KEYSTONE
Re f E FERENCE
ALGEBRA II FORMULA SHEET
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Shapes
Logarithmic Properties
loga x = y ↔ x = a y
A = lw
w
log x = y ↔ x = 10 y
In x = y ↔ x = ey
loga (x · y ) = loga x + loga y
l
loga x p = p · loga x
x
loga y = loga x − loga y
h
V = lwh
w
l
Quadratic Functions
f(x) = ax 2 + bx + c
General Formula:
Data Analysis
f (x) = a(x − h )2 + k
Standard (Vertex) Form:
Permutation:
nPr
Combination:
=
n!
(n − r)!
n!
nCr =
r !(n − r )!
f(x ) = a(x − x 1)(x − x 2)
Factored Form:
Quadratic Formula:
x=
ˉb ± b 2 − 4ac
2a
when ax 2 + bx + c = 0 and a Þ 0
Exponential Properties
am · an = am + n
(a m )n = a m · n
am
= am − n
an
a ¯1 =
1
a
Compound Interest Equations
Annual:
A = P (1 + r ) t
Periodic:
A =P 1+
i3 = ¯ i
i 2 = ¯1
nt
n
P = principal amount
r = annual rate of interest
t = time (years)
Continuous:
¯1
r
( )
Powers of the Imaginary Unit
i=
A = account total after t years
A
= Pert
n = number of periods interest
is compounded per year
i4 = 1
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