# the ultimate cheat sheet for math & physics · pdf fileimplicit differentiation ... visually...

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TheUltimateCheatSheetforMath&PhysicsPreview

TableofContentsAlgebra..............................................................................................................................................2Arithmetic......................................................................................................................................................................................................2Exponents......................................................................................................................................................................................................3

Trigonometry.....................................................................................................................................4DoubleAngleFormulas...........................................................................................................................................................................4HalfAngleFormulas..................................................................................................................................................................................5SumandDifferenceFormulas..............................................................................................................................................................6

Precalculus.........................................................................................................................................7EquationofaLine......................................................................................................................................................................................7EquationofParabola................................................................................................................................................................................7EquationofCircle.......................................................................................................................................................................................7EquationofEllipse.....................................................................................................................................................................................7EquationofHyperbola.............................................................................................................................................................................7EquationofHyperbola.............................................................................................................................................................................7

Calculus..............................................................................................................................................8Tangentline..................................................................................................................................................................................................8Implicitdifferentiation............................................................................................................................................................................9

LinearAlgebra..................................................................................................................................10Rankofmatrixandpivots...................................................................................................................................................................10Lengthofavectorandtheunitvector...........................................................................................................................................11SolutionsofAugmentedMatrices....................................................................................................................................................12CoefficientMatrix....................................................................................................................................................................................12UniqueSolution.......................................................................................................................................................................................13InfiniteSolution.......................................................................................................................................................................................13NoSolution.................................................................................................................................................................................................13DifferentialEquations......................................................................................................................14First-OrderLinearNon-Homogeneous..........................................................................................................................................14OrderandLinearity................................................................................................................................................................................14ReductionofOrder.................................................................................................................................................................................15

Physics.............................................................................................................................................16Vectors.........................................................................................................................................................................................................16DotProduct................................................................................................................................................................................................16CrossProduct............................................................................................................................................................................................16MagnitudeorLengthofavector......................................................................................................................................................17ResultantVector......................................................................................................................................................................................17

AlgebraArithmetic

= = 10 6 = 2 5 2 3 = 2 5 3 = 5 3 2_________________________________________________________________________________________________________________

_

=

123 =

1231=12 13 =

12 3 =

16

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=

12

34 =

1 4 2 32 4 =

4 68

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=

1 23 4 =

(1+ 2)(3+ 4) =

2 14 3

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+

= + , 0 12 16

4 =124

164 = 3 4

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=

165 =

4 45 = 4

45

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=

1

=

234

=2134

=21 43 =

83

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=

12 165 =

125

165

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= =