Summary
Summary Wiskunde Graad 9 (Vandag-handboek)
Hierdie notas is die oorspronklike werk van die Vandag Wiskunde Graad 9 handboek wat slegs deur Skool_Notas opgesom is.
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Graad 9Hierdie is die oorspronklike
werk van die Vandag Graad 9
Wiskunde handboek wat slegs deur
skool_notas opgesom is.
Dit mag nie herverkoop/versprei of
onder n nuwe lisensie verkoop word nie.
, Skool Instagram : @skool_notas
Epos : skoolnotas@icloud.com
Notas
Webtuiste : https://skoolnotas.company.site/
Whatsapp : 081 369 9131
Hierdie notas mag nie herverkoop, gekopieer, versprei of onder ‘n nuwe lisensie verkoop word nie.
Telgetalle ....................................................................................................................................................................................3
Die eienskappe van getalle ........................................................................................................................................... 3
Veelvoude, faktore en priemfaktore ..................................................................................................................... 4
Probleemoplossing ............................................................................................................................................................... 5
Heelgetalle ................................................................................................................................................................................9
Berekeninge met heelgetalle ....................................................................................................................................... 9
Die eienskappe van heelgetalle ............................................................................................................................... 10
Probleemoplossing ...............................................................................................................................................................11
Gewone breuke .................................................................................................................................................................... 12
Berekeninge en probleemoplossing ....................................................................................................................12
Ekwivalensie ...............................................................................................................................................................................13
Desimale breuke ................................................................................................................................................................ 14
Berekeninge .............................................................................................................................................................................. 14
Ekwivalensie en probleemoplossing....................................................................................................................16
Eksponente ............................................................................................................................................................................. 17
Die eksponentwette .............................................................................................................................................................17
Berekeninge en eenvoudige vergelykings ......................................................................................................18
Wetenskaplike notasie .....................................................................................................................................................19
Probleemoplossing ..............................................................................................................................................................19
Patrone ...................................................................................................................................................................................... 20
Numeriese patrone ............................................................................................................................................................20
Meetkundige patrone ......................................................................................................................................................20
Funksies en verwantskappe ...................................................................................................................................... 21
Inset- en uitsetwaardes ...................................................................................................................................................21
Ekwivalente vorme ...............................................................................................................................................................21
Algebraïese uitdrukkings ............................................................................................................................................ 23
Algebraïese taal ....................................................................................................................................................................23
Uitbreiding en vereenvoudiging van algebraïese uitdrukkings ...............................................23
Algebraïese vergelykings ............................................................................................................................................25
Ontleed, interpreteer en stel vergelykings op .......................................................................................... 25
Verskillende metodes om vergelykings op te los ................................................................................... 25
Konstruksies .......................................................................................................................................................................... 28
Lyne, hoeke, spesiale hoeke en driehoeke ................................................................................................... 28
Die Stelling van Pythagoras...................................................................................................................................... 30
Bereken onbekende sye van ’n driehoek ........................................................................................................30
1
, Skool Instagram : @skool_notas
Epos : skoolnotas@icloud.com
Notas
Webtuiste : https://skoolnotas.company.site/
Whatsapp : 081 369 9131
Hierdie notas mag nie herverkoop, gekopieer, versprei of onder ‘n nuwe lisensie verkoop word nie.
