Math Conventions Flashcards
Become familiar with math conventions used in GRE Quantitative Reasoning section
one billion
1,000,000,000; or 10^9
one dozen
12
pi (π)
3.14
ratio of circumference to diameter for a circle
rounding
When a positive number is to be roudned to a certain decimal place adn the number is halfway between the two nearest posibilities, the number should be rounded to the greater possibility;
When negative, number should eb roiunded to the lesser possibility
Example A: 23.5 rounded to nearest integer is 24
Example B: 123.985 rounded to nearest 0.01 is 123.99
Example C: -36.5 rounded to nearest integer is -37
repeating decimals are written with _______ over the repeating digits
a bar
terminology:
“factor”, “divisor”, “multiple”, or “divisible by”
definition:
if r, s, and t are integers and rs=t, then r and s are “factors”, or “divisors” of t; also, t is a “multiple” of r (and of s) and t is “divisible by” r (and by s).
The factors of an integer include positive and negative integers
Ex: -7 is a factor of 35
Ex: 4 has six factors: -4, -2, -1, 1, 2, 4
least common multiple (LCM)
the least common multiple of two nonzero integers “a” and “b” is teh least positive integer that is a multiple of both “a” and “b”
Ex: LCM of 2 and 5 is 10
greatest common divisor (GCD); or
greatest common factor (GCF)
the greatest common divisor/factor of “a” and “b” is the greatest positive integer that is a divisor of both “a” and “b”
Ex: for the set of numbers [18, 30, 42], the GCF = 6
if an integer “n” is divided by a nonzero integer “d” resulting in quotient “q”, then
n = _________
n = qd + r
where 0 <= r < |d|
Also, r = 0 if an only if “n” is a multiple of “d”
prime number
a “prime number” is an integer greater than 1 that has only two positive divisors: 1 and itself
first five prime numbers:
2, 3, 5, 7, and 11
composite number
a “composite number” is an integer greater than 1 that is not a prime number
The first five composite numbers are:
4, 6, 8, 9, and 10
odd and even integers are not necessarily ________
“positive”
unless otherwise restricted, the possible values of numbers/constants/variables are “__________”
“all real numbers”
x**0 = _____
for all nonzero numbers “x”
x**0 = 1
for all nonzero numbers “x”
order of operations
- parentheses
- exponentiation
- negation
- multiplication and division (from left to right)
- addition and subtraction (from left to right)
Ex: -32 means “the negative of ‘3 squared’” because exponentiation takes precedence over negation; therefore, -32 = -9 but (-3)**2 = 9 because parentheses take precedence over exponentiation
The following are examples of_______:
(x/0)
sqrt(x); where x < 0
0**0
“undefined expressions”
because all numbers are assumed to be real
compossition of functions “g” and “f” is written as ______
g(f(x))
sum of the measures of interior angles fo a triangle is ________
180 degrees
“Lines” are assumed to be “_________”
“straight” lines that extend in both directions without end
angle measures in ________ are assumed to be _________
“degrees”;
“positive and less than or equal to 360 degrees”
when a square, circle, polygon or other closed geometric figure is described in words but not shown, the figure is assumed to enclose _______
a convex region
area of a shape
the area of the region enclosed by the shape
distance between a point and a line
is the lenght of the perpendicular line segment from the point to the line, which is the shortest distance between the point and line
in a geometric context, the phrase “similar triangles” (or other figures) means _________
the figures have the same shape
geometric figures [are / are not] always drawn to scale
are not
coordinate systems [are / are not] always drawn to scale
are
(therefore, you can read, estimate, or compare quantities in such figures by sight or by measurement, including geometric figures that appear in coordinate systems)
elements of a set are also called _________
members
sets are denoted by:
curled brackets, i.e. { }
if A and B are sets, the “intersection of A and B” is ________
the set of elements that are in both A and B
if A and B are sets, the “union of A and B” is __________
the set of elements that are in A or B, or both
A is a subset of B if ________
all elements of A are also in B
by convention, the empty set, { }, is a subset of every set
“disjoint” or “mutually exclusive” sets are _____________
sets with no elements in common
in SETS of numbers or other elements, repetitions [are / are not] counted as additional elements
are not
in LISTS of numbers or other elements, repetitions [are / are not] counted as additional elements
are
in SETS of numbers or other elements, order [is / is not] relevant
is not
in LISTS of numbers or other elements, order [is / is not] relevant
is
sequences are _________
lists
the terms “data set” and “set of data” [are / are not] “sets” according to the mathematical definition
are not;
rather, they refer to a list of data
{statistics}
measures of central tendency
- mean
- median
- mode
{statistics}
measures of position
- quartiles
- percentiles
{statistics}
measures of dispersion
- standard deviation
- range
- interquartile range
“average (arithmetic mean)” of a data set
the sum of the data divided by the number of data
for a finite set or list of numbers, the “mean” refers to the “arithmetic mean” unless otherwise noted
“average [not qualified by “(arithmetic mean)”]
can refer to the rate or ratio of one quantity to another
e.g. “average number of miles per hour” or “average weight per truckload”
the term “average” is never used to refer to ______ or ________
“median”;
“mode”
median
for an odd number of data: the middle number when listed in increasing order
for an even number of data: the arithmetic mean of the two middle numbers when listed in increasing order
“mode” of a data set
the most frequently occurring number in the list
thus, there may be more than one mode for a list of data
percentiles
for data listed in increasing order, the “percentiles” of the data are 99 numbers that divide the data into 100 groups of roughly equal size
1st quartile = 25th percentile
2nd quartile = 50th percentile
3rd quartile = 75th percentile
first, second, and third quartile
are three numbers that divide the data into four groups
(NOTE: the four groups may be referred to as quartiles; this is clarified by the use of the word “in”, e.g. ‘the cow’s weight was in the third quartile of the weights of the herd)
standard deviation
the non-negative square root of the mean of the squared differences between “m” (the arithmetic mean) and each of the data
AKA, the “population standard deviation”
range
the “range” of a list of data is the greatest number in the list minus the least number
interquartile range
the “interquartile range” of the data is the third quartile minus the first quartile
frequency distribution
display of data where discrete data values are repeated with various frequencies or where preestablished intervals of possible values have frequencies corresponding to the numbers of values in the intervals
relative frequency distributions
a display of data where each frequency of a frequency distribution is divided by the total number of data in the distribution, resulting in a relative frequency
random selection/sample
all possible samples of equal size have the same probability of being selected unless there is information to the contrary
probability experiments (aka random experiments)
have a finite number of possible outcomes;
any particular set of outcomes is called an event;
every event (E) has a probability, P(E) where 0<=P(E)<=1
if E and F are two mutually exclusive events, then P(E adn F) = ______
P(E and F) = 0
independent events
E and F are two events such that the occurrence of either event does not affect the occurrence of the other;
events E and F are independent if and only if P(E and F) = P(E)P(F)
random variable
a random variable is a variable that represents values resulting from a random experiment
discrete random variable
is a random variable from an experiment with only a finite number of possible outcomes also has only a finite number of values
continuous random variable
when the values of a random variable form a continuous interval of real numbers, such as all of the numbers betwee 0 and 2, the random variable is called “continuous random variable”
