Formula Booklet AISL
Prior Learning
A=bh
A=21(bh)
A=21(a+b)h
A=πr2
C=2πr
V=lwh
V=πr2h
V=Ah
A=2πrh
d=√(x2−x1)2+(y2−y1)2
(2x1+x2,2y1+y2)
Sequences Series
un=u1+(n−1)d
Sn=2n(2u1+(n−1)d)=2n(u1+un)
un=u1rn−1
Sn=r−1u1(rn−1)=1−ru1(1−rn),r=1
Financial Mathematics
FV=PV(1+100kr)kn
Exponents & Logs
logab=x⟺ax=b, where a>0, b>0, a=1
Approximations Error
ε=∣∣∣∣vEvA−vE∣∣∣∣×100%
Coordinates & Lines
y=mx+c
ax+by+d=0
y−y1=m(x−x1)
m=x2−x1y2−y1
Modelling
x=−2ab
2&3D Geometry
d=√(x2−x1)2+(y2−y1)2+(z2−z1)2
(2x1+x2,2y1+y2,2z1+z2)
V=31Ah
V=31πr2h
A=πrl
V=34πr3
A=4πr2
l=360∘θ⋅2πr
A=360∘θ⋅πr2
Trig IDs
sinAa=sinBb=sinCc
c2=a2+b2−2abcosC
cosC=2aba2+b2−c2
A=21absinC
Descriptive Statistics
IQR=Q3−Q1
xˉ=ni=1∑kfixi
Probability
P(A)=n(U)n(A)
P(A)+P(A′)=1
P(A∪B)=P(A)+P(B)−P(A∩B)
P(A∪B)=P(A)+P(B)
P(A∣B)=P(B)P(A∩B)
P(A∩B)=P(A)P(B)
Distributions & Vars
E(X)=∑xP(X=x)
X∼B(n,p)
E(X)=np
Var(X)=np(1−p)
Differentiation
f(x)=xn⟹f′(x)=nxn−1
Integration
∫xndx=n+1xn+1+C,n=−1
A=∫abydx
∫abydx≈2h(y0+2(y1+⋯+yn−1)+yn)
Prior Learning
A=bh
A=21(bh)
A=21(a+b)h
A=πr2
C=2πr
V=lwh
V=πr2h
V=Ah
A=2πrh
d=√(x2−x1)2+(y2−y1)2
(2x1+x2,2y1+y2)
Sequences Series
un=u1+(n−1)d
Sn=2n(2u1+(n−1)d)=2n(u1+un)
un=u1rn−1
Sn=r−1u1(rn−1)=1−ru1(1−rn),r=1
Financial Mathematics
FV=PV(1+100kr)kn
Exponents & Logs
logab=x⟺ax=b, where a>0, b>0, a=1
Approximations Error
ε=∣∣∣∣vEvA−vE∣∣∣∣×100%
Coordinates & Lines
y=mx+c
ax+by+d=0
y−y1=m(x−x1)
m=x2−x1y2−y1
Modelling
x=−2ab
2&3D Geometry
d=√(x2−x1)2+(y2−y1)2+(z2−z1)2
(2x1+x2,2y1+y2,2z1+z2)
V=31Ah
V=31πr2h
A=πrl
V=34πr3
A=4πr2
l=360∘θ⋅2πr
A=360∘θ⋅πr2
Trig IDs
sinAa=sinBb=sinCc
c2=a2+b2−2abcosC
cosC=2aba2+b2−c2
A=21absinC
Descriptive Statistics
IQR=Q3−Q1
xˉ=ni=1∑kfixi
Probability
P(A)=n(U)n(A)
P(A)+P(A′)=1
P(A∪B)=P(A)+P(B)−P(A∩B)
P(A∪B)=P(A)+P(B)
P(A∣B)=P(B)P(A∩B)
P(A∩B)=P(A)P(B)
Distributions & Vars
E(X)=∑xP(X=x)
X∼B(n,p)
E(X)=np
Var(X)=np(1−p)
Differentiation
f(x)=xn⟹f′(x)=nxn−1
Integration
∫xndx=n+1xn+1+C,n=−1
A=∫abydx
∫abydx≈2h(y0+2(y1+⋯+yn−1)+yn)