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MAIN DEFINTIONS
A-secton
Absolute Expression: An algebraic statement that contains at least one absolute value.
Absolute Value: It is the result of a number that will always not be negative. It is always positive because it is only explaining how far a value is from zero.
Addition: It is an operator denoted as the "+" symbol. It determines the result from two or more numbers or amounts, such as 5 + 2 = 7. It is the process on increasing one addend value (5) with another addend value (2). The two addends (5, 2) are combined or calculated together to form the result called the sum (7).
Algebraic Expression (expression): A statement that must contain at least one term. These terms can be written as a combination of terms separated by at least one operator, except the equal sign. ex. 3x + 1
Associate Property: The result of two expressions that when added or multiplied into groups will have the same result no matter how they are grouped. Different arranged numbers will provide the same result. ex. (3 + 4 + c) = (c + 4 + 3)
B-secton
b-value (y-intercept): It is any y-value that intercepts the y-axis, when x = 0. This is the initial y-value in a linear equation or function.
Base: The number that must be multiplied by itself repeatedly to provide a result to the exponential term.
c-Section
Coefficient: The known value of a term that is multiplied by a unknown variable. ex (Term 3x, 3 is the coefficient). If there isn't a number associated with the variable it is assumed to be 1. (ex. x is the same as 1x, where 1 is the coefficient)
Communitive Property: This is a property rule that allows the number or variable of a expression, equation or function to be multiplied or added in any order, not effecting the product or sum of a expression. This property rule cannot be utilized with division nor subtraction. (ex. 1 + 3 + 4 = 4 + 1 + 3)
Common Difference: The constant amount of change from one number to the next in a arithmetic sequence.
Common Factor (CF): The common factors of two or more numbers.
Common Multiple (CM): The common multiple of two or more numbers.
Constant: The value of a expression or equation that will remain and not to be changed. (ex. 3x + 1, 1 is the constant)
Continuous: It is a value that can be any infinite in an interval of numbers [0.43782. . . . . ]. The values are always changing but are not countable. (ex. temperature, sea level)
Coordinate Plane: It presents points (x, y), or multiple points that are called lines, which are graphed to display the unique position of those points on a x- and y-axis.
d-Section
Dependent variable: The unknown number which is presented as a variable value. It depends on another variable for its value. This means that the value of y depends on the value of x.
Difference: The result of the subtraction of numbers.
Direction: It is the position of one location as it relates to another location. It is the position that something is pointing towards or the way that you should go to reach a location.
Discrete: These values are finite and countable. (ex. number of trees in a forest)
Distance Formula: It provides the length from one location (point) to another location (point) on a coordinate plane.
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Distributive: This is when the outer number is multiplied by each number within a parenthesis. The result is the sum of the product. (ex. 4(3 + 2) = 12 + 8 = 20)
Divide: It is an operator denoted as "/" symbol. It determines the result of two numbers, such as 20/5 = 4. It is the process of separating the dividend value (20) into two or more parts based the divisor value (5). The result is the called the quotient (4).
Domain: This is the independent values of a function (F(x)) that are allowed to provide a result for that function. (NOTE: some function will not allow values, such as 1/x, when x =0).
e-Section
Eliminate: The process of getting rid of one variable (eliminate) to solve for one variable, in which that result is substituted to solve for the other variable, so as to solve a system of equations.
Equal: The operator that states that two numbers, terms, expressions, or equations are the same.
Equation: It are two expressions that contains at least one variable, value, and constant. Each expression can be written as a combination of terms separated by at least one operator. The two expressions are separated by the equal sign and should result in equal values results. ex. if x = 2, then 3x + 1 = 7y.
Exponent: It is the number in the upper right corner of a number that tells the base number how many times it must multiply by itself, repeatedly. ex. 3x , 2 is the exponent.
Expression: These values are expressed as numeric or algebraic. Numerical expressions have only numbers, while algebraic expression have numbers and variables.
Evaluate: Is to solve an expression or equation by substituting a value for a variable to get a result.
f-Section
Factor: It is two numbers that when are multiplied together will provide a product as a number or expression. (ex. factors of 27x (1, 3, 9, 27, x), factors of 18(1,2, 3 6, 9, 18), factors of 20(1, 2, 4, 5, 10, 20))
Finite: A specific set of numbers that are countable. This means that they do not continue or reach a end, such as {1,2,3}.
FOIL: A method similar to distributive property, in which you multiply the values of to combined expresses by multiply the first value of the first expression by the first and outer values of the second expression, then multiply the last expression by the first and outer values of the second expression. This is the acronym: F (first), O (outer, I (inner), L (last).
