Finals

Question 1

Arithmetic Sequence

Answer 1

A sequence in which the difference of consecutive terms in constant

Question 2

Asymptote

Answer 2

An line that a graph approaches more and more closely

Question 3

Change of base formula

Answer 3

A formula that allows you to rewrite logarithms in terms with another base.

Question 4

Circle

Answer 4

Consists of all points in a plane, that are a given distance from a given point.

Question 5

Combined variation

Answer 5

Describes a situation where a variable depends on two other variables, and varies directly with some of them and varies inversely with others.

Question 6

Common difference

Answer 6

The constant difference d between consecutive terms of an arithmetic sequence.

Question 7

Common logarithm

Answer 7

A logarithm with base 10, denoted by log.

Question 8

Common ratio

Answer 8

The constant ratio r between consecutive terms of geometric sequence.

Question 9

Completing the square

Answer 9

To add a term c to an expression of the form x^2+bx such that that x^2+bx+c is a perfect square trinomial.

Question 10

Complex conjugates

Answer 10

Pairs of complex numbers of the forms a+bi and a-bi, where x cannot =0

Question 11

Complex fraction

Answer 11

A fraction that contains a fraction in its numerator and denominator.

Question 12

Complex number

Answer 12

A number written in the form a+bi, where a and b are real numbers.

Question 13

Composition of fractions

Answer 13

A function that takes up operations, that uses g and f.

Question 14

Compound inequality

Answer 14

Is a compound that combines two simple inequalities.

Question 15

Conic Section

Answer 15

A figure formed by intersection of a plane and a right circular cone.

Question 16

Consistent

Answer 16

A linear on non linear system of equations. if there is one value that satisfies the equation.

Question 17

Constant of variation

Answer 17

The constant a in the inverse variation is on bottom

Question 18

Continuos relation

Answer 18

A set of data is said to be continuous if the values belonging to the set can take on ANY value within a finite or infinite interval. Definition: A set of data is said to be discrete if the values belonging to the set are distinct and separate (unconnected values).

Question 19

Correlation coefficient

Answer 19

A number that is a measure of the strength and direction of the correlation between two variables.

Question 20

Dependent

Answer 20

variable is the one that depends on the value of some other number. If, say, y = x+3, then the value y can have depends on what the value of x is. An

Question 21

Diminsions of a matrix

Answer 21

are the number of rows by the number of columns. If a matrix has a rows and b columns, it is an a×b matrix. For example, the first matrix shown below is a 2×2 matrix; the second one is a 1×4 matrix; and the third one is a 3×3 matrix.

Question 22

Direct variation

Answer 22

describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k , called the constant of variation or constant of proportionality .

Question 23

Discriminant

Answer 23

of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. It is generally defined as a polynomial function of the coefficients of the original polynomial

Question 24

Ellipse

Answer 24

an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.

Question 25

End behavior

Answer 25

of a graph is defined as what is going on at the ends of each graph. ... As the function approaches positive or negative infinity, the leading term determines what the graph looks like as it moves towards infinity.

Question 26

Exponential equation

Answer 26

are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by . To solve exponential equations with same base, use the property of equality of exponential functions . ... In other words, if the bases are the same, then the exponents must be equal.

Question 27

Extraneous solution

Answer 27

are values that we get when solving equations that aren't really solutions to the equation.

Question 28

Extrema

Answer 28

the maxima and minima of a function,

Question 29

Factor theorem

Answer 29

is used when factoring polynomials "completely". ... Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus "x minus the number" is a factor.

Question 30

finite sequence

Answer 30

is a list of terms in a specific order. The sequence has a first term and a last term.

Question 31

function

Answer 31

a relationship or expression involving one or more variables

Question 32

geometric sequence

Answer 32

is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Question 33

greatest integer function

Answer 33

, also called step function, is a piecewise function whose graph looks like the steps of a staircase. The greatest integer function is denoted by f(x) = [x] and is defined as the greatest integer less or equal to x. Example #1. [2.5] is the greatest integer less or equal to 2.5.

