NATIONAL SENIOR CERTIFICATE/ NASIONALE …

1 NATIONAL . SENIOR certificate /. NASIONALE . SENIOR SERTIFIKAAT. GRADE/GRAAD 12. september 2014 . mathematics P1/ wiskunde V1. MEMORANDUM. MARKS/PUNTE: 150. Hierdie memorandum bestaan uit 16 This memorandum consists of 16 pages. 2 mathematics P1/ wiskunde V1 ( september 2014 ). NOTE/LET OP: If a candidate answered a question TWICE, mark the FIRST attempt ONLY. Indien kandidaat vraag TWEE keer beantwoord het, merk SLEGS die EERSTE poging. Consistent accuracy applies in ALL aspects of the memorandum. Volgehoue akkuraatheid geld deurgaans in ALLE aspekte van die memorandum. If a candidate crossed out an attempt of a question and did not redo the question, mark the crossed-out attempt. Indien kandidaat poging vir vraag deurgetrek het en nie die vraag weer beantwoord het nie, merk die poging wat deurgetrek is. The mark for substitution is awarded for substitution into the correct formula. Die punt vir substitusie word toegeken vir substitusie in die korrekte formule. QUESTION 1/VRAAG 1. Note/Let op: ( ) factors/faktore If divided by /indien or/of deel deur -values/waardes only/slegs, OR/OF 0 marks/punte.

2 ( ) ( ) ( )( ). ( ). substitution/substitusie or/of -values/waardes (2). Penalise 1 mark for standard form/standaardvorm incorrect rounding off. ( ) ( ) ( )( ). Penaliseer 1 punt vir substitution/substitusie ( ) verkeerde afronding.. -values/waardes or/of (4). factors/faktore ( )( ). or/of or/of or/of answer/antwoord OR/OF. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 3. Let/stel ( )( ). or/of factors/faktore or/of or/of or/of answer/antwoord (3). ( )( ) factors/faktore . or/of OR/OF. ( ] or/of [ ). answer/antwoord OR/OF.. Note/Let op: If/As and/en max/maks. 3 marks/punte. If/As or/of max/ maks. 2 marks/punte. If correct graphical solution but concludes incorrectly, max 3. As korrekte grafiese oplossing, maar maak verkeerde gevolgtrekking, maks. 3 punte. If omits or , max 3 As of uitlaat, maks 3 punte. (4).. OR/OF. (2). [15]. Copyright reserved Please turn over 4 mathematics P1/ wiskunde V1 ( september 2014 ). QUESTION 2/VRAAG 2.. 2.. ( ) substitution/substitusie standard form/standaardvorm ( )( ) factors/faktore or/of -values/waardes or/of If a candidate makes a -values/waardes mistake and both equations OR/OF become linear, max.

3 3 marks. Indien kandidaat fout begaan en beide vergelykings word line r, maks. 3 punte.. 2.. Substitution/substitusie ( ) ( ). Standard form/standaardvorm ( )( ) Factors/faktore or/of -values/waardes or/of -values/waardes (7). ( ) ( )( ) . roots are nonreal/wortels is nie-re el conclusion/gevolgtrekking (2). Note/Let op: If a candidate states nonreal' and eg. irrational', max 1 Indien kandidaat nie-re el' en bv. irrasionaal' meld, maks 1 punt. [9]. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 5. QUESTION 3/VRAAG 3. answer/antwoord (1). Second difference/Tweede verskil = Second difference/ Tweede verskil -value/waarde -value/waarde -value/waarde OR/OF. ( ). ( ). ( ). ( ) ( ) method/metode ( ) ( ). -value/waarde -value/waarde -value/waarde (4). [5]. Copyright reserved Please turn over 6 mathematics P1/ wiskunde V1 ( september 2014 ). QUESTION 4/VRAAG 4.. (2). ( terms/terme). (GS/MR 17 terms/terme) identifies two patterns/. identifiseer twee patrone (( ) ).

4 Substitution/substitusie ( ).. answer/antwoord (5). ; Answer ONLY: 1 mark SLEGS antwoord: 1 punt -value/waarde -value/waarde If a candidate substitutes incorrect -value, CA only if < <. Indien kandidaat verkeerde -waarde vervang, CA slegs as < <. substitution/substitusie or/of answer/antwoord (4). [11]. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 7. QUESTION 5/VRAAG 5. answer/antwoord (1).. ( ) substitution/substitusie -value/waarde [ ( ) ]. [ ( ) ( )] substitution/substitusie answer/antwoord Answer ONLY: Full marks OR/OF SLEGS antwoord: Volpunte . ( ) substitution/substitusie -value/waarde [ ]. substitution/substitusie [ ]. answer/antwoord (5). ( ) substitution/substitusie ( ). Answer ONLY: 1 mark ( ) SLEGS antwoord: 1 punt ( ). ( ) ( ) simultaneous equation/. gelyktydige vergelykings ( ) factors/faktore ( ). answer/antwoord (4). [10]. Copyright reserved Please turn over 8 mathematics P1/ wiskunde V1 ( september 2014 ). QUESTION 6/VRAAG 6. ( ). ( ) substitution/substitusie ( ) Wrong formula: 0 marks simplification/vereenvoud.

