Math III Final Exam Review. Name. Unit 1 Statistics. Definitions Population: Sample: Statistics: Parameter: Methods for Collecting Data Survey:

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1 Math III Fial Exam Review Name Uit Statistics Defiitios Populatio: Sample: Statistics: Paamete: Methods fo Collectig Data Suvey: Obsevatioal Study: Expeimet: Samplig Methods Radom: Statified: Systematic: Cluste: Coveiece: The five umbe summay cosist of: Label o the Box ad Whiske Plot below

2 Measues of cetal tedecy Mea: Media: Mode: Nomal Distibutio Complete the omal distibutio cuve below: Z-Scoe Uit Polyomials ad Factoig Sets of Numbes: Ratioal Itege Whole Natual Real Iatioal Polyomial Opeatios - addig, subtactig, multiplyig, ad dividig (log divisio ad sythetic divisio) Factoig: Always look fo a GCF st! Tems 3 Tems 4 Tems Diffeece of Squaes Tiomial a= T Chat Goupig Diffeece of Cubes (SOAP) Tiomial a> T Chat ad Box Sum of Cubes (SOAP) Ratioal Expessios: (Factios!!) Simplify Facto Numeato, Facto Deomiato, Cacel Multiply Facto Numeatos, Facto Deomiatos, Cacel Divide Flip, Facto, Cacel Uit 3 Quadatic Fuctios Radicals ad Complex Numbes Simplifyig Look fo the highest pefect squae. Addig/Subtactig Must be the same # ude the adical Multiplyig Multiply Isides, Multiply Outsides, Simplify Dividig/Ratioalizig No adical i the deomiato, Cojugates (a + b) (a b) Complex No egative #s ude the adical.

3 Solvig Quadatic Fuctios. Gaphig. Factoig 3. Squae Root Popety 4. Complete the Squae 5. Quadatic Fomula Quadatic Applicatios ad Regessios Gaphig Paabolas Stadad Fom f ( x) = ax + bx + c y-itecept: c axis of symmety: b x = x-coodiate of vetex: a b a Vetex Fom y = (x h) + k 4p Vetex: p = Diectio: Focus: Diectix: AOS: x = (y k) + h 4p Witig the Equatio Give: Roots wok backwads o sum ad poduct method Poit, Vetex, Focus, o Diectix Uit 4 Cubic, Radical, ad Ratioal Fuctios Ivese Fuctio Switch x ad y Facto Polyomial Fuctio. Fid oot i calculato (if ot give). Use sythetic divisio to fom a quadatic 3. Facto ad solve the quadatic Witig the equatio give oots Applicatios ad Regessio Ope Box poblem Domai will be betwee 0 ad half of the logest side Solvig Ratioal Equatios Fid a commo deomiato Multiply each tem by the CD to get id of the factios Solve fo x. Gaphig Ratioal Fuctios (Quotiet of Polyomials) Roots Vetical Asymptote (x = #) / Domai x # Hoizotal Asymptote (y = #) / Rage y #

4 Gaphig Recipocal Fuctios (y = /x) Shifts Vetical Asymptote (x = #) / Domai x # Hoizotal Asymptote (y = #) / Rage y # Gaphig Radical Fuctios Solvig Radical Equatios Applicatio Wok poblems Tavel poblems d = t Uit 5 Logaithmic ad Expoetial Fuctios Commo Log base 0 Natual Log - base e Log Popeties log(x) + log(y) = log (x) log(y) = log(x) = Chage of Base Fomula = Expoetial Regessio Gowth/Decay If 0 < b < If b > Fomulas Gowth y = a( + ) t kt y = ae Decay ( ) t y = a y = ae kt Compoud Iteest t A = P + Compoud Cotiuous t A = Pe Solvig Expoetial Fuctios If bases ae the same the the expoets ae equal If the bases ae ot the same the take the log of both sides Solvig Logaithmic Fuctios Codese to a sigle logaithm If log o ONE side oly Cicle Method If log o both sides with the same base the set them equal Uit 6 Systems, Sequeces, ad Seies To solve a Systems of Noliea equatios look fo the of Solve by: Gaphig, Substitutio, o Elimiatio Applicatio