Fraction: A number that contains a numerator and an denominator. It expresses the parts of a whole number. ex. 2/7 of a pie is 2 slices of out of 7 slices of pie
Function: It contians a specific number of x-values (one or more) that will output one specific y-values. The y-value (dependent variable) depends on the x-value (independent variable), where the x-value is the domain and the y-value is the codomain. The result is the function (F(x)). This means that for every one or more x-values there is one y-value. This is usually expressed in the slope-intercept format, y = mx + b.
g-Section
Graphing: This is a way of presenting points, and lines on a coordinate plane. Points are displayed as locations. Points that are connected form lines. The lines are expressed as expression, equations and functions that are displayed to show the change from one point to another along a linear liner or curve.
Greater Than: A number that is more than another number and is presented as the operator >. ex. 5 is greater than 2, expressed as 5 > 2.
Greatest Common Factor (GCF): It is comparing two or more numbers by discovering the largest common factor among them. ex. factors of 15(1, 3, 5, 15), factors of 20(1, 2, 4, 5, 20, 20); common factors are (1, 5); the GCF is 5. It is the largest common integer that divides into each number.
Horizontal line: It is a special linear line that is displayed horizontal on a coordinate plane. It is parallel to the x-axis. It is expressed as y = c, when x = any number, and y is the same constant number.
H-Section
I-Section
Independent Variable: The unknown number whose value are not effected by another value. This means that it does not depend on another variable for its value. This means that the x-value determines what the y-value will be.
Inequality: They are two numbers or two expressions that are either <, >, <, or > each other. The expressions contain at least one variable, value, and constant. Each expression can be written as a combination of terms separated by at least one operator. The two expressions are separated by the<, >, <, or > signs and should result in equations or expressions that do not equal each other. ex. 2 < 4 OR 3x + 1 > 7. (NOTE: if one side of the equation or expression is multiplied by a neg. number, the sign switches.
Infinity (infinite): A specific set of numbers that are NOT countable. This means that they continue or does not reach a end, such as {1,2,3, . . . . . ). This means that the set of number will not end. It also means a number will never end. ex. 3.149209. . . This means that this number is endless and cannot be defined as a specific number values. In addition, lines and curves can be infinite presented as the domain and range of points on a line, such as [1, ). This means that the points starts at at point one, however, the range (y-value) is infinite.
Intersecting line: They are lines that intersect at one point. The point formulates into one solution to a problem (equation or function).
Irrational: It is any number that cannot be written as a simple fraction, such as the 2, PI or 9.94687 of a number.
Known Variable: The variable that has a specific or unchangeable number that assist in solving a problem.
K-Section
Less Than: A number that is smaller than another number and is presented as the operator <. ex. 2 is less than 5, expressed as 2 < 5.
Linear equation: They are equations that have numbers that are expressed with only one degree and graph form a straight line on a coordinate plane. It forms a relationship amongst variables where the y-value (dependent) depends on the x-value (independent).
Least Common Multiple (LCM): It is when you compare two or more numbers by discovering the smallest common multiple among them. ex. multiples of 9(9, 18, 27. . .), multiples of 3(3, 6, 9, 12, 18 . . .). Both have 9, 18, 27 . . as a multiples, however, the least common multiple is 9.
L-Section
Multiple: It is a is the number that can be divided into another number without leaving a remainder. The numbers accepted must be expressed as a whole number of that product or when divided does not contain a remainder. ex. multiples of 9(9, 18, 27. . .), multiples of 3(3, 6, 9, 12. . .).
Multiplication: It is a operator denoted by "*". determines the result of two numbers, such as ex. 5 * 3 = 10. It is the process of adding the multiplicand value (5) to itself by a certain number of times, called the multiplier value (3). This means that 5 is added 3 times (5 + 5 + 5= 15). The result is called the product (15).
M-Section
N-Section
Non-linear (equation): They are equations that have numbers that are expressed with radical and rational numbers. It must be at least two degrees. When graphed it does not form a straight line on a coordinate plane. This means that the rate of change of variable do not change at a constant rate.
Number: It is an arithmetic value expressed as words that are used to count or calculate
Number line: The line is horizontal and displays a range of real numbers that stretch into infinity. It explains how these numbers correspond with each other.
Numeric expression: It is a statement that contains only numbers and operators. ex. 3(2 + 1)
o-Section
One-Variable Equation: They are equations that have the same variable. This one variable is the variable to solve the equation. It should result in equal values results. ex. 3x + 1 + 5x = 7.
Operator: It indicates the mathematical process to determine a solution t a math problem. These are denoted by such symbols as, multiply(*), add(+), substract (-), divide(/), equal(=), less than (<), etc.
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Ordered Pair (x, y): These are two values presented as (x, y). The order of the values are important. The x-value is considered, first, then the y-value. Combined they presents the location of one point on a coordinate plane or it can present the solution to a equation.
p-Section
Pattern: It is the repetition of a sequence of events (numbers, colors, shapes).
Parallel line (equation): They are two linear lines that do not intersect at any point. No points intersecting means that their is not a solution to the equation or function. It results in equal slope, but unequal y-intercepts.
PEMDAS: It is the acronym used to assist in remembering the order of arithmetic. The order is P(parenthesis), E(exponent), M(multiply), D(divide), A(addition), S(subtract).
