Numbers, Sequences, Factors
Integers:
. . .
, 3, 2, 1, 0, 1, 2, 3,
. . .
Rationals:
fractions, that is, anything expressable as a ratio of integers
Reals:
integers plus rationals plus special numbers such as
√
2,
√
3 and
π
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
,
. . .
Example:
d
= 4 and
t
1
= 3 gives the sequence 3, 7, 11, 15,
. . .
Geometric Sequences:
each term is equal to the previous term times
r
Sequence:
t
1
,
t
1
·
r
,
t
1
·
r
2
,
. . .
Example:
r
= 2 and
t
1
= 3 gives the sequence 3, 6, 12, 24,
. . .
Factors:
the factors of a number divide into that number
without a remainder
Example: the factors of 52 are 1, 2, 4, 13, 26, and 52
Multiples:
the multiples of a number are divisible by that number
without a remainder
Example: the positive multiples of 20 are 20, 40, 60, 80,
. . .
Percents:
use the following formula to ±nd part, whole, or percent
part =
percent
100
×
whole
Example: 75% of 300 is what?
Solve
x
= (75
/
100)
×
300 to get 225
Example: 45 is what percent of 60?
Solve 45 = (
x/
100)
×
60 to get 75%
Example: 30 is 20% of what?
Solve 30 = (20
/
100)
×
x
to get 150
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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
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 Spring '10
 RazaSuleman
 Pythagorean Theorem, triangle, Math MustKnow Facts

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