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samenvatting Wiskunde A
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volledige samenvatting van het vak
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Samenvatting WiskundeInhoud
Hoofdstuk 1: getallenkennis...................................................................................................................2
Functies van getallen..........................................................................................................................2
Talstelsels...........................................................................................................................................2
Getalverzamelingen............................................................................................................................3
Breuken..............................................................................................................................................4
Kommagetallen..................................................................................................................................5
Procenten...........................................................................................................................................5
Veelvouden en delers.........................................................................................................................5
Bewerkingen...........................................................................................................................................6
Basisbegrippen...................................................................................................................................6
Volgorde van de bewerkingen............................................................................................................6
Eigenschappen van bewerkingen.......................................................................................................7
Hoofdrekenen.....................................................................................................................................7
Cijferen...............................................................................................................................................8
Controlestrategieën............................................................................................................................9
Meetkunde.............................................................................................................................................9
Basisbegrippen...................................................................................................................................9
Vormleer...........................................................................................................................................10
Meetkundige relaties........................................................................................................................12
Ruimtelijke oriëntatie.......................................................................................................................13
meten en metend rekenen...................................................................................................................15
basisbegrippen.................................................................................................................................15
Grootheden en eenheden................................................................................................................16
Formules...........................................................................................................................................17
Samengestelde grootheden..............................................................................................................17
Toepassingen....................................................................................................................................18
Geïntegreerde oefeningen...................................................................................................................19
heuristieken......................................................................................................................................19
Tabellen en grafieken.......................................................................................................................19
Patronen...........................................................................................................................................20
Ongelijke verdeling en mengsels......................................................................................................20
1
, Telproblemen...................................................................................................................................20
kansrekenen.....................................................................................................................................20
Hoofdstuk 1: getallenkennis
Functies van getallen
Getal als hoeveelheid
o Aantal
o Kardinale getallen
Getal als rangorde
o Volgorde
o Ordinale getallen of rangtelwoorden
Getal als code
o Unieke combinatie
Getal als verhouding
o Als breuk of procent
o Geen absolute hoeveelheid
o Maatgetal
Talstelsels
Wiskundig systeem om getallen voor te stellen
Additief systeem
o Op tellen
o Egyptisch talstelsel -> hiërogliefen
o Romeinse cijfers
Positioneel stelsel
o plaats bepaald de waarde
grondtal of basis
o Babylonische symbolen
o Maya’s
10-delig talstelsel
Grondtal 10
Waarde is afhankelijk van de positie in het getal
Andere talstelsels
binaire of tweetallig talstelsel
o grondtal 2
octale
o grondtal 8
hexadecimale
o grondtal 16
o 0-9 & A-F
2
, Romeinse talstelsel
o I, X, C en M max 3x na elkaar
o Hogere waarde voor lagere waarde = optellen
o Lagere waarde voor hogere waarde = aftrekken
o I = 1, V = 5, X = 10, C = 100, L = 50, M = 1000, D = 500
Getalverzamelingen
Natuurlijke getallen
Positief getal > 0
Strikt positief getal ≥ 0
N
Gehele getallen
N + de negatieve getallen
Z < zahlen
Rati onale getallen
Z + breuken
Q
3 representaties
o Breuk, kommagetal en percentage
Begrensd kommagetal = eindig aantal decimale
o Repeterend kommagetal
Eindig aantal decimalen die zich herhalen
o Zuiver repeterend kommagetal
Periode begint na komma
o Gemengd repeterend kommagetal
Niet repeterend deel na kommagetal
Reële getallen
Kommagetallen met oneindig veel en niet-repeterende decimalen
R
Imaginaire getallen = complexe getallen C
3
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