Linear Equations
Slope-InterceptForm:๐ = ๐๐ + ๐Slope=๐๐ฆ-intercept=๐
Point-SlopeForm:๐ โ ๐๐ = ๐(๐ โ ๐๐)
StandardForm:๐จ๐ + ๐ฉ๐ = ๐ช
Slope=โ12
๐ฆ-intercept= 32
SlopeFormula:๐ = ๐๐5๐๐๐๐5๐๐
MidpointFormula:6๐๐7๐๐๐
, ๐๐7๐๐๐:
DistanceFormula:๐ = <(๐๐ โ ๐๐)๐ + (๐๐ โ ๐๐)๐
Systems of Equations
Intersectinglinesร onesolution
Parallellinesร nosolutions
Samelineร infinitesolutions
Quadratic Equations / Parabolas
Standard/QuadraticForm:๐(๐) = ๐๐๐ + ๐๐ + ๐
๐ฅ-valueofvertex= โ ABC
๐ฆ-valueofvertex= ๐ 6โ ABC:
Minimumwhen๐ > 0Maximumwhen๐ < 0
๐ฆ-intercept= ๐ โโconstantorcoefficientโ
VertexForm:๐(๐) = ๐(๐ โ ๐)๐ + ๐
Vertex:(โ, ๐)โโconstantsorcoefficientsโMinimum(when๐ > 0):๐Maximum(when๐ < 0):๐
FactoredForm:๐(๐) = ๐(๐ โ ๐)(๐ โ ๐)
๐ฅ-intercepts:๐ and๐กโโconstantsorcoefficientsโ
๐ฅ-valueofvertex= S7TB
๐ฆ-valueofvertex= ๐ 6S7TB:
Minimumwhen๐ > 0
Maximumwhen๐ < 0
ESSENTIAL FORMULAS FOR SAT MATH
Circles ArcLength= 6 ๐
๐๐๐:๐๐ ๐SectorArea= 6 ๐
๐๐๐:๐ ๐๐
๐ =centralangleofarc/sector
Center-RadiusEquation:(๐ โ ๐)๐ + (๐ โ ๐)๐ = ๐๐Center:(โ, ๐)Radius=๐
Powers/Exponents/Roots ๐ฅC ร ๐ฅA = ๐ฅC7A ๐ฅ5C = ^
_`
_`
_a= ๐ฅC5A ๐ฅ
`a = โ๐ฅCa
(๐ฅC)A = ๐ฅCA (๐ฅ๐ฆ)C = ๐ฅC๐ฆC
<๐ฅ๐ฆ = โ๐ฅ ร <๐ฆ ๐ฅc = 1
(โ1)e = f 1, ๐๐๐๐๐ ๐๐ฃ๐๐โ1, ๐๐๐๐๐ ๐๐๐
Exponential Equations
GeneralForm: ๐(๐) = ๐๐๐ โข If๐ > 1,exponentialgrowthโข If0 < ๐ < 1,exponentialdecay
Growth/DecayFormula:๐จ(๐) = ๐ท6๐ + ๐๐๐๐:๐
โข ๐ =Principle(initialamount)โข ๐ =%increase/decreaseโข ๐ก =timeinterval(inanyunit)
Trigonometry ๐ ๐๐๐ = noo
pqo ๐๐๐ ๐๐๐ = Crs
pqo ๐ก๐๐๐๐๐๐ก = noo
Crs
๐๐โ ๐ด + โ ๐ต = 90ยฐ, ๐กโ๐๐ z๐ ๐๐๐ด = ๐๐๐ ๐ต๐๐๐ ๐ด = ๐ ๐๐๐ต
Percentages % = oC|T
}pn~๏ฟฝร 100 %๐โ๐๐๐๐ = e๏ฟฝ}5n~r
n~rร 100
Miscellaneous ๐ท๐๐ ๐ก๐๐๐๐ = ๐ ๐๐ก๐ ร ๐๐๐๐
Quadratic Identities
(๐ฅ + ๐)(๐ฅ + ๐) = ๐ฅB + (๐ + ๐)๐ฅ + ๐๐ ๐B โ ๐B = (๐ + ๐)(๐ โ ๐)(๐ + ๐)B = ๐B + 2๐๐ + ๐B(๐ โ ๐)B = ๐B โ 2๐๐ + ๐B
Eliminatebothvariables!
A mentor can change everything.
Components of Experiment Design
Population: Asetofitemsofinterestforsomequestionorexperiment.
RandomSample: Asubsetofthepopulationthatcanreasonablybestudiedinwhicheachitemhasanequalchanceofbeingselected.
Requiredinordertogeneralizesurveyresultstotheentirepopulation.
SampleBias: Whensomemembersofpopulationarelesslikelytobeincludedthanothers.
Randomsampling=nosamplebias
MarginofError: Howmanypercentagepointsasampleโsresultswilldifferfromtherealpopulationโsvalue.
ConfidenceInterval: A95%confidenceintervalwitha4%marginoferrormeansthatyourstatisticwillbewithin4pointsoftherealpopulationvalue95%ofthetime.
Statistical Measures
Mean: ๐ ๐ข๐๐๐๐๐ก๐๐๐ #๐๐๐๐ก๐๐๐
Median: Themiddlenumberofanorderedsetofitems.
Median#term: e7^B,๐ =numberofitemsinset.
Range: Maximumโminimum
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(๐ค๐ + โ๐ + โ๐ค)
SurfaceAreaofCylinder= 2๐๐B + 2๐๐โ
AreaofEquilateralTriangle=โ๏ฟฝ๏ฟฝ๐ B
Complex Numbers
๐^ = ๐ ๐B = โ1 ๐๏ฟฝ = โ๐ ๐๏ฟฝ = 1
๐๏ฟฝ = ๐ ๐๏ฟฝ = โ1 ๐๏ฟฝ = โ๐ ๐๏ฟฝ = 1
Direct/Inverse Variation DirectVariation:๐ฆ = ๐๐ฅ
InverseVariation:๐ฆ = ๏ฟฝ_
Complex Examples of Variation
๐ฆ = ๐โ๐ฅ โถ 9๐ฅ โ 3๐ฆ ๐ฆ = ๐๐ฅB โถ 3๐ฅ โ 9๐ฆ
๐ฆ = ๏ฟฝโ_ โถ 9๐ฅ โ ^
๏ฟฝ๐ฆ ๐ฆ = ๏ฟฝ
_๏ฟฝ โถ 3๐ฅ โ ^
๏ฟฝ๐ฆ
Arithmetic Sequences
๐e = ๐^ + (๐ โ 1)๐ ๐e =eB(๐^ + ๐e)
๐ = constantofvariation