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Samenvatting Wiskunde A vwo 6 alle examenstof
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Een korte duidelijke samenvatting van de wiskunde A examenstof
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CSE VWO 2021 Wiskunde ADomein A Vaardigheden
Rekenregels machten:
ga ∙ gb = ga+b
( g a) b = gab
ga / gb = ga –b
(g ∙ h)a = ga ∙ ha
g0 =1
-n
g = 1 / gn
gp/n = 𝑛√𝑔^𝑛
Rekenregels logaritmen:
g
log(g) =1
g
log(1) =0
g g
log(a)+ log(b) = glog(ab)
g g
log(a) – log(b) = glog(a/b)
g
P ∙ log(a) = glog(aP)
ln(x) = elog(x)
x
a =G = alog(G) = x
4
3 + log(x) → 4log(43) + 4log(x) → 4log(64x)
1/g
log(a) = – glog(a)
ABC-formule
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
Algebraïsche vaardigheden
A∙B=A∙C A = 0 of B = C
2 2
A =B A = B of A = -B
A/B = C/D A∙D=B∙C
, CSE VWO 2021 Wiskunde A
Domein B1 Algebra
Absolute verandering = Verandering in aantal, hoeveelheid
Relatieve verandering = Verandering in procenten
Breuken:
𝑡𝑒𝑙𝑙𝑒𝑟 𝑑𝑒𝑒𝑙
𝑛𝑜𝑒𝑚𝑒𝑟 𝑔𝑒ℎ𝑒𝑒𝑙
Rekenregels breuken:
𝐴 𝐶 𝐴∙D 𝐶∙B 𝐴D+BC
𝐵
+ 𝐷 = 𝐵∙D + 𝐵 ∙D = 𝐵𝐷
𝐴 𝐶 𝐴𝐶
∙
𝐵 𝐷
= 𝐵𝐷
Percentages:
𝑑𝑒𝑒𝑙
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 = ∙ 100%
𝑔𝑒ℎ𝑒𝑒𝑙
𝑛𝑖𝑒𝑢𝑤−𝑜𝑢𝑑
𝑝𝑟𝑜𝑐𝑒𝑛𝑡𝑢𝑒𝑙𝑒 𝑣𝑒𝑟𝑎𝑛𝑑𝑒𝑟𝑖𝑛𝑔 = 𝑜𝑢𝑑
∙ 100%
Domein B2 Telproblemen
EN = keer
OF = plus
Permutatie = Volgorde doet ertoe
= 5 * 4 * 3 * 2 *1 (5!)
Combinatie = Volgorde doet er NIET toe, het aantal mogelijke combinaties
= nCr -> ( 𝟓𝟐) -> Uit 5 in totaal kies ik 2 mensen
Voorbeeld permutatie:
Een lotnummer bestaat uit 5 cijfers. Elk cijfer mag maximaal 1x in het lot staan.
5*4*3*2*1
10 deelnemers aan een wedstrijd. Hoeveel manieren brons, zilver, goud geven?
Volgorde doet er dus toe: 10 * 9 * 8
Voorbeeld combinatie:
10 leerlingen in de klas, 3 moeten gaan opruimen. De volgorde doet er hier niet toe: ongeacht welke
plek iemand krijgt, hij moet hetzelfde doen als de anderen. -> 10nCr3
5 jongens in de klas en 5 meisjes in de klas. 2 jongens moeten opruimen OF 2 meisjes:
5nCr2 + 5nCr2
5 jongens in de klas en 20 meisjes in de klas. 3 jongens EN 3 meisjes moeten opruimen:
5nCr3 * 20nCr3
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