Letter F
FACTORIAL
-the product of n integers from n to 1or 1 through n can be expressed by the symbol n! (read as n factorial).
FACTORING
-is it the process of finding the factor of a product. this is the inverse operation of special product.
FACTORS
-they are the numbers multiplied i.e, both the multiplicand and the multiplier.
FINAL AMOUNT
-it is the sum of the principal and the interest as computed. it is also called maturity value.
FINITE SERIES
-It is a series containing a fixed number of terms.
FINITE SET
-it is a set whose element can be counted or has a limited number of elements.

FOOT
-a measure of lenth.
FOOT-POUND
-it is a unit of work. it is the work done in raising 1 lb, a height of 1 ft., ot it is the pressure of 1 lb. xerted over a distance of 1 ft. in any direction.
Face of a Polyhedron
One of the flat surfaces making up a polyhedron. Note: The faces of a polyhedron are all polygons.

Factor of a Polynomial
Factorization of a Polynomial
A factor of polynomial P(x) is any polynomial which divides evenly into P(x). For example, x + 2 is a factor of the polynomial x2 – 4.
The factorization of a polynomial is its representation as a product its factors. For example, the factorization of x2 – 4 is (x – 2)(x + 2).
Factor Theorem
The theorem that establishes the connection between the zeros and factors of apolynomial.

Factor Tree
A structure used to find the prime factorization of a positive integer.

Factoring Rules
Algebra formulas for factoring. 1. x2 – (r + s)x + rs = (x – r)(x – s) | 2. x2 + 2ax + a2 = (x + a)2 and x2 – 2ax + a2 = (x – a)2 | 3. Difference of squares: a2 – b2 = (a – b)(a + b) | 4. Difference of cubes: a3 – b3 = (a – b)(a2 + ab + b2) | 5. a4 – b4 = (a – b)(a3 + a2b + ab2 + b3) = (a – b) [ a2(a + b) + b2(a + b) ] = (a – b)(a + b)(a2 + b2) | | or, more simply, a4 – b4 = (a2 – b2)(a2 + b2) = (a – b)(a + b)(a2 + b2) | 6. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4) | 7. an – bn = (a – b)(an – 1 + an – 2b + an – 3b2 + ··· + abn – 2 + bn – 1) | 8. Sum of cubes: a3 + b3 = (a + b)(a2 – ab + b2) | 9. a5 + b5 = (a + b)(a4 – a3b + a2b2 – ab3 + b4) | 10. a7 + b7 = (a + b)(a6 – a5b + a4b2 – a3b3 + a2b4 – ab5 + b6) | 11. If n is odd, then an + bn = (a + b)(an – 1 – an – 2b + an – 3b2 – ··· + a2bn – 3 – abn – 2 + bn – 1) | 12. Sum of squares: a2 + b2 = (a – bi)(a + bi) Note: a2 + b2 does not factor using real numbers. | 13. |
First Derivative Test
A method for determining whether an inflection point is a minimum, maximum, or neither.

LETTER G
Odds in Gambling
A way of representing gambling payoffs of an event by a method similar to odds against. If the gambling odds are m:n (read aloud "m to n"), then a bet of n dollars paysm dollars profit if the bettor wins.
Note: Gambling odds are not probabilities. See odds in favor.

Standard Form for the Equation of a Line
General Form for the Equation of a Line
Ax + By = C, where A > 0 and, if possible, A, B, and C are relatively prime integers. The standard form is used in some algebra classes for practice in manipulatingequations. Otherwise it is used far less often than other forms for the equation of a line.
Note: An alternate standard form, Ax + By + C = 0, is used as part of the formula fordistance from a point to a line.
Geometric Figure
Any point, line, segment, ray, angle, polygon, curve, region, plane, surface, solid, etc. Formally, a geometric figure is any set of points on a plane or in space. Geometric Sequence
Geometric Progression
A sequence such as 2, 6, 18, 54, 162 or which has a constant ratiobetween terms. The first term is a1, the common ratio is r, and the number of terms isn.

Geometric Series
A series such as 2 + 6 + 18 + 54 + 162 or which has a constantratio between terms. The first term is a1, the common ratio is r, and the number of terms is n.

Solid
Geometric Solid
Solid Geometric Figure
The collective term for all bounded three-dimensional geometric figures. This includespolyhedra, pyramids, prisms, cylinders, cones, spheres, ellipsoids, etc.

