Mathematics Grade 10 P1 Gauteng November 2022 Memo (Afr)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION PROVINSIALE EKSAMEN NOVEMBER 2022 GRADE 10/GRAAD 10 MARKING GUIDELINES/ NASIENRIGLYNE MATHEMATICS (PAPER 1)/WISKUNDE (VRAESTEL 1) 9 pages/bladsye NOTE/LET WEL: • If a candidate answered a QUESTION TWICE, mark only the FIRST attempt. • If a candidate crossed out an answer and did not redo it, mark the crossed-out answer. • Consistent accuracy applies to ALL aspects of the marking guidelines. • Assuming values/answers in order to solve a problem is unacceptable. • As ʼn kandidaat ʼn VRAAG TWEE KEER beantwoord het, merk slegs die EERSTE poging. • As ʼn kandidaat ʼn antwoord deurgehaal het en dit nie oorgedoen het nie, merk die deurgehaalde antwoord. • Konsekwente akkuraatheid is van toepassing op ALLE aspekte van die nasienriglyne. • Om waardes/antwoorde te aanvaar om ʼn probleem op te los is onaanvaarbaar.

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 1 1.1 1.1.1 2 x6 − 8 = 2( x 6 − 4) ✓ factorise/faktoriseer ✓ factorise/faktoriseer = 2 ( x3 + 2 )( x3 − 2 ) (2) 1.1.2 − x + ( x − y )3 + y ✓ −( x − y) = ( x − y )3 − ( x − y ) ✓ common factor ( x − y) gemeenskaplike faktor = ( x − y )[( x − y )2 − 1] ( x − y) = ( x − y )( x − y + 1)( x − y − 1) ✓ [( x − y ) 2 − 1] ✓ diff. of two squares/ verskil tussen twee vierkante (4) 2 1.2 1.2.1  12  1 ✓ x 4 and/en 9  x − 3   1 1 1 ✓ −6x 2 = x 4 − 6x 2 + 9 (2) 1.2.2 x −3  x −5 + ( x −2 )−1 ✓ division x −3+5 = x −3−( −5) + x 2 and brackets/ deel x −3+5 en hakies = x2 + x2 = 2 x2 ✓ simplify/vereenvoudig (2) 1.2.3 5x +1.(4 x )3 25 x −2.10 x −1 5x +1.(22 x )3 = 5 x−2 ✓ bases primefactors/ 2 .(5.2) x −1 basisse priemfaktore 5x +1.26 x = 5 x − 2 x −1 x −1 2 .5 .2 ✓ simplify numerator/ = 5x +1− x +1.26 x −5 x + 2− x +1 vereenvoudig teller = 52.23 ✓ simplify denominator/ = 200 vereenvoudig noemer ✓ final answer/ finale antwoord (4) 2

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 1.2.4 − 11 1 – ✓ Factorise trinomial/ 2 x − 5 x − 12 4 − x 2 Faktoriseer drieterm − 11 1 = + (2 x + 3)( x − 4) x − 4 ✓ Change of sign/ − 11 + 2 x + 3 Verandering van teken = (2 x + 3)( x − 4) 2x − 8 ✓ Numerator/Teller = ✓ LCD/KGV (2 x + 3)( x − 4) 2( x − 4) ✓ Simplified answer/ = (2 x + 3)( x − 4) Vereenvoudigde 2 antwoord = 2x + 3 (5) 1.3 (3 x + 2)(2 x − 5) ✓ (2 x − 5) = 6 x − 11x − 10 2 ✓ Simplify/Vereenvoudig  d = −11 ✓ Answer/Antwoord (3) [22] QUESTION/VRAAG 2 2.1 2.1.1 (3x − 1)( x + 2) = 0 1 ✓ 1 3 x= or/of x = –2 3 ✓ ̶2 (2) 2.1.2 3x − 2.3x−1 = 3 3x (1 − 2.3−1 ) = 3 If answer ONLY ✓ Factorise/Factorise NO marks/ 1 3x   = 3 SLEGS antwoord 3 GEEN punte nie ✓ Simplify/Vereenvoudig 3x = 32 ✓ Answer/Antwoord x=2 (3) 2.2 2.2.1 2x ✓ Subtract 1 on both sides/ −1  1 − 5 Trek 1 aan albei kante af 3 2x ✓ 3 −2  − 4 3 ✓ (−2) and change of −6  −2 x  12 inequalities/en 3  x  −6 verandering van −6  x  3 ongelykhede (3) 2.2.2 9 integers satisfy the equation/9 heelgetalle voldoen ✓ Answer/Antwoord aan die vergelyking (1) 3

