Samenvatting Overzicht Wiskunde en Systeemanalyse

Wiskunde en Systeemanalyse
06-09-2018 hoorcollege

www.dwo.nl/ho/en/student

fraction = break
3 = numerator
4 = denominator
Power = macht
Square root = wortel
Domein = alle waarden van x
Bereik (Range) = alle waarden van y




q
Ap/q = (Ap)1/q of (A1/q)p= √ Ap

log 25
125x = 25 = =x
log 125
.√ a∗√ b= √ a∗b
a a 12 1 /2 1 12 √ a∗1 √ a
√ =
b b ()
a = √ a2
¿a ∗
b() = =
√b √b

, a2 + a2 = 2a2

voorbeelden:
‘√ 98=√ 2∗√ 49=7 √ 2
3 1
2 2∗5 10 √ 10 1
‘ 2 = 3 2∗5∗5 = √ 50 = 1 √
√ √ √
‘
5
=
5∗5
=
25
=
5
= √ 10
5 √ √
3

5 5∗5∗5 5
3
5
50. → die5=(5∗5∗5) 3




Expand brackets:


Decompose in factors:



(a + b)2 = a2+ 2ab + b2
(a – b) = a2-2ab + b2
(a + b)(a - b) = a2 – b2

A C = AD CB AD +CB
+ + = A2=C → A=√ C∨−√ C
B D BD DB DB

A
∗C
B
=
AC A2=B2 → A=B∨ A=−B
D BD

A A
/C ∗D
‘B B
=
D C

Abc-formule:
Bij ax2 + bx + c = 0
−b ± √ b2−4 ac
‘ x= D = discriminant = b 2−4 ac
2a

Bij intersection de discriminant berekenen  D < 0 geen intersect, D > 0 2 intersect punten D = 0 1
intersect punt

Of
Y = ax2 + bx +c  Y = a(x-xt)2 + yt

Som-product methode Transformaties
X2-6x+5 = 0 omhoog: y = x2 + 2
(x-5)(x-6) = 0 omlaag: y = x2 - 2
X=5vx=6 links: y = (x+2)2
Rechts: y = (x-2)2
Multiplication: y= 2x2