Een duidelijke samenvatting van alles wat je moet weten voor de Landelijke kennistoets wiskunde. De samenvatting is gebaseerd op, op de oefentoets op 10voordeleraar, oefentoetsen op Brightspace en mijn aantekeningen.
Landelijke kennistoets formule overzicht
Inhoud
Functies..................................................................................................................................................2
Algemeen............................................................................................................................................2
Goniometrie.......................................................................................................................................2
Logaritmes..........................................................................................................................................4
Inverse functies...................................................................................................................................5
Exponentiële functies.........................................................................................................................5
Dynamische modellen............................................................................................................................6
Statistiek en Combinatoriek....................................................................................................................7
Statistiek.............................................................................................................................................7
Combinatoriek....................................................................................................................................7
Analytische meetkunde..........................................................................................................................9
Integreren.............................................................................................................................................10
Getallen................................................................................................................................................11
Getaltheorie.....................................................................................................................................11
Complexe getallen............................................................................................................................12
Aanschouwelijke meetkunde................................................................................................................13
Synthetische meetkunde......................................................................................................................14
Kansverdelingen...................................................................................................................................15
Differentiëren.......................................................................................................................................16
Problemen en Bewijzen........................................................................................................................17
Matrices en Grafen...............................................................................................................................18
,Functies
Algemeen
Functies met de bijbehorende inverse, afgeleide en primitieve
Functie f (x) Inverse f −1 (x) Afgeleide f ’ ( x ) Primitieve ∫ f ( x ) dx
1 −¿ 0 x +c
x x 1 1 2
x +c
2
x2 √x 2x 1 3
x +c
3
√x x2 1 2 2
3
x +c
2√ x 3
1 1 −1 ln ( x ) +1
x x x2
xn 1
n x n−1 nn +1
xn +c
n+1
e
x
ln ( x ) e
x x
e +c
a
x
ln ( x ) x
a ln ( a ) ax
+c
ln ( a ) ln ( a )
ln ( x ) ex 1 xln ( x ) +c
x
sin ( x ) arcsin ( x ) oftewel sin−1 ( x ) cos ( x ) −cos ( x ) +c
cos ( x ) arccos ( x ) oftewel cos−1 ( x ) −sin ( x) sin ( x ) +c
tan ( x ) arctan (x) ofterwel tan −1 (x ) 1+ tan 2 (x) −ln|cos ( x )|+ c
arcsin ( x ) sin ( x) 1 −¿
√1−x2
arccos ( x ) cos ( x ) −1 −¿
√1−x 2
arctan (x) tan ( x ) 1 −¿
1+ x2
f ( g ( x )) g
−1
( f −1 ( x ) ) f ( g ( x )) g ( x )
' '
−¿
f ( x ) + g(x ) −¿ ' '
f ( x )+ g ( x ) ∫ f ( x ) dx +∫ g ( x ) dx
Het vinden van oplossingen van vergelijkingen met absoluut tekens
Goniometrie
De periode van een trigonometrische functie bepalen:
2π
Er geldt altijd: periode=
|a|
o Hierbij is a het getal voor de variabele. Dit is bruikbaar voor zowel de sinus als voor
de cosinus
, Als het een samengestelde functie is ga je opzoek naar de KGV (kleinste gemeenschappelijke
veelvoud)
o Dit doe je door ze los van elkaar te berekenen en dan de KGV te vinden.
Exacte waardentabel voor de sinus, cosinus en de tangens
sin ( x )=sin ( x +2 π ) =sin ( π −x)
−sin ( x )=sin ( x + π )=sin (−x)
(
sin ( x )=cos π−x
1
2 )
sin ( 2 x ) =2 sin ( x ) cos ( x )
2 2
sin ( x )=1−cos ( x)
o Komt uit deze cos 2 ( x ) +sin2 ( x )=1
Rekenregels cosinus formules
cos ( x )=cos ( x+ 2 π )=cos (−x )
−cos ( x )=cos ( x+ π )=cos ( x−π )
( 1
) (
cos ( x )=sin π−x =sin π + x
2
1
2 )
2 2 2
cos ( 2 x )=2 cos ( x )−1=1−2sin ( x )=cos ( x ) −sin ( x )
cos 2 ( x )=1−sin2 ( x)
o Komt uit deze cos 2 ( x ) +sin2 ( x )=1
Rekenregels tangens formules
tan ( x )=tan ( x+ 2 π )=tan ( x+ π )
−tan ( x )=tan (−x )=tan ( π −x )
1
tan ( x )=cot ( π−x )
2
sin ( x )
tan ( x )=
cos (x )
Sinus, cosinus en tangensvergelijkingen oplossen
sin ( x )=sin ( y )
o x= y +2 kπ ∨ x=π − y +2 kπ
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