GLOSSARY OF MATH TERMS
ALGEBRA AND GEOMETRY
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| Word | Definition | Examples |
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| Radical | The symbol that encloses a square root or any other given root. |
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| Radical equation | Any equation with an expression with variables inside a radicand or variables raised to a rational number. |
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| Radical function | Any function whose equation is also a radical equation. | |
| Radicand | The number that is under the radicand sign. |
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| Radius | For a circle the radius is the segment with endpoints at the center of the circle and the circle. | 
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| Radius of a regular polygon | The radius of the circumscribed circle to a regular polygon. |
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| Range | All possible values in the set that constitutes the output for the function. |
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| Ratio | A fraction that compares two numbers. |
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| Rational exponent | Given that the nth root of x is a real number
and m is an integer,
we have that x1/n = nÖx and xm/n = nÖxm= (nÖa)n |
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| Rational expression | An expression with fractions, especially when there is a variable in the denominator. The variable can not make the denominator equal to zero |
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| Rational function | A rational function is a function of the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions and Q(x) ¹ 0 | |
| Rational number | Any number that may written as a fraction; including whole numbers (written as fractions with 1 as denominator) and decimals that truncate or repeat (may be expressed as fractions). |
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| Rational root theorem | A theorem which states that in a polynomial the different combinations of the factors of the numerator and denominator of the quotient [constant term]/[leading coefficient] contains all the possible rational real zeros in the polynomial. In other words: If 0 = anxn + an-1xn-1 +...+ a1x + a0 then p/q in its simplest form is a rational root of this polynomial equation, where all coefficients an ...a0 are integers, and p must be a factor of a0 and q must be a factor of an . |
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| Rationalize the denominator | The process of changing the denominator of a fraction from radical expression to rational number without changing the value of the expression. |
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| Ray | The section of a line that has one endpoint in one side and it never ends at the other side. (flash light beam pointing to the space) | |
| Real number |
Any number rational or irrational. With exception of the imaginary numbers all numbers are real numbers. |
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| Reciprocal | Multiplicative inverse of a number different than zero. The multiplication of a number and its inverse is 1. | |
| Rectangle | Any parallelogram that has 4 right angles. |
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| Recursive formula | A recursive formula in a sequence is defined in a way that the output of the first iteration is the input of the second iteration and so on. |
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| Reduction | Reduce a fraction to its simplest terms. | |
| Reflection | It is a transformation known as a flip that maps a point in the plane to its mirror image, by means a specific line as the mirror line. | |
| Reflectional symmetry | A type of symmetry where a figure reflects onto itself using a line of reflection or line of symmetry. | |
| Reflexive | Refers to reflexive property: | a = a ; Ðb=Ðb |
| Regular polygon | A polygon that is both equilateral and equiangular. |
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| Relation | A set of ordered pairs. |
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| Remainder theorem | Given a polynomial P(x) of degree n ³ 1; when divided by a linear factor (a - 1) and having a to be a constant, then the remainder is P(a). |
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| Remote interior angles | The two nonadjacent angles to any exterior angle in a triangle. |
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| Resultant | The sum of two given vectors is the resultant. | |
| Rhombus | Any parallelogram with 4 congruent sides. |
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| Right Angle | An angle measuring 90°. |
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| Right Triangle | A triangle with one 90° angle. The other two angles are complementary that is add up to 90°. | 
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| Rotation | A rotation is a transformation where a geometric figure is rotated around a point. | |
| Rotational symmetry | It is a transformation consisting of a turn of x degrees around a point K in a way that for any point Y in the figure KY=KY' and mÐYKY' is x degrees. The image of Y is Y' and the image of K is K itself. | |
| Same-side interior angles | Also known as consecutive interior angles; they lie in the interior of parallel lines cut by a transversal and at the same side of this transversal. | 
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| Sample | Gathered information from just a part of the population. | |
| Sample proportion | Having an event occurring y times in a sample of size x, the sample proportion then is y/x. | |
| Sample Space | All possible ways an event may happen. |
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| Scalar multiplication | It is the multiplication of each entry in a given matrix by the same number, called the scalar. | |
| Scale | It is the ratio of any length of the corresponding side of one figure to the length of the corresponding side of another similar figure. The length may be given in different units. | 1 km to 1mile 1 m to 1 ft |
| Scale drawing | A drawing for which all lengths are proportional to the corresponding lengths. | |
| Scalene triangle | A triangle with all sides of different length. |
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| Scientific Notation | A number of the form a x 10n where n is 1<a<10. For numbers greater than 0 and less than 1 n is negative. |
62,300,000 = 6.23 x 106 0.000311 = 3.11 x 10-4 |
| Secant | Line, line segment or ray that intersects the circle in two different points. | |
| Secants and a tangents intersecting at an exterior point. (angle) | The angle formed by secants and/or tangents intersecting at an exterior point is given by half the positive difference of the two included intersected arcs in the circle. |
