GRADE/ GRADE 12 SEPTEMBER 2012 MATHEMATICS P1 (WISKUNDE V1) MEMORANDUM
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1 Province of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE/ GRADE 12 SEPTEMBER 2012 MATHEMATICS P1 (WISKUNDE V1) MEMORANDUM MARKS/ PUNTE: 150 This memorandum consists of 11 pages. Hierdie memorandum bestaan uit 11 bladsye.
2 2 MATHEMATICS P1 (Memo) (SEPTEMBER 2012) QUESTION/VRAAG a + a a a 2 2a (a 1)(a 1) 0 a x + 5x 1 4x 2 4x + 1 4x 2 9x (4x 1)(x 2) 0 x or/of x 2 Correct solution/korrekte oplossing: x 2 standard form standaard vorm factorisation faktorisering value of a waarde van a (4) transpose and square both sides bring om en kwadreer beide kante standard form standaard vorm factorise faktoriseer both values of x beide waardes van x correct value of x korrekte waarde van x (5) x 3 or/of x 6 one mark for each value of x een punt vir elke waarde van x (4) 1.2 y 2x y 2x 1 (1) Substitute/Vervang (1) in xy 2y + x 2 + 3x 10 x(2x 1) 2(2x 1) + x 2 + 3x 10 2x 2 x 4x 2 + x 2 + 3x 10 x 2 8x (x 6)(x 2) 0 x 6 or/of x 2 and/en y 2(6) 1 or/of y 2(2) y 2x 1 substitution vervanging standard form standaard vorm both values of x beide waardes van x both values of y beide waardes van y (5)
3 (SEPTEMBER 2012) WISKUNDE V1 (Memo) write in factors skryf in faktore factorise faktorisering antwoord (5) 1.4 equate values vergelyk waardes QUESTION/VRAAG 2 antwoord (2) [25] ; 4 ; 11 ; 22 ; 37 ; 56 ; 79 1 mark for each term 1 punt vir elk term (2) T n an 2 + bn + c and/en 2a 4 a 2 T n 2n 2 + bn + c n 1 T 1 2(1) 2 + b(1) + c b + c (1) n 2 (2) (1): -3 b b -3 (1) c c 2 T n 2n 2 3n b + c T 2 2(2) 2 + b(2) + c b + c -4 2b + c (2) Identification of 2 nd difference Identifisering van 2 de verskil value of a waarde van a 1 st equation 1 ste vergelyking 2 nd equation 2 de vergelyking value of c waarde van c formula formule (6) [8]
4 4 MATHEMATICS P1 (Memo) (SEPTEMBER 2012) QUESTION/VRAAG T 1 1 T 2-2 T 3-5 sequence is arithmetic/ry is meetkundig 1 st 3 terms 1 ste 3 terme antwoord (2) d -3 value of d waarde van d (1) S n n(-3n + 5) n 2 + 5n 3n 2 5n (3n + 25)(n 10) 0 or/of n 10 n 10 n N (0,2) + (0,2) 2 + (0,2) 3 a 1, r 1,25 substitution in correct formula standard form standaard vorm factorization faktorisering correct value of n korrekte waarde van n. (5) expansion uitbreiding ratio verhouding substitution in antwoord (4) ratio verhouding substitution vervanging
5 (SEPTEMBER 2012) WISKUNDE V1 (Memo) ratio verhouding substitution in QUESTION/VRAAG T n ar n-1 T n S n a 1900 T 7 400(1,1) (1,1) 6 708,62 7 th month/7 de maand R708,62 Saves in 7 months/spaar in 7 maande R3 794,87 r ,5% R ,93 0,0776 Alternative/Alternatief a 1911,875 r 1,00525 Effective annual interest rate 7,76% Effektiewe jaarlikse rentekoers 7,76% R ,93 [18] substitution in the substitution into korrekete formule the value of a die waarde van a the value of r die waarde van r substitution in antwoord (4) antwoord (1) substitution substitusie Simplification Answer [14]
6 6 MATHEMATICS P1 (Memo) (SEPTEMBER 2012) QUESTION/VRAAG y R ; y 5 antwoord (1) 5.2 y -3x + 2 (1) (-3x + 2) y (2) -3x 2 x (x + 1) -3x 2 6x 0-3x(x + 2) 0 x 0 or/of x -2 y -3(0) + 2 or/of y -3(-2) (0 ; 2) and/en (-2 ; 8) equating f(x) and g(x) vergelyk f(x) en g(x) simplification standard form Standaard vorm for both x values Vir beide x waardes for both y values vir beide y waardes for each correct coordinates 1 mark vir elke regte koördinaat 1 punt (7) 5.3 f(x) QUESTION/VRAAG 6 reflection about asymptote: refleksie in die asimptote: x -1 or/of reflection about asymptote: refleksie in die asimptote: y 5 for description vir beskrywing (1) [9] 6.1 (3;-2): (0;0) : substituting (3;-2) substitusie (0;0) 9a 2 a value of a die waarde van a (3) 6.2 B(6 ; 0) coordinate of B koördinaat van B (1) 6.3 g(x) is a one-too-many function; for every y-value there are two corresponding x-values. g(x) is een-te-veel funksie; vir elke y-waarde is daar twee ooreenstemmende x-waardes for answer/vir antw. substantiation/ regverdiging (2)
