MATHS P1 MEMO GR11 NOV2015 EA_hlayiso.com_.pdf

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 11 NOVEMBER 2015 MATHEMATICS P1/WISKUNDE V1 MEMORANDUM MARKS/PUNTE: 150 Hierdie memorandum bestaan uit 14 bladsye./ This memorandum consists of 14 pages.

Downloaded from hlayiso.com 2 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) 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  factors/faktore or/of  -values/waardes Answer ONLY: 1 mark. SLEGS antwoord: 1 punt. (2) 1.1.2 Penalise 1 mark for incorrect rounding off. Penaliseer 1 punt vir  standard form/standaardvorm verkeerde afronding. √  substitution/substitusie √ or/of  -values/waardes If answer left in surd form: 3 marks. Indien antwoord in wortelvorm gelaat: 3 punte. (4) 1.2.1  standard form/standaardvorm  factors/faktore  critical values/kritieke waardes OR/OF [ ]  solution/oplossing OR/OF (4) 𝑥 Note/Let op: 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. Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2015) MATHEMATICS P1/WISKUNDE V1 3 1.2.2   solution/oplossing (2) 1.2.3 { }  4 values/waardes  7 values/waardes If/As 𝑥 , 1 mark/punt. (2) 1.3.1 Answer ONLY: 1 mark.  squaring/kwadrering ( ) SLEGS antwoord: 1 punt.  simplification/vereenvoudiging  answer/antwoord (3) If answer = 8: 2 marks./As antwoord = 8: 2 punte. Used/gebruik 𝑚 𝑚 If answer = 10: 1 mark./As antwoord = 10: 1 punt 1.3.2 ( )( )  factors/faktore  answer/antwoord (2) If no factors shown but correct answer: 0 marks. As geen faktore maar regte antwoord: 0 punte. [19] Copyright reserved Please turn over

Downloaded from hlayiso.com 4 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) QUESTION 2/VRAAG 2 2.1.1 √ √ √ √ √  √ √ √ √  √ √ Answer ONLY: 0 marks. SLEGS antwoord: 0 punte.  answer/antwoord OR/OF √ √ √ ( ) ( )  [ ]   answer/antwoord (3) 2.1.2 [ ] √ [ ]  and/en [ ] OR/OF  rule/reël  rule/reël  answer/antwoord (4) 2.2    answer/antwoord (3) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2015) MATHEMATICS P1/WISKUNDE V1 5 2.3      OR/OF Answer ONLY: 0 marks. SLEGS antwoord: 0 punte. If/As then/dan      (5) [15] Copyright reserved Please turn over

Downloaded from hlayiso.com 6 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) QUESTION 3/VRAAG 3 3.1  /  substitution/substitusie  standard form/standaardvorm  factors/faktore or/of or/of  -values /-waardes or/of or/of  -values/-waardes (6) 3.2.1  method/metode Roots are rational and unequal Wortels is rasionaal en ongelyk  rational AND unequal/ rasionaal EN ongelyk No mark for answer if no method is shown. Geen punt vir antwoord as geen metode aangedui word nie. If candidate includes “non-real”: max 1 mark. As kandidaat “nie-reëel’ insluit: maks 1 punt. (2) 3.2.2  No mark for answer if no method is shown. Geen punt vir antwoord as geen metode aangedui word nie. No marks if contradictions are given, e.g. unequal. Geen punt as teenstrydighede genoem word nie, bv. ongelyk. Roots are nonreal/Wortels is nie-reëel.  answer/antwoord (2) 3.3  substitution/substitusie For non-real solution/ Vir nie-reële wortels:  statement/stelling ( √ )( √ )  critical values/kritieke waardes  answer/antwoord √ √ (4) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2015) MATHEMATICS P1/WISKUNDE V1 7 QUESTION 4/VRAAG 4 4.1  ; (1) 4.2   OR/OF   substitution/substitusie (2) 4.3 OR/OF  substitution/substitusie  answer/antwoord (2) 4.4  substitution/substitusie  answer/antwoord OR/OF Answer ONLY: 1 mark. SLEGS antwoord: 1 punt.  expansion/uitbreiding  answer/antwoord (2) [7] Copyright reserved Please turn over