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| Secant and a tangent intersecting at the point of tangency in the circle. (angle) | The angle formed by a secant and a tangent intersecting at the point of tangency in the circle is given by half the measure of the included intersected arc. |
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| Secant and a tangent intersecting at the exterior of the circle. (segments) | The square of the tangent's length is equal to the product of the secant's length and the length of the secant's exterior segment. Lengths are taken from the exterior point to points in the circle. |
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| Secants intersecting at an exterior point of the circle. (segments) | The product of the secant's length and the length secant's exterior segment is equal to the product of length of the other secant and the length of its respective exterior segment. Lengths are taken from the exterior point to points in the circle. |
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| Secants intersecting at the interior of the circle (angles) | Two secants intersecting at the interior of a triangle form vertical angles whose measure is half the sum of the arc's angular measure for the included intersected arcs. |
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| Sector of a circle | The area of the interior of a circle that is intercepted by a central angle. |
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| Segment | A section of a line, defined by two end points and all the points between them. | 
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| Segment of a circle | The area bounded by an arc and its chord. | |
| Segment parallel to the third side in a triangle. | If a segment connecting two sides of a triangle is parallel to the third side, then the segments produced in one connecting side are proportional to the segments in the other connecting side. (The converse is also true) |
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| Semicircle | Exactly half a circle | |
| Sequence | Defined as an ordered list of numbers. | |
| Series | Implies the sum of all the terms in a sequence. It may be finite if the sequence is finite or infinite if the sequence is infinite. | |
| Side-angle-side similarity | Two triangles are similar if two of their corresponding sides are proportional and the included corresponding angles congruent. |
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| Similar figures | Figures with all corresponding angles congruent and corresponding sides proportional. Same shape, but different size. | |
| Similar polygons | Similar polygons have congruent corresponding angles and proportional sides. |
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| Side-side-side similarity | Two triangles that have all the corresponding sides proportional and the corresponding angles congruent are similar. |
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| Similar solids | Solids with the same shape and all their corresponding dimensions proportional. |
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| Similar Triangles | Triangles that have all corresponding angles and corresponding sides proportional. Same shape, but different size. | |
| Similarity ratio | Ratio written using the lengths of corresponding sides in similar polygons. | |
| Simple fraction | Fraction with a whole number in the numerator and a whole number in the denominator. | |
| Simple Interest | Interest obtained using the formula I = prt, where I is generated, p is principal, r is the interest rate per period of time, and t is the time period. | |
| Simplest form | Simplest form of a rational expression implies that the polynomial in the numerator and the polynomial in the denominator don't have any common divisors. | |
| Simplify | Done by combining all like terms and eliminating all grouping symbols like parenthesis to get the least number of terms in an expression. | 4(9 – 5) changes to 16 when simplified. |
| Simulation | Cases in which probabilities are difficult to get experimentally; it is common to resource to models of the involved events. | |
| Sine |
Ratio of the length of the opposite side to a reference angle in a right triangle and the hypotenuse. Opposite/hypotenuse. |
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| Skew lines | 2 lines in different planes that don’t intersect. | 
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| Slope | The measure of
how steep a line is. The change in y (rise) divided by the change in x
(run). Slope = m |
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| Slope Formula | m = (y2 - y1)/(x2 - x1) | 
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| Slope cases | Horizontal, vertical, tilted to the right, tilted to the left. | 
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| Slope-Intercept form |
A linear equation of the form y = mx + b, where m is the slope and b is the y-intercept |
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| Solids | Cones, cylinders, prisms, pyramids and spheres. |
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| Solution of an equation | The solution of the equation are all the values for the independent variable(s) that make the equation a true statement when they are plugged into the equation. |
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| Solution or root | The value that makes an equation a true statement, a root refers particularly to the value of x for which y = 0, this value is also the x-intercept of the graph. |
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| Solution set | Set of all values that make an algebraic statement true. |
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| Solve | To find the solution, to find the answer, to get to know the value for which a variable stands for. | |
| Space | All existent points in the universe. | |
| Special right triangle
30-60-90 |
A special right triangle 30-60-90 has the hypotenuse equal to twice the length of the side opposite to the 30 degree angle, and the length of the side opposite to the 60 degree angle; equal to the product of the square root of three and the length of the side opposite to the 30 degree angle. |
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| Special right triangle 45-45-90 |
A special right triangle 45-45-90 has congruent legs and the hypotenuse length equal to the product of square root of two and the length of the leg. |
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| Sphere | A sphere is properly defined as the set of points in the space that are equidistant of one point called center. Planes that go through the center of the sphere, intersect GREAT CIRCLES. The circumference of the sphere is the perimeter of any of its great circles. |
