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# Core 4

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## Nick Turnbull

on 19 May 2010

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#### Transcript of Core 4

CALCULUS Algebra Partial Fractions Parametric Equations Differentiation Integration Vectors Implicit Connected rates Standard Substitution By Parts Vols of Rev Trig identities Numerical Inspection Areas To cartesian Chain Rule Equation of a line Point of intersection of two lines Angle between vectors Angle between lines About y axis About x axis CORE 4 Differentiation Binomial expansions 2 Eg write:
2sinxcosx as sin2x
tanx as sinx/cosx
sin x as 1/2 - 1/2cos2x
before integrating eg 2 Integration (1 + x) = 1 + nx + n(n+1)x/2! + .......

eg (1 - 2x) = 1 + (1/2)(-2x) + (1/2)(-1/2)(-2x) /2! + ......

(8 - x) = 2(1 + (-x/8)) etc n 1/2 2 1/3 1/3 Differential Equations f(x) g(y) dy/dx = p(x)q(y)
gives: )
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