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
