Act Formula Sheet
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1
2
3ACT FORMULA SHEET
Arithmetic and Algebra
Properties of Exponents and Radicals
a
n
__
a
∙ a
= a
(a
)
= a
(ab)
= a
b
n
m
n+m
n
m
nm
n
n
n
= a
n-m
a
m
(
)
(
)
(
)
1 __
a __
b __
=
a __
a
1 __
n
-n
n
__
n
a
n
=
=
a
=
-n
a
a
-n
a
b
n
b
b
n
_
__
__
__
__
__
__
___
n
m __
a
n
1 __
n
n
a _
=
= a
√
= a
=
n
√
n
n
∙
a
n
m
n
__
a
√
ab
a
√
b
√
√
√
b
n
√
b
Generic Formulas
_____
________
-b ± √
-4ac
b
2
Sum of Terms
_____________
Quadratic Formula: For ax
Arithmetic Mean:
+ bx + c = 0, x =
2
2a
Number of Terms
Desired Outcomes
_____________
Distance: Distance = Rate ∙ Time
Event Probability:
Possible Outcomes
New - Old
_______
∙ 100%
Percent Growth/Decay: Original(1 ± r
)(1 ± r
)...
Percent Change:
1
2
Old
In Percent Growth or Decay, r
, r
, ... are the
1
2
percents an amount is being changed by each
year, month, etc.
Arithmetic Sequence/Series
Geometric Sequence/Series
a
___
Common Difference: d = a
- a
Common Ratio: r =
n+1
a
n+1
n
n
Find the n
Find the n
term: a
term: a
th
= a
+ (n - 1)d
th
= a
r
n -1
n
1
n
1
(
)
n __
1 - r
n
___
Sum the first n terms: S
Sum the first n terms: S
=
(a
+ a
)
= a
2
1 - r
n
1
n
n
1
Counting and Ordering
Properties of Logarithms
n!
______
log
a
x
= x
Combination (Order Doesn’t Matter):
C
=
r!(n - r)!
a
n
r
n!
______
xlog
y = log
y
x
Permutation (Order Does Matter):
P
=
a
a
(n - r)!
n
r
Remember, n is the number of choices you
log
x + log
y = log
(xy)
a
a
a
have, and r is how many you are going to
choose.
(
)
x _
log
x - log
y = log
y
a
a
a
1
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