Mathematics Grade 12 Paper 1 Eastern Cape Mock 2014 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 SEPTEMBER 2014 MATHEMATICS P1/WISKUNDE V1 MEMORANDUM MARKS/PUNTE: 150 Hierdie memorandum bestaan uit 16 bladsye./ This memorandum consists of 16 pages.

Downloaded from hlayiso.com 2 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) NOTE/LET OP:  If a candidate answered a question TWICE, mark the FIRST attempt ONLY. Indien ʼn kandidaat ʼn 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 ʼn kandidaat ʼn poging vir ʼn 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 1.1.1 Note/Let op: ( )  factors/faktore If divided by 𝑥/indien or/of deel deur 𝑥  -values/waardes ∴𝑥 only/slegs, OR/OF 0 marks/punte. ( ) √( ) ( )( ) ( )  substitution/substitusie or/of  -values/waardes (2) 1.1.2 Penalise 1 mark for  standard form/standaardvorm incorrect rounding off. ( ) √( ) ( )( ) Penaliseer 1 punt vir  substitution/substitusie ( ) verkeerde afronding. √  -values/waardes or/of (4) 1.1.3  factors/faktore ( )( ) or/of  or/of or/of  answer/antwoord OR/OF Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 3 Let/stel ( )( ) or/of  factors/faktore or/of or/of  or/of  answer/antwoord (3) 1.2.1 ( )( )  factors/faktore  or/of OR/OF ( ] or/of [ )  answer/antwoord OR/OF 𝑥 Note/Let op: If/As 𝑥 and/en 𝑥 max/maks. 3 marks/punte. If/As 𝑥 or/of 𝑥 max/ maks. 2 marks/punte. If correct graphical solution but concludes incorrectly, max 3 marks./ As korrekte grafiese oplossing, maar maak verkeerde gevolgtrekking, maks. 3 punte. If omits “or”, max 3 marks./ As “of” uitlaat, maks 3 punte. (4) 1.2.2   OR/OF 𝑥 (2) [15] Copyright reserved Please turn over

Downloaded from hlayiso.com 4 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) QUESTION 2/VRAAG 2 2.1  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 marks. Indien ʼn kandidaat ʼn fout begaan en beide vergelykings word lineêr, maks. 3 punte.  2   Substitution/substitusie ( ) ( )  Standard form/standaardvorm ( )( )  Factors/faktore or/of  -values/waardes or/of  -values/waardes (7) 2.2 ( ) ( )( )  ∴ roots are nonreal/wortels is nie-reëel  conclusion/gevolgtrekking (2) Note/Let op: If a candidate states ‘nonreal’ and eg. ‘irrational’, max 1 mark./ Indien kandidaat ‘nie-reëel’ en bv. ‘irrasionaal’ meld, maks 1 punt. [9] Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 5 QUESTION 3/VRAAG 3 3.1  answer/antwoord (1) 3.2 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

Downloaded from hlayiso.com 6 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) QUESTION 4/VRAAG 4 4.1.1   (2) 4.1.2 ( terms/terme) (GS/MR 17 terms/terme)  identifies two patterns/ identifiseer twee patrone (( ) )  substitution/substitusie ( )    answer/antwoord (5) 4.2 ; Answer ONLY: 1 mark SLEGS antwoord: 1 punt  -value/waarde  -value/waarde If a candidate substitutes incorrect 𝑟-value, CA only if <𝑟< Indien kandidaat verkeerde 𝑟-waarde vervang, CA slegs as <𝑟<  substitution/substitusie or/of  answer/antwoord (4) [11] Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 7 QUESTION 5/VRAAG 5 5.1.1  answer/antwoord (1) 5.1.2  ( )  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) 5.2 ∴ ( )  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

Downloaded from hlayiso.com 8 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) QUESTION 6/VRAAG 6 6.1 ( ) ( )  substitution/substitusie ( ) Wrong formula: 0 marks  simplification/vereenvoud. ( ) ( ) 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) 6.2.1  ∴ Loan amount/Leningsbedrag =  answer/antwoord OR/OF Loan amount/Leningsbedrag   (2) 6.2.2 [ ( ) ]  Wrong formula: max 1 mark (𝑖)  correct formula/formule [ ( ) ] Verkeerde formule:  substitution/substitusie maks. 1 punt (𝑖)  answer/antwoord (4) 6.2.3 [ ( ) ]  method/metode Balance/balans [ ( ) ]  substitution/substitusie =  answer/antwoord If no rounding from 6.2.2 balance = 𝑅 Indien geen afronding uit 6.2.2 OR/OF balans = 𝑅 [( ) ] Bal. = ( ) (3) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 9 QUESTION 7/VRAAG 7 7.1.1 ( )   (2) 7.1.2 Let/stel   ( ) OR/OF ( ) OR/OF ( ) (2) 7.1.3  ( )  substitution/substitusie ( )  -value/waarde  equation/vergelyking OR/OF ( ) , ( )  substitution/substitusie and ( )  -value/waarde   equation/vergelyking (4) 7.1.4  setting up equation/opstel van vergelyking ( )  standard form/standaardvorm ( )  factors/faktore or/of ∴( ) answer/antwoord (4) Answer ONLY: Full marks SLEGS antwoord: Volpunte Copyright reserved Please turn over