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| Sphere: Surface area and volume. | The surface area of an sphere is 4 times the area of one of its great circles. The volume is equal to the volume of 4 right cones with base and height equal to radius of the sphere. |
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| Square | Parallelogram with four congruent sides and four congruent angles. |
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| Square Root | If x2 = y, then x is the square root of y. Square root is the opposite of square. |
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| Standard deviation | It is the measure of how far or close the values in the data are from the mean. | |
| Standard form of an equation of a circle | (x - h)2 + (y - k)2 = r2 where (h,k) is the center and r is the radius. |
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| Standard Form of a Polynomial | When the degree of the terms in a polynomial are ordered from left to right in decreasing order. |
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| Standard form of a quadratic function | The standard form of a quadratic equation is f(x)= ax2 + bx + c, where a ¹ 0. | |
| Standard normal curve | It is defined as a normal distribution that is centered in the y-axis and for which standard deviation is 1. | |
| Straight angle |
An angle measuring 180°, formed by to opposite rays. An angle that measures 180°, a straight line. |
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| Subtraction | Adding the opposite | 7x - 3x = 7x + (-3x) = 4x |
| Supplementary angles | Two positive angles whose measures add to 180 degrees. | 
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| Surface area | For a solid different that the sphere is the sum of the area of the bases and the lateral areas. For a sphere is 4 times the area of any of the great circles. | |
| Symmetric | A figure that has some type of symmetry. | |
| Symmetry | A figure with symmetry needs to have an isometry that allows to map the figure onto itself. | |
| Synthetic division | A process of dividing a polynomial by a linear factor, using the coefficients and ignoring the variable and the exponents (they are relevant just as the position to place the coefficients). When dividing the sign of the divisor is reversed to avoid subtracting and to allow just to add. |
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| System of equations | A given set of equations with the same variables per equation. To solve it you need the same number of variables as equations you have. |
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| System of Linear Equations | Two or more linear equations for which goal is to find a common solution. The system may be unique, independent and consistent; dependent and consistent with infinite number of solutions or independent and inconsistent with no solutions. |
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| Table of Values | A method of finding points in the coordinate plane to graph a relation. A set of values for x is selected and plugged in the equation to find the corresponding value for y. A column is given to x, another to the equation, another to the values for y, and the final for the coordinate points (x,y) generated. |
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| Tangent | The ratio of the length of the opposite side of a reference angle to the adjacent side to the same angle. Opposite over adjacent. |
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| Tangent to a circle | A line, line segment, or ray that intersects the circle in just one point. |
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| Tangents intersecting at an exterior point of a circle. | Two tangents that intersect at an exterior point of a circle have have the same length from the intersection to the point of tangency. They are perpendicular to the radius at the point of tangency. |
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| Term | A form of grouping one or more numerical and/or variable factors by means of multiplication and division. Addition and subtraction symbols separate terms. |
6kj is one term
4k2u + 6k |
| Terminal point | A vector has to go through 2 points, the second is the terminal point. | |
| Tessellation | A pattern of geometric plane figures that covers a plane without overlapping or leaving any gaps. A pure tessellation is made up of copies of a congruent figure. | |
| Theorem | A conjecture that has been proven and may be used in proofs to prove other statements. | |
| Theoretical Probability | The computation of the possibility that something will occur based on the number of possible outcomes. | |
| Tiling | A pattern of geometric plane figures that covers a plane without overlapping or leaving any gaps. A pure tessellation is made up of copies of a congruent figure. | |
| Tolerance | The difference in the desired value, above and below the value. The tolerance is one and a half the difference between the maximum and minimum values. | |
| Trace | The set of values that result from plugging in zero into the equation of a plane. | |
| Transformation | It is defined as the change experimented by a geometric figure. There are four types: Translations, rotations, dilations, and reflections. | |
| Translation | Shifting a graph horizontally or vertically. | |
| Translational symmetry | A translation that allows mapping a figure onto itself. | |
| Transversal | A line cutting two coplanar lines. | 
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| Transverse axis | A segment in the hyperbola goes from vertex to vertex of the two branches, and it is contained in the line that goes through the foci. |
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| Trapezoid | Quadrilateral with exactly one pair of parallel sides. |
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| Triangle | A polygon that has three sides and three angles | |
| Triangle classification by angles | Triangles may be classified as acute, right, and obtuse. |
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| Triangle classification by sides | Triangles may be classified as scalene, isosceles and equilateral. |
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| Triangle inequality theorem | The sum of two given sides of a triangle is always greater that the remaining side. |
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| Trigonometry ratios | The trigonometry ratios for a right triangle are sine, cosine and tangent. |
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| Truth table | A table containing the truth values of a Boolean expression. Boolean operators are "and", and "or." | |
| Two column proof | A two column proof consist of proving a statement in a logical way by using statements already proven before. |
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