Graad 12 Wiskunde November Vraestel 1 en Memo:
Totaal: 150 punte.
Hierdie Vraestel dek die volgende werk:
Algebr. | Getalpatrone. | Funksies. | Finansies. | Calculus. | Waarskynlikheid.
Hierdie is 'n oefenvraestel met memorandum bedoel om die leerling se kennis te toets, en sal nie dies...
1.1.1 x 2−9 x +20=0 (3)
1.1.2 x ( x +3 ) −1=0 (korrek tot 2 desimale plekke) (3)
1.1.3 x 2+ 7 x <0 (3)
−5
1.1.4 2 x 3 =64 (4)
1.2 Los gelyktydig x en y op, indien:
2 x− y=8 , and
2 2
x −xy + y =19 (7)
1.3 Los die volgende uitdrukking op sonder die gebruik van ‘n sakrekenaar: (4)
√ 41024 + √ 4 1022
√ 16510
[24]
VRAAG 2
2.1 Die terme p ;(2 p+2);( 5 p+3) vorm ‘n rekenkundige reeks.
Bepaal:
2.1.1 Die waarde van p. (4)
2.1.2 Die reël in die vorm van a n=a+(n−1) d . (2)
2.1.3 Die 15de term van die reeks. (4)
2.2 x ; y ; 81 is ‘n meetkundige reeks .
En y=2 x−5
Al die terme in die reeks is heelgetalle.
Bepaal die waardes van x en y . (10)
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Graad 12 November Vraestel 1
,VRAAG 3
Gegee die reeks: 2; 6; 10; 14; ….
3.1 Watter tipe reeks is dit? Staaf jou antwoord deur ‘n berekening. (2)
3.2 Bereken T 55. (3)
3.3 Wat term het ‘n waarde van 322? (3)
3.4 Bepaal deur ‘n berekening of 1204 ‘n term in die reeks is? (4)
VRAAG 4
−3
Die skets hieronder wys die grafiek van f ( x )= + q. Die asymptote van f sny by B (−1; y ) . Die
x+ p
(
punt D 5 ; 4
1
2)is ‘n punt op die grafiek.
4.1 Bepaal die waarde van p. (1)
4.2 Bewys dat q=5. (2)
4.3 Bereken die x -afsnit van f . (2)
4.4 Bepaal die vergelyking van die vertikale asimptoot van h as h ( x )=f ( x +4) (2)
4.5 Een van die simmetrie-asse van f is ‘n stygende funksie. Bepaal die vergelyking van die
simmetrie-as. (3)
4.6 Gee die waardes van x vir f ( x ) ≥ x +6 . (2)
4.7 Bepaal die vergelyking van g, die refleksie van f in die x -as en skuif twee eenhede regs.(3)
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Graad 12 November Vraestel 1
, VRAAG 5
Die funksies f ( x )=−x2 −2 x +3 en g ( x )=mx+ c word hieronder getoone,
met g wat beweeg deur punte E, C en A. A en B is die x -afsnitte van f , en CD is die simmetrie-as
van f . E is die y -afsnit van g .
5.1 Bepaal die koördinate van C, die draaipunt van grafiek f . (3)
5.2 Bepaal die vergelyking van g. (4)
5.3 Bereken die lengte van CE. (2)
5.4 Bepaal die stel notasies vir f −1 (x). (2)
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Graad 12 November Vraestel 1
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