Geometry
The study of geometric figures in two dimensions (plane geometry) and three dimensions (solid geometry). It includes the study of points, lines, triangles,quadrilaterals, other polygons, circles, spheres, prisms, pyramids, cones, cylinders, andpolyhedra. Geometry typically includes the study of axioms, theorems, and two-column proofs.
Among the various types of geometry are analytic geometry, Euclidean geometry, andnon-Euclidean geometry.
Geometric Mean
A kind of average. To find the geometric mean of a set of n numbers, multiply the numbers and then take the nth root of the product.

LETTER H

Half Angle Identities
Half Number Identities
Trig identities that show how to find the sine, cosine, or tangent of half a given angle. Half Angle Identities | or or or or |
Half-Closed Interval
Half-Open Interval
An interval that contains one endpoint but not the other.

Half-Life
For a substance decaying exponentially, the amount of time it takes for the amount of the substance to diminish by half.

Harmonic Mean
A kind of average. To find the harmonic mean of a set of n numbers, add thereciprocals of the numbers in the set, divide the sum by n, then take the reciprocal of the result. The harmonic mean of {a1, a2, a3, a4, . . ., an} is given below.

Harmonic Sequence
Harmonic Progression
The sequence .
Note: The harmonic mean of two terms of the harmonic sequence is the term halfway between the two original terms. For example, the harmonic mean of and is . Harmonic Series
The series . Note: The harmonic series diverges. Its sequence of partial sums is unbounded. Altitude
Height
The shortest distance between the base of a geometric figure and its top, whether that top is an opposite vertex, an apex, or another base. Altitude of a Cylinder
Height of a Cylinder
The distance between the bases of a cylinder. Formally, the shortest line segmentbetween the (possibly extended) bases. Altitude also refers to the length of this segment.

Altitude of a Parallelogram
Height of a Parallelogram
The distance between opposite sides of a parallelogram. Formally, the shortest line segment between opposite sides. Altitude also refers to the length of this segment.

LETTER I

Independent Events
Events for which the probability of any one event occurring is unaffected by the occurrence or non-occurrence of any of the other events. Formally, A and B are independent if and only if P(A|B) = P(A).

Independent Variable
A variable in an equation that may have its value freely chosen without considering values of any other variable. For equations such as y = 3x – 2, the independent variable is x. The variable y is not independent since it depends on the number chosen for x.
Formally, an independent variable is a variable which can be assigned any permissible value without any restriction imposed by any other variable.

Indeterminate ExpressionAn undefined expression which can have a value if arrived at as a limit.Note: Another way to think about indeterminate expressions is to see them as a disagreement between two rules for simplifying an expression. For example, one way to think about is this: The 0 in the numerator makes the fraction "equal" 0, but the 0 in the denominator makes the fraction "equal" ±∞. This conflict makes the expression indeterminate. Common indeterminate expressions: 00 1∞ ∞0 ∞ – ∞ | Example: | The limitseems to evaluate to , which is indeterminate. In fact,since sin x and x are approximately equal to each other for values of x near 0.Note that this limit can also be computed usingl’Hôpital’s rule. | |
Proof by Contradiction
Indirect Proof
Proving a conjecture by assuming that the conjecture is false. If this assumption leads to a contradiction, the original conjecture must have been true. This technique employs the logical method known as modus tolens.

Induction
A method for proving a proposition that is valid for infinitely many different values of avariable. For example, it can be used to prove the formula 1 + 2 + 3 + 4 + . . . + n = .

InequalityDefinition 1: Any of the symbols <, >, ≤, or ≥.Definition 2: A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥. Examples: | x + y < 14 ≤ a ≤ 7m2 – 3m + 2 ≥ 0 | |
Inequality Rules
Algebra rules for manipulating inequalities are listed below.

Infinite
Describes a set which is not finite. Formally, a set is infinite if it can be placed in one-to-one correspondence with a proper subset of itself.

Infinite Geometric Series
An infinite series that is geometric. An infinite geometric series converges if its common ratio r satisfies –1 < r < 1. Otherwise it diverges.

LETTER J

Joint Variation
Jointly Proportional
When we say z is jointly proportional to a set of variables, it means that z is directly proportional to each variable taken one at a time.
If z varies jointly with respect to x and y, the equation will be of the form z = kxy (where kis a constant). Equation: c = 5abVariable c is jointly proportional to a and b. That meansc is directly proportional to both a and b.Doubling a causes c to double. Doubling b causes c to double. Doubling both a and b causes c to quadruple. | a | b | c | 1 | 1 | 5 | 2 | 1 | 10 | 1 | 2 | 10 | 2 | 2 | 20 | | Step Discontinuity
Jump Discontinuity
A discontinuity for which the graph steps or jumps from one connected piece of the graph to another. Formally, it is a discontinuity for which the limits from the left andright both exist but are not equal to each other.