PRAXIS II: MATH CONTENT

These are not official mathematics definitions.

Cardinal number	a count of how many ( 4 ducks)
Ordinal number	position (2^nd duck in the row)
Nominal number	Relative position such as a house number. Does not indicate number before it as does the ordinal number. Also identifiers such as numbers on athletic jerseys.
Distributive property	Distributes multiplication over addition or subtraction. 2( x+4) = 2x+8
Commutative property	A change in order does not affect the outcome. Multiplication and addition, but not for subtraction or division. A+B=B+A and A*B=B*A
Associative Property	A change in grouping but not order. Addition and Multiplication but not division or subtraction. A + (B+C) = (A+B)+C and A*(B*C)=(A*B)*C
Prime number	Only factors are 1 and itself 2 ,3 ,5, 7, 11, 13, etc
Composite number	Factors in addition to 1 and itself 4, 6, 8, 9 etc
GCF	Greatest Common Factor: Largest number that will divide into 2 or more numbers Example: 4 is the GCF of 8 and 12
LCM	Least Common Multiple: Smallest number that 2 or more numbers will divide into. Example: 24 is the LCM of 8 and 12.
Order of operations	Powers, multiplication and division, addition and subtraction unless otherwise indicated by parentheses.
Reciprocal	The product of a number and its reciprocal is 1. The reciprocal of a/b is b/a.
Algorithm	A routine process used to obtain a result to a problem.
Pascal’s Triangle	A triangular array of numbers representing the coefficients of a binomial expansion.
Series	A list of numbers with a common definition. Example: the odd or even numbers, prime numbers, Fibonacci numbers.
Arithmetic Series	Not all series are arithmetic or geometric, but arithmetic and geometric are two common series of numbers. An arithmetic series is a series with a common difference between terms, e.g., 3, 7, 11, 15, 19,… a1 is the first term ( 3), d is the difference between terms (4) and n is the number of the term (the fourth term: a4 is 15 in this case) The general rule for finding a term is an = a1 + d(n-1). If we want the 10^th term: a10 = 3 + 4(9) thus a10 = 39 for this series of numbers.
Geometric Series	A geometric series is a series with a common factor between terms, e.g., 3, 6, 12, 24, 48,… or 8, 4, 2, 1, ½, ¼, 1/8, … Once again the first term is a1, n is the number of the term, and r is the common factor between terms. In the first example, r = 2 and in the second example r = 1/2 . The general rule for finding a term is an = a1r^(n-1) For example from the first series a8= 3(2)^7 thus the 8^th term is 3(128) which equals 384.
Sequence	The sum of a series. Example: sum of the odd numbers 1 thru 7 is 16.
Perpendicular	Lines meeting to form right angles
Parallel	Coplanar lines which do not intersect. Planes that do not intersect
Transformations	Common transformations in Geometry are the Rotation (turn), Reflection (flip) (how it would appear in a mirror), and the Slide.
Common System of Measurement	Common units: inches, feet, yards, miles, pints, quarts, gallons, ounce, pound, ton, and degree Fahrenheit. These used to be called the English System of Measurement.
Metric System of Measurement	Common units: meters, liters, grams, and degree Celsius. Used with common prefixes of milli, centi, kilo.
Mean	Most commonly used measure for average. Sum of terms divided by number of terms. The value if all terms were the same.
Median	Less commonly used measure of average. Middle term in a list of ordered terms. Example: Seven is the median of 1, 4, 7, 8, 9
Mode	Least commonly used measure of average. Most frequently appearing item or number in a list of terms. Example: 3 is the mode for 1,1,3,3,3,3,5,6,6,7,8,9,9

Weighted average	Mean calculated after some scores a given more value than others. Example: test grades may count for two grades.
Range	Highest score minus lowest score. Also can be defined as highest score minus lowest score plus one. The latter form is rare.
Additive Inverse	Number added to another number to get zero. Example -3 and 3
Multiplicative identity	A number multiplied by something to make the result one. The product of a number and its reciprocal. Example: 3 and 1/3
Scalene triangle	No sides the same length
Isosceles triangle	Two sides the same length
Equilateral triangle	Three sides the same length. Also is equiangular.
Acute triangle	All angles are less than 90 degrees
Obtuse triangle	One angle is greater than 90 degrees
Right triangle	One angle is 90 degrees
Volumes Cylinder or Prism:	V = Bh (B is area of the base and h is the height) Example: Rectangular Based Prism: V=lwh. Triangular Based Prism: V=1/2(abh). Cylinder: V=πr^2h.
Volumes Cones and Pyramids	V = 1/3 Bh (B is area of the base and h is the height) Example: Rectangular Based Pyramid: V=1/3 lwh. Triangular Based Pyramid: V=1/3(1/2abh). Cone: V=1/3(πr^2h).
Factor tree	Simple diagram of prime factors of a number.
Celsius to Fahrenheit	F = 9/5(C) + 32
Fahrenheit to Celsius	C = 5/9(F -32)
	NOTE: -40 degrees C is equal to -40 degrees F