Math III-Formula Sheet
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1 Math III-Formula Sheet Statistics Z-score: Margi of Error: To fid the MEAN, MAXIMUM, MINIMUM, Q 3, Q 1, ad STANDARD DEVIATION of a set of data: 1) Press STAT, ENTER (to eter our data) Put it i L 1 ) Press STAT 3) To Calc 4) Press 1, ENTER = mea, s = stadard deviatio, = # of values i the data, Med = media Normal Distriutio Percetage Normalcdf(lower limit, upper limit, mea, SD) Radom Sample-lotter method (everoe has a equall likel chace to e chose) Coveiece Sample- eas to reach (poll people i the luchroom) Sstematic-Eample: wat 150 studets, 1800 studets ames are put i the list, choose the 8 th perso, the ever 1 th (ecause 1800/150=1) after that util 150 are chose. Stratified- Sugroups- a desired umer is chose from EACH sugroup. (E: Fresh, Soph, Ju, Se-100 chose from all) Cluster-couties- all people i chose couties participate, oe of the people i o-chose couties participate. Self-Selected- perso chooses to participate (olie surve) Surve-questioaire Eperimet-used to prove cause ad effect; cotrolled (1) how sujects are assiged to groups, ad () which treatmets each received Oservatioal Stud- researcher CANNOT cotrol (1) ad/or () (from aove defiitio of eperimet)
2 Geometr Parallel Lies ad Trasversals Agles that are cogruet: correspodig, alterate-iterior, vertical Agles that are supplemetar (add up to 180 degrees): Same-side iterior Other reasos used: CPCTC (Correspodig parts of cogruet triagles are cogruet)-used after triagles are prove cogruet, Refleive Triagle cogruec: SSS, SAS, ASA, AAS Quadrilaterals: Parallelogram, rhomus, rectagle, square Slope: m 1 rise or ru Distace Formula: d ( 1 ) ( 1) Midpoit Formula: 1 M, 1 Polomials Stadard form of a quadratic: a c Verte form: a( h) k (h, k) is verte 1 1 Directri: k Focus: hk, 4a 4a Ais of Smmetr: (ou ca also fid the - a coordiate of the verte with this formula) Quadratic Formula: 4ac a Comple # s: 1 i i 1 Imagiar umers come i pairs. Equatio of a Circle with ceter at (h, k): h k r Eve ad Odd DEGREE Odd degree has opposite ed ehavior Eve degree has the same ed ehavior Compositio: Sum/Differece of cues: 3 3 a ( a )( a a ) a 3 3 ( a )( a a Polomial Idetities: ( a ) a 3a 3a 3 3 ( a ) a a Eve ad Odd Fuctio Eve Fuctios: f ( ) f ( ) Odd Fuctios: f ( ) f ( ) )
3 Epoetial ad Log Fuctios Iverse: Switch ad (solve for ) Chagig to/from epoetial ad log forms: (Brick ad Feather ) If, the. Chage of Base Formula Epoetial Equatio: Epoetial Growth/Deca (Value of a Item): Cotiuousl Compouded: No-cotiuousl Compouded: = # of times compouded (mothl = 1, quarterl=4) Log Properties (also used with atural logs) Product Propert: Quotiet Propert: Power Propert: Sequeces ad Series Arithmetic Sequece A() = a 1 + ( 1 ) d Geometric Sequece A() = a 1 r -1 S Fiite Arithmetic Series ( a a 1 ) Fiite Geometric Series S a r (1 1 1 r ) a 1 = first term = # of term d = commo differece r = commo ratio a = th term Degree, Radias, ad Poits Uit Circle Covert degrees to radias: Covert radias to degrees:
4 Sie Curve-starts at 0 Cosie Curve-starts at 1 Trig Graphs: a si d a cos d a = Amplitude = Chage i Period Period = d = Vertical Shift ( + is up ad is dow) Trigoometric Idetities Reciprocal Idetities (csc = cosecat, sec = secat, cot = cotaget) Taget ad Cotaget Idetities Pthagorea Idetities Similarit ad Circles Cetral agle: a agle whose verte is the ceter of the circle. It is equal to the arc it forms. Arc: part of a circle s circumferece (the crust of a slice of pizza) Sector: regio ouded a arc of the circle ad the two radii to the arc s edpoits. (slice of pizza) Taget: a lie i the plae of a circle that itersects the circle i eactl oe poit. Forms 90 degree agles with radius of circle. Chord: a segmet whose edpoits are o a circle Secat: a lie that itersects a circle at two poits. A secat also does NOT pass through the ceter of a circle.
5 Agles i a Circle Cetral Agle Agle = Arc Iscried Agle Agle = ½ Arc Triagle Iscried i a Semicircle Quadrilateral Iscried i a Circle ⁰ a Diameter c d a + c = d = 180 Two Secats Two Tagets Two Chords Chord ad Taget Agle = ½ Arc m 1 m 1 m 1 If a lie is taget to a circle, it is perpedicular the radius draw to the poit of tagec. If a diameter or radius is perpedicular to a chord, the it isects the arc ad isects the chord. If two segmets from the same eterior poit are taget to a circle, the are cogruet. Circumferece of a Circle: or Area of a Circle: Arc Legth (i degrees): Arc legth (i radias):
6 Calculator Hits Regressio Equatios How to tur o R: Catalog, Diagostic ON, eter, eter Liear Regressio - Stat Calc 4 Quadratic Regressio - Stat Calc 5 Epoetial Regressio - Stat Calc 0 Cuic Regressio - Stat Calc 6 Itersectios d Trace 5 Move liker to itersectio Eter Eter Eter Normal Distriutio Percetage Normalcdf(lower limit, upper limit, mea, SD) Kow how to: 1) Fid the Zeros ) Fid the ma ad mi 3) Tur aes off 4) Chage Tale Set 5) Radia vs Degree Mode Vocaular Domai Rage Eact Solutios cotai Approimate solutios decimals Itegers: -3,-,-1,0,1,,3
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