NLN PAX: Mathematics Test: Algebra,
Complete Solution
Numbers
basic building blocks of mathematics.
Integers
set of whole positive and negative numbers, including zero. These do not include
fractions, decimals, or mixed numbers.
Prime Number
whole number greater than 1 that has only two factors, itself and 1; a number that can
be divided evenly by 1 itself.
Composite Number
whole number greater than 1 that has more than two different factors; any whole
number that is not a prime number.
Even Number
any integer that can be divided by 2 without leaving a remainder.
Odd Number
any integer that cannot be divided evenly by 2.
Decimal Number
a number that uses a decimal point to show the part of the number that is less than one.
Decimal Point
symbol used to separate the ones place from the tenths place in decimals or dollars
from cents in currency.
Decimal Place
position of a number to the right of the decimal point.
Decimal or Base 10 System
number system that uses ten different digits.
Rational Number
all integers, decimals, and fractions. Any terminating or repeating decimal number is a
rational number.
Irrational Number
cannot be written as fractions or decimals because the number of decimal places is
infinite and there is no recurring pattern of digits within the number.
Real Numbers
set of all rational and irrational numbers.
Mathematical Operations
addition, subtraction, multiplication, division
Addition
increases the value of one quantity by the value of another results in sum
Subtraction
opposite operation to addition; it decreases the value of one quantity by the value of
another quantity results in difference.
Multiplication
repeated addition; one number tells how many times to add the other number to itself
(order doesn't matter).
Division
, opposite operation to multiplication; one number tells us how many parts to divide the
other number into (order does matter)
Exponent
superscript number placed next to another number at the top right that indicates how
many times the base number is to be multiplied by itself.
Squared
number with an exponent of 2
Power
value of a number raised to an exponent
Cubed
number with an exponent of 3
Negative Exponent
reciprocal of a positive exponent.
Parentheses
designate which operations should be done first when there are multiple operations.
Order of Operations
set of rules that dictates the order in which we must perform each operation in an
expression so that we will evaluate it accurately.
P
operations inside the parentheses
E
simplify the exponents
MD
multiplication and division from left to right.
AS
addition and subtraction from left to right.
Root
another way of writing a fractional exponent; uses radical symbol to indicate the
operation.
Radical
number underneath the bar, and sometimes have a number in the upper left.
Square Root
a number raised to the one-half power.
Perfect Square
number that has an integer for its square root.
Scientific Notation
way of writing large numbers in a shorter form.
Absolute Value
distance away from zero a number is on the number line.
Signs are the same
add the absolute values.
Signs are different
take absolute values of the addends and subtract the smaller value from the larger
value, then apply the original sign of the larger value to the difference.
Factors
numbers that are multiplied together to obtain a product.
Complete Solution
Numbers
basic building blocks of mathematics.
Integers
set of whole positive and negative numbers, including zero. These do not include
fractions, decimals, or mixed numbers.
Prime Number
whole number greater than 1 that has only two factors, itself and 1; a number that can
be divided evenly by 1 itself.
Composite Number
whole number greater than 1 that has more than two different factors; any whole
number that is not a prime number.
Even Number
any integer that can be divided by 2 without leaving a remainder.
Odd Number
any integer that cannot be divided evenly by 2.
Decimal Number
a number that uses a decimal point to show the part of the number that is less than one.
Decimal Point
symbol used to separate the ones place from the tenths place in decimals or dollars
from cents in currency.
Decimal Place
position of a number to the right of the decimal point.
Decimal or Base 10 System
number system that uses ten different digits.
Rational Number
all integers, decimals, and fractions. Any terminating or repeating decimal number is a
rational number.
Irrational Number
cannot be written as fractions or decimals because the number of decimal places is
infinite and there is no recurring pattern of digits within the number.
Real Numbers
set of all rational and irrational numbers.
Mathematical Operations
addition, subtraction, multiplication, division
Addition
increases the value of one quantity by the value of another results in sum
Subtraction
opposite operation to addition; it decreases the value of one quantity by the value of
another quantity results in difference.
Multiplication
repeated addition; one number tells how many times to add the other number to itself
(order doesn't matter).
Division
, opposite operation to multiplication; one number tells us how many parts to divide the
other number into (order does matter)
Exponent
superscript number placed next to another number at the top right that indicates how
many times the base number is to be multiplied by itself.
Squared
number with an exponent of 2
Power
value of a number raised to an exponent
Cubed
number with an exponent of 3
Negative Exponent
reciprocal of a positive exponent.
Parentheses
designate which operations should be done first when there are multiple operations.
Order of Operations
set of rules that dictates the order in which we must perform each operation in an
expression so that we will evaluate it accurately.
P
operations inside the parentheses
E
simplify the exponents
MD
multiplication and division from left to right.
AS
addition and subtraction from left to right.
Root
another way of writing a fractional exponent; uses radical symbol to indicate the
operation.
Radical
number underneath the bar, and sometimes have a number in the upper left.
Square Root
a number raised to the one-half power.
Perfect Square
number that has an integer for its square root.
Scientific Notation
way of writing large numbers in a shorter form.
Absolute Value
distance away from zero a number is on the number line.
Signs are the same
add the absolute values.
Signs are different
take absolute values of the addends and subtract the smaller value from the larger
value, then apply the original sign of the larger value to the difference.
Factors
numbers that are multiplied together to obtain a product.
