑔 1 mark for vertical horizontal change change./1 punt vir 1 vertikale − (1) ✓𝐌 𝑚= 2 verandering. 2 1 mark for −2 − (− 3) ✓𝐌 1 horizontal change./ −2 1 punt vir 𝑚= horisontale 4 −3 verandering. 3 𝑚 = 8 ✓CA Learner may use any two of the three points given. Award full marks for the usage of any two of the three points correctly./ Leerder mag enige twee van gegewe drie punte gebruik. Ken 1 mark for correct volpunte toe vir die korrekte gebruik van enige twee punte. gradient/slope./ y = mx + c 1 punt vir korrekte 3 gradient of helling. 3 = (0) + 𝑐 8 1 mark for answer./ 3=c Learner may use any of the three points given. Award full 1 punt vir marks for the usage of any of the three points correctly. antwoord. Leerder mag enige van die drie gegewe punte gebruik. Ken volpunte toe vir die korrekte gebruik van enige van die drie punte. y-intercept = 3/y-afsnit = 3 3 ∴ 𝑦 = 𝑥 + 3 ✓ 𝐂𝐀 8 (4) [11] 6

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 9 QUESTION 8/ VRAAG 8 8.1 a=2✓A 1 mark for answer./1 punt vir antwoord. (1) 8.2 8.2.1 −8 + 2y = –6 ; y ≠ 0 y 1 mark for multiplying all terms by y./ –8 + 2y2 = –6y ✓ M 1 punt vir vermenigvuldiging van alle 2y2 + 6y – 8 = 0 ✓ M terme met 𝑦. 2(y2 + 3y – 4) = 0 ✓ M 1 mark for the standard form./1 punt vir 2(y – 1)(y + 4) = 0 ✓✓ M standaardvorm. y = 1 or y = –4 ✓ CA 1 mark for factoring out 2./1 punt vir gemene faktor 2. 1 mark for each factor./1 punt vir elke faktor. 1 mark for both answers./1 punt vir beide antwoorde. (6) 8.2.2 4y + 3 = 5 y − 12 1 mark for multiplying all terms by 5./ 5 4𝑦+3 5𝑦−12 1 punt vir vermenigvuldiging van elke = 1 5 term met 5. 4y + 3 = 5(5y – 12) ✓ M 1 mark for simplification./1 punt vir 4y + 3 = 25y – 60 vereenvoudiging. 4y – 25y = –60 – 3 ✓ M 1 mark for subtracting like terms./ –21y = –63 ✓ M 1 punt vir aftrekking van gelyksoortige y = 3 ✓ CA terme. 1 mark for answer./1 punt vir antwoord. (4) 8.3 If/ as 𝒔 ∎ 𝒕 equals/ gelyk is aan 𝒕𝟐 + 𝒔𝒕, and/en 𝟒 ∎ 𝒙 = −𝟑, then/dan is 1 mark for substituting./1 punt vir x2+ 4x = –3 ✓ M vervanging. x2 + 4x + 3 = 0 ✓ CA 1 mark for quadratic trinomial form./ (x + 1) (x + 3) = 0 ✓✓ CA 1 punt vir kwadratiese drieterm. x = –1 or/of x = –3 ✓ CA 1 mark for each factor./1 punt vir elke faktor. 1 mark for both answers./1 punt vir beide antwoorde. (5) [16] TOTAL/ TOTAAL: 75 7