Identifiseer reghoekige driehoeke ........................................................................................................................30
Tweedimensionele vorms ............................................................................................................................................ 31
Driehoeke .....................................................................................................................................................................................31
Vierhoeke ......................................................................................................................................................................................31
Gelykvormige en kongruente driehoeke .........................................................................................................33
Reguit lyne ............................................................................................................................................................................. 34
Verwantskappe tussen hoeke ................................................................................................................................. 34
Probleemoplossing ............................................................................................................................................................ 34
Omtrek en oppervlakte ................................................................................................................................................35
Omtrek en oppervlakte van veelhoeke ........................................................................................................... 35
Omtrek en oppervlakte van ’n sirkel ...................................................................................................................36
Funksies en verwantskappe ..................................................................................................................................... 37
Ekwivalente vorme ..............................................................................................................................................................37
Algebraïese uitdrukkings ............................................................................................................................................ 38
Uitbreidings en vereenvoudiging van uitdrukkings ............................................................................ 38
Algebraïese vergelykings ............................................................................................................................................ 41
Los vergelykings op ........................................................................................................................................................... 41
Grafieke.................................................................................................................................................................................... 42
Interpreteer en ondersoek grafieke ................................................................................................................... 42
Teken grafieke en bepaal die vergelykings van grafieke ............................................................... 43
Volume kapasiteit en buite-oppervlak ........................................................................................................... 44
Buite-oppervlakke van kubusse, prismas en silinders ...................................................................... 44
Volumes van kubusse, prismas en silinders ............................................................................................... 45
Transformasie-meetkunde ....................................................................................................................................... 46
Transformasies in ’n koördinaatvlak ................................................................................................................. 46
Vergrotings en verkleinings ....................................................................................................................................... 46
Driedimensionele voorwerpe .................................................................................................................................. 48
Klassifisering van driedimensionele vorms ................................................................................................. 48
Datahantering .................................................................................................................................................................... 49
Versamel, organiseer en som data op ............................................................................................................ 49
Stel data voor ......................................................................................................................................................................... 50
Ontleed, interpreteer en doen verslag oor data .................................................................................... 52
Waarskynlikheid ................................................................................................................................................................ 54
Waarskynlikheid, frekwensie en relatiewe frekwensie ........................................................................ 54
Waarskynlikhede van saamgestelde gebeurtenisse .......................................................................... 54
2
, Skool Instagram : @skool_notas
Epos : skoolnotas@icloud.com
Notas
Webtuiste : https://skoolnotas.company.site/
Whatsapp : 081 369 9131
Hierdie notas mag nie herverkoop, gekopieer, versprei of onder ‘n nuwe lisensie verkoop word nie.
Natuurlike getalle
→ Natuurlike getalle (N) word gebruik om alledaagse dinge soos appels of boeke te
tel.
→ Natuurlike getalle is 1, 2, 3, 4, 5, 6, 7, 8, 9, ensovoorts.
→ Hier is 3 en 8, twee natuurlike getalle op die getallelyn.
→ Ons wys die twee getalle as kolletjies op die getallelyn, aangesien hulle elk ’n
spesifieke waarde het.
Telgetalle
→ Die groep telgetalle (N0) sluit al die natuurlike getalle in plus die getal 0.
→ Sommige wiskundiges sluit nul by die natuurlike getalle in en gebruik nie
telgetalle as ’n versameling nie.
Heelgetalle
→ Heelgetalle (Z) sluit nul en al die positiewe en negatiewe telgetalle in.
→ Ons gebruik heelgetalle byvoorbeeld om temperature onder vriespunt aan te
toon.
→ Heelgetalle word wiskundig gebruik in berekeninge soos hierdie : 5 - 8.
→ Hierdie berekeninge is in die formaat a - b, waar a < b.
→ Die getallelyn toon vir ons dat 5 - 8 = - 3.
Rasionale getalle
a
→ Rasionale getalle (Q) is getalle wat as breuke geskryf kan word in die vorm ,
b
waar a en b telgetalle is en b ≠ 0.
1
→ Die getal 2 (1 deel uit 2 dele) is ’n rasionale getal.
Irrasionale getalle
→ Irrasionale getalle (Q’) kan nie as ’n heelgetal gedeel deur ’n heelgetal uitgedruk
word nie.
→ ’n Getal kan nie irrasionaal sowel as rasionaal wees nie.
a
→ Irrasionale getalle kan nie in die vorm b geskryf word nie.
→ Hulle is nie-herhalende, nie-eindige desimale getalle.
22
→ Wanneer ons berekeninge met π doen, gebruik ons ’n benaderde waarde, soos 7
of 3.14.
3
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