1. Die vraestel bestaan uit 5 vrae. Beantwoord alle vrae. 3. n Goedgekeurde sakrekenaar mag gebruik word.
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1 CAMI Education (Pty) Ltd Reg. No. 1996/017609/07 CAMI House Fir Drive, Northcliff P.O. Box 1260 CRESTA, 2118 Tel: +27 (11) Fax : web: info@camiweb.com GRAAD 12 WISKUNDIGE GELETTERDHEID VRAESTEL 2 NOVEMBER 2011 TOTAAL: 150 TYD: 3 UUR INSTRUKSIES 1. Die vraestel bestaan uit 5 vrae. Beantwoord alle vrae. 2. Nommer antwoorde korrek volgens die vrae. 3. n Goedgekeurde sakrekenaar mag gebruik word. 4. Alle berekeninge moet aangetoon word. 5. Alle finale antwoorde moet afgerond word tot twee desimale plekke, tensy anders vermeld. 6. Alle eenhede moet aangedui word in die antwoorde.
2 VRAAG 1: Twee vriende is au pairs maar verdien verskillende pakkette as betaling. Pakket A Basiese loon R400 per week 40 uur per week R20 per uur vir addisionele ure Pakket B Basiese loon R300 per week 30 uur per week R25 per uur vir addisionele ure Bereken die normale loon per uur vir beide persone Bereken die loon as beide dames 5 addisionele ure per week werk Teken die grafieke op dieselfde rooster wat die verskillende lone sal aandui tot 55 uur per week Definieer die konsep gelykbreekpunt Bepaal die aantal ure wat beide dames moet werk om dieselfde aantal geld te verdien per week. 1.2 n Mediese dokter, Dr Bones, verdien n bruto salaris van R93 287,26 per maand. Bereken die maandelikse aftrekking in die gegewe tabel Maandelikse aftrekkings Bedrag Huislening R PAYE (Tax) (Bruto salaris R6500) x 35% Mediese fonds R3 800 Assuransie R2 870 Pensioen fonds 7% van Bruto Salaris n Motor paaiement mag nie meer as 30% van n persoon se bruto salaris wees nie. Bereken die bedrag wat Dr Bones toegelaat sal word om op n motor af te betaal Dr Bones wil graag n nuwe BMW vir R % saamgestelde rente word maandeliks gehef oor n tydperk van 5 jaar. Wat sal die paaiement op die BMW wees? Formule: Pi x = [ 1 ( 1 + i) n ]
3 1.2.4 Sal die lening deur die bank goedgekeur word? Gee n rede. [30] VRAAG 2: 2.1 n Skrynwerker,Woody, koop n vel hout met afmetings, 3 m by 2 m. Hy wil ronde tafeltjies uit die stuk hout maak waarvan die radius 0,5 m is. Slegs die blaaie word uit die vel hout gesny Hoeveel tafelblaaie kan Woody uit die vel hout sny? Die vel hout kos R930. Bereken die koste van elke tafelblad as die afval stukkies hout buite berekening gebring word. (3) Bereken die omtrek van n tafelblad. Formule: Omtrek = 2 π radius, waar π = 3, Elke tafelblad moet n afwerking kry en die koste is R3,78 per meter. Bereken die koste om al die tafelblaaie af te werk Elke tafel sal drie pote kry. Die koste per tafelpoot is R23,55. Bereken die totale koste om een tafeltjie te maak Woody wil 20% wins op elke tafel maak. Bereken die verkoopprys van so n tafeltjie. (3) 2.2 n Groente boer, Mnr Vegg, bou n dam op sy plaas sodat water opgegaar kan word vir besproeiing. Gebruik onderstaande diagram wat die dam voorstel om die vrae te beantwoord Bereken die kapasiteit van die dam.. (3) Formule: Volume = π r 2 h, waar π = 3, Hoeveel liters water kan die dam hou indien 1000 liter = 1 m 3? Die eerste liters water is elke maand verniet. Addisionele water kos daarna R0,65 per liter. Bereken die koste om die dam te vul met
