Chapter 1, 2, 3 & 4

Parabola

In mathematics, a parabola is a plane curve, which is mirror-symmetrical, and is approximately U-shaped when oriented as shown in the diagram below.

Box Plot

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum. The term "box plot" comes from the fact that the graph looks like a rectangle with lines extending from the top and bottom.

Continuous Graph

A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values. A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers.: Graph the continuous function: y = x2 for all Reals

Input

A function can be defined by any mathematical condition relating each argument (input value) to the corresponding output value. If the domain is finite, a function f may be defined by simply tabulating all the arguments x and their corresponding function values f(x).

Output

A function can be defined by any mathematical condition relating each argument (input value) to the corresponding output value. If the domain is finite, a function f may be defined by simply tabulating all the arguments x and their corresponding function values f(x).

Histogram

A histogram is an accurate representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson. It is a kind of bar graph.

Proportion

A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways: two equal fractions, or, using a colon, a:b = c:d.

Variable

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x , y , and z are common generic symbols used for variables.

Quadrant

Also by convention they are often numbered using Roman numerals: I II III IV. Pages referring to 'quadrant' The Coordinate Plane. The coordinate plane defined with description of x,y axis, quadrants, origin. (C) 2011 Copyright Math Open Reference.

Equation Mat

An Expression Mat is an organizational tool that is used to represent algebraic expressions. Pairs of Expression Mats can be modified to make an Equation Mat.

Rule

An algebraic rule is a method for describing the relationship between two variables. This lesson will give a definition of an algebraic rule, show some examples and give you the steps to create rules when given a set of data. CAHSEE Math Exam: Tutoring Solution / Math Courses.

Integer

An integer is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 ¹⁄₂, and √2 are not.

Solution

Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities. With a system of equations or system of inequalities, the solution set is the set containing value(s) of the variable(s) that satisfy all equations and/or inequalities in the system. See also.

Perimeter

Calculating the area and the perimeter. The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle

Expression Comparison Mat

Combining two Expression Mats into an Expression Comparison Mat creates a concrete model for simplifying (and later solving) inequalities and equations. ... After moving and simplifying the Expression Comparison Mat, students are asked to tell which side is greater.

Coordinates

Coordinates are a set of values that show an exact position. On maps and graphs it is common to have a pair of numbers to show where a point is: the first number shows the distance along and the second number shows the distance up or down. Example: the point (12,5) is 12 units along, and 5 units up.

5-D Process

Declare. Define. "Define," is the second step in the 5D process. Defining is the part of this process where you will get to make an educated guess/estimate on what you are trying to figure out.On this section you will be making trials. "Do," is the next step to completing the 5D process

Evaluate

Evaluate expressions. A variable is a letter, for example x, y or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Growth Factor

Growth rate is the addend by which a quantity increases (or decreases) over time. For example, compound interest is a growth factor situation: If your investment yields 10% annually, then that means that each year, your total has multiplied itself by 110% (the growth factor is 1.10).

Term

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

Distributive Property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from elementary algebra. In propositional logic, distribution refers to two valid rules of replacement.

Commutative Property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it.

Multiplicative Inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a.

Associative Property

In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

y-intercept

In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).

Origin

In two dimensions. On the flat coordinate plane, there are two axes, the vertical y-axis and the horizontal x-axis. The origin is the point where they intersect. This point has the coordinates 0,0 and is usually labelled with the letter O.

Order of Operations

It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to the mnemonic "Please Excuse My Dear Aunt Sally". ... Most common in the UK, India and Australia are BODMAS meaning Brackets, Of or Order, Division, Multiplication, Addition and Subtraction.

Mean

Mean, median, and mode are three kinds of "averages". ... The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers.

Parameter

Parameter definition. A parameter is a quantity that influences the output or behavior of a mathematical object but is viewed as being held constant. Parameters are closely related to variables, and the difference is sometimes just a matter of perspective.

Tile Pattern

Pattern. Things that are arranged following a rule or rules. Example: these tiles are arranged in a pattern. Another Example: there is a pattern in these numbers: 2, 7, 12, 17, 22, ... they follow a rule "start at 2 and add 5 each time"

Area

Perimeter is 1-dimensional and is measured in linear units such as inches, feet or meters. Area is 2-dimensional: it has a length and a width. Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width.

Proportional Relationship

Proportions are the comparison of two equal ratios. Therefore, proportional relationships are relationships between two equal ratios. For example, oranges are sold in a bag of 5 for $2. The ratio of oranges to their cost is 5:2 or .

Unit Rate

Rates. ... When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. If you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.

Stem-and-Leaf PLot

Stem-and-Leaf Plot. more ... A plot where each data value is split into a "leaf" (usually the last digit) and a "stem" (the other digits). For example "32" is split into "3" (stem) and "2" (leaf). The "stem" values are listed down, and the "leaf" values are listed next to them.

Multiplicative Identity

The Multiplicative Identity Property. For a property with such a long name, it's really a simple math law. The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.

Additive Identity

The additive identity property says that if you add a real number to zero or add zero to a real number, then you get the same real number back. The number zero is known as the identity element, or the additive identity. ... Here is an illustration of the additive identity property for 18 + 0= 18.

Combine Like Terms

The central limit theorem (CLT) is a statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

Vertex

The common endpoint of two or more rays or line segments. Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices.

x-intercept

The graphical concept of x-intercepts is pretty simple. The x-intercepts are where the graph crosses the x-axis.

Median

To find the Median, place the numbers you are given in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. Put them in order: {10, 11, 13, 15, 16, 23, 26} The middle number is 15, so the median is 15. (If there are two middle numbers, you average them.)

x-y Table

XY tables are motorized linear slides with linear motion based in bearings which are driven by a drive mechanism, typically a linear motor. XY tables are built and configured to provide high-performance positioning along multiple axis.

Graph

a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles

Ordered Pair

a pair of elements a, b having the property that ( a, b) = (u, v ) if and only if a = u, b = v.

Independent Variable

a variable (often denoted by x ) whose variation does not depend on that of another

Non-Commensurate

corresponding in amount, magnitude, or degree: Your paycheck should be commensurate with the amount of time worked. 2. proportionate; adequate: a solution commensurate to the seriousness of the problem.

Additive Inverse

so in other words, the additive inverse of x is another number, y, as long as the sum of x + y equals zero. The additive inverse of x is equal and opposite in sign to it (so, y = -x or vice versa). For example, the additive inverse of the positive number 5 is -5. That's because their sum, or 5 + (-5) = 0.

x-axis

the principal or horizontal axis of a system of coordinates, points along which have a value of zero for all other coordinates.

y-axis

the secondary or vertical axis of a system of coordinates, points along which have a value of zero for all other coordinates.

Dependent Variable

variable (often denoted by y ) whose value depends on that of another.