Math Conventions

Question 1

one billion

Answer 1

1,000,000,000; or 10^9

Question 2

one dozen

Answer 2

12

Question 3

pi (π)

Answer 3

3.14

ratio of circumference to diameter for a circle

Question 4

rounding

Answer 4

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

Question 5

repeating decimals are written with _______ over the repeating digits

Answer 5

a bar

Question 6

terminology:

“factor”, “divisor”, “multiple”, or “divisible by”

Answer 6

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

Question 7

least common multiple (LCM)

Answer 7

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

Question 8

greatest common divisor (GCD); or

greatest common factor (GCF)

Answer 8

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

Question 9

if an integer “n” is divided by a nonzero integer “d” resulting in quotient “q”, then
n = _________

Answer 9

n = qd + r
where 0 <= r < |d|

Also, r = 0 if an only if “n” is a multiple of “d”

Question 10

prime number

Answer 10

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

Question 11

composite number

Answer 11

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

Question 12

odd and even integers are not necessarily ________

Answer 12

“positive”

Question 13

unless otherwise restricted, the possible values of numbers/constants/variables are “__________”

Answer 13

“all real numbers”

Question 14

x**0 = _____

for all nonzero numbers “x”

Answer 14

x**0 = 1

for all nonzero numbers “x”

Question 15

order of operations

Answer 15

1. parentheses
2. exponentiation
3. negation
4. multiplication and division (from left to right)
5. 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

Question 16

The following are examples of_______:
(x/0)
sqrt(x); where x < 0
0**0

Answer 16

“undefined expressions”

because all numbers are assumed to be real

Question 17

compossition of functions “g” and “f” is written as ______

Answer 17

g(f(x))

Question 18

sum of the measures of interior angles fo a triangle is ________

Answer 18

180 degrees

Question 19

“Lines” are assumed to be “_________”

Answer 19

“straight” lines that extend in both directions without end

Question 20

angle measures in ________ are assumed to be _________

Answer 20

“degrees”;

“positive and less than or equal to 360 degrees”

Question 21

when a square, circle, polygon or other closed geometric figure is described in words but not shown, the figure is assumed to enclose _______

Answer 21

a convex region

Question 22

area of a shape

Answer 22

the area of the region enclosed by the shape

Question 23

distance between a point and a line

Answer 23

is the lenght of the perpendicular line segment from the point to the line, which is the shortest distance between the point and line

Question 24

in a geometric context, the phrase “similar triangles” (or other figures) means _________

Answer 24

the figures have the same shape

Question 25

geometric figures [are / are not] always drawn to scale

Answer 25

are not

Question 26

coordinate systems [are / are not] always drawn to scale

Answer 26

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)

Question 27

elements of a set are also called _________

Answer 27

members

Question 28

sets are denoted by:

Answer 28

curled brackets, i.e. { }

Question 29

if A and B are sets, the “intersection of A and B” is ________

Answer 29

the set of elements that are in both A and B

Question 30

if A and B are sets, the “union of A and B” is __________

Answer 30

the set of elements that are in A or B, or both

Question 31

A is a subset of B if ________

Answer 31

all elements of A are also in B

by convention, the empty set, { }, is a subset of every set

Question 32

“disjoint” or “mutually exclusive” sets are _____________

Answer 32

sets with no elements in common

Question 33

in SETS of numbers or other elements, repetitions [are / are not] counted as additional elements

Answer 33

are not

Question 34

in LISTS of numbers or other elements, repetitions [are / are not] counted as additional elements

Answer 34

are

Question 35

in SETS of numbers or other elements, order [is / is not] relevant

Answer 35

is not

Question 36

in LISTS of numbers or other elements, order [is / is not] relevant

Answer 36

is

Question 37

sequences are _________

Answer 37

lists

Question 38

the terms “data set” and “set of data” [are / are not] “sets” according to the mathematical definition

Answer 38

are not;

rather, they refer to a list of data

Question 39

{statistics}

measures of central tendency

Answer 39

• mean
• median
• mode

Question 40

{statistics}

measures of position

Answer 40

• quartiles

- percentiles

Question 41

{statistics}

measures of dispersion

Answer 41

• standard deviation
• range
• interquartile range

Question 42

“average (arithmetic mean)” of a data set

Answer 42

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

Question 43

“average [not qualified by “(arithmetic mean)”]

Answer 43

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”

Question 44

the term “average” is never used to refer to ______ or ________

Answer 44

“median”;

“mode”

Question 45

median

Answer 45

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

Question 46

“mode” of a data set

Answer 46

the most frequently occurring number in the list

thus, there may be more than one mode for a list of data

Question 47

percentiles

Answer 47

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

Question 48

first, second, and third quartile

Answer 48

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)

Question 49

standard deviation

Answer 49

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”

Question 50

range

Answer 50

the “range” of a list of data is the greatest number in the list minus the least number

Question 51

interquartile range

Answer 51

the “interquartile range” of the data is the third quartile minus the first quartile

Question 52

frequency distribution

Answer 52

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

Question 53

relative frequency distributions

Answer 53

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

Question 54

random selection/sample

Answer 54

all possible samples of equal size have the same probability of being selected unless there is information to the contrary

Question 55

probability experiments 
(aka random experiments)

Answer 55

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

Question 56

if E and F are two mutually exclusive events, then P(E adn F) = ______

Answer 56

P(E and F) = 0

Question 57

independent events

Answer 57

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)

Question 58

random variable

Answer 58

a random variable is a variable that represents values resulting from a random experiment

Question 59

discrete random variable

Answer 59

is a random variable from an experiment with only a finite number of possible outcomes also has only a finite number of values

Question 60

continuous random variable

Answer 60

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”