4 water tot sy volle kapasiteit Om te voorkom dat alge op die bodem van die dam begin groei, moet die bodem met n swart emulsie bedek word Bereken die oppervlakte van die dam se bodem. Formule: Oppervlakte = π r 2, waar π = 3, Die swart emulsie kan gekoop word in 5 liter houers. As een houers 15 m 2 kan bedek, bereken die aantal houers wat benodig sal word om die bodem daarmee te bedek Die koste van n 5 liter houer is R340. Hoeveel sal Mnr Vegg moet betaal vir die emulsie? Die verwer ontvang n loon van R65 per uur. Dit neem hom 3h40 om die bodem te verf met die swart emulsie. Bereken sy totale loon vir die werkie. (3) Formule: Loon = (R65 aantal ure gewerk) + (R65 60 x minute) 2.5 Na n maand begin die dam se wal lek teen n tempo van 20 liters water per uur. Mnr Vegg ontdek die lekkasie na 48 uur Hoeveel liters water het uitgelek? Hoeveel sal die Mnr Vegg kos om die dam weer heeltemal vol te maak? 2.6 Nadat die lekkasie reggemaak is begin die verwer die buitekant van die dam verf. Bereken die totale buite oppervlakte wat geverf moet word. Formule: Area = 2π r h, waar π = 3, Die normale temperatuur van die water is 23 0 C. Herlei Celsius na Fahrenheit. (3) 9 Formule: F = C [49] VRAAG 3: 3.1 Die inkomste en uitgawe vir Febr 2010 van Maatskappy X is in n tabel saamgevat. Uitgawes 02/2010 Inkomste 02/2010 Huurgeld R Handel rekening R Skryfbehoeftes R4 400 Rente op beleggings R Herstelwerk R Advertensie R Assuransie R Salarisse R
5 Lone R Verbruikbare R5 500 goedere Telefoon R Brandstof R Gebruik die gegewe tabel om die wins vir Febr 2010 te bereken. (3) Formule: Wins = Inkomste - Uitgawe Bereken die persentasie wins Febr Formule: Vanaf 1 Maart sal daar bepaalde verhogings wees Bereken die nuwe bedrag vir huurgeld as die huur verhoog met 3% Die personeel het n salaris verhoging van 3,6% ontvang. Bereken die uitgawe vir die maatskappy ten op sigte van die nuwe salarisse Die brandstof prys verhoog met 5%. Bereken die brandstof uitgawe Indien die ander uitgawes en inkomste dieselfde bly vir Maart, bepaal of die maatskappy genoeg geld sal ontvang om die verhoogde uitgawes te dek Identifiseer twee uitgawes wat aangespreek kan word om die uitgawes te verminder. Motiveer. [21] VRAAG 4: 4.1 Vergelyk die distribusie van data van die gemiddelde aantal leerders per gekwalifiseerde onderwyser in twee verskillende provinsies in Suid Afrika. Provinsie A: Provinsie B: Bereken die gemiddeld vir elke provinsie Maak n afleiding uit bogenoemde gemiddeldes. (3) Watter waarde(s) in Provinsie A sal die gemiddeld beïnvloed? Bereken die omvang van elke provinsie.
6 4.2 n Grafiek is opgestel om die elektrisiteits rekeninge van Mnr Spark voor te stel. Gebruik die grafiek om die vrae te beantwoord Die koste van elektrisiteit gedurende 2010 is opgeteken in die tabel: Jan Febr Mrt Apr Mei Jun Jul Aug Sept Okt Nov Des R150 R250 - R300 R350 R350 R500 R350 R300 R300 R250 R150 Voeg hierdie inligting by op die gegewe grafiek (8) Gee n moontlike rede waarom die rekening R550 was gedurende Julie Gee n moontlike rede waarom daar geen rekening in Maart was nie As Mnr Spark dieselfde hoeveelheid krag elke maand gebruik, bereken hoeveel die krag hom in Desember 2011 sal kos as die elektrisiteit met 5% toeneem. (3)
7 4.3 Die veranderinge in brandstof pryse is opgeteken in die onderstaande tabel. Tydperk is April 2010 tot April Tydens watter maande het die brandstof prys afgeneem? As die brandstof prys R9,40 per liter in Maart 2011 was, wat was die prys in Desember 2010? Wat is die verskil in brandstof pryse per liter in April 2010 in vergelyking met April 2011? Gedurende watter maand was die brandstof prys die laagste? Noem 2 faktore wat n invloed het op die brandstof prys. [38] VRAAG 5: 5.1 In n restaurant kan mense hul eie spyskaart saamstel. Die keuses kan gemaak word uit die volgende: VLEIS: Hoender (Ch) of Lam(La) GROENTE: Wortels (Ca) of Groenbone(Gb) SLAAIE: Gemengde slaai (Mi) of Aartappelslaai(Po)
8 5.1.1 Voltooi die boom diagram om die moontlike kombinasies aan te dui. (8) As die kombuis se voorraad van aartappelslaai op is, bepaal die waarskynlikheid (in desimale vorm) dat die geregte die volgende sal bevat: Hoender, groenbone en gemengde slaai of Lam, groen bone en gemengde slaai. [12] TOTAAL: 150
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