Absolute value: The distance a number is native $0$.
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Algebra: The research of math symbols and also the rules for manipulating thosesymbols.Algebra grid: A grid provided to illustrate values that algebraic expressions.Arithmetic sequence: A succession of numbers in which every number have the right to be computed byadding the exact same amount come the previous number.Associative law of addition: For any three numbers $a$, $b$, and also $c$, that is alwaystrue the $(a+b)+c = a+(b+c)$.Associative regulation of multiplication: For any kind of three number $a$, $b$, and also $c$, it isalways true the $(a(b))(c) = a(b(c))$.Axis of symmetry: A line the you deserve to flip (or reflect) a graph throughout that results inthe same graph.Base: A number the is increased to a power.Best fit line: as soon as the points on a grid room not every on a right line, however seem tohave a somewhat direct pattern, you can find a line that is the “best fit” (closest) come thepoints.Box plot: A box with “whiskers” showing the median, quartiles, and extremes (least andgreatest values) of a collection of data values.Break even: have a benefit of zero (that is, make exactly as much money as you spend).Ceiling function: $ceiling(x)$ is the closest integer i m sorry is better than or equalto $x$.Clearing denominators: multiplying both political parties of an equation by some nonzero numberthat turns all the fractions in the equation into integers.Coefficient: A constant that a change or expression is multiply by.Combining choose terms: making use of the distributive legislation to add any two multiplesof an expression such as $x$. For example, you deserve to simplify $4x+5x$ into $9x$.Common difference: In one arithmetic sequence, the quantity that have the right to be included to eachnumber to obtain the next one.Common ratio: In a geometric sequence, the amount that each number deserve to be multipliedby to get the next number.Commutative regulation of addition: For any kind of two numbers $a$ and $b$, $a + b = b + a$.Commutative regulation of multiplication: For 2 numbers $a$ and $b$, $a(b) = b(a)$.Completing the square: Rewriting the equation $x^2+2mx=n$ together $(x+m)^2 = n + m^2$so the it have the right to be much more easily solved.Composition: The ingredient of two attributes $f$ and $g$ is the duty $f ∘ g$ thattransforms $x$ into $f(g(x))$.Conditional family member frequency: A joint frequency separated by the complete of its heat orcolumn in a two-way frequency table.Constant: A solitary fixed number (unlike a variable, who value deserve to vary).Constant coefficient: A constant term, believed of as a coefficient of $1$.Constant term: A term that is a constant. For a polynomial in $x$, it’s the termwithout one $x$.Coordinates: A point on a 2-dimensional plane is described by a pair $(x, y)$. Thecoordinate $x$ is given by the labels listed below the grid, and also the coordinate $y$ is offered by thelabels to the left of the grid.Coordinate plane: A 2-dimensional level surface used for plot points, lines,curves, and regions. It consists of an $x$ and also a $y$ axis which intersect at the origin.Coordinate grid: A network of lines on a coordinate aircraft that renders it easy to see$(x, y)$ collaborates of locations in that plane.Correlation coefficient: A number in between $1$ and also $-1$ the indicates exactly how muchincreasing one variable will have tendency to boost or to decrease the other variable. If the best fitlinear model for $x$ and also $y$ is $y=mx+b$, the correlation coefficient $r$ that $x$ and also $y$satisfies $$r^2=1-( ext"root-mean-square error that model")^2 /( ext"standard deviation the " y ext" data")^2$$. The correlation coefficient $r$ has actually the samesign (positive, negative, or 0) together $m$. If $x$ and also $y$ have method $m_x$ and $m_y$ andstandard deviations $σ_x$ and $σ_y$, that is likewise true that the correlation coefficient is themean that $(x-m_x)(y-m_y)$ divided by $σ_x σ_y$.Cost: In economics, how much money a firm spends to create a product.Cube root: The cube source of $a$, composed $√^3 a$, is the number whose cube is $a$.That is, $(√^3 a)^3 = a$.Data: A repertoire of associated measurements.Decimal: A fractional amount written v a decimal allude (like $0.5$).Denominator: The bottom number or expression in a fraction.Difference: The distance in between two quantities, or the answer to a subtractionproblem.Dilation: A dilation through a hopeful number $r$ around a allude $A$ is atransformation that moves every other allude $B$ along the ray from $A$ that passes with $B$,and multiplies