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 2.3 Solve for x and y simultaneously/Los vir x en y gelyktydig op: x y ✓ Make x the subject of x− y =4 and/en + =5 the equation (1)/Maak 5 2 x = y + 4……(1) 2x + 5y = 50……..(2) x die onderwerp van die vergelyking (1) subst/vervang (1) into/in (2) ✓ LCD/KGV 2(y+ 4)+ 5y = 50 2y + 8 + 5y = 50 ✓ Substitute/Vervang 7y = 42 y=6 ✓ y value/y-waarde x=6 x = 10 ✓ x value/x-waarde OR/OF ✓ Make y the subject of y = x – 4……(1) the equation (1)/Maak subst/vervang (1) into/in (2) y die onderwerp van die 2x+ 5(x – 4) = 50 vergelyking (1) 2x + 5x – 20 = 50 ✓ Substitute/Vervang 7x = 70 ✓ Simplify/Vereenvoudig x = 10 ✓ x value/x-waarde y = 10 – 4 y=6 ✓ y value/y-waarde (5) [14] 4

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 3 3.1 3.1.1 Zain’s formula/Zain se formule: Tn = 4(n − 1) + 2 ✓ Method/Metode = 4n − 4 + 2 = 4n − 2 ✓ Answer/Antwoord This is the same as Letti’s formula. They are both correct./ ✓ Reason/Rede Dit is dieselfde as Lettie se formule. Hulle is albei korrek. (3) 3.1.2 T27 = 4(27) –2 ✓ ✓ Substitution/ Vervanging = 106 ✓ ✓ Answer/Antwoord (2) 3.2 3.2.1 Tn = 5n – 8 ✓✓ ✓ 5n ✓–8 (2) 3.2.2 The 52th number to end in a 7 will be T105/Die 52ste getal ✓ n=105 wat op ʼn 7 einding sal T105 wees. T105 = 5(105) – 8 ✓ Substitute/Vervang = 517 ✓ 517 OR/OF 7 ; 17 ; 27 ; 37 Tn = 10n –3 ✓ Tn ✓ Substitute/Vervang T52 = 10(52) – 3 ✓ 517 = 517 OR/OF ✓ Pattern/Patroon 7 ; 17 ; 27 ; 37 ✓✓ 517 By inspection the 52nd term will be 517 Deur inspeksie is die 52ste term gelyk aan 517 (3) [10] 5

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 4 4.1 4.1.1 xR ✓ Answer/Antwoord (1) 4.1.2 y  −4 OR/OF y  (−4; ) ✓ Answer/Antwoord (1) 4.1.3 y = −3 ✓ Answer/Antwoord (1) 4.2 f (x) = ax – 3 subst/vervang (–2;6) ✓ Substitution/Vervanging 6 = a–2 – 3 a–2 = 9 1 a–2 = 9 1 1 a = = 3–1 ✓ = 3–1 3 3 (2) 4.3 x-intercept exponential graph:/x-afsnit eksponensiële grafiek: 3–x – 3 = 0 3–x = 3 ✓ Let/Stel x = 0 x = –1 C( ̶ 1 ; 0) OR/OF x-intercept hyperbola:/x-afsnit hiperbool: ✓ x value/x-waarde −4 –4=0 x −4 4 ✓ co-ordinate/koördinaat = C( ̶ 1 ; 0) x 1 x = –1 (3) 4.4 −1  x  0 OR/OF x  (−1;0) ✓ x  −1 ✓ x0 (2) 4.5 4.5.1 A(–2 ; 6) C(–1 ; 0) 6−0 m= −2 + 1 y2 − y1 ✓ subst into m = m = −6 x2 − x1 y = –6x + c y −y subst/vervang (–1;0) OR/OF subst/vervang (–2;6) vervang in m = 2 1 x2 − x1 0 = –6(–1) + c 6 = –6(–2) + c ✓m= ̶6 c = –6 ✓ subst m and co-ordinate/ vervang m en koördinaat  y = –6x – 6 ✓ equation/vergelyking (4) 4.5.2 y = −x − 4 ✓ –x ✓ –4 (2) 6

