Mathematics Grade 12 Paper 1 Eastern Cape Mock 2015 Memo

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR SERTIFIKAAT GRADE/GRAAD 12 SEPTEMBER 2015 MATHEMATICS P1/WISKUNDE V1 MEMORANDUM MARKS/PUNTE: 150 This memorandum consists of 15 pages./ Hierdie memorandum bestaan uit 15 bladsye.

Downloaded from hlayiso.com 2 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 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 ( )( ) ( )( ) or/of  -values/waardes If a candidate removes brackets and factorised incorrectly, maximum 1 mark if both 𝑥-values are correct./ As kandidaat hakies verwyder en verkeerd faktoriseer, maksimum 1 punt indien beide 𝑥-waardes korrek is. (2) 1.1.2 ( )( ) ( )( )  simplification/vereenvoudiging  standard form/standaardvorm √( ) ( )( )  substitution/substitusie ( ) Penalise 1 mark for √ incorrect rounding off./ Penaliseer 1 punt vir or/of verkeerde afronding.  -values/waardes √ If stopped at : max 3 marks √ As stop by : maks 3 punte (5) 1.1.3 (a) The graph should be shifted units upwards / Die  grafiek moet eenhede opwaarts geskuif word.  upwards/opwaarts (2) (b)  answer/antwoord (1) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 3 1.2  ( ) ( )  substitution/substitusie ( )  standard form/standaardvorm If formula is used, award factor’s mark for ( )( ) substitution.  factors/faktore or/of As formule gebruik word,  -values/waardes ken faktore-punt toe vir  -values/waardes or/of substitusie. OR/OF If a candidate makes a mistake and both equations become linear, max. 3 marks. Indien ʼn kandidaat ʼn fout begaan en beide vergelykings word lineêr, maks. 3 punte.  ( ) ( )  substitution/substitusie ( ) ( )  standard form/standaardvorm ( )( )  factors/faktore or/of  -values/waardes  y-values/waardes or/of (6) 1.3 ( )( ) or/of  or/of or/of or/of OR/OF   use of logs/gebruik van logs  (4) Copyright reserved Please turn over

Downloaded from hlayiso.com 4 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 2015) 1.4 ( )( )  factors/faktore  critical values/kritieke waardes  solution/oplossing OR/OF OR/OF 𝑥 Note/Let op: If/As 𝑛 and/en 𝑛 Full marks/volpunte If/As <𝑛< max/maks 2 punte. If/As 𝑛 or/of 𝑛 max/maks 2 marks/punte. If/As 𝑛 or/of 𝑛 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. (4) [24] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 5 QUESTION 2/VRAAG 2 2.1.1 ( )  ( )( ) Answer ONLY: 3 marks  substitution/substitusie SLEGS antwoord: 3 punte  answer/antwoord (3) 2.1.2 ( ) ( )( )  substitution/substitusie  answer/antwoord If a candidate expands series but gives incorrect answer: 0 marks/ OR/OF Indien ’n kandidaat reeks uitbrei, maar gee verkeerde antwoord: 0 punte Answer ONLY: 2 marks  substitution/substitusie SLEGS antwoord: 2 punte  answer/antwoord (2) 2.2 BOTH answers ONLY:  ( ) 4 marks SLEGS ALBEI antwoorde:  standard form/standaardvorm ( )( ) 4 punte  factors/faktore or/of  answers/antwoorde ONE answer ONLY: 1 mark SLEGS EEN antwoord: 1 punt (4) 2.3.1  < <  < < < < < <  answer/antwoord (3) 2.3.2 Wrong formula/verkeerde formule 0 marks/punte  substitution/substitusie  simplification/vereenvoudiging  answer/antwoord or/of or/of OR/OF  substitution/substitusie ( )  simplification/vereenvoudiging or/of or/of  answer/antwoord (3) Copyright reserved Please turn over