5 Liea Pogammig Gaph all iequalities give (shade appopiate egio) Fid the poits of itesectio that make up the feasible egio (polygo i which all shades ovelap) Substitute the poits ito the objective fuctio to fid the max/mi Liea Pogammig Wod Poblems Detemie vaiables by fidig the objective fuctio (most of the time pofit) Wite algebaic iequalities to epeset the situatio Gaph all iequalities Fid the poits of itesectio of the feasible egio Substitute the poits ito the objective fuctio to fid solutio Sequeces ad Seies Aithmetic Sequece: Fomula fo th tem: a = a + ( ) d A ecusive defiitio cosists of pats:.. Aithmetic Seies: Sum of a fiite aithmetic seies: S = ( a + a ) Geometic Sequece: Fomula fo th tem: Geometic Seies: a = a a a a( ) Sum of a fiite geometic seies: S = o S = **Note ** a If we kow the fist ( a ) tem, last ( a ) tem, ad but ot use a S = Sigma Notatio 5 = Uit 7-Paallel Lies ad Tiagles Give: l m. coespodig agles: alteate iteio agles: alteate exteio agles: same-side iteio agles(also called cosecutive): All elatioships ae except fo, which is.

6 Tiagles Tiagle Sum: All of the iteio agles of a tiagle add to. Midsegmet: Pats of a tiagle ad thei poits of cocuecy: Pat of a Tiagle Pictue Poit of Cocuecy Pictue Pepedicula Bisecto Agle Bisecto Media Altitude Tiagle Similaity Sepaate the tiagle ito tiagles (small/lage). Popotio will be pat (small tiagle) to whole (lage tiagle). Tiagle Popotioality Theoem: If a lie to oe side of a tiagle itesects the othe, the it divides the sides. Popotio: Povig Tiagles ae simila: AA, SAS, SSS

7 Quadilateals Paallelogam Rectagle Rhombus Squae Paallelogam Rhombus Rectagle Opposite sides paallel Opposite sides coguet Opposite agles ae coguet Cosecutive agles ae supplemetay Diagoals bisect each othe All sides ae coguet Diagoals ae pepedicula Diagoals bisect opposite agles Diagoals ae coguet 4 ight agles Uit 8 Cicles Covetig fom adias to degees adia = 80 π Covetig fom degees to adias = π adias 80 Cotemial Agles: Two agles i stadad positio have the same temial side. Add o subtact 360 if i degees o if i adias Refeece Agle: The acute agle fomed by the temial side of a agle i stadad positio ad the x-axis. Tigoometic atios: si θ = y cos θ = x Pythagoea Idetity: si y ta θ = x + y = x θ + cos θ = Pythagoea Theoem: θ x y Tigoometic Idetities Recipocal Idetities: Quotiet Idetities: Cosecat Secat Cotaget csc θ = siθ sec θ = cosθ cot θ = taθ ta θ = siθ cosθ cosθ cot θ = siθ

8 Gaphig Tig Fuctios Peiod: The hoizotal distace fo the gaph of a peiodic fuctio to complete oe cycle. Amplitude: The absolute value of half the diffeece betwee a peiodic fuctio s maximum value ad its miimum value. 360 π Fo fuctios of the fom y = asi bx ad y = a cos bx the amplitude is a, ad the peiod is o b b Fo fuctios of the fom y = a ta bx the amplitude is ot defied, ad the peiod is 80 π o. b b Phase Shift: A hoizotal taslatio of a tigoometic fuctio. Vetical Shift: A vetical taslatio of a tigoometic fuctio Midlie: A hoizotal axis used as the efeece lie about which the gaph of apeiodic fuctio oscillates. y = a si b( x h) + k y = a cos b( x h) + k y = a ta b( x h) + k Phase Shift (h): Vetical Shift(k): The midlie is y = k If x-h, the shift is to the ight. If k > 0, the shift is to up If x+h, the shift is to the left. If k < 0, the shift is to dow.. Cicles ad Tagets (mak pictue) Acs ad Agles Cetal: Agle = ac O: Agle = ac I: Agle = (ac + ac) Out: Agle = (ac ac) x x Ac Legth Aea of Secto π π = s θ O π = 360 s θ π = π θ Aea Secto O π = 360 θ Aea Secto Gaphig Cicles Vetex Fom: Stadad Fom: Cete: Radius: To chage fom stadad to vetex you must complete the squae fo both x ad y.