Volledige samevatting van die konteks van Graad 12 Wiskunde op hoërvlak (skoon wiskunde). Hierdie dokument voldoen aan die vereistes soos uiteengesit in die SAGS deur IEB en DBE. Behels die hele jaar se werk rakende Meetkunde en Algebra , is goeie voorbereiding vir VRAESTEL 1 & VRAESTEL 2.
Egte breuke (breuke Egte breuke (breuke
wat lê tussen -1 en 1 wat lê tussen -1 en 1
d.w.s teller < noemer) d.w.s teller < noemer)
Onegte breuke Onegte breuke
(waardes minder as (waardes minder as
-1 of groter as 1) -1 of groter as 1)
Rasionale en irrasionale getalle:
RASIONALE GETALLE – enige getal wat as ‘n breuk geskryf kan
word d.w.s ‘n of waar A & B ∈ Z ; B ≠ 0
ℎ𝑒𝑒𝑙𝑔𝑒𝑡𝑎𝑙 𝐴
ℎ𝑒𝑒𝑙𝑔𝑒𝑡𝑎𝑙 𝐵
Alle heelgetalle
Alle breuke
Alle eindigende desimale breuke
Alle repeterende desimale breuke
IRRASIONALE GETALLE- Kan slegs in ‘n getalvorm met
oneindigende, nie-repeterende syfers na die desimale komma
geskryf word, die getalle kan NIE AS ‘N BREUK geskryf word NIE
• Alle nie-eindigende , nie-repeterende desimale getalle
• Pi (π)
• √𝑃𝑜𝑠𝑖𝑡𝑖𝑒𝑤𝑒 𝑛𝑖𝑒 − 𝑣𝑖𝑒𝑟𝑘𝑎𝑛𝑡
3
• √𝑃𝑜𝑠𝑖𝑡𝑖𝑒𝑤𝑒 𝑛𝑖𝑒 − 𝑘𝑢𝑏𝑖𝑒𝑘𝑒
2
, Reële en nie-reële getalle:
REËLE GETALLE – Die getalle lyn bestaan uit al die Rasionale (Q) en
Irrasionale (Q’) getalle wat saam die versameling Reële (ℝ) getalle
vorm
NIE-REËLE GETALLE - √−25 is ‘n voorbeeld van ‘n nie-reële getal.
Daar is geen getal wat, as dit gekwadreer word, gelyk sal wees
aan -25 nie. √−25 bestaan nie op die getalle lyn nie. Die reële en nie-
reële getalle vorm gesamentlik die komplekse getalle.
Bodmas / HVDVOA
B Brackets () H Hakkies ()
0 Of / Orders √x x²
V Van
D Division ÷
D Deling ÷
M Multiplication x V Vermenigvuldiging x
A Addition + O Optel +
S Subtraction -
A Aftrek -
3
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