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Linear Equations
Slope-InterceptForm:𝒚 = 𝒎𝒙 + 𝒃Slope=𝑚𝑦-intercept=𝑏
Point-SlopeForm:𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏)
StandardForm:𝑨𝒙 + 𝑩𝒚 = 𝑪
Slope=−12
𝑦-intercept= 32
SlopeFormula:𝒎 = 𝒚𝟐5𝒚𝟏𝒙𝟐5𝒙𝟏
MidpointFormula:6𝒙𝟏7𝒙𝟐𝟐
, 𝒚𝟏7𝒚𝟐𝟐:
DistanceFormula:𝒅 = <(𝒙𝟐 − 𝒙𝟏)𝟐 + (𝒚𝟐 − 𝒚𝟏)𝟐
Systems of Equations
Intersectinglinesàonesolution
Parallellinesànosolutions
Samelineàinfinitesolutions
Quadratic Equations / Parabolas
Standard/QuadraticForm:𝒇(𝒙) = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
𝑥-valueofvertex= − ABC
𝑦-valueofvertex= 𝑓 6− ABC:
Minimumwhen𝑎 > 0Maximumwhen𝑎 < 0
𝑦-intercept= 𝑐 →“constantorcoefficient”
VertexForm:𝒇(𝒙) = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌
Vertex:(ℎ, 𝑘)→“constantsorcoefficients”Minimum(when𝑎 > 0):𝑘Maximum(when𝑎 < 0):𝑘
FactoredForm:𝒇(𝒙) = 𝒂(𝒙 − 𝒔)(𝒙 − 𝒕)
𝑥-intercepts:𝑠and𝑡→“constantsorcoefficients”
𝑥-valueofvertex= S7TB
𝑦-valueofvertex= 𝑓 6S7TB:
Minimumwhen𝑎 > 0
Maximumwhen𝑎 < 0
ESSENTIAL FORMULAS FOR SAT MATH
Circles ArcLength= 6 𝒏
𝟑𝟔𝟎:𝟐𝝅𝒓SectorArea= 6 𝒏
𝟑𝟔𝟎:𝝅𝒓𝟐
𝑛 =centralangleofarc/sector
Center-RadiusEquation:(𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐Center:(ℎ, 𝑘)Radius=𝑟
Powers/Exponents/Roots 𝑥C × 𝑥A = 𝑥C7A 𝑥5C = ^
_`
_`
_a= 𝑥C5A 𝑥
`a = √𝑥Ca
(𝑥C)A = 𝑥CA (𝑥𝑦)C = 𝑥C𝑦C
<𝑥𝑦 = √𝑥 × <𝑦 𝑥c = 1
(−1)e = f 1, 𝑖𝑓𝑛𝑖𝑠𝑒𝑣𝑒𝑛−1, 𝑖𝑓𝑛𝑖𝑠𝑜𝑑𝑑
Exponential Equations
GeneralForm: 𝒇(𝒙) = 𝒂𝒃𝒙 • If𝑏 > 1,exponentialgrowth• If0 < 𝑏 < 1,exponentialdecay
Growth/DecayFormula:𝑨(𝒕) = 𝑷6𝟏 + 𝒓𝟏𝟎𝟎:𝒕
• 𝑃 =Principle(initialamount)• 𝑟 =%increase/decrease• 𝑡 =timeinterval(inanyunit)
Trigonometry 𝑠𝑖𝑛𝑒 = noo
pqo 𝑐𝑜𝑠𝑖𝑛𝑒 = Crs
pqo 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 = noo
Crs
𝑖𝑓∠𝐴 + ∠𝐵 = 90°, 𝑡ℎ𝑒𝑛 z𝑠𝑖𝑛𝐴 = 𝑐𝑜𝑠𝐵𝑐𝑜𝑠𝐴 = 𝑠𝑖𝑛𝐵
Percentages % = oC|T
}pn~�× 100 %𝑐ℎ𝑎𝑛𝑔𝑒 = e�}5n~r
n~r× 100
Miscellaneous 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑅𝑎𝑡𝑒 × 𝑇𝑖𝑚𝑒
Quadratic Identities
(𝑥 + 𝑎)(𝑥 + 𝑏) = 𝑥B + (𝑏 + 𝑎)𝑥 + 𝑎𝑏 𝑎B − 𝑏B = (𝑎 + 𝑏)(𝑎 − 𝑏)(𝑎 + 𝑏)B = 𝑎B + 2𝑎𝑏 + 𝑏B(𝑎 − 𝑏)B = 𝑎B − 2𝑎𝑏 + 𝑏B
Eliminatebothvariables!
A mentor can change everything.
Components of Experiment Design
Population: Asetofitemsofinterestforsomequestionorexperiment.
RandomSample: Asubsetofthepopulationthatcanreasonablybestudiedinwhicheachitemhasanequalchanceofbeingselected.
Requiredinordertogeneralizesurveyresultstotheentirepopulation.
SampleBias: Whensomemembersofpopulationarelesslikelytobeincludedthanothers.
Randomsampling=nosamplebias
MarginofError: Howmanypercentagepointsasample’sresultswilldifferfromtherealpopulation’svalue.
ConfidenceInterval: A95%confidenceintervalwitha4%marginoferrormeansthatyourstatisticwillbewithin4pointsoftherealpopulationvalue95%ofthetime.
Statistical Measures
Mean: 𝑠𝑢𝑚𝑜𝑓𝑖𝑡𝑒𝑚𝑠#𝑜𝑓𝑖𝑡𝑒𝑚𝑠
Median: Themiddlenumberofanorderedsetofitems.
Median#term: e7^B,𝑛 =numberofitemsinset.
Range: Maximum–minimum
StandardDeviation: Measuresspreadofdataset
HighSD: dataspreadoutfrommeanLowSD: dataclosetomean
Outlier: Avaluethatissignificantlylargerorsmallerthantherestofthedata.
HighOutlier: Mean>Median
LowOutlier:Mean<Median
ESSENTIAL FORMULAS FOR SAT MATH
A mentor can change everything.
Box Plots
LowerQuartile: Lowest25%ofdata.
UpperQuartile: Highest25%ofdata
Extra Geometry Formulas
SurfaceAreaofRectangularPrism= 2(𝑤𝑙 + ℎ𝑙 + ℎ𝑤)
SurfaceAreaofCylinder= 2𝜋𝑟B + 2𝜋𝑟ℎ
AreaofEquilateralTriangle=√��𝑠B
Complex Numbers
𝑖^ = 𝑖 𝑖B = −1 𝑖� = −𝑖 𝑖� = 1
𝑖� = 𝑖 𝑖� = −1 𝑖� = −𝑖 𝑖� = 1
Direct/Inverse Variation DirectVariation:𝑦 = 𝑘𝑥
InverseVariation:𝑦 = �_
Complex Examples of Variation
𝑦 = 𝑘√𝑥 ∶ 9𝑥 → 3𝑦 𝑦 = 𝑘𝑥B ∶ 3𝑥 → 9𝑦
𝑦 = �√_ ∶ 9𝑥 → ^
�𝑦 𝑦 = �
_� ∶ 3𝑥 → ^
�𝑦
Arithmetic Sequences
𝑎e = 𝑎^ + (𝑛 − 1)𝑑 𝑆e =eB(𝑎^ + 𝑎e)
𝑘 = constantofvariation