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Linear Equations
Slope-InterceptForm:π = ππ + πSlope=ππ¦-intercept=π
Point-SlopeForm:π β ππ = π(π β ππ)
StandardForm:π¨π + π©π = πͺ
Slope=β12
π¦-intercept= 32
SlopeFormula:π = ππ5ππππ5ππ
MidpointFormula:6ππ7πππ
, ππ7πππ:
DistanceFormula:π = <(ππ β ππ)π + (ππ β ππ)π
Systems of Equations
IntersectinglinesΓ onesolution
ParallellinesΓ nosolutions
SamelineΓ infinitesolutions
Quadratic Equations / Parabolas
Standard/QuadraticForm:π(π) = πππ + ππ + π
π₯-valueofvertex= β ABC
π¦-valueofvertex= π 6β ABC:
Minimumwhenπ > 0Maximumwhenπ < 0
π¦-intercept= π ββconstantorcoefficientβ
VertexForm:π(π) = π(π β π)π + π
Vertex:(β, π)ββconstantsorcoefficientsβMinimum(whenπ > 0):πMaximum(whenπ < 0):π
FactoredForm:π(π) = π(π β π)(π β π)
π₯-intercepts:π andπ‘ββconstantsorcoefficientsβ
π₯-valueofvertex= S7TB
π¦-valueofvertex= π 6S7TB:
Minimumwhenπ > 0
Maximumwhenπ < 0
ESSENTIAL FORMULAS FOR SAT MATH
Circles ArcLength= 6 π
πππ:ππ πSectorArea= 6 π
πππ:π ππ
π =centralangleofarc/sector
Center-RadiusEquation:(π β π)π + (π β π)π = ππCenter:(β, π)Radius=π
Powers/Exponents/Roots π₯C Γ π₯A = π₯C7A π₯5C = ^
_`
_`
_a= π₯C5A π₯
`a = βπ₯Ca
(π₯C)A = π₯CA (π₯π¦)C = π₯Cπ¦C
<π₯π¦ = βπ₯ Γ <π¦ π₯c = 1
(β1)e = f 1, πππππ ππ£ππβ1, πππππ πππ
Exponential Equations
GeneralForm: π(π) = πππ β’ Ifπ > 1,exponentialgrowthβ’ If0 < π < 1,exponentialdecay
Growth/DecayFormula:π¨(π) = π·6π + ππππ:π
β’ π =Principle(initialamount)β’ π =%increase/decreaseβ’ π‘ =timeinterval(inanyunit)
Trigonometry π πππ = noo
pqo πππ πππ = Crs
pqo π‘ππππππ‘ = noo
Crs
ππβ π΄ + β π΅ = 90Β°, π‘βππ zπ πππ΄ = πππ π΅πππ π΄ = π πππ΅
Percentages % = oC|T
}pn~οΏ½Γ 100 %πβππππ = eοΏ½}5n~r
n~rΓ 100
Miscellaneous π·ππ π‘ππππ = π ππ‘π Γ ππππ
Quadratic Identities
(π₯ + π)(π₯ + π) = π₯B + (π + π)π₯ + ππ πB β πB = (π + π)(π β π)(π + π)B = πB + 2ππ + πB(π β π)B = πB β 2ππ + πB
Eliminatebothvariables!
A mentor can change everything.
Components of Experiment Design
Population: Asetofitemsofinterestforsomequestionorexperiment.
RandomSample: Asubsetofthepopulationthatcanreasonablybestudiedinwhicheachitemhasanequalchanceofbeingselected.
Requiredinordertogeneralizesurveyresultstotheentirepopulation.
SampleBias: Whensomemembersofpopulationarelesslikelytobeincludedthanothers.
Randomsampling=nosamplebias
MarginofError: Howmanypercentagepointsasampleβsresultswilldifferfromtherealpopulationβsvalue.
ConfidenceInterval: A95%confidenceintervalwitha4%marginoferrormeansthatyourstatisticwillbewithin4pointsoftherealpopulationvalue95%ofthetime.
Statistical Measures
Mean: π π’πππππ‘πππ #ππππ‘πππ
Median: Themiddlenumberofanorderedsetofitems.
Median#term: e7^B,π =numberofitemsinset.
Range: Maximumβminimum
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(π€π + βπ + βπ€)
SurfaceAreaofCylinder= 2ππB + 2ππβ
AreaofEquilateralTriangle=βοΏ½οΏ½π B
Complex Numbers
π^ = π πB = β1 ποΏ½ = βπ ποΏ½ = 1
ποΏ½ = π ποΏ½ = β1 ποΏ½ = βπ ποΏ½ = 1
Direct/Inverse Variation DirectVariation:π¦ = ππ₯
InverseVariation:π¦ = οΏ½_
Complex Examples of Variation
π¦ = πβπ₯ βΆ 9π₯ β 3π¦ π¦ = ππ₯B βΆ 3π₯ β 9π¦
π¦ = οΏ½β_ βΆ 9π₯ β ^
οΏ½π¦ π¦ = οΏ½
_οΏ½ βΆ 3π₯ β ^
οΏ½π¦
Arithmetic Sequences
πe = π^ + (π β 1)π πe =eB(π^ + πe)
π = constantofvariation
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