TExES Math 4-8

Associative property of multiplication

(a*b)*c = a*(b*c)

Associative property of addition

(a+b)+c = a+(b+c)

Real part

Given the complex number a+bi, a is this

simple Interest

I = Prt. Interest is paid only on the principle and is not paid on previous earned interest.

Whole numbers

all natural numbers plus the number 0.

Average rate of change

an interpretation of slope that applies to many linear models. The slope of the line gives this term in the y-units per change in the x-units

open interval

an interval that includes all the points in between the ending points but does not include either of its ending points.

closed interval

an interval that includes both of its ending points and all the points between these ending points is a closed interval.

Ordered pair

an ordered pair consists of two components separated with a comma, written inside parenthesis, where the first element is the x-value and the second element is the y-value ().

Supplementary angles

Two angles whose measures add to a total of 180 degrees

Complementary angles

Two angles whose measures add to a total of 90 degrees

Terms

Values separated with plus or minus signs in an expression

parabola

a curve that is the graph of a quadratic function

Tree diagram

a diagram with branches used to systematically list all the outcomes of a probability or counting situation experiment or factors of a composite number is called a tree diagram

Scatter diagram

a graph of specific ordered pairs of data is a scatter diagram.

Linear programming

a method of finding an optimum value such as minimum cost or maximum profit particularly used in application in business and social science

Oblique (slant) asymptote

a nonvertical and nonhorizontal line that the graph approaches as the absolute value of x gets larger without bound. These asymptotes are formed when the degree of the numerator is larger than the degree of the denominator.

Monomial

a polynomial containing only one term

Annuity

a sequence of equal payments or deposits made at equal periods of time is called an annuity.

Infinite set

a set having an unending list of distinct elements

Interval notation

a simplified form of writing intervals by using parenthesis and brackets to show whether the endpoints are included.

combination

a subset of elements selected from a set, where order does not matter.

Equilateral Triangle

a triangle that has three sides of equal length and three angles of equal degrees (60)

Vertical asymptote

a vertical line that a graph approaches but never touches or crosses. In a rational function, find the value for x in the denominator that will make the function undefined. The vertical asymptote will be x = that value. f(x) = 1/x-3. x=3 is the (blank)

commutative property of multiplication

a*b = b*a

Commutative property of addition

a+b = b+a

leading coefficient

the coefficient in front of the term with the greatest degree

absolute value

the distance on the number line from that number to zero

Quadrants

The four regions of the coordinate plane divided by the x- and y-axis.

Trapezoid

A quadrilateral that has two parallel sides.

Scalar

A a real number used with the multiplication operation in working with matrices. Example: 3[2 3 5] with a product of [6 9 15], 3 would be this term

Composite number

A composite number is a natural number that is not a prime number, thus it is divisible by another number other that itself and one. Thus it has more than two factors.

Histogram

A form of bar graph used in statistics having observed values on the horizontal axis and frequencies on the vertical axis

Frequency Polygon

A form of line graph used in statistics having observed values on the horizontal axis and frequencies on the vertical axis.

Rational function

A function that can be written as a polynomial divided by a polynomial.

Piecewise-defined function

A function that is defined over different parts of the domain by different rules is called a piecewise-defined function.

Natural logarithm

A natural logarithm is a base e logarithm

Complex number

A number of the form a + bi. The a and b are real numbers, and i = the square root of -1

Prime number

A number that is a natural number greater than one that is divisible by only two numbers: itself and one. Thus, it has two factors.

Random Sampling

A sampling procedure used in statistical analysis where a sample is drawn in such a way that each time an item is drawn from the population every item in the population has an equal chance of being drawn.

Scalene Triangle

A scalene triangle does not have any sides of equal length

Closure of sets

A set is closed under a given operation if when the operation is performed on any two members; the result gives a member of the same set.

Synthetic Division

A shortcut method used in dividing a polynomial by a binomial of the form x-k. It can be used to find f(k)

Venn Diagrams

A technique where set relationships are put in pictorial form.

Undefined term

A term with a zero in the denominator

Right Triangle

A triangle with one right angle (90 degrees)

Integers

All wholes numbers, plus all negative numbers such as -1, -2, -3 etc.

Natural numbers

Also, called the set of counting numbers or the positive integers e.g. 1,2,3,4,.....

Acute triangle

An acute triangle has three acute angles (less than 90 degrees)

Equation

An equation is a statement where two expressions are equal. A specific value(s) can be determined for the variable in the equation.

Quadratic Equation

An equation that represents the graph of a parabola and is a second-degree equation (ax^2 + bx + c = 0)

Isosceles Triangle

An isosceles triangle has two sides of equal length and two angles of equal degrees.

Standard form of the equation of a line

Ax + By + C

Disjoint Sets

Disjoint sets do not have any common elements.

Fundamental Theorem of Arithmetic

Every composite number can be expressed as a unique product of prime numbers

Rationalizing the Denominator

Expressions should not be left with a radical in the denominator. You should simplify the radial expression and eliminate the radical in the denominator. Multiply by 1 (the square root in the denominator over the same square root).

parallelogram

In a parallelogram, both pairs of opposite sides are parallel. Also, both pairs of opposite sides are equal in length.

