Algabria 2 Vocab

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Exsperimental probability of evnt

P(event) = number of times that an event occurs over number of trials

Factoring

rewriting an expression as the product of its factors

center

middle

Monomial

A number, a variable, or a product of a number and one or more variables

Trinomial

A polynomial with 3 terms

Matrix

A rectangular array of numbers. You usually display the array of numbers within the columns in the array.

function

A relation in which each element of the domain corresponds with exactly the one element of the range

combination

A selection of numbers or objects in which order does not matter

Domain

A set of inputs, also called x coridinants, of the orderd pairs

diffrence of two squares

A squred - b squred

Equation

A statement where the two expressions are equal

How to factor the diffrence of two squres

A sured - b squred = (a + b)(a -b)

Variable

A symbol, usually a letter, that represents one or more numbers Exsanmples: n, x

row operations

A system used to solve a matrix

Constant term

A term with no variables

zero of a function

A value of x where f (x) = 0

data point

A value that originates in a worksheet cell and that is represented in a chart by a data marker

box and whisker plot

A way to display dat that uses -quartertiles to bound the center box and -the minimum and maxim values that form the whiskers

Distrubutive Property for subtraction

A(b-c) = ab-ac

Asscociate Property

Addition: (a + b) + c = a + (b + c) Multiplication: (ab)c = a(bc)

Communitive property

Addition: A + b = b + a Subtraction: ab = ba

Property of clousure

Addition: a + b is a real number Subtraction: ab is a real number

consecutive

All in a row or pattern, 123 ect.

permutation

An arrangement of items in a particular order.

literal equation

An eqaion that uses two different letters as variables

Outlier

An outlier is a value that is substantially different from the rest of the data in a set. If the data is in one variable, outliers can occur at the ends. They can be misleading because they affect measures of central tendency.

And and Or

And means that a solution is always true Or means that a solution makes either inequality true,

n factorial

N! = n(n-1) * ... * 3 * 2 * 1. Zero factorial is 0! = 1.

Complex conjagations

Number pairs of the form a + bi and a - bi

irrational numbers

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.

Unnatural numbers

Odd numbers basiclly

Open and closed circles

Open circles stand for greater then Closed stand for less then or equal to

Inverse operations

Operations that undo each other

Zero Product Property

if ab=0, then a=0 or b=0

vertex of a parabola

(H, k) the intersection of the parabola and it's axsis summery

standard form of a circle

(x-h)2 + (y-k)2 = r2

Opposite of an Opposite

-(-a) = a [If a is a positive number, then the answer will be positive as well]

Opposite of a Sum Property

-(a+b)=(-a)+(-b)

Opposite of a Difference

-(a-b) = -a + b = a -b

Opposite of a product

-(ab) = -a x b = a x (-b)

multiplication by -1

-1 x a = -a

Opposite or additive inverse

-a Examples: 12 + (-12) = 0 where -12 is -a -7 + 7 = 0 where -7 is -a

Multiplication by 0

0 x a = 0

Reciprocal or multiplication inverse

1/a Examples: 8(1/8 = 1 where 1/8 is 1/a -5(-1/5) = 1 where -1/5 is 1/a

distibutive property for subtraction

A (b - c) = ab - ac

Definition of Division

A / b = a over b = a . 1 over b, b is not equal to o

Bimodal

A bimodal set has two modes. If a data set has more then two modes, then the modes are probably not statistically useful. If no value occurs more frequently then any other, then there is no mode.

Equally likely sample space

A combination of equally likely events in a set

greatest common factor (GCF)

A common factor of the terms in the exspression. It is the common factor with the greatest coefficent and the greatest exsponent. You can factor any exspression that has a GCF not equal to 1.

positive correlation

A correlation where as one variable increases, the other also increases, or as one decreases so does the other. Both variables move in the same direction.

Translation

A function that moves an object a certain distance

linear function

A function whose graph is a line

Scatter plot

A graph that relates two sets of detail by plotting the data as ordered pairs.