distances from $A$ through $r$. $A$ is dubbed the facility of the dilation.Discriminant: The discriminant that the equation $ax^2+bx+c=0$ is the quantity$b^2-4ac$. A quadratic equation has actually two services if the discriminant is positive, onesolution if that discriminant is zero, and no real solutions if that discriminant is negative.Distributive law of multiplication end addition: For any type of threenumbers $a$, $b$, and $c$, $a(b+c) = a(b)+a(c)$, and $(b+c)(a) = b(a)+c(a)$.Distributive law of multiplication end subtraction: For any three numbers $a$, $b$,and $c$, $a(b−c) = a(b)−a(c)$, and also $(b−c)(a) = b(a)−c(a)$.Domain: The set of entry ($x$-coordinates) the a relationship or function.Dot plot: A diagram showing data worths as dots above a number line.Equation: A math sentence v an equates to sign (like $3x+5=11$).Equivalent: two fractions are equivalent if they have actually the same numerical value. Twoequations or inequalities are indistinguishable if they have actually the same solution set.Even function: A duty $f$ through $f(x)=f(-x)$ for all $x$. $f(x) = x^n$ is an evenfunction if $n$ is an even integer. A duty is also if and only if that graph has actually the $y$-axisas an axis of symmetry.Expanding an expression: using the distributive legislation to revolve expressionswhich require parentheses (like $3(x+2)$) right into expressions which perform not (like $3x+6$).Exponent: In a power, the variety of times the basic is multiplied by itself.Exponential: utilizing exponents, specifically using variables in exponents.Exponential decay: Decreasing toward $0$ because of a variable in one exponent, such as in$y=2^-x$.Exponential growth: raising rapidly as result of a variable in one exponent, such as in$y=2^x$.Expression: A mix of variables and numbers using arithmetic (like $6-x$).Factor: one expression that is multiply by another expression, or that deserve to bemultiplied by an additional expression to create a stated result.Factoring: Rewriting an expression together a product.Fibonacci sequence: The succession 1, 1, 2, 3, 5, ... With staying terms $F(n)$ givenby $F(n) = F(n-1) + F(n-2)$ for $n > 2$.First quartile: because that $n$ data values, the average of the $$n/2$$ smallest worths if $n$is even, and also of the $$n-1/2$$ smallest worths if $n$ is odd.Floor function: $floor(x)$ is the closestly integer i beg your pardon is less than or equal to $x$.Formula: an expression that is supplied to compute a value.Fraction: A numerator separated by a denominator (like $$1/2$$). Normally we need thenumerator and denominator to both it is in integers.Frequency: In statistics, the number of times something occurs, or is observed.Function: A relation in i beg your pardon no $x$-coordinate shows up in an ext than one $(x, y)$ordered pair. This method you can think of a duty as a revolution that takes each$x$-coordinate to its single corresponding $y$-coordinate.Fundamental theorem of arithmetic: any integer better than $1$ deserve to be created as aproduct of prime numbers, ordered the smallest to largest, in exactly one way.Geometric sequence: A succession of numbers in which each number have the right to be computed bymultiplying the vault number by the same amount.Graph: photo formed by plot the options to one equation or inequality, or someother set of pairs of numbers, on a coordinate plane. Come graph one expression comprise thevariable $x$, set $y$ equal to the expression.Histogram: Rectangles of same width over a number line, wherein each rectangles’sheight shows the number of data values in that portion of the number line.Horizontal: walk from next to side, favor the horizon.Improper fraction: A fraction in which the numerator is bigger than the denominator(like $$3/2$$).Inequality: A mathematics sentence that supplies one of the symbols $$, $≤$, or $≥$.Infinite: more than any type of finite (real) number.Input: A number that have the right to be “put into” a relation to produce one or an ext “outputs.” Ifa relationship is given by a two tower table that rows $(x, y)$, friend “look up” the input $x$ value inthe first column, and the output(s) are offered by the $y$ values in those equivalent row(s).Integer: A whole number or the an unfavorable of a totality number. Because that instance, $37$ and also $0$and $-5$ space integers, however $2.7$ and $$-3/2$$ space not.Interquartile range: The third quartile minus the very first quartile.Inverse functions: attributes $f$ and $g$ such that $g ∘ f(x)=x$ forevery $x$ in the domain that $f$, and also $f ∘ g(y)=y$ for every $y$ in the domain that $g$.Irrational number: A number that cannot be