Mathematics Grade 10 P1 Gauteng June 2024 Memo (Afrikaans)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION PROVINSIALE EKSAMEN JUNE/JUNIE 2024 GRADE/GRAAD 10 MARKING GUIDELINES/ NASIENRIGLYNE MATHEMATICS/WISKUNDE (PAPER/VRAESTEL 1) 6 pages/bladsye NOTE/LET WEL: • If a candidate answers a question TWICE, mark only the FIRST attempt. As ʼn kandidaat ʼn vraag TWEE keer beantwoord, sien slegs die EERSTE poging na. • If a candidate crossed OUT an answer and did not redo it, mark the crossed-out answer. Indien ʼn kandidaat ʼn antwoord DOODTREK en dit nie OORDOEN nie, sien die deurgehaalde antwoord na. • Consistent accuracy (CA) applies to ALL aspects of the marking guidelines. Konsekwente akkuraatheid (CA) is van toepassing op ALLE aspekte van die nasienriglyne. • Assuming values/answers in order to solve a problem is UNACCEPTABLE. Aannames van waardes/antwoorde om ʼn probleem op te los, is ONAANVAARBAAR.

Downloaded from hlayiso.com MARKING GUIDELINES/ MATHEMATICS/WISKUNDE NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 1 1.1 𝑥=4 ✓ answer/antwoord (1) 1.2 𝑥 = 0 or/𝑜𝑓 𝑥 = 3 ✓ any one/enigeen (1) 1.3 𝑥 = 1 or/𝑜𝑓 𝑥 = 2 ✓ any one/enigeen (1) [3] QUESTION/VRAAG 2 2.1 2.1.1 2b(b − 5c) 2 = 2b(b 2 − 10bc + 25c 2 ) ✓square the binomial/kwadreer = 2b3 − 20b 2 c + 50bc 2 binoom ✓distribute 2b/versprei 2b (2) 2.1.2 3x − 2.3x −1 3x + 2 + 2.3x +1 ✓ factorise numerator/ faktoriseer teller 3x (1 − 2.3−1 ) ✓ factorise denominator/ = x 2 3 (3 + 2.3) faktoriseer noemer 1 = 3 15 1 = 45 ✓final answer/finale antwoord (3) 2.2 a 2 − ax − 1 + x = a 2 − 1 − ax + x ✓sum and difference/ som en verskil = (a + 1)(a − 1) − x(a − 1) ✓factorise/faktoriseer = (a − 1)(a + 1 − x) ✓factorise/faktoriseer (3) [8] 2

Downloaded from hlayiso.com MARKING GUIDELINES/ MATHEMATICS/WISKUNDE NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 QUESTION/VRAAG 3 3.1 3.1.1 3𝑥 2 − 2𝑥 = 0 𝑥(3𝑥 − 2) = 0 ✓factorise/faktoriseer 2 ✓both x values/ 𝑥 = 0 or/of 𝑥 = beide 𝑥 waardes (2) 3 3.1.2 7 5 4 = + 2 3−𝑥 𝑥+3 𝑥 −9 ✓factorise/faktoriseer −7 5 4 = + ✓change of sign/ 𝑥 − 3 𝑥 + 3 (𝑥 + 3)(𝑥 − 3) verander teken LCD/KGV (𝑥 + 3)(𝑥 − 3); 𝑥 ≠ ±3 −7(𝑥 + 3) = 5(𝑥 − 3) + 4 ✓ −7( x + 3) = 5( x − 3) + 4 −7𝑥 − 21 = 5𝑥 − 15 + 4 −12𝑥 = 10 5 𝑥=− 6 ✓answer/antwoord (4) 3.1.3 16.2 x −1 = (0,5) x − 4 24.2 x −1 = (2−1 ) x − 4 ✓ 24.2x−1 2 x +3 = 2− x + 4 ✓ (2−1 ) x −4 x+3= 4− x ✓ x+3= 4− x 2x = 1 1 ✓answer / antwoord x= 2 (4) 3.2 3.2.1 3x 2−  14 4 ✓subtract 2/trek 2 af −3x  12 −4 4 ✓multiply 3 / x  −16 −4 (2) vermenigvuldig met 3 3.2.2 𝑥=1 answer/antwoord (1) 3

