Intro to Pre-Cal - Definitions

SI (Systeme international d’unites)

Measurement system in which all units are based on multiples of ten

Referent

An item used as a unit for estimating measurement

Imperial System

Measurement based on British units (base measure in an inch)

Area

2-D calculation or a shape

The amount of space a flat shape takes up

Surface Area

Measured area of all surfaces on a 3-D object

Cone

3-D object w/a circular base and a curved lateral surface from the base to the vertex

Slant Height

Shortest distance from the base of a cone or pyramid to the highest point

Lateral Height

Surface on a 3-D object that joings the bases or the base to the highest point

Sphere

Round ball-shaped 3-D object

Pyramid

3-D object w one base and same amount of triangular faces as sides on the base

Volume

Amount of space a 3-D object occupies

Apex

The highest point of a pyramid or a cone

Hypontenuse

Side opposite of the right angle in a right triangle

Always the longest side

Opposite Side

Side across from the acute angle being considered in a right triangle

Adjacent Side

Side that forms one of the arms to the acute angle being considered (not the hypotenuse)

Tangent Ratio

Ratio of the length of the opposite side to the length of the adjacent side

tan = opposite over adjacent

Sine Ratio

Ratio of the length of the opposite side to the length of the hypotenuse

sin = opposite over hypotenuse

Cosine Ratio

Ratio of the length of the adjacent side to the length of the hypotenuse

cos = adjacent over hypotenuse

Primary Trigonometric Ratio

The three ratios defined in a right triangle

SOH CAH TOA

Angle of Elevation

Angle formed by the horizontal and a line of sight ABOVE the horizontal

Angle of Depression

Angle formed by the horizontal and a line of sight BELOW the horizonal

Perfect Square

Number that can be expressed as the product of 2 equal factors (same factor twice)

Square Root

One of the 2 equal factors of a number

Perfect Cube

A number that can be expressed as the product of 3 equal factors (same number three times)

Cube Root

One of the 3 equal factors of a number

Prime Factorization

Process of writing a number as a product of its prime factors

Base

Number or variable that is being multiplied repeatedly in expanded form

Exponent

Value that specifies how many times the base will be multiplied by itself

Irrational Number

A number that cannot be expressed in the form a/b where a & b are integers, and b does not equal 0

cannot be a terminating or repeating decimal

Radical

consists of a root symbol, index & a radicand

can be rational and irrational

Radicand

the value under the radical sign

Index

Indicates what root to take

Mixed Radical

Product of a rational number and a radical

Entire Radical

Product of 1 and a radical

Monomial

A number, a product of 1+ variables or a product of a number and 1+ variables

Numerical Coefficient

the number being multiplied by the variable(s)

Polynomial

Algebraic expression formed by adding or subtraction monomials (each called a term)

Degree of a Term

Sum of exponents of the variables (highest term degree is taken for the entire polynomial)

Binomial

A polynomial w/ only 2 terms

Trinomial

A polynomial w/ 3 terms

Distribution Property

Rule that distributes a number into brackets (multiplied with everything in that bracket)

FOIL (Firsts, Outsides, Insides, Lasts)

Greatest Common Factor (GCF)

Largest factor shared by 2 or more terms

Least Common Multiple

Smallest multiple shared by 2 or more terms

Difference of Squares

Expression of the form a squared - b squared that involves the subtraction of 2 squares

Graph

Effective way of showing the relationship between 2 quantities

Constant Rate of Change

Represented graphically as a straight line

Steepness of Line

Indiecates rate @ which 1 quantity is changing in relation to the other

rising & to the right = increasing; down & to the right = decreasing

Relation

Association between two quantities, expressed in words, equations, ordered pairs, or graphs

Linear Relation

Relation that forms a straight line when data is plotted on a graph

Degree of Equation = 1

Non-Linear Relation

Relation that DOES NOT form a straight line when plotted on a graph

Degree of Equation = NOT 1

Discrete Data

Data values that are NOT connected (tickets, objects)

Continuous Data

Data values that ARE connected (both quantities have values in between)

Independent Variables

Variable for which the values are selected

x variable, first column of table of values, horizontal axis

Dependent Variable

Variable whose value depends on the independent variable

y variable, second column of table of values, vertical axis

Domain

Set of all possible values for the independent variable in a relation

Listed in increasing order: words, number lines, lists, set notation, interval notation

Range

Set of all possible values for the dependent variables in a relation

Listed in increasing order:words, number lines, lists, set notation, interval notation

Function

A relation in which each value of the independent variable is associated w/only one value of the dependent variable

No vertical line through the points when graphed

Function Notation

Symbolic notation used for writing a function

f(x) = f of x, value of the function at x (replaces the y)

Slope

Ratio of the vertical change, to the horizontal change of a line or line segment

m = rise over run

Y - Intercept

y coordinate of the point where a line or curve crosses the y axis

value of y when x=0

Slope Intercept Form

Equation of a line: y = mx + b

General Form

Equation of a line in the form Ax + By + C = 0

X- Intercept

x coordinate of the point where a line or curve crosses the x axis

value of x when y=0

Slope Point Form

Equation of a non-vertical line in the form y - y₁ = m(x - x₁)

Parallel Lines

Lines in the same plane that do NOT intersect

Same slope but different intercepts

0 solutions

Perpendicular Lines

Two lines that intersect at a right angle

Slope = negative reciprocals of each other

1 solution

Points of Intersection

A point @ which 2 lines touch/cross

Systems of Linear Equations

2 or more linear equations involving common variables

Solutions

A point of intersecition of lines on a graph

An ordered pair that satisfies both equations

A pair of values occuring in both equations’ tables of values

Coincident Lines

Lines that occupy the same position

Infinite solutions, equations are the exact same