Downloaded from hlayiso.com 6 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 2015) 2.4   ( )  common factor/gemene factor ( )  substitution/substitusie Answer ONLY: 1 mark SLEGS antwoord: 1 punt  answer/antwoord (5) [20] QUESTION 3/VRAAG 3 3.1  common 2nd difference/gemene tweede verskil  -value/waarde ( )  -value/waarde  -value/waarde OR/OF ( ) ( ) ( ) ( ) ( )  method/metode ( ) ( )  -value/waarde ( )  -value/waarde Answer ONLY: 4 marks SLEGS antwoord: 4 punte  -value/waarde (4) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 7 3.2 ( ) ( )  Fifth term in Row 20/Vyfde term in Ry 20:  method/metode If 𝑛 , answer = : 1 mark  answer/antwoord OR/OF As 𝑛 , antwoord = : 1 punt Ry 1 3 Ry 2 6 9 Ry 3 12 15 18 Ry 4 21 24 27 30 Ry 5 33 36 39 42 45 Ry 6 48 51 54 57 60 63 Ry 7 66 69 72 75 78 81 84 Terms in 5th column/terme in 5de kolom  method/metode  ( ) ( )+33  answer/antwoord If 𝑛 , answer = : 1 mark As 𝑛 , antwoord = : 1 punt (3) [7] Copyright reserved Please turn over

Downloaded from hlayiso.com 8 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 2015) QUESTION 4/VRAAG 4 4.1.1 [( ) ]  ( )  ( )  in [( ) ] If used present value formula: max 2 marks  As huidige waarde formule gebruik: maks 2 punte  answer/antwoord OR/OF [( ) ]  ( )  ( )  in If ONLY compound formula or ONLY future value [( ) ] formula used: max 3 marks  Indien SLEGS saamgestelde formule of SLEGS toekomstige waarde formule gebruik: maks 3 punte  answer/antwoord (5) 4.1.2  ( ) Wrong formula/ Verkeerde formule  substitution/substitusie 0 marks/punte  answer/antwoord or/of (3) 4.2.1 [ ( ) ]  ( )  ( )  If/Indien: If used present value formula: [ ( ) ] 𝑥[ ( ) ] max 2 marks  As huidige waarde formule gebruik: maks 2 punte  answer/antwoord 𝑥 𝑅 4 marks/punte (5) 4.2.2  substitution/substitusie ( ) Wrong formula: 0 marks Verkeerde formule: 0 punte  answer/antwoord OR/OF ( )  substitution/substitusie  answer/antwoord (2) [15] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 9 QUESTION 5/VRAAG 5 5.1 ( ) ( ) Answer ONLY: 2 marks SLEGS antwoord: 2 punte ( )  swop and /ruil en om or/of or/of  answer/antwoord or/of (2) 5.2  answer/antwoord (1) 5.3 ( ) √ ( ) √  ( ) √ ( )  Answer ONLY: 1 mark  answer/antwoord SLEGS antwoord: 1 punt OR/OF ( ) √ ( ) √  ( ) √ √ ( )   answer/antwoord (3) 5.4 ( )  ( ) range/terrein  (2) 5.5  ( )  (2) Copyright reserved Please turn over

Downloaded from hlayiso.com 10 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 2015) 5.6 ( )   ( )  substitute/vervang ( )  ( ) (4) 5.7  answer/antwoord (1) [15] QUESTION 6/VRAAG 6 6.1 ( )  answer/antwoord (1) 6.2 ( )  ( ) ( )( )  factors/faktore or/of –  -values/waardes (3) 6.3 ( )  ( ) OR/OF ( ) OR/OF ( ) ( ) ( ) ( ) –  – ( ) (2) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 11 6.4 𝑦  intercepts/asse 𝑥  turning point/draaipunt (2) 6.5 ( )  ( )  ( )  ( ) ( ) ( ) –  ( ) (4) 6.6 ( ) and/en ( )  ( ) ( ) or/of ( )  substitution/substitusie ( ) ( ) ( ) or/of ( )  answer/antwoord OR/OF ( ) ( ) or/of ( ) ( ( )) ( ) ( ) ( ) (3) 6.7 translates 2 units left and 3 down/  transleer 2 eenhede links en 3 af  / ( ) ( )  answer/antwoord (3) [18] Copyright reserved Please turn over