composed as a fraction$$m/n$$ wherein $m$ and also $n$ are integers.Isolate: make a variable show up alone on one next of one equation or inequality, andnot happen in the other side of the equation or inequality.Joint frequency: The number of events that meet both of two stated criteria.Joint relative frequency: A joint frequency divided by the total variety of events.Laws the exponents: $$a^c + d = a^c a^d$$, $$(a b)^d = a^d b^d$$, and$$(a^c)^d = a^cd$$. This are constantly true once $c$ and also $d$ are optimistic integers. If $a$ and$b$ room nonzero, then they room true for any kind of integers $c$ and $d$, together is$$a^c - d = a^c / a^d$$. If $a$ and $b$ are positive, climate all four laws are true for any type of $c$and $d$.Linear: A directly line, or one equation or expression who graph is a directly line.If $m$ and $b$ room constants, climate $mx+b$ is a direct expression, and also a function $f$ characterized by$f(x)=mx+b$ is a direct function.Linear coefficient: for a polynomial in $x$, the number that $x$ (without an exponent)is multiplied by.Linear model: An calculation for a variable making use of a straight expression in anothervariable.Linear optimization: Maximizing or minimizing a straight goal or expense expression, whileremaining within some constraints provided by straight inequalities.Marginal frequency: The complete of a row or shaft in a two-way frequency table.Marginal loved one frequency: A marginal frequency separated by the full number ofevents.Mean: The typical of a repertoire of data values. This have the right to be computed by including allthe values and also then dividing by the number of values.Mean absolute deviation: The median distance that data values from some main value,such together the mean, median, or mode of the collection. In various other words, the typical of $|x-m|$ where$x$ is every data value and $m$ is the mean, median, or setting of all the data values.Mean squared deviation: The typical squared distance of data worths from some centralvalue, such as the mean, median, or setting of the collection. In other words, the mean of$(x-m)^2$ wherein $x$ is each data value and $m$ is the mean, median, or setting of every the datavalues.Median: The middle number in one ordered perform of data values. If there space an evennumber the values, the typical is halfway in between the two center numbers in the list.Mode: The most typical value in a collection, or “modes” if an ext than one are tied.Monic: A polynomial whose leading (first) coefficient is $1$.Monomial: A product that variables and numbers, like $3x$ or $5x^2$. A monomial is alsosometimes called a term.Negate: take it the the contrary of a number, by multiplying it through $-1$.Negative number: A value less than zero (like $-3$).$n$th root: an $n$th source of $a$ is a number $b$ whose $n$th power is $a$. That is,$b^n = a$. If $a ≥ 0$ and also $n$ is an integer and also $n > 0$, climate “the” $nth source of $a$, written$√^na$, is the $n$th root of $a$ the is hopeful or zero.Numerator: The peak number or expression in a fraction.Odd function: A function $f$ v $-f(x)=f(-x)$ for all $x$. $f(x) = x^n$ is one oddfunction if $n$ is one odd integer. A role is strange if and also only if the graph has the point$(0, 0)$ as a point of symmetry.One-to-one: A function $f$ for which $f(x)$ has a different value for every distinct(different) value of $x$.Origin: The allude on a coordinate plane where the $x$-axis and $y$-axis intersect.It is stood for by the collaborates $(0, 0)$.Outlier: A value that “lies outside” (is lot smaller or larger than) many of theother worths in a collection.Output: A number produced by applying a relationship or role to an input.Parabola: The shape of the graph of $y=x^2$.Parallel: two lines are parallel if they constantly have the same distancebetween them, for this reason they never intersect. If 2 lines space parallel, they have actually the very same slope.Perfect square: A number the is the square the a reasonable number. For example, $1$,$4$, $$25/16$$, and $0$ are perfect squares. An integer is a perfect square just if that is thesquare of one integer, which deserve to be proven utilizing the an essential theorem the arithmetic.Period: for a periodic function, the quantity of time prior to it repeats. The is, if $f$is a periodic function, its period is the smallest possible positive $h$ where $f(x+h)=f(x)$ forevery $x$.Periodic function: A function that repeats after ~ a certain duration $h$ with $h > 0$, sothat $f(x+h)=f(x)$ because that every $x$.Perpendicular: 2 lines space perpendicular if they develop a 90-degree angle. If twolines space