Content
Formula Booklet AASL
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=√(x1−x2)2+(y1−y2)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
FV=PV(1+100kr)kn
S∞=1−ru1,∣r∣<1
Exponents & Logs
logab=x⟺ax=b, where a,b>0 and a=1
logaxy=logax+logay
logayx=logax−logay
logaxm=mlogax
logax=logbalogbx
Counting
(a+b)n=an+nC1an−1b+⋯+nCran−rbr+bn
nCr=r!(n−r)!n!
Coordinates & Lines
y=mx+c
ax+by+d=0
y−y1=m(x−x1)
m=x2−x1y2−y1
Quadratics
x=−2ab
x=2a−b±√b2−4ac
Δ=b2−4ac
Exponents & Logs
ax=exlna
logaax=x=alogax
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
Trig IDs
sinAa=sinBb=sinCc
c2=a2+b2−2abcosC
cosC=2aba2+b2−c2
A=21absinC
l=rθ
A=21r2θ
tanθ=cosθsinθ
sin2θ+cos2θ=1
sin2θ=2sinθcosθ
cos2θ=cos2θ−sin2θ=2cos2θ−1=1−2sin2θ
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)=0⇒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)
E(X)=np
Var(X)=np(1−p)
z=σx−μ
Differentiation
f(x)=xn⟹f′(x)=nxn−1
f(x)=sinx⟹f′(x)=cosx
f(x)=cosx⟹f′(x)=−sinx
f(x)=ex⟹f′(x)=ex
f(x)=lnx⟹f′(x)=x1
dxdy=dudy×dxdu
y=uv⟹dxdy=udxdv+vdxdu
y=vu⟹dxdy=v2vdxdu−udxdv
a=dtdv=dt2d2s
Integration
∫xndx=n+1xn+1+C,n=−1
A=∫abydx
distance =∫t1t2∣v(t)∣dt
displacement =∫t1t2v(t)dt
∫x1dx=lnx+C
∫sinxdx=−cosx+C
∫cosxdx=sinx+C
∫exdx=ex+C
A=∫ab∣y∣dx
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=√(x1−x2)2+(y1−y2)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
FV=PV(1+100kr)kn
S∞=1−ru1,∣r∣<1
Exponents & Logs
logab=x⟺ax=b, where a,b>0 and a=1
logaxy=logax+logay
logayx=logax−logay
logaxm=mlogax
logax=logbalogbx
Counting
(a+b)n=an+nC1an−1b+⋯+nCran−rbr+bn
nCr=r!(n−r)!n!
Coordinates & Lines
y=mx+c
ax+by+d=0
y−y1=m(x−x1)
m=x2−x1y2−y1
Quadratics
x=−2ab
x=2a−b±√b2−4ac
Δ=b2−4ac
Exponents & Logs
ax=exlna
logaax=x=alogax
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
Trig IDs
sinAa=sinBb=sinCc
c2=a2+b2−2abcosC
cosC=2aba2+b2−c2
A=21absinC
l=rθ
A=21r2θ
tanθ=cosθsinθ
sin2θ+cos2θ=1
sin2θ=2sinθcosθ
cos2θ=cos2θ−sin2θ=2cos2θ−1=1−2sin2θ
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)=0⇒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)
E(X)=np
Var(X)=np(1−p)
z=σx−μ
Differentiation
f(x)=xn⟹f′(x)=nxn−1
f(x)=sinx⟹f′(x)=cosx
f(x)=cosx⟹f′(x)=−sinx
f(x)=ex⟹f′(x)=ex
f(x)=lnx⟹f′(x)=x1
dxdy=dudy×dxdu
y=uv⟹dxdy=udxdv+vdxdu
y=vu⟹dxdy=v2vdxdu−udxdv
a=dtdv=dt2d2s
Integration
∫xndx=n+1xn+1+C,n=−1
A=∫abydx
distance =∫t1t2∣v(t)∣dt
displacement =∫t1t2v(t)dt
∫x1dx=lnx+C
∫sinxdx=−cosx+C
∫cosxdx=sinx+C
∫exdx=ex+C
A=∫ab∣y∣dx