Origin

In a rectangular coordinate system, the intersection of the x-axis and y-axis, where the ordered pair (0,0) is located

Fibonacci sequence

In a sequence where starting with the third term, each term is a sum of the two previous terms

Imaginary part

In the complex number a + bi. b is the (blank)

Base of a logarithm

In the logarithm logax, this refers to the a

Permutation

One of the arrangements of elements r from a set of n elements is a permutation of n elements taken r at a time where order does matter

Collinear

Points that lie on the same line.

Quadratic Formula

The Quadratic Formula is used to determine the zeros (or solutions) are where the parabola crosses the x-axis

Half-life

The amount of time it takes for a quantity to decay exponentially to become half of its initial amount

Common Logarithm

The base 10 logarithm

Complement of a Set

The complement A' of a set are the elements in the universal set, but not in the original set A

Distance Formula

The distance formula is used to determine the distance between two points in the coordinate plane d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Midpoint Formula

The midpoint formula is used to locate the midpoint of a line segment. (x₁+x₂)/2, (y₁+y₂)/2

Break-even point

The point where the revenue from selling a product is equal to the cost of producing the product is the break-even point.

Vertices

The point where two line segments meet.

Present value

The principle in an investment paying compound interest can be called this

Radius of a circle

The radius of a circle is the square root of the r^2 value in the equation of a circle (x-h)^2 + (y-k)^2 = r^2

Expression

The result of adding, subtracting, multiplying, dividing (except by zero) on any combination of variables or constants as well as raising to powers and taking roots. An equal sign does not exist. A specific value cannot be determined for the variables in the expression.

Intersection of Sets

The set contains all the elements that are members of both set A and Set B. It is symbolized by A C B. The Word "and" is associated with this term.

Union of Sets

The set contains all the elements that are members of set A or set B. This includes the members that are in the intersection of these two sets. It is symbolized by A E B. the word "or" is associated with this term.

Rational numbers

The set of all numbers formed by the quotient of two integers where the divisor is not 0. Any number in this set when expressed as a decimal number will be either a terminating or repeating decimal number.

Hyperbola

The set of all points in a plane where the absolute value of the difference of the distances from two fixed points is constant is a hyperbola

Sample space

The set of all possible outcomes of a given experiment in probability is called a sample space.

Real numbers

The set of points that corresponds to the numbers on the number line including all rational and irrational numbers. Includes the disjoint sets of rational and irrational numbers.

Range

The set of real numbers values of the dependent variable y in a relation

Vertex of a circle

The vertex of a circle is the order pain (h,k) in the equation of the circle (x-h)^2 + (y-k)^2 = r^2. The values of h and k will have opposite signs from what they appear to have in the formula.

point-slope form of the equation of a line

This form of the equation of a line is used to write the equation of a line given a point and a slope.

Rhombus

both pairs of opposite sides in this quadrilateral are parallel. Also, the four sides are equal in length.

cos - adjacent over hypotenuse

cah

Descriptive statistics

concerns the description of the collection process (sampling procedures), organization, and analysis of the data

Inferential Statistics

deals with making generalizations and predictions from the data collected

Reciprocal Function

f(x) = 1/x is the (blank) of x.

Standard form of the equation of a Parabola

f(x) = ax^2 + bx + c

base of an exponent

in the exponent a^x, this refers to the a

Logarithm

log base a X. the power to which the base a must be raised to obtain x.

Stem and leaf Display

organizes and gropus data for quicker analysis.

sign = opposite of hypotenuse

soh

Horizontal asymptote

the horizontal line that a graph approaches as the absolute value of x gets larger without bound. Different from the vertical asymptote, the graph may cross this asymptote. This asymptote is formed in two ways from a rational function. When the degree of the numerator is less than the degree of the denominator.

Completing the square

the process of adding to a binomial the number that will make it a perfect square trinomial

Slope

the ratio of the change in y to the change in x referring to a nonvertial and nonhorizontal line.

Probability of an event

the ratio of the number of outcomes in the sample space belonging to the event to (over) the number of outcomes in the sample space is the probability of an event. It follows the same format of part expressed in the numerator and whole expressed in the denominator

System of equations

the set of equations that are considered at the same time. If there are two unknown variables, a system of two equations is required to find both of these values. If there are three unknown variables, a system of three equations is required to find these three values and etc.

Irrational numbers

the set of numbers within the real numbers when expressed in decimal form will be nonterminating and nonrepeating decimal numbers

Domain

the set of real numbers for which an expression is defined over the independent values of x

Universal Set

the universal set (U) contains all the elements appearing in any set used in the given problem.

Argument

the x in the expression logax

tan - opposite over adjacent

toa

Mutually exclusive events

two events that cannot occur simultaneously in probability.

Slope-intercept form of the equation of a line

y=mx+b In this equation, m represents the slope of the line and b represents the y-intercept