Downloaded from hlayiso.com 8 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) QUESTION 5/VRAAG 5 5.1.1 2  answer/antwoord (1) 5.1.2  -value/waarde  -value/waarde  -value/waarde  answer/antwoord OR/OF Answer ONLY: 3 marks. SLEGS antwoord: 3 punte.  -value/waarde  -value/waarde  -value/waarde  answer/antwoord (4) 5.1.3  is also a factor/ is ook ʼn faktor. Factors/faktore: and/en  argument is not prime/nie priem nie. (2) 5.1.4 Units digits/enesyfers:  identify pattern/identifiseer patroon Answer ONLY: 2 marks. Decimal/desimaal SLEGS antwoord: 2 punte.  answer/antwoord Units digit/enesyfer (2) 5.2.1    answer/antwoord (3) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2015) MATHEMATICS P1/WISKUNDE V1 9 5.2.2 If ONLY/Indien SLEGS:  𝑘 𝑘  answer/antwoord 𝑘 4 marks/punte.  If continues and mentions that 𝑘 is uneven: 5 marks. As voortgaan en meld dat 𝑘  answer/antwoord is onewe: 5 punte  choice/keuse (5) [17] If expansion that leads to correct answer: 5 marks. As uitbreiding wat tot korrekte antwoord lei: 5 punte. If ONLY expansion: 2 marks. Indien SLEGS uitbreiding: 2 punte. 1 3 5 7 9 11 13 15 5 -3 -19 -43 -75 -115 -163 -219 2 4 6 8 10 12 14 16 18 20 22 24 26 28 -14 -24 -34 -44 -54 -64 -74 -84 -94 -104 -114 -124 -134 -144 30 32 34 36 38 40 42 44 -154 -164 -174 -184 -194 -204 -214 -224 QUESTION 6/VRAAG 6 6.1  substitution/substitusie  answer/antwoord Wrong formule/verkeerde formule: 0 marks/punte. (2) 6.2  substitution/substitusie ( ) Wrong formule/verkeerde formule: 0 marks/punte.   answer/antwoord If answer given as : 2 marks. Indien antwoord gegee as : 2 punte. (3) 6.3.1   If ONLY/Indien SLEGS: R25 890  answer/antwoord 1 mark/punt. (3) 6.3.2  ( ) Wrong formule/ R26 009,69 Verkeerde formule:  substitution/substitusie 1 mark/punt for/vir 𝑖  answer/antwoord (3) Copyright reserved Please turn over

Downloaded from hlayiso.com 10 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) 6.4 𝑇 𝑇 𝑇  𝑃 𝑃  ( ) [ ( ) ]( )  R14 642,83 ( )  answer/antwoord OR/OF Wrong formule/ verkeerde formule: ( ) 1 mark/punt for/vir 𝑖  ( )  ( ) ( )   ( ) ( )  answer/antwoord OR/OF  [ ( ) ]( )  ( ) ( ) ( )  ( ) ( )  answer/antwoord (5) [16] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2015) MATHEMATICS P1/WISKUNDE V1 11 QUESTION 7/VRAAG 7 7.1  Let/stel Answer ONLY 𝑥 : 2 marks.  simplify/vereenvoudig SLEGS antwoord 𝑥 : 2 punte.  answer/antwoord (3) 7.2 𝑦  -intercept/afsnit  asymptote/asimptoot 𝑔  shape/vorm 𝑦  -intercept/afsnit  -intercept/afsnit 𝑂 𝑥 (5) 7.3  answer/antwoord (1) 7.4  equation/vergelyking  simplify/vereenvoudig  -values/waardes or/of or/of   (5) 7.5   (2) 7.6   (2) [18] Copyright reserved Please turn over

Downloaded from hlayiso.com 12 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) QUESTION 8/VRAAG 8 8.1  substitution/substitusie  simplify/vereenvoudig (2) 8.2   (2) 8.3  answer/antwoord (1) 8.4  substitution/substitusie  answer/antwoord (2) 8.5   (2) [9] QUESTION 9/VRAAG 9 9.1 Let/stel  Do not penalise if not in coordinate form. Moenie penaliseer indien nie in koördinaatvorm nie.  answer/antwoord (2) 9.2  setting up equation/ opstel van vergelyking  substitution/substitusie NOTE/LET WEL: No reference can be made to 9.3/Geen verwysing kan na 9.3 gemaak word nie.  -value/waarde (  simplification/vereenvoudiging (4) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2015) MATHEMATICS P1/WISKUNDE V1 13 9.3  OR/OF ( ) ( ) ( ) ( ) or/of or/of 6,125  ( ) Do not penalise if not in coordinate form. Moenie penaliseer indien nie in koördinaatvorm nie. (2) 9.4 : Let/stel  substitute/vervang  units/eenhede  answer/antwoord (3) 9.5 ;  answer/antwoord (1) 9.6 or/of   (2) [14] QUESTION 10/VRAAG 10 10.1   𝐶𝐴: 𝑏 𝑎   equation/vergelyking 𝐶𝐴: 𝑒 𝑎 𝑑 OR/OF 𝐶𝐴: 𝑓 𝑑    (7) 10.2 at least 2 out of 3/ten minste 2 uit 3)  or/of or/of  answer/antwoord (2) [9] Copyright reserved Please turn over

Downloaded from hlayiso.com 14 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2015) QUESTION 11/VRAAG 11 11.1 For independent events/vir onafhanklike gebeurtenisse: and/en  rule/reëel  substitution/substitusie   -value/waarde  -value/waarde (5) 11.2.1  female failing/vroulik druip)  (2) 11.2.2  pass, given male/slag, gegee manlik)  (2) 11.3 or and  rule/reël of en  0,7 fails both/druip albei)  answer/antwoord OR/OF Answer ONLY: 1 mark. SLEGS antwoord: 1 punt. 𝑀/𝑊 𝐴/𝑅    fails both/druip albei)  answer/antwoord (3) [12] TOTAL/TOTAAL: 150 Copyright reserved Please turn over