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 |
Order Of Operations: |
PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract) |
Arithmetic Sequences: |
each term is equal to the previous term plus d Sequence: t1, t1 + d, t1 + 2d, . . . Example: d = 4 and t1 = 3 gives the sequence 3, 7, 11, 15, . . . |
Geometric Sequences: |
each term is equal to the previous term times r Sequence: t1, t1 · r, t1 · r2, . . . Example: r = 2 and t1 = 3 gives the sequence 3, 6, 12, 24, . . . |
Factors: |
the factors of a number divide into that number without a remainder |
Multiples: |
the multiples of a number are divisible by that number without a remainder |
Percents: |
use the following formula to find part, whole, or percent part = percent 100 × whole |
Averages, Counting, Statistics, Probability
average |
average = sum of terms number of terms |
average speed |
total distance/total time |
sum |
Average*number of teerms |
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. |
SAT Prep |
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