total distance
total time
Factoring
You may need to apply these types of factoring:
Probability
Probability refers to the chance that a specific outcome can
occur. When outcomes are equally likely, probability can be
found by using the following definition:
For example, if a jar contains 13 red marbles and 7 green
marbles, the probability that a marble selected from the jar
at random will be green is
If a particular outcome can never occur, its probability is 0.
If an outcome is certain to occur, its probability is 1. In
general, if
p
is the probability that a specific outcome will
occur, values of
p
fall in the range
. Probability
may be expressed as either a decimal, a fraction, or a ratio.
Functions
A function is a relation in which each element of the
domain is paired with
exactly
one element of the range. On
the SAT, unless otherwise specified, the domain of any
function
is assumed to be the set of all real numbers
for which
is a real number. For example, if
, the domain of
is all real numbers
greater than or equal to
. For this function, 14 is paired
with 4, since
.
Note:
the
symbol represents the positive, or principal,
square root. For example,
, not ± 4.
number of ways that a specific outcome can occur
total number of possible outcomes

SAT Preparation Booklet
16
MATHEMATICS REVIEW
Exponents
You should be familiar with the following rules for
exponents on the SAT.
For all values of
:
For all values of
Also,
.
For example,
.
Note:
For any nonzero number
, it is true that
.
Sequences
Two common types of sequences that appear on the SAT
are arithmetic and geometric sequences.
An
arithmetic sequence
is a sequence in which successive
terms differ by the same constant amount.
For example: 3, 5, 7, 9, . . . is an arithmetic sequence.
A
geometric sequence
is a sequence in which the ratio of
successive terms is a constant.
For example: 2, 4, 8, 16, . . . is a geometric sequence.
A sequence may also be defined using previously defined
terms. For example, the first term of a sequence is 2, and
each successive term is 1 less than twice the preceding
term. This sequence would be 2, 3, 5, 9, 17, . . .
On the SAT, explicit rules are given for each sequence. For
example, in the sequence above, you would not be expect-
ed to know that the 6th term is 33 without being given the
fact that each term is one less than twice the preceding
term. For sequences on the SAT, the first term is
never
referred to as the zeroth term.
Variation
Direct Variation:
The variable
is directly proportional
to the variable
if there exists a nonzero constant
such
that
.
Inverse Variation:
The variable
is inversely proportional
to the variable
if there exists a nonzero constant
such
that
Absolute Value
The absolute value of
is defined as the distance from
to zero on the number line. The absolute value of
is
written as
. For all real numbers
:
For example:
GEOMETRIC CONCEPTS
Figures that accompany problems are intended to provide
information useful in solving the problems. They are
drawn as accurately as possible EXCEPT when it is stated
in a particular problem that the figure is not drawn to
scale. In general, even when figures are not drawn to scale,

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- Spring '17
- karish
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