7 (SEPTEMBER 2012) WISKUNDE V1 (Memo) y both x intercepts Beide x-afsnitte. (-2 ; 3) (0 ; 6) turning point draaipunt (0 ; 0) x 6.5 Range/Wydte : y 3 or/of y 3 range/wydte (1) 6.6 g: y QUESTION/VRAAG For inverse/vir inverse : x : y lo for base 7.2 y g: y 2 -x 1. O P. 1-2 (3) correct equation korrekte vergelyking (2) [14] vir basis antwoord (2) for curve vir kurwe y-intercept y-afsnit g -1 : for curve vir kurwe y lo x-intercept x-afsnit (4) 7.3 see graph/sien grafiek dotted line gebroke lyn (1) 7.4 y x y x (1) x 7.5 see graph/sien grafiek (1) [9]
8 8 MATHEMATICS P1 (Memo) (SEPTEMBER 2012) QUESTION/VRAAG P v ; i n 18 F v 2860 P v (1 + i) n F v correct value of i korrekte waarde van i substitution into Vervanging in or/of 24% 8.2 F v No, he will be R55,01 short Nee, hy sal R55,01 kort ( value of i waarde van i substitution into (correct conclusion) antwoord (korrekte afleiding) (3) The deposit/die deposito 15% of R ,00 R The loan/die lening R or/of The loan/die lening 85% of R R P v value of loan waarde van value of i waarde van i (1) ,476x x R2 104,96 substitution into Vervanging in [10]
9 (SEPTEMBER 2012) WISKUNDE V1 (Memo) 9 QUESTION/VRAAG a 2 x + 2a 2 x + antwoord (1) one mark for each correct term een punt vir elke korrekte term (2) 1 mark for each derivative 1 punt vir elke afgeleide (2) 9.4 f(x) x 3 f (x) 3x 2 substitution into simplification simplification antwoord (4) [9] QUESTION/VRAAG y x(x 2 27) x 3 27x At turning points/by draaipunt: 3x x 2 9 x 3 or -3 y (3) or/of y (-3) 3-27(-3) Turning points/draaipunte (3 ; -54) or/of (-3 ; 54) both values of x Beide waardes van x both values of y Beide waardes van y 1 mark for both coordinates 1 punt vir koördinate vir beide draaipunte. (4)
10 10 MATHEMATICS P1 (Memo) (SEPTEMBER 2012) 10.2 f(x) x 3x 2 2x 3 f (x) 12 6x 6x 2 f (x) -6 12x At point of inflection/by punt van infleksie: f (x) x 0-12x 6 x 1 st derivative 1 ste afgeleide 2 nd derivative 2 de afgeleide value for x waarde van x y ( coordinate are/koördinate is mx 2 6x 12 QUESTION/VRAAG Volume 3mx 2 6x m(2) 2 6(2) m m 24 m Exterior area/buite oppervlakte A y 2x 3 3x 2 12x + n At x 2 is y (2) 3 3(2) 2 12(2) + n n n n 17 value for y waarde van y coordinate koördinate (5) differentiation differensiasie substitution vervanging value of m waarde van m substitution of x and y vervanging van x en y value of n waarde van n (5) [14] formula formule substitution vervanging h (3) formula formule substitution of h vervanging van h (2)
11 (SEPTEMBER 2012) WISKUNDE V1 (Memo) For minimum/vir minimum: and/en differentiation of A differensiasie van A simplification value of r waarde van r 23,35 Allow/Laat toe: 23,33 or/of 23,34 QUESTION/VRAAG 12 value of h. waarde van h (4) [9] x + y 10 x + 3y x 0 for 1 st inequality vir 1 ste ongelykheid 2 nd inequality 2 de ongelykheid y x 0 y 0 (4) 10 F F : Feasible region Gangbare gebied feasible region gangbare gebied line/lyn 2x + y line/lyn x + 3y A (6) 12.3 Minimum number of capsules and tablets: Minimum aantal kapsule en tablette 3 tablets/tablette Read at A./Gelees by A. 4 capsules/kapsules tablets tablette capsules kapsules (3) [13] TOTAL/TOTAAL: 150
NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 SEPTEMBER 2014 MATHEMATICS P1/WISKUNDE V1 MEMORANDUM
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