Axises of summery

A line that divides the parabola line into two mirror images. The equation of the axis summery is x = h

Numeric exspression

A mathematical phrase that contains numbers and open sybols Exsamples: 3 + 5 (8-2 + 5)

Algebraic exspression

A mathematical phrase that contains one or more variables Exsamples: 3n + 5 (8x-2 + 5n)

simulation

A model of an event

function rule

A n eqasion that represnts an output value in terms of an input value

Percentile

A number from 0 to 100 that you can associate x value from a data set. it shows the percent of the data that are less then or equal to x. If x is at the 63erd percentile, then 63% of the data are less then or equal to x.

principal root

A number that has a positive and a negative root

Imiginary number

Any number in the form of A + bi where a and b are real numbers and b does not equal 0

Matrix element

Any number within a matrix

standerd form of a linear equation

Ax + By = C where A, B and C are real numbers and A and B are not both 0.

Complex number

Coplex numbers in the form of a + bi where a and b are real numbers and b is not = to 0 If b = 0 the number a + bi is a real number If a = 0 and b does not equal zero the number a + bi is a pure imiginary number

Transformation

Each function in a family

Quadratic function, which you can write in the form of f(x) = ax to the second power + bx + c

F(x) = ax to the second power + bx + c

Key concepts box: The parent quadratic function

F(x) = x to the second power is the parent quadric function. It's graph shows is the parabola shown in the box see photos The axis of symmetry is x = 0. The vertex is (0,0)

dependent variable

F(x); it represents the output of the function. It is called the dependent variable because its value depend on the input value.

Median

For a data set listed in order, the middle value for an odd number of data values; the mean of the two middle values for an even number of data values Exsample: for 1, 2, 3, 4, 5, 5, 9, the middle two values are 3 and 4. The median is their mean 3 + 4 over 2 = 3.5

nth root

Given the sequence of equasions a(n) = b,a is the nth root of b

Like terms

Have the same variables raised to the same powers

theorectical probability

If a sample space has n equally likely outcome and an event A occurs in m of these outcomes, then the theoretical probability of event A is P(A) = m over n.

Measure Of central tendency

Indicates the middle of a data set. The mean median and mode are the most common uses of central tendency

verticle line test

It sates that if a vericle line passed es through more than one point of the graph of a relation, then the relation is not a function

Slope of a line

Positive slope, line rises left to right. Negative slope, line falls from left to right Zero slope, horizontal line. Unidentified slope, vertical line.

Variable Quantity

Quantities whose values change or vary

Constant

Quantities whose values do not change

correlation coefficient

R; indicates the strength of a correlation.

Slope

Ratio of horizontal vs vertical change or rise over run in a graph

verticle compression

Ruduces all y values of a function to the same function between 0 and 1.

Concept Summery: Writing Equations of Lines

Slope Intercept form: y = mx + b Use this form when you know the slope and y intercept. Point Slope Form: y - y1 = m(x - x1) Use this form when you know the slope and a point, or points. Standard Form: Ax + By = C A, B and C are real numbers. A and B cannot both be zero.

mean

Sum of data values over number of data values Example: 1 + 2+ 3 + 3 + 4 + 5 + 5 + 9 over 8 = 4

imaginary unit

The complex number whose squre is -1. So i squred = -1 and i = the saure route of -1

Range of a set of data

The difference between the greatest value to the least value. If you order the data from least value to greatest value, the. The median divides the data into two parts. The median of each part divides rhe data further and tou have four parts in all.

interquartile range

The difference between the third and first quantities

Discrimanent

The discriminant of a quadratic equasion is in the form of ax squred + bx + c = 0 is the value of the exspression b squred - 4ac

perimeter

The distance around a figure

Radius

The distance from the center of a circle to any point on the circle

linear equation

The equation that represents a linear function

Parabola

The graph of a quaderatic function

Parabla

The graph of a quadratic function which you can write in the form of f(x) = ax squred + bx + c where a is not = 0

Fundimental Counting Principle

The method of using multiplication to count

Mode

The most frequently occurring values Exsample: two modes: in 1, 2, 3, 4, 5, 5, 9, both 3 and 5 occerd twice

Index

The number that gives the degree of the root

Radicand

The number under the radical sign

Complex number plaine

The point (a,b) represents the complex number a + bi. To graph a complex number, locate the rewal part on the horizontial axsis and the imaginary part of the y axsis

Reflection

The process by which a graph of a function is flipped across the line, such as the x or y axis. Each point on the graph of the reflected function is the same distance from the line of reflection as it's corresponding point on the graph of the original function.

experimental probability

The ratio of the number of times an event occurs to the total number of trials, or times that the activity is performed.