Downloaded from hlayiso.com MARKING GUIDELINES/ MATHEMATICS/WISKUNDE NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 3.3 2 x + y = 8 and/en and 2 y + 3x = −2.........(2) y = 8 − 2 x...........(1) ✓equation (1)/ vergelyking (1) subst (1) into (2) /vervang (1) in (2) 2(8 − 2 x) + 3 x = −2 ✓subst (1) into (2) 16 − 4 x + 3 x = −2 vervang (1) in (2) − x = −18 ✓x value/𝑥 − 𝑤𝑎𝑎𝑟𝑑𝑒 x = 18 subst x = 18 into (1) /vervang x = 18 in (1) ✓y value/𝑦 − 𝑤𝑎𝑎𝑟𝑑𝑒 y = 8 − 2(18) y = −28 (4) [17] QUESTION/VRAAG 4 4.1 Sub point A (–1;–3)/Vervangpunt A(–1;–3) –3 = a + c ….. eq 1/vgl 1 ✓✓ correct sub of both Sub point B(2; 0)/vervangpunt B(2;0) points 0 = 4a + c ….. eq 2/vgl 2 𝑘𝑜𝑟𝑟𝑒𝑘𝑡𝑒 𝑣𝑒𝑟𝑣 𝑣𝑎𝑛 eq 1 − eq 2/𝑣𝑔𝑙 1 − 𝑣𝑔𝑙 2 𝑏𝑒𝑖𝑑𝑒 𝑝𝑢𝑛𝑡𝑒 –3 = −3 𝑎 a = 1 sub in eq 1/𝑣𝑒𝑟𝑣 𝑖𝑛 𝑣𝑔𝑙 1 ✓ 𝑎=1 –3 = 1 + c c = –4 ✓ 𝑐 = −4 or sub in eq 2/of vervang in vgl 2 0=4+c c=–4 (4) 4

Downloaded from hlayiso.com MARKING GUIDELINES/ MATHEMATICS/WISKUNDE NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 𝑦 −𝑦 4.2 b= 𝑥1−𝑥2 1 2 −3−0 b = −1−2 ✓ correct answer for b=1 b/korrekte antwoord vir 𝑏 𝑔(𝑥) = 𝑥 + 𝑞 sub/vervang (-1;-3) –3 = –1 + 𝑞 ✓ sub (-1;-3) or (2;0)/ 𝑞 = −2 vervang (-1;-3) of (2;0) OR/OF sub (2;0)/vervang (2;0) ✓ correct answer for 0=2+𝑞 q/korrekte antwoord vir 𝑞 𝑞 = −2 Method 2/Metode 2 Sub (2;0) into 𝑔/Vervang (2;0) in 𝑔 0 = 2𝑏 + 𝑞 …… eq 1/vgl 1 Sub (-1;-3) into 𝑔/verv (-1;-3) in 𝑔 −3 = −𝑏 + 𝑞 ….. eq 2/vgl 2 eq 1 – eq 2/𝑣𝑔𝑙 1 − 𝑣𝑔𝑙 2 3𝑏 = 3 ✓ correct answer for b/ 𝑏=1 korrekte antwoord vir 𝑏 Sub/vervang (2;0) into/in 𝑔(𝑥) = 𝑥 + 𝑞 ✓ sub/verv (-1;-3) 0=2+𝑞 OR/OF (2;0) 𝑞 = −2 OR/OF ✓ correct answer for q/ Sub/vervang (-1;-3) into/in 𝑔 korrekte antwoord vir 𝑞 –3 = –1 + 𝑞 𝑞 = −2 (3) 4.3 ✓✓✓ x and y intercepts for f/x en y-afsnitte van f ✓✓✓ x and y intercepts for g/x en y-afsnitte van g. (6) 4.4 –2 – (–4) = 2 ✓ –2 – (– 4) ✓ answer/antwoord (2) 5

Downloaded from hlayiso.com MARKING GUIDELINES/ MATHEMATICS/WISKUNDE NASIENRIGLYNE (PAPER/VRAESTEL 1) GRADE/GRAAD 10 4.5 −1 ≤ 𝑥 ≤ 2 ✓ mark for values Or punt vir waardes 𝑥 ∈ [ −1; 2] ✓ mark for correct notation ONLY if values were correct./punt vir notasie SLEGS as waardes korrek was. (2) [17] QUESTION/VRAAG 5 5.1 2 x +2 + k = 2 x.2 2 + k ✓ mark for splitting exponent/punt vir opbreek = 4.2 x + k van eksponente ✓ answer/antwoord (2) 5.2 Sub point (0;5)/vervangpunt (0;5) ✓ sub point correctly/vervang 5 = 4. 20 + 𝑘 punt korrek 𝑘=1 ✓ correct answer/korrekte antwoord (2) 5.3 𝑦=1 ✓ answer/antwoord (1) [5] TOTAL/TOTAAL [50] 6