perpendicular and also the slope of one of them is $m$, then the slope of the other line is$$-1/m$$.Piecewise-defined function: A duty that is defined by different formulas atdifferent inputs.Point: A ar in the name: coordinates plane. A suggest has coordinates $(x,y)$, whereby $x$is offered by the labels below a name: coordinates grid, and $y$ is given by the brand to the left ofa name: coordinates grid.Point the symmetry: A suggest that you deserve to rotate a graph about by 180° that outcomes inthe very same graph.Point-slope form: If a line contains the allude $(x_1,y_1)$ and also has slope $m$, then itsequation have the right to be written as $y−y_1=m(x−x_1)$. An equation in the type $y−y_1=m(x−x_1)$ is said tobe in point-slope form.Polynomial: A amount of monomials. Typically terms with greater powers are written first.Positive number: A value greater than zero (like 3).Power: an expression that the kind $a^d$. $a$ is called the base, $d$ is referred to as theexponent, and $a^d$ is dubbed “the $d$th strength of $a$”. If $d$ is a positive integer, $a^d$means $a$ multiplied by itself $d$ times.Prime number: one integer better than $1$ that have the right to only be written as a product the twowhole number in one way: as itself multiply by $1$.Product: The answer to a multiplication problem.Profit: Revenue minus cost.Quadrant: each of the four sections that a coordinate airplane made by the intersecting$x$- and $y$-axes. The four quadrants room labeled I, II, III, and IV, counterclockwise from thetop right.Quadratic: an expression or equation in i beg your pardon the highest power the a change hasexponent $2$.Quadratic coefficient: for a polynomial in $x$, the number the $x^2$ is multipliedby.Quartiles: The very first quartile, median, and third quartile space values which divide adata collection into four roughly equal parts.Quotient: The answer come a department problem.Range: The set of outputs ($y$-coordinates) that a relationship or function.Rate the change: The speed at i m sorry a variable alters over a period of time. This isgiven by the change in the variable divided by the adjust in (amount of) time.Rational number: A number that deserve to be composed as a fraction $$m/n$$where $m$ and also $n$ are integers.Reflection: strict motion throughout a resolved line $AB$ in a plane, like amirror image.Relation: A collection of ordered bag $(x, y)$.Relative frequency: A frequency separated by the total variety of events, regularly expressedas a percentage.Residual: an observed worth minus its estimated value.Restriction: A role $g$ is a limit of the role $f$ if $g(x) = f(x)$for every $x$ in the domain of $g$, yet that domain might be smaller sized than the domain that $f$.Revenue: exactly how much money a company receives in sales.Rigid motion: A movement that conservation distances and angle measures, through nostretching, shrinking, or bending. A rigid movement in the plane is a succession of one or moretranslations, rotations, and/or reflections.Root-mean-square error: A number the tells you how far away a line or curve is native aset of clues (a smaller sized number way the heat is a far better “fit” come the points). Much more precisely,it is the square root of the average of the squared residuals (differences) in between observed andestimated values.Roots: The values of $x$ where a polynomial is zero. These space the$x$-coordinates the the $x$-intercepts of the polynomial’s graph.Rotation: strict motion about a fixed center $A$, with transforming but noreflection.Scatter plot: Dots in the coordinate plane representing bag of connected measurements,such as heights and also weights because that a team of people.Sequence: A list of numbers that may be produced by some rule.Set: one unordered collection of numbers or various other mathematical objects, withoutrepetitions.Similar: two geometric numbers are similar if they have actually the exact same shape however possiblydifferent sizes, with equivalent lengths different by a single common range factor.Simplify: come rewrite one expression in a means that method the exact same thing but is simpler(or shorter). You deserve to simplify $3x - x + 6$ into $2x + 6$.Slope: A number the measures how steep a line is. It reflects the lot of readjust inthe height of the line together you walk 1 unit to the right. The slope of the line $y=mx+b$ is $m$.Slope-intercept form: The kind $y=mx+b$ because that a direct equation, wherein $m$ and $b$ areconstants. The numbers $m$ and also $b$ give the slope and $y$-intercept of the line that is thegraph of the equation.Solution: In an equation or inequality, a number that