Sample space

The set of all possible outcomes to an experiment or activity

Range

The set of outputs, also called y coridinanents of the orderd pairs

parent function

The simplest form of a set of functions that form a family.

Slope

The slope of a non-vertical line through set of points (x1, y1) and (x2, y2) is the tratio of the vertical change to the corissponding horizontal change.

parelell lines

The slope of parallel lines are equal.

perpindicular lines

The slope of these lines are negative reciprocals of each other.

Correlation

The strenth of a relationship between two points.

Cube root

The third root of a number

quantities

The values that separate a set of data.

verticle stretch

The vertice stretch is the thing that manipulates all y values of a function by the same factor greater than 1.

fuction notation

The way to write a function rule

minimum value

The y codinate of the vertewx If a < 0, the parabola opens downwards

maximum value

The y coordinate of the vertex.

maximum value

The y cordinate of the vertex

Minimum value

The y cordinate of the vertex.

Evaluate

To evaluate an expression, substitute a number for each variable in the equation. Then simplify using order of operations.

Solution of an equasion

To find the solution of an equasion, isolate the variables on each side of the equasion using inverse operations

compound inequality

Two inequalities with the words and and or To solve a compound inequality, containing and, find all values of the inequality that make both inequalities true.

Theoretical Probability

What should occur or what we expect to happen in an experiment

Equally likely outcomes

When each outcome in a sample space has the same chance of occurring

combined variation

When one quantity varies directly and/or inversely as two or more other quantities

X >/= 4

X is greater than or equal to 4 To graph: draw a closed circle above the 4 on the number line and then draw an arrow to the right.

X > 4

X is greater then 4 To graph: place a open circle above the 4 on a number line a draw an arrow going to the right

X < 4

X is less than 4 To graph: draw a open circle above the 4 on a number line and then draw a line going to the left.

X </= 4

X is less than or equal to 4 To graph: draw a closed circle above the 4 on a number line then draw a line going to the left.

How to form a perfect square trinomial from x squred by adding b/2 squred.

X squred + bx + (b/2) squred = (x + b/2) squred

independent variable

X; it represents the input of the function

The equation of a line through point (x1, y1) with the slope as m

Y - y1 = m(x - x1)

direct variation

Y = kx or y over x = k where k is not equal to 0

slope intercept

Y = mx + b where m is the slope of a line and (0, b) is the y intercept

Sample Space (Probability)

list of all possible outcomes

diagram

a drawing intended to explain how something works

cubic

a polynomial with a degree of 3

Quintic

a polynomial with a degree of 5

Relation

a set of pairs of input and output values

perfect square trinomial

a trinomial that is the square of a binomial For exsample, x squred + 10x + 25 = (x + 5) squred

simulation

a way to model random events

distibutive property

a(b+c)=ab+ac

Definition of Subtraction

a-b=a+(-b)

Inverse Variation

an equation of the form y = k/x, where k is not equal to zero

Identity

an equation that is true for every value of the variable

Term

an expression that is a number, a variable, or the product of a number and one or more variables

Negative correlation

as one variable increases, the other decreases

Natural Numbers

counting numbers

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

absolute value of a complex number

distance from the origin on the complex number plane Or I a + b I = the square route of a squared + b squared

Bimodal

distributions with two modes

Vertex form

f(x) = a(x-h)^2 + k

plotting

finding the data point for an ordered pair

Linear

straight line

Coefficent

the numerical factor of a term

complete the square

the process of adding a term to a quadratic expression to make it a perfect square trinomial

Constant of a variation

the ratio of all output-input pairs equals the constant k (except for (0, 0) )

parent graph

the simplest of the graphs in a family of graphs

Binomial

the sum of two monomials

line of best fit

the trend line that gives the most accurate model of related data

x-intercept

the x-coordinate of a point where a graph crosses the x-axis

y-intercept

the y-coordinate of a point where a graph crosses the y-axis

Integers

whole numbers and their opposites

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

joint variation

y varies jointly as x and z if there is some nonzero constant k such that y=kxz


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