Math

Real part

Given the complex number a + bi, a is the real part.

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.

Mutually exclusive events

Two events that cannot occur simultaneously in probability are called mutually exclusive.

Congruent Figures

Two figures are congruent if they have the same shape and size.

Terms

Values separated with plus or minus signs in an expression.

Commutative property of addition

a + b = b + a

Commutative property of multiplication

a x b = b x a

Domain

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

Reciprocal Function

The function f(x) = 1⁄x is a reciprocal function of x.

Prime number

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

Polygon

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

Regular Polygon

A polygon that has all sides and all angles equal.

Monomial

A polynomial containing only one term is a monomial.

Equation of a circle

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

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 is has more than two factors.

Parabola

A curve that is the graph of a quadratic function is a parabola.

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.

Line of Symmetry

A figure has a line of symmetry if it is possible to fold the figure over a line drawn on its interior in such a way that half of the figure folds exactly onto the other half.

Point of Symmetry

A figure has a point of symmetry if there exists a point on the figure itself so that you can rotate the figure about that point and the figure coincides with itself.

Symmetric Figure

A figure that can be folded flat along a line so that the two halves match perfectly is a symmetric figure; such a line is called a line of symmetry.

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 of form f (x) = p(x) , q(x) where both p(x) and q(x) are polynomials and q(x) is not equal to zero is a rational function.

Piecewise-defined function

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

Scatter diagram

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

Horizontal asymptote

A horizontal asymptote is 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 a horizontal asymptote. Horizontal asymptotes are formed in two ways from a rational function. When the degree of the numerator is less than the degree of the denominator

Logarithm

A logarithm is an exponent loga x is the power to which the base a must be raised to obtain x.

Natural logarithm

A natural logarithm is a base e logarithm.

Complex number

A number of the form a + bi is a complex number. The a and b are real numbers and i = √-1 .

Percent

A percent is a ratio that compares a number to 100. You can write a percent with the percent symbol or as a fraction or decimal. For example, you can write 40% as 40/100 or as .40.

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.

Scalar

A scalar is a real number used with the multiplication operation in working with matrices.Example: In the following example, 3 is the scalar 3 [2 3 5]. The product is [6 9 15].

Scalene Triangle

A scalene triangle does not have any sides of equal length.

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 is an infinite set.

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. Example: The set of natural numbers is closed under the operation of addition or multiplication. The set of natural numbers is not closed under the operation of subtraction (3 - 8) or division (23/22).

Combination

A subset of elements selected from a set is called a combination were order does not matter.

System of equations

A system of equations is 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.

Venn Diagrams

A technique where set relationships are put in pictorial form.

Transformation

A term that applies to moving geometric figures in such a way that they keep their congruency; three types of transformations are: slide, flip and rotate.

Undefined term

A term with zero in the denominator.

Trapezoid

A trapezoid is a quadrilateral that has two parallel sides.

Vertical asymptote

A vertical asymptote is 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.

Absolute value

Absolute value |x| is the distance on the number line from that number to zero. Example: |-3| is three units from 0.

Natural numbers

Also, called the set of counting numbers or the positive integers {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 (ax2 + bx + c = 0 ).

Equilateral Triangle

An equilateral triangle has three sides of equal length and three angles of equal degrees (60).

Average rate of change

An interpretation of slope that applies to many linear models is an average rate of change. The slope of the line gives the average change 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 is called an open interval.

Closed Interval

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

Isosceles Triangle

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

Oblique (slant) asymptote

An oblique asymptote is a nonvertical and nonhorizontal line that the graph approaches as the absolute value of x gets larger without bound. Oblique asymptotes are formed when the degree of the numerator is larger than the degree of the denominator. In the rational function, use synthetic division omitting the remainder to determine the oblique asymptote (y = x + 1).

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 ( ).

Standard form of the equation of a line

Ax + By + C

Circumference

Circumference is the distance around a circle. Circumference is used with closed curves like circles and ellipses, while perimeter is used for polygons and other figures. This distance is equal to Pi times the diameter of the circle. Pi is a number that is approximately 3.14159.

Completing the square

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

Descriptive Statistics

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

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. Rationalizing the denominator is a process of simplifying the radial expression and eliminating the radical in the denominator.

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 is called the origin where the ordered pair (0, 0) is located.

Rhombus

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

Imaginary part

In the complex number a + bi, b is the imaginary part.

Base of an exponent

In the exponent, ax, a is the base which is the number that is a repeated factor.