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 4.6 4 g ( x) = − − 4 and/en B(x ; 6) x 4 ✓ Subst y = 6/Vervang y = 6 − −4=6 x 4 ✓ x value/ − = 10 x x-waarde x = −0, 4 AB = 2 ̶ 0,4 ✓ 1,6 = 1,6 units/eenhede (3) [19] QUESTION/VRAAG 5 5.1 ✓ Shape/Vorm ✓ x intercepts/ x-afsnitte ✓ Turning point/ Draaipunt (0 ;–8) (3) 5.2 q = –8 Substitute (–4;0) or (4;0) to calculate a Vervang (–4;0) of (4;0) om a te bereken ✓Subst coordinate y = ax 2 − 8 and q = –8/ Vervang koördinaat 0 = a (4) 2 − 8 en q = –8 16a = 8 1 ✓a= 1 a= 2 2 1 ✓ Equation/ Vergelyking  y = x2 − 8 2 (3) 5.3 –4  x  4 OR/OF x [–4;4] ✓ x  –4 ✓x4 (2) 5.4 1 ✓ – 1 x2 k ( x) = − x 2 + 2 2 2 ✓ +2 (2) [10] 7

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 6 6.1 A = (1 + in) = 7 990(1 + (0,15  4)) ✓✓ ✓ Substitution in correct formula/Vervanging in korrekte formule ✓ Converting 48 months to 4 years/ Omskakeling 48 maande tot 4 jaar = 7 990(1,60) = R12 784,00✓ ✓ Total amount including interest/ Totale bedrag insluitend rente = R12 784,00 ÷ 48 ✓ Monthly repayment/ = R 266,33 ✓ Maandelikse terugbetaling Monthly payment including fees/Maandelikse betalings insluitend fooie = R266,33 + R13,50 = R 279,83 ✓ ✓ Total monthly repayment/ Totale maandeliks terugbetaling (5) 6.2 A= P(1+ i)n ✓ ✓ Correct formula/ Korrekte formule = 5000(1 + 0,2)31 ✓✓✓ ✓ 20% to/na 0,2 ✓ 60 – 29, n=31 ✓ Substitution/ Vervanging = R 1 424 257,88 ✓ ✓ Answer/Antwoord (5) [10] 8

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 7 7.1 7.1.1 P(A or/of B) = 1 – P(A or/of B)' ✓ 1 – P(A or/of B)' = 1 – 0,05 = 0,95 ✓ Answer/Antwoord (2) 7.1.2 NO/NEE ✓ no/nee ✓ Justification/ P(A) + P(B)  P(A or/of B) Regverdiging (2) 7.1.3 P(A or/of B) = P(A) + P(B) – P(A and/en B) Formula/formule P(A and/en B) = 0,25 + 0,89 – 0,95 = 0,19 Answer/Antwoord (2) 7.1.4 P(B) = 0,89 – 0,19 ✓ 0,89 – 0,19 = 0,6 ✓ Answer/Antwoord (2) 7.2 7.2.1 ADD MULTIPLIER ✓ 600 – 285 = 315(ADD) ✓ 950 – 285 = 665 (MULTIPLIER) ✓ 600 + 950 + 235 – 600 – 285 = 315 *285 950 – 285 = 665 1 500 = 285 ✓ Correct diagram used/ Korrekte diagram gebruik 235 600 + 950 + 235 – 1 500 = 285 (4) 7.2.2 285 19 ✓ Answer only/ = Slegs antwoord 1 500 100 (1) 7.2.3 1 500 − 950 550 1 500 − 950 = ✓ 1 500 1 500 1 500 11 11 = ✓ 30 30 OR/OF OR/OF 315 + 235 550 11 315 + 235 = = 1 500 1 500 30 1 500 (2) [15] TOTAL/TOTAAL : 100 9

Downloaded from hlayiso.com MATHEMATICS/WISKUNDE MARKING GUIDELINES/ NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 10