algebra ii math notes

8/13/2019 Algebra II Math Notes

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ALG II MATH NOTES

Chapter 1 Equations and InequalitiesVariable Symbols, usually letters, used to represent unknown quantities.Algebrai E!pression E!pressions that ontain at least one "ariable.

#olynomial A monomial or sum o$ monomials.%onomial An e!pression that is a number, a "ariable, or a produt o$ number and"ariable.Coe$$iient &he number in $ront o$ a "ariable. 'umerial $ator o$ monomial.(egree )o$ monomial* Is the sum o$ the e!ponents o$ its "ariable. (egree o$ a onstant is+ero.Constants %onomials wo "ariables.(egree )o$ a polynomial* Equal to the monomial with greatest degree.&erms Eah indi"idual monomial in the polynomial.-ike &erms &erms with the same degree o$ "ariables.

inomial A polynomial with two unlike terms.&rinomial A polynomial with three unlike terms.

#ower E!pression in the $ormxn with an e!ponent. Also re$ers to the e!ponent itsel$./ormula A mathematial sentene that e!presses the relationship between quantities.0eal 'umbers A number that is $ound on a number line. Either rational or irrational.

'atural 'umbers Also known as ounting numbers. #ositi"e integers. 1, 2, 3...45hole 'umbers 'atural numbers as well as +ero. 6, 1, 2...4Integers 5hole 'umbers as well as their negati"e ounterparts. 7 82, 81, 6, 1,

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0ational 'umber A number that an be e!pressed as a $ration in the $orm a/bwhere b 0. Inludes 'atural, 5hole, and Integers. (eimal representation eitherterminates or repeats. 9, 81, 23, 6.1:::::::74

Irrational 'umber A number that;s not rational. (eimal neitherterminates orrepeats. 2, , e74#roperties o$ 0eal 'umberspen Sentene A mathematial sentene that ontains at least one "ariable.Equation A mathematial sentene stating two e!pressions are equal.#roperties o$ Equalityther letters like @g(x)may also be used.-inear Equation A equation with only "ariables that ha"e 1 as an e!ponent.

-inear /untion A $untion whose ordered pairs satis$y a linear equation.Standard /orm An equation in the $ormAx+By+C=0whereA, B, and Careintegerswith a GC=1andAandBare not both+ero.J8interept &he y8oordinate at whih the graph o$ an equation interepts the y8


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Substitution >ne equation is sol"ed $or one "ariable in terms o$ the other. >nee!pression is substituted $or a "ariable in the other equation.

E!ampleasionally, you may ha"e to multiplydi"ide eah equation to be ableto eliminate.System o$ Inequalities >rdered pairs that satis$y both sets o$ inequalities. Solutions arewhere the two graphs interset.

Constraints oundaries o$ systems./easible 0egion &he area where the graphs interset.ounded 5hen the area $ormed is a polygon.nbounded 5hen the area is open)unbounded on one side*.

-inear #rogramming /inding ma!imum and minimum "alues inside an area.

%a!imum Value &he highest point that is within the $easible region.Always at"erte!.%inimum Value &he lowest point that is within the $easible region. Alwaysat"erte!.

System o$ Equations in &hree Variables Systems that ha"e three "ariables.>rdered &riple Solution to systems with three "ariables. (x,y,).

RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR

Chapter %atries%atri! A retangular array o$ onstants andor "ariables in rows and olumns usuallyenlosed in brakets.

Element Eah "alue in the matri!.(imensions (esribing the si+e o$ a matri!. Row x Column.

Speial %atriesperations with %atries0and all negati"es i$ a1.E!p. (eay &he base is 0byi$$x>yand bx1, and :gbx>y, thenx>by.FI$ b


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a plane that are equidistant $rom a gi"en point alled the #ousand a gi"en line alledthe "iretrix. (esribed asy"-=1/a(x")#.

-atus 0etum A line perpendiular to the a!is o$ symmetry going throughthe $ous.

Cirle Set o$ all points in a plane that are equidistant $rom a gi"en point, known as theenter.

0adius &he distane $rom any point on the irle to the enter./ormula &he equation o$ a irle with enter (,-)and radius is )x")#+

(y"-)#=#.Ellipses Set o$ all points in a plane suh that the sum o$ the distanes $rom two $i!ed

points, the #oi, is onstant. &he graph is in the shape o$ a strethed irle. &he pointsat whih the ellipse intersets the a!is o$ symmetry $orm two lines alled the ma'oraxisand minor axis. &hese two a!is interset at the enter. &he $oi o$ the ellipse arealways caway $rom the enter and in an ellipse, c#=a#"b#.

Eentriity Zow muh the ellipse is @strethed. c/a.

Zyperbola &he set o$ all points in a plane suh that the absolute "alue o$ di$$ereneo$ the distanes $rom two $i!ed points, the #oi(are onstant. &he graph is in the shape o$two branhes pointed away $rom eah other and approahing asymptotes. In ahyperbola, c#=a#+b#.Eentriityis c/a.

Verte! &he endpoint o$ the branhes. &hey are caway $rom the enter.&rans"erse A!is -ength #awith endpoints as "erties o$ hyperbola.ConDugate A!is -ength #band perpendiular to trans"erse a!is.

'onretangular Asymptotes aren;t perpendiular.0etangular Asymptotes are perpendiular.


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