5 ( ) ( ) Verkeerde formule: 0 punte correct use of logs/korrekte ( ) gebruik van logs ( ). years/jare Accept/Aanvaar answer/antwoord years/jare; 8 years/jare or/of 7 years/jare 9 months/maande (4).. Loan amount/Leningsbedrag =. answer/antwoord OR/OF. Loan amount/Leningsbedrag .. (2). [ ( ) ] . Wrong formula: max 1 mark ( ). correct formula/formule [ ( ) ]. Verkeerde formule: substitution/substitusie maks. 1 punt ( ). answer/antwoord (4). [ ( ) ] method/metode Balance/balans [ ( ) ] substitution/substitusie = answer/antwoord If no rounding from balance = . Indien geen afronding uit OR/OF balans = . [( ) ]. Bal. = ( ). (3). [13]. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 9. QUESTION 7/VRAAG 7. ( ) .. (2). Let/stel .. ( ) OR/OF ( ) OR/OF ( ) (2).. ( ). substitution/substitusie ( ). -value/waarde equation/vergelyking OR/OF. ( ) , ( ). substitution/substitusie and ( ). -value/waarde . equation/vergelyking (4). setting up equation/opstel van vergelyking ( ).

6 Standard form/standaardvorm ( ). factors/faktore or/of ( ) answer/antwoord (4). Answer ONLY: Full marks SLEGS antwoord: Volpunte Copyright reserved Please turn over 10 mathematics P1/ wiskunde V1 ( september 2014 ). Decreasing function/afnemende funksie decreasing/afnemend decreases as increases/ neem af soos wat reason/rede toeneem. If sketch is given as reason: Max 1 mark As skets as rede gegee is: Maks 1 punt (2). answer/antwoord (1). ( ). ( ) interchange and OR/OF ruil en OR/OF equation/vergelyking (2). -intercept/ -afsnit . shape/vorm Do not award shape- mark if graph is not asymptotic. Moenie vormpunt toeken as grafiek nie asimptoties is nie. (2). < .. (2). [21]. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 11. QUESTION 8/VRAAG 8. ( ). ( )( ) factors/faktore or/of both/albei (3). ( ) -value/waarde ( ). ( ) ( ) ( ) -value/waarde OR/OF. -value/waarde ( ) ( ) ( ) -value/waarde OR/OF. ( ). -value/waarde -value/waarde ( ) ( ) ( ). OR/OF. -value/waarde ( )( ) ( ).

7 =. ( ). -value/waarde or/of (2). ( ) setting up equation/opstel van vergelyking standard form/standaardvorm ( )( ) factors/faktore or/of ( ) answer/antwoord (4). Copyright reserved Please turn over 12 mathematics P1/ wiskunde V1 ( september 2014 ). < or/of < < <. < <. (2). < < < <. < <. < <. < <. (2). ( ) ( ) ( ).. (2). [15]. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 13. QUESTION 9/VRAAG 9. ( ). ( ) ( ). ( ) formula/formule ( ) ( ) ( ) substitution of/substitusie van ( ). ( ) ). simplification to/. vereenvoudiging na ( ). ( ) common factor/gemene faktor ( ). Answer ONLY: 0 marks SLEGS antwoord: 0 punte answer/antwoord Penalise 1 mark for incorrect use of formula. Must show ( ). Penaliseer 1 punt vir verkeerde gebruik van formule. Moet ( ) toon. (5).. Penalise 1 mark for incorrect notation.. Penaliseer 1 punt vir verkeerde notasie.. (4). ( ). ( ). ( ) ( ). ( )( ) standard form/standaardvorm factors/faktore or/of answer/antwoord (5). [14]. Copyright reserved Please turn over 14 mathematics P1/ wiskunde V1 ( september 2014 ).

8 QUESTION 10/VRAAG 10. ( ). ( )( ) ( ) ( ). ( )( )( ) ( )( ). or/of or/of ( ) and/en ( ) coordinates of and /. ko rdinate van en (4). ( ) ( ) ( ). ( )( ) factors/faktore or/of coordinates/ko rdinate ( ) and/en ( ) coordinates/ko rdinate (5). ( ) ( ). Answer ONLY: Full marks ( ) SLEGS antwoord: Volpunte ( ). OR/OF. ( ) ( ). ( ) ( ). (2).. ( ) Answer ONLY: Full marks ( ). SLEGS antwoord: Volpunte answer/antwoord (2). Point of inflection/Infleksiepunt at/by . ( )< if/as answer/antwoord (2). Answer ONLY: Full marks [15]. SLEGS antwoord: Volpunte QUESTION 11/VRAAG 11.. ( ). ( ) ( ) ( ) ( ). ( ). ( ) ( ). ( ) . ( ) ( ). (4).. Copyright reserved Please turn over ( september 2014 ) mathematics P1/ wiskunde V1 15. -value/waarde ( ) ( ). answer/antwoord (3). [7]. QUESTION 12/VRAAG 12. answer/antwoord (1). If incorrect -value/Indien verkeerde -waarde: answer/antwoord CA: . (1). (first client takes a loaf of white bread) = answer/antwoord (eerste kli nt vat witbrood) = (1). ( ) . = or/of or/of (3).

9 ( ) ( ) ( ) ( ) ( ) ( ). or/of answer/antwoord (3). Copyright reserved Please turn over 16 mathematics P1/ wiskunde V1 ( september 2014 ). answer/antwoord (1). (E's next to each other/E's langs mekaar). = . = 80 640 80 640. (E's next to each other/E's langs mekaar). = or/of or/of (3). (starting with ; repeating letters the same). (begin met ; herhaalde letters dieselfde). = . =.. (2). [15]. TOTAL/TOTAAL: 150. Copyright reserved Please turn over