The Official Handy-Dandy Academy Math Cheat Sheet

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THE OFFICIAL HANDY–DANDY
ACADEMY MATH CHEAT SHEET
Rules of Exponents
0
For any nonzero x, x
= 1.
For any integers p and q,
p
p
q
p
q
x
=
x
= (
x)
.
q
If p is positive this is defined for all x when q is odd and for nonnegative x when q is even. If p/q is negative,
p
the power x
is never defined for x = 0.
q
Other exponent rules include
r+s
r
s
r
s
rs
x
= x
x
(x
)
= x
r
r
x
x
r
r
r
(xy)
= x
y
=
r
y
y
1
−r
x
=
r
x
Rules of Logarithms
For any positive numbers, the following hold. Two caveats: log
(x) is only defined for x > 0 and c = 1,
c
c > 0.
x
log
(b) = x
⇐⇒
a
= b
a
log
(xy) = log
(x) + log
(y)
c
c
c
x
log
= log
(x) − log
(y)
c
c
c
y
y
log
(x
) = y log
(x)
c
c
For any bases a and b we have
log
(x)
b
log
(x) =
a
log
(a)
b
The Binomial Theorem
If n is a positive integer and a and b are any numbers,
n
n
n
k
n−k
(a + b)
=
a
b
.
k
k=0
Recall that
n
n!
=
.
k
k!(n − k)!
Trig Identities
opposite
adjacent
sin(θ) =
cos(θ) =
hypotenuse
hypotenuse
opposite
tan(θ) =
adjacent

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