SAT Math Facts & Formulas
Numbers, Sequences, Factors
Integers:
. . .
, 3, 2, 1, 0, 1, 2, 3,
. . .
Reals:
integers plus fractions, decimals, and irrationals (
√
2,
√
3,
π
, etc.)
Order Of Operations:
PEMDAS
(Parentheses / Exponents / Multiply / Divide / Add / Subtract)
Arithmetic Sequences:
each term is equal to the previous term plus
d
Sequence:
t
1
,
t
1
+
d
,
t
1
+ 2
d
,
. . .
The n
th
term is
t
n
=
t
1
+ (
n
−
1)
d
Number of integers from
i
n
to
i
m
=
i
m
−
i
n
+ 1
Sum of
n
terms
S
n
= (
n/
2)
·
(
t
1
+
t
n
)
(optional)
Geometric Sequences:
each term is equal to the previous term times
r
Sequence:
t
1
,
t
1
·
r
,
t
1
·
r
2
,
. . .
The n
th
term is
t
n
=
t
1
·
r
n
−
1
Sum of
n
terms
S
n
=
t
1
·
(
r
n
−
1)
/
(
r
−
1)
(optional)
Prime Factorization:
break up a number into prime factors (2, 3, 5, 7, 11,
. . .
)
200 = 4
×
50 = 2
×
2
×
2
×
5
×
5
52 = 2
×
26 = 2
×
2
×
13
Greatest Common Factor:
multiply common prime factors
200 = 2
×
2
×
2
×
5
×
5
60 = 2
×
2
×
3
×
5
GCF(200
,
60) = 2
×
2
×
5 = 20
Least Common Multiple:
check multiples of the largest number
LCM(200
,
60): 200 (no), 400 (no), 600 (yes!)
Percentages:
use the following formula to find part, whole, or percent
part =
percent
100
×
whole
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SAT Math Facts & Formulas
Averages, Counting, Statistics, Probability
average =
sum of terms
number of terms
average speed =
total distance
total time
sum = average
×
(number of terms)
mode = value in the list that appears most often
median = middle value in the list (which
must
be sorted)
Example: median of
{
3
,
10
,
9
,
27
,
50
}
= 10
Example: median of
{
3
,
9
,
10
,
27
}
= (9 + 10)
/
2 = 9
.
5
Fundamental Counting Principle:
If an event can happen in
N
ways, and another, independent event
can happen in
M
ways, then both events together can happen in
N
×
M
ways. (Extend this for three or more:
N
1
×
N
2
×
N
3
. . .
)
Permutations and Combinations (Optional):
The number of permutations of
n
things taken
r
at a time is
n
P
r
=
n
!
/
(
n
−
r
)!
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 Spring '10
 RazaSuleman
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