deserve to be substituted because that thevariable to make that equation or inequality true. If the equation or inequality has more thanone variable, a equipment is a list of number that as soon as substituted for the list of variablesmakes the equation or inequality true. For a mechanism of much more than one equation or inequality, asolution need to make all of the equations or inequalities true. In chemistry, a equipment is aliquid mixture.Solution set: All solutions to an equation, inequality, or system.Solve: discover the options to an equation, inequality, or system.Square root: A square source of $a$ is a number $b$ who square is $a$. The is,$b^2 = a$. If $b$ is a square source of $a$, climate so is $- b$. If $a ≥ 0$, “the” square root of$a$, created $√a$, is the square root of $a$ that is optimistic or zero.Standard deviation: The square root of the variance.Standard form: for a straight equation, the type $Ax+By=C$ wherein $A$, $B$, and $C$ areconstants. For a quadratic equation, either the kind $y=ax^2+bx+c$ or $ax^2+bx+c=0$, whereby $a$,$b$, and also $c$ space constants.Statistic: A number provided to describe or summary data.Statistics: The research of data, and the approaches used to describe or summarize data.Step function: A piecewise-defined duty where every piece’s formula is a constant(doesn’t change with $x$). A step function’s graph looks choose stair steps.Substitution: In one expression or equation, removed a variable by replacing itwith one more expression the it is equal to.Sum: The answer come an addition problem.Symmetry: Repeating pattern or shape.System: because that equations or inequalities, two or much more equations or inequalities the areall required to be true.Table: In mathematics, a rectangular setup of rows and columns.Term: facet in a sum, difference, or sequence.The quadratic formula: The formula $$x = -b ± √b^2-4ac / 2a$$, which gives thesolutions to any type of equation in the form $ax^2+bx+c=0$ through $a ≠ 0$. The equation has actually two solutionswhen $b^2-4ac > 0$; it has actually one solution once $b^2-4ac=0$; and it has actually no actual solutions as soon as $b^2-4ac Third quartile: for $n$ data values, the average of the $$n/2$$ largest values if $n$is even, and also of the $$n-1/2$$ biggest values if $n$ is odd.Translation: Rigid movement by a continuous distance in a single direction,with no rotation or reflection.Two-way frequency table: For events that deserve to be divided into categories two differentways, a table of joint frequencies, utilizing rows of the table to team the events one way, andcolumns the the table to group the events the various other way.Unit: A typical measurement, such as a meter or one hour.Value: A number the a change or expression have the right to equal.Variable: A letter (like $x$) that we have the right to use to mean various numbers in ~ differenttimes.Variance: The average squared street of data values from their mean $m$. This deserve to becomputed by including $(x-m)^2$ for each data worth $x$, and also then dividing by the variety of datavalues $n$. When measuring a sample indigenous a population, for instance heights that people, thevariance that the sample is usually different than the variance of the whole population. Toestimate the population’s variance, it is usually much better to divide by $n-1$ instead of $n$.Vertex: The point where a parabola the cross its axis the symmetry, or an end of a sideof a polygon, or the corner allude of one angle.Vertex form: A quadratic equation in the type $y=a(x-h)^2+k$.Vertical: walking up and down.Whole number: one of the numbers 0, 1, 2, 3, ... .$x$-axis: The horizontal line running with the origin on a coordinate plane.$x$-coordinate: The horizontal value in a name: coordinates pair. It speak how much to theleft or best the suggest is. The $x$-coordinate is always written an initial in the name: coordinates pair.$x$-intercept: A suggest where a curve meets the horizontal axis (the $x$-axis).$y$-axis: The vertical line running with the origin on a name: coordinates plane.$y$-coordinate: The vertical worth in a coordinate pair. It speak how far up or downthe point is. The $y$-coordinate is always written last in the coordinate pair.$y$-intercept: A point where a line or curve meets the upright axis (the $y$-axis).The $y$-intercept the the heat $y=mx+b$ is the suggest $(0,b)$.
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Zeros: The worths of $x$ wherein an expression is zero. These room the$x$-coordinates the the $x$-intercepts of the expression’s graph. Because that a polynomial expression,these space usually referred to as roots.