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GLOSSARY OF MATH TERMS

ALGEBRA AND GEOMETRY

Word Definition Examples

D

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Decay factor For an exponential decay function of the form y = abx, where 0 < b < 1, with b the decay factor.
Deductive reasoning It is the process of thinking logically going from facts (in geometry proven statements) to a conclusion (statement to prove)
Dependent events The outcome of a dependent event is affected by the outcome of the previous event.
Dependent system If a system of equations have unlimited solutions then the system is dependent.
Depressed polynomial The resulting numbers of the synthetic division that correspond to the quotient of the division; these are the coefficients for the depressed polynomial that is one degree less than the divisor polynomial.
Descartes' rule of signs The rule states that ordering the terms of a single-variable polynomial with real coefficients in descending order as to the exponents, then we have that the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or less than it by a multiple of 2. This multiply of 2 refers to the fact that the number of imaginary roots is always even. Multiple roots of the same value are counted separately. To find the number of negative roots we substitute the variable by its opposite (if variable is x then -x); then the number of negative roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients or less than it by a multiple of 2.
Dilation It is an enlargement or reduction of a geometric figure.
Diameter The chord in a circle that goes through the center; it is the longest chord in a circle.
Difference of two squares a2 - b2 = (a +b)(a - b)
Directrix The line outside the parabola that runs perpendicular to the axis of symmetry and it is at the same distance from the parabola than the focus in all its points.
Discriminant In a quadratic equation is the expression inside the radical: b2 - 4ac.
Distance Formula (2 points) Formula that uses two points in the coordinate plane to find the distance in between them.
Distance from a point to a line The perpendicular distance from a point not on a line to the line in question.
Diverge Given an infinite geometric series, this diverges if |r|³1, where r is the common ratio of the sequence in question.

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Ellipse All the points in a plane for which the distance to the foci (each focus) is constant.
Enlargement Get a figure larger keeping all its proportions (requires a scale factor to be multiplied by each dimension to enlarge the figure)
Equation A mathematical statement that has to expressions joined by the = sign. It has the right side of the equation (expression1) and the left side of the equation (expression 2)

m + 7 = 23

2x3  6y = 4

Equiangular polygon Polygon in which all angles are congruent (equal). Regular polygons are equiangular.
Equiangular triangle A triangle in which all angles are congruent (equal)
Equilateral polygon A polygon in which all sides are congruent (equal). Regular polygons are equilateral.
Equilateral triangle A triangle in which all sides are congruent.
Equivalent statements Statements  that have the same truth value.
Equivalent systems Equivalent systems are systems of equations that have the same solution.
Evaluate Given an expression and values for the variables, it is the process of substituting these values in the expression and simplify it following the order of operations.
Even function A function for which the graph has the y-axis as axis of symmetry. y = 6x2 + 4x + 1
Event

Any given group of possible outcomes we have in probability.

Possible results in one experiment.

Flipping a coin the outcomes are Head and Tail.
Experimental data It is the data collected from an experiment in statistics to specifically find the answer of a question.
Experimental probability

It is given by the ratio of the number of times an event occurs and the number of times the experiment is done to find the probability.

Results we get from an experiment.

Explicit formula In sequences, an explicit formula shows the nth term of a given sequence in terms of n.
Exponent It is a raised number representing the repeated multiplication of a given factor. 103 = 10x10x10
Exponential equation Equation with variables in the exponent (s)
Exponential function Any equation of the form y = bx that has a variable as exponent. Exponential functions and logarithmic functions are inverses each other.
Expression Any combination of numbers and operations without the = sign.
Extended proportion An extended proportion is when three or more ratios are equal.
Exterior angle (polygon) It is the angle formed in a polygon by the side and an extension to this side.
Exterior angle sum theorem All the exterior angles in a polygon, one per vertex, added together are 360 degrees.
Exterior angle theorem triangle The exterior angle of a triangle is equal to the sum of the remote interior angles.
Extraneous Solution After an equation is solved, sometimes the number yielded in the solution doesnt work for the original equation. This is an extraneous solution. Rational, radical, logarithmic and absolute value equations need to be verified for this kind of solutions.

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Factoring The process to brake a polynomial down into the product of several factors.
Factorial!

n! represents the product of all the whole numbers from n to 1.

n! is the product of all the whole numbers from n down to 1 - used in probability.

5! = 5  4  3 2  1 = 120
Factors All whole numbers that are multiplied together to yield another number.

5 and 6 are factor of 30.

30 = 5x6

Factor theorem Given a polynomial if (x - a) is a factor, then f(a) = 0.
Factored Form Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial. y = (x + 5)(x  1) is the factored form of
y= x2 + 4x  5
Favorable outcome The desired results of an experiment in probability. Getting an even number when rolling a dice {2,4,6}
Fraction

The ratio of two numbers that represents the part of a whole. A fraction is a rational number, and rational numbers is a subset of the real numbers.

Fraction bars in algebra indicate division.

4/7
Feasible region Given a set of inequalities with a set of constrains; the area in the graph that satisfies all the inequalities and constrains is the feasible region.
Flow proof A process of proving a statement with previously proven statements and representing the process in a flow of statement/reason blocks joined by arrows indicating the flow.
Focus of a hyperbola The point inside the branch of the hyperbola that is connected to each point in the branch, as these connect with the other focus in the other branch; so that the absolute value of the difference in these two lengths is constant.
Focus of a parabola The midpoint in the Latus Rectum and on the axis of symmetry of the parabola. The distance from this point inside the parabola to a point in the parabola, is the same as the length of the perpendicular segment that connects the directrix to this point in the parabola.
Focus of an ellipse Each one of the points in the major axis of the ellipse, from which sum of the distance from each to the set of points in the ellipse is constant.
Foundation drawing Drawing that is made to show the base of an object known as the foundation and the height of each part.
Function A relation of the type that has exactly one value in the domain (independent variable) matching a value in the range (dependent variable).
Function notation

A function written with the symbol f(x) instead of y.

It is read as f of x.

f(x) = 5  4x
y = 5  4x

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Geometric Mean The geometric mean of two numbers a and b is the square root of (a)(b)
Geometric probability A probability that uses the ratio of segments, areas and volumes to find the probability of points, segments, areas or volumes.
Geometric Sequence A series of numbers for which each consecutive number is the previous one times a constant known as common ratio.
Geometric series Given the terms of a geometric series; the geometric series is the indicated sum of the terms.
Glide reflection It is the composition of a translation followed by a reflection in a line that is parallel to the translation vector.
Glide reflectional symmetry A type of symmetry in which there is a glide reflection that allows mapping a figure onto itself.
Golden ratio The ratio of the length of a golden rectangle to its width. It is more or less 1.62.
Golden rectangle A rectangle that may be divided into a square and a rectangle. The resulting rectangle is similar to the original rectangle.
Graph of an equation The set made of all the ordered pairs or points that when substituted in an equation yield a true equality statement.
Greatest common factor GCF Given several whole numbers; the largest number that is a factor of all of them.
Growth factor For an exponential growth function of the form y = abx, where b > 1, with b the decay factor.

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