Question 34

growth factor

Answer 34

is the factor by which a quantity multiplies itself over time

Question 35

hyperbola

Answer 35

is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Question 36

identity function

Answer 36

is a function that always returns the same value that was used as its argument.

Question 37

imaginary unit

Answer 37

is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1. The square of an imaginary number bi is −b². For example, 5i is an imaginary number, and its square is −25. Wikipedia

Question 38

inconsistent

Answer 38

is the study of commonplace mathematical objects, like sets, numbers, and functions, where some contradictions are allowed. ...

Question 39

independent

Answer 39

is a variable that represents a quantity that is being manipulated in an experiment. A dependent variable represents a quantity whose value depends on those manipulations.

Question 40

infinite sequence

Answer 40

s a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, .

Question 41

interval notation

Answer 41

is a way to describe continuous sets of real numbers by the numbers that bound them. Intervals, when written, look somewhat like ordered pairs. However, they are not meant to denote a specific point. Rather, they are meant to be a shorthand way to write an inequality or system of inequalities.

Question 42

inverse function

Answer 42

s a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y. The inverse function of f is also denoted as f^{-1}. Wikipedia

Question 43

inverse relation

Answer 43

is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.

Question 44

inverse variation

Answer 44

mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

Question 45

joint variation

Answer 45

occurs when a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz.

Question 46

latus rectum

Answer 46

of a conic section is the chord through a focus parallel to the conic section directrix (Coxeter 1969). "Latus rectum" is a compound of the Latin latus, meaning "side," and rectum, meaning "straight."

Question 47

linear programming

Answer 47

is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.

Question 48

logarithm

Answer 48

is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Question 49

logistic growth model

Answer 49

is a common S-shaped curve with equation {\displaystyle f(x)={\frac {L}{1+e^{-k}}}, } where x_{0}, the x value of the sigmoid's midpoint; L, the curve's maximum value; k, the logistic growth rate or steepness of the curve

Question 50

matrix

Answer 50

is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is 2 × 3, because there are two rows and three columns: {\displaystyle

Question 51

n^th root

Answer 51

of a number x is a number r which, when raised to the power n, yields x: {\displaystyle r^{n}=x, } where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Wikipedia

Question 52

natural logarithm

Answer 52

is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459.

Question 53

negative exponent

Answer 53

how many times to divide by the number.

Question 54

parabola

Answer 54

s a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line.

Question 55

parent function

Answer 55

is the simplest function of a family of functions that preserves the definition of the entire family. For example, for the family of quadratic functions having the general form

Question 56

piece wise defined function

Answer 56

is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself. Wikipedia

Question 57

point slope form

Answer 57

the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form.

Question 58

quadratic function

Answer 58

a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree. Wikipedia

Question 59

radicand

Answer 59

an nth root of a number x is a number r which, when raised to the power n, yields x: {\displaystyle r^{n}=x, } where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root.

Question 60

rate of change

Answer 60

is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.

Question 61

rational exponent

Answer 61

is an exponent that is a fraction. For example, can be written as . ... Let's explore the relationship between rational (fractional) exponents and radicals.

Question 62

rationalizing the denominator

Answer 62

means to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals.

Question 63

recursive formula

Answer 63

is a formula that defines each term of a sequence using preceding term(s).

Question 64

regression line

Answer 64

is an estimate of the line that describes the true, but unknown, linear relationship between the two variables.

Question 65

relative minimum

Answer 65

is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood. These are points in which the first derivative is 0 or it does not exist.

Question 66

relative maximum

Answer 66

point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph)

Question 67

root

Answer 67

a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

Question 68

scatter plot

Answer 68

chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

Question 69

sequence

Answer 69

is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence. Wikipedia

Question 70

set builder notation

Answer 70

is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Usually with infinite number sets.

Question 71

step function

Answer 71

a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces.

Question 72

synthetic division

Answer 72

is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.

Question 73

vertex form

Answer 73

is a point where two or more curves, lines, or edges meet. ... Vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle, which is the 'top' corner opposite its base, but this is not its strict mathematical definition

Question 74

vertical line test

Answer 74

is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. Wikipedia

Question 75

zeros

Answer 75

a zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Wikipedia