Base of a logarithm

In the logarithm loga x, a is the base which is the number that is a repeated factor.

Inferential Statistics

Inferential statistics deals with making generalizations and predictions from the data collected.

Interval notation

Interval notation is a simplified form of writing intervals by using parenthesis and brackets to show whether the endpoints are included. The inequality x < 3 written in interval notation is (- ∞,3) whereas the inequality x£ 3 written in interval notation is (- ∞,3].

Stem-and-Leaf Display

It organizes and groups data for quicker analysis. The display below shows # of individuals per age group:

Linear programming

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

Associative property of addition

Notice in this one the terms will always be in the same order.

Associative property of multiplication

Notice in this one the terms will always be in the same order.Distributive property of multiplication over addition

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 are collinear if they lie on the same line.

Synthetic Division

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

Equality

Term used to denote whether two numerical values are the same.

Fibonacci sequence

The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, .....) is a sequence where starting with the third term, each term is a the sum of the two previous terms.

Quadratic Formula

The Quadratic Formula is used to determine the zeros (or solutions) to a quadratic equation. The zeros (or solutions) are where the parabola crosses the x-axis. - b ± √ b2 - 4ac ---------------- 2a

Pythagorean Theorem

The a and b represent the legs of a right triangle and c represents the hypotenuse. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Half-life

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

Argument

The argument is the x in the expression loga x.

Common Logarithm

The base 10 logarithm (log10x ) is called the common logarithm.

Probability

The chance that an event will occur ( probabilities will be a value between 0 and 1).

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(A,B) = √ (x2 - x1)2 + (y2 -y1)2

Leading coefficient

The leading coefficient of a polynomial is the coefficient in front of the term with the greatest degree. In the polynomial (4x3 + 5x -9), 4 is the leading coefficient.

Midpoint Formula

The midpoint formula is used to locate the midpoint of a line segment.

Whole numbers

The number zero is added to the set of Natural (or counting) numbers to form the whole numbers. {0, 1, 2, 3, 4, 5, ....}

Integers

The numbers -1, -2, -3, and so on, are added to the set of whole numbers to form the set of integers. {....-3, -2, -1, 0, 1, 2, 3.....}

Perimeter

The perimeter of a polygon is the sum of the lengths of all its sides.

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 is a vertex. The plural form of vertex is vertices. Example: The vertices of a triangle are where the line segments meet to form the three corners.

Present value

The principle in an investment paying compound interest can be called the present value.

Probability of an event

The probability of an event is 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.

Quadrants

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

Radius of a circle

The radius of a circle is the square root of the r2 value in the equation of a circle (x - h)2 + (y - k )2 = r2. For example: in the circle (x - 3)2 + (y + 2 )2 = 17 , r is equal to √17 .

Range

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

Odds

The ratio of the probalility that an event will occur to the probability that it will not occur.

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. Intersection is symbolized by A Ç B. The word "and" is associated with intersection.

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. Union is symbolized by A È B . The word "or" is associated with union.

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. The set of integers is a subset of the set of rational numbers, the set of whole numbers is a subset of the set of integers, and the set of natural numbers is a subset of the set of whole numbers. Example: {-3, -0.5, 0, 1, 1/3, 2/3, 5, 6}

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.

Irrational numbers

The set of numbers within the real numbers when expressed in decimal form will be nonterminating and nonrepeating decimal numbers.Example { - √3 ,√2 ,π ,√5 }

Real numbers

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

Simple Interest

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

Slope

The slope (m) of a nonvertial and nonhorizontal line is the ratio of the change in y to the change in x.

Universal Set

The universal set (U) contains all the elements appearing in any set used in the given problem. Used in labeling with the Venn diagram, the rectangle is the universal set.

Vertex of a circle

The vertex of a circle is the order pair (h, k) in the equation of the circle (x - h)2 + (y - k)2 = r2. The values of h and k will have opposite signs from what they appear to have in the formula. For example: in the circle (x - 3)2 + (y + 2)2 = 92, the vertex is (3, -2). They appear opposite in the equation of the circle due to the minus signs in front of the h and k.

Representation

The way mathematical information is presented (written, symbolic or graphical).

Standard form of the equation of a Parabola

f (x) = ax2 + bx + c where a ¹ 0

Vertex form of the equation of a Parabola

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

Point-slope form of the equation of a line

y - y1 = m(x - x1) This form of the equation of a line is used to write the equation of a line given a point and a slope.

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.