Shormann Algebra 1 and 1/2 Geometry Vocabulary ‧₊ ᵎᵎ 🍒 ⋅ ˚✮

The Shormann math for 9th grade set available not only on Quizlet!

Square Root

if x is greater than 0, than the square root of x is the unique positive real number such that the square root of x squared equals x

Digit

any of the Hindu-Arabic numerals 1 through 9, and 0

Counting (Natural) Numbers

numbers used to count objects (like 1, 2, 3, etc.)

Whole Numbers

counting numbers and the number 0

Integers

whole numbers, and all negative numbers

Real Numbers

any number used to describe a positive or negative number - includes all integers, decimals, and fractions

Imaginary Numbers

the result of taking the square root from a negative number - normally, the square root of -1 is factored out and exchanged for the symbol “i” - i2 = -1

Absolute Value Symbol

two vertical bars enclosing a number, like this: IaI

Algebraic Subtraction

if a and b are real numbers, then a-b = a + (-b), and -b is the opposite of b

Ratio

the size of one thing relative to another

Prime Number

a number that is only divisible by itself and one

Numerator

the top value in a fraction

Denomenator

the bottom value in a fraction

%

symbol for percent, which means “per 100”

Proportional

having a constant ratio

Analogy

resemblance in some particulars between things otherwise unlike; similar

Algebra

a generalization of arithmetic, where letters representing numbers are combined according to the rules of arithmetic, often to solve for an unknown value

Don’t Write the 1

1x = x and x to the power of 1 = x

X to the Power of 0 = 1

anything (except 0) raised to the power of 0 equals 1

X.X.X.X…. = X to the Power of “N”

for example, x.x = x squared, x.x.x = x cubed, etc.

X to the Power of -N = 1/X to the Power of N

anything (except 0) raised to a negative power equals 1 over anything raised to the opposite of that power

Polynomial in One Unknown

one term, or the sum of individual terms of the form ax to the power of n, where a is a real number, x is an unknown quantity, and n is a whole number

Polynomial in More than One Unknown

one term, or the sum of individual terms of the form ax to the power of n y to the power of m z to the power of p where a is a real number, and the rest are unknown quantaties

Axiom

a self-evident statement about something obvious, normally common to all sciences

Postulate

a construction (drawing) of something, normally common to a particular science, that may be obvious — assumed to be true without proof

Point

that which has no part — its location is represented by a dot

Line

a widthless length — its location is represented on paper by using a pencil and a straight edge

Line Segment

a line with a start point and end point

Plane

a flat surface having length and width only

Ray

a line with a starting point but no end point

Angle

two rays in the same plane that share a common starting point and do not overlap

Right Angle

formed when two lines or line segments intersect, forming 4 adjacent angles that are equal and perpendicular to each other

Obtuse Angle

an angle greater than a right angle

Acute Angle

an angle less than a right angle

Parallel

two lines that never intersect

Circle

a plane figure contained by one line called the circumference, such that all the straight line segments falling upon it are equal to each other, and have one point in common, the center

Diameter

any line segment drawn through the center of a circle and terminated in both directions by the circumference

Radius

half the diameter

Polygon

simple, closed, coplanar geometric figures whose sides are straight lines

Equilateral Triangle

all sides are congruent (equal)

Isosceles Triangle

two sides are congruent

Scalene Triangle

no sides are congruent

Right Triangle

one right angle

Obtuse Triangle

one angle greater than a right angle

Acute Triangle

three acute angles

Parallelogram

two pairs of parallel sides

Trapezoid

one pair of parallel sides

Rectangle

a parallelogram with four right angles

Rhombus

an equilateral parallelogram

Square

a rhombus with four right angles

Polyhedron

formed by four or more polygons that intersect only at their edges

Solid

three dimensional figures

Cone

circular base and a lateral surface that comes to a point

Cylinder

two parallel circular bases connected by a lateral surface

Sphere

the set of points a given distance from a given point called the center

Deductive Reasoning

applying rules

Inductive Reasoning

finding rules

Mathematical Proof

a deductive argument where rules and definitions are applied to reach a logical conclusion

Theorem

also called propositions, these are true mathematical statements requiring proof — theorems particular to a certain discipline are sometimes called lemma, such as the lemma found in Newton’s science book, Principia

Side

a segment of a polygon

Vertex

where two sides of a polygon, or two rays of an angle, meet

Convex Polygon

a polygon with no indentations

Concave Polygon

a polygon that has at least one indentation

Hypotenuse

in a right triangle, it is the side opposite the right angle

Transversal

a line that intersects two or more parallel lines, and is not perpendicular to those lines

Tesselation

a repeating pattern of shapes that covers a plane with no gaps or overlaps

Fractal

an object or quantity that displays self similarity on all scales

Analytical Geometry

where algebra and geometry meet on the coordinate plane

Ordered Pair

a pair of numbers, written in a specific order — on a coordinate plane, an ordered pair is used to identify the location of a point, and has the form (x,y)

Function

a relationship where the output (y) depends on the input (x) — each input, or domain value, maps to one, and the only one value in the output, or range

Relation

like a function, except the input (x), can map to more than one output (y)

Undefined

a function is said to be undefined when a value is not part of its domain

Indeterminate

when both the numerator and denominator equal zero

y = mx + b

the standard form for the equation of a line; where m is the slope and y is the y-intercept

Slope

a ratio expressing the change in the dependent variable (y) with respect to the independent variable (x) — also referred to as “rise over run”

Y-Intercept

the location where a function crosses the y-axis

Cartesian Coordinate System

also called a coordinate plane, it is a plane containing a horizontal “x” axis and a vertical “y” axis — it is used to graph pairs, functions, experimental data, etc.

Data

a collection of facts and information recorded during an experiment, from which conclusions and decisions can be made

Right Solid

any geometric solid whose sides are perpendicular to its base

Calculus

the mathematical study of rates of change

Delta

the symbol used in calculus that means “change in”

Infinitesimal

the idea that a quantity can be close to, but not equal to zero

Limit

the application of infinitesimals to evaluating a function

Tangent Line

a line that touches a function essentially at one point

Derivative

the slope for a line drawn between two points on a function that are an infinitesimally small delta x apart

Integral

the use of infinitesimals to calculate area

Mean

the average of a set of numbers

Median

the middle number in a set of numbers

Mode

the most often occurring number in a set of numbers

Range

the difference between the smallest and largest numbers in a set of numbers

Statistics

mathematics related to the collection, organization, and interpretation of mathematical data

Histogram

a type of bar graph where each set of data is organized into groups, and the frequency of values in each group is graphed

Normal Distribution

also called a bell curve, this is a common pattern obtained from a histogram

Bit

a digit in a binary number system — it can have two values, 1, or 0 — in computer memory, this is a small electrical switch which is either on (value 1) or off (value 0)

Byte

in computer memory, this equals 8 bits

Pixel

abbreviation for “picture element,” the small discrete elements of digital photography and computer/television screens containing color information

Matrix

a two-dimensional array consisting of rows and columns of numbers

Array

like a matrix, but not limited to two dimensions — used in computer data storage

Sequence

numbers ordered in a way that they form a definite pattern