Downloaded from hlayiso.com 12 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 2015) QUESTION 7/VRAAG 7 7.1 ( ) ( ) ( )  substitute/vervang ( ) ( ) ( ) ( )  formula/formule ( ) Penalise 1 mark for incorrect use of ( ) formula. Must show 𝑓 (𝑥) Penaliseer 1 punt vir verkeerde gebruik van formule. Moet 𝑓 (𝑥) toon.  simplification/vereenvoudiging ( )  common factor/gemene faktor ( )  answer/antwoord Answer ONLY: 0 marks (5) SLEGS antwoord: 0 punte 7.2.1 Penalise 1 mark for incorrect  answer/antwoord notation in 7.2. Penaliseer 1 punt vir (1) verkeerde notasie in 7.2. 7.2.2 √   answer/antwoord (2) 7.2.3 ( ) ( )  substitute/vervang   answer/antwoord (3) 7.3 ( ) ( ) ( ) ( )  ( ) ( )  ( ) ( ) ( ) ( )  answer/antwoord (3) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 13 QUESTION 8/VRAAG 8 8.1 ( )  answer/antwoord ( )( )( ) (1) 8.2 ( )  ( )  ( ) ( )( )  factors/faktore ( ) or/of ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )  ( )  ( ) ( ) and/en ( ) (5) 8.3 ( )  ( ) or/of or/of  answer/antwoord (2) 8.4 Maximum where/maksimum waar ( ) at/by  ( ) ( ) ( ) ( ) or/of  or/of ( ) or/of ( ) (2) 8.5 or/of or/of    (3) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com 14 MATHEMATICS P1/WISKUNDE V1 (EC/SEPTEMBER 2015) QUESTION 9/VRAAG 9 9.1 ( )  answer/antwoord (1) 9.2 ( )   and method/en metode (2) 9.3  ( )  factors/faktore or/of  -values/waardes ( ) ( ) square units/vierkante eenhede  area/oppervlakte (4) [7] QUESTION 10/VRAAG 10 10.1.1 ( ) ( / ) ( ) ( )  answer/antwoord (1) 10.1.2 Mutually exclusive events/onderling uitsluitende gebeurtenisse: ( / ) ( ) ( )  rule/reël  answer/antwoord (2) 10.1.3 Independent events/onafhanklike gebeurtenisse: ( / ) ( ) ( )  rule/reël or/of 0,19  answer/antwoord (2) Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/SEPTEMBER 2015) MATHEMATICS P1/WISKUNDE V1 15 10.2.1  first branch/eerste vertakking 𝑊 𝐵𝑊  second branch from /tweede vertakking uit 𝐵  second branch from /tweede vertakking uit 𝑅 𝐵𝑅  outcomes/uitkomste If probabilities not listed, 𝑊 𝐺𝑊 maximum 1 mark Indien waarskynlikhede nie 𝐺 gelys is nie, maksimum 1 punt 𝑅 𝐺𝑅 (4) 10.2.2 ( ) ( ) ( ) ( )( ) ( )( )  ( )( )  ( )( )  answer/antwoord (3) [12] QUESTION 11/VRAAG 11 11.1 (codes/kodes)    answer/antwoord (3) 11.2 (syfers ongelyke ewe getalle/digits unequal even numbers)  (syfers ongelyke ewe getalle/digits unequal even numbers) or/of  answer/antwoord OR/OF (syfers ongelyke ewe getalle/ digits unequal even  numbers) or/of  answer/antwoord (2) [5] TOTAL/TOTAAL: 150 Copyright reserved Please turn over