Point-slope: It is a method used to discover the straight line of a equation. If the slope and one point on that line is known, then other points can be discovered. The equation is written as :
Positive (pos.): A number greater than zero.
Perpendicular line: They are two linear lines that intersects at one point. The intersecting point forms a right angle. The point formulates into one solution to a equation or function. It results in unequal y-intercepts and unequal neg. reciprocal slope values.
Point: A point describes the exact position on a coordinate plane.
Power (exponent): It is another way of expressing the word exponent. It is the number in the upper right corner of a number that tells the base number how many times it must multiply by itself, repeatedly. ex. 3x , 2 is the exponent.
Product: tt is the result of number multiplied together.
(y - y )
1
=
m
x
1
(x - )
Quadratic equation: They are equations that have numbers that are expressed with two or more degrees. The graph formed are not straight, but curved. It may also include, radicals and rational numbers. The result is a non-linear equation that can have more than one solution. It is often presented as ax + bx + c = 0, where a, b and c are known variables, and x is an unknown variable.
Quadratic formula: It is one of many methods of solving a quadratic formula. It is the extension of the standard quadratic equation, written as x
where a is the coefficient of x , b is the coefficient of x and c = c. The result are all the solution to the equation.
Q-Section
R-Section
Rational Number: It is any number that can be written as a fraction (9.45667 . . , 7/8, etc.). This includes integers (. . ,-1, 0, 1, . .), whole numbers (0, 1, 2 . . . ) and natural numbers (1,2 3, . . . ).
Radical: It is the opposite of the exponent. It is one number that creates another number when multiplied. It can be signified as the square root, cubed root, etc. of a number. ex. .
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Reverse Signs: It is the method of solving for inequalities, that, if the final operation is neg., the signs should be switched. This ensures the correct solution or direction of the inequalities.
Raised (power): It is another way of expressing the word exponent. It is the number in the upper right corner of a number that tells the base number how many times it must multiply by itself, repeatedly. ex. 3x , 2 is the exponent.
Range: This is the output of a function (F(x)) presented as the codomain. It is all the possible results of the initial y-value (dependent value)
Rise: It is the vertical distance of change from one point to another on a graph.
Run: It is the horizontal distance of change from one point to another on a graph.
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s-Section
x - x
Same Linear Line: They are lines that intersect at every point. The point formulates into one solution to a problem (equation or function). It results in equal slope, but equal y-intercepts.
Sequence: It is a set of numbers, object or events that are the arranged in a specific order and follow a certain rule. ex. 4, 7, 10, 13 follows the rule: add 3 to each number.
Slope: It is the steepest (high, low or remain constant) of a linear line denoted as the rise/run or the change of the vertical distance over the horizontal distance, denoted by the form:
Slope-intercept: Solving an equations that is presented as a straight-line, in the form of:
Solution: The value that when substituted for a unknown variable makes the expression or equation correct. ex. 3 + x = 5 has solution of 2, when substituted makes 3 + 2 = 5 correct.
Substitute: When one equation is in standard form and the other in slope-intercept form, the y result of the slope-intercept can be substituted into the standard form as x. Once x is discovered, it can then be substituted to solve for the other variable, so as to solve a system of equations.
Subtraction: It is a operator denoted by the "-" symbol. It determines the result of two numbers, such as 5 - 2 = 3. It is the process of taking away the subtrahend value (2) from the minuend value (5). The result is the called the difference (2).
System of Equation: They are two or more equations that when combined together will either form one solution, no solution, or infinite solutions.
m =
1
1
y - y
2
2
y = mx + b
where,
x, y = variables
m = slope
b = y-intercept
T-Section
Table (linear equation): A table that contains at least one input row and one output row of values. These rows and columns form solution to a equation or function. The results display some kind of common pattern or sequence from the output values.
Terms: These can be any number, variable or any combinations a number and variable that creates a product. ex. (3, x, and 3x)
Two-Variable Equation: They are equations that have two or more different variables. ex. x + 3n - 4w = -7.
Unknown variable: it is the variable that is substituted for the unknown value. The unknown variable is what is to be solved.
U-Section
V-Section
Value: It is a number or the output of a calculation.
Variable: This can be any letter of the alphabet that is presented as the unknown value of an expression or equation.
Vertical line: It is a special linear line that is displayed vertically on a coordinate plane. It is parallel to the y-axis. It is expressed as x = a, when y = any number, and x is the same constant number.
Word Expressions: A basic sentence stating an expression in words. ex. twice a number: 3, 2n; five more than three times a number: 5 + 3x.
Word Problem: It is one or sentences that explain an expression or equation. It it used to solve a real-world problem.
W-Section
X-Section
X-axis: The x-axis the horizontal line in the coordinate plane.
X-intercept: The point on the x-axis where the function intercept when y=0.
Y-Section
Y-axis: The x-axis the vertical line in the coordinate plane.
Y-intercept: The point on the y-axis where the function intercept when x=0.
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