Downloaded from hlayiso.com 10 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) 7.2.1 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) 7.2.2  answer/antwoord (1) 7.2.3 ( ) ( )  interchange and OR/OF ruil en OR/OF  equation/vergelyking (2) 7.2.4  -intercept/ -afsnit 𝑦  shape/vorm Do not award shape- mark if graph is not asymptotic. 𝑂 𝑥 Moenie vormpunt toeken as grafiek nie asimptoties is nie. (2) 7.2.5 <   (2) [21] Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 11 QUESTION 8/VRAAG 8 8.1  ( ) ( )( )  factors/faktore or/of  both/albei (3) 8.2 ( )  -value/waarde ( ) ( ) ( ) ( )  -value/waarde OR/OF  -value/waarde ( ) ( ) ( )  -value/waarde OR/OF ( )  -value/waarde  -value/waarde ( ) ( ) ( ) OR/OF  -value/waarde ( )( ) ( ) = ( )  -value/waarde or/of (2) 8.3 ( )  setting up equation/opstel van vergelyking  standard form/standaardvorm ( )( )  factors/faktore or/of ( )  answer/antwoord (4) Copyright reserved Please turn over

Downloaded from hlayiso.com 12 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) 8.4 < or/of < <  <  < < (2) 8.5 < <  < < < < < <  < < (2) 8.6 ( ) ( )  ( )  (2) [15] Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 13 QUESTION 9/VRAAG 9 9.1 ( ) ( ) ( ) ( )  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 𝑓 (𝑥) Penaliseer 1 punt vir verkeerde gebruik van formule. Moet 𝑓 (𝑥) toon. (5) 9.2 √ Penalise 1 mark for incorrect notation.   Penaliseer 1 punt vir verkeerde notasie.   (4) 9.3 ( ) ( )  ( ) ( ) ( )( )  standard form/standaardvorm  factors/faktore or/of  answer/antwoord (5) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com 14 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) QUESTION 10/VRAAG 10 10.1.1 ( ) ( )( ) ( ) ( ) ( )( )( ) ( )( ) or/of or/of ( ) and/en ( )  coordinates of and / koördinate van en (4) 10.1.2 ( )  ( )  ( ) ( )( )  factors/faktore or/of  coordinates/koördinate ( ) and/en ( )  coordinates/koördinate (5) 10.2.1 ( )  ( ) Answer ONLY: Full marks ∴ ( ) SLEGS antwoord: Volpunte  ( ) OR/OF ( )  ( ) ( )  ( ) (2) 10.2.2  ( ) Answer ONLY: Full marks ( ) SLEGS antwoord: Volpunte  answer/antwoord (2) 10.2.3 Point of inflection/Infleksiepunt at/by  ( )< if/as  answer/antwoord (2) Answer ONLY: Full marks [15] SLEGS antwoord: Volpunte QUESTION 11/VRAAG 11 11.1 √ √  √ ( ) ( ) ( )  ( ) ( ) ( ) √ ( )  √ ( ) √ ( ) √ ( )  ( ) (4) 11.2  Copyright reserved Please turn over

Downloaded from hlayiso.com (SEPTEMBER 2014) MATHEMATICS P1/WISKUNDE V1 15  -value/waarde ( ) ( )  answer/antwoord (3) [7] QUESTION 12/VRAAG 12 12.1.1  answer/antwoord (1) 12.1.2 If incorrect 𝑥-value/Indien verkeerde 𝑥-waarde:  answer/antwoord CA: 𝑦 𝑥 (1) 12.2.1 (first client takes a loaf of white bread) =  answer/antwoord (eerste kliënt vat ʼn witbrood) = (1) 12.2.2 ( )   = or/of  or/of (3) 12.2.3 𝑊 𝑊 𝐵 𝑊 𝐵 𝐵 ( ) ( ) ( ) ( ) ( ) ( ) or/of  answer/antwoord (3) Copyright reserved Please turn over

Downloaded from hlayiso.com 16 MATHEMATICS P1/WISKUNDE V1 (SEPTEMBER 2014) 12.3.1  answer/antwoord (1) 12.3.2 (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) 12.3.3 (starting with ; repeating letters the same) (begin met ; herhaalde letters dieselfde) =  =  (2) [15] TOTAL/TOTAAL: 150 Copyright reserved Please turn over