Maths - Core 3

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  • Created by: Georgia
  • Created on: 14-04-13 15:23

What are the trig identities involving sin^2(x) an

Sin^2(x) + Cos^2(x) = 1

Sin^2(x) = 1 - Cos^2(x)

Cos^2(x) = 1 - Sin^2(x)

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What are the trig identities involving Cot^2(x) an

1 + Cot^2(x) = Cosec^2(x)

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What are the trig identities involving Tan^2(x) an

Tan^2(x) + 1 = Sec^2(x)

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What is the trig identity for Sin(2x)?

2Sin(x)Cos(x)

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What are the three trig identities for Cos(2x)?

Cos(2x) = Cos^2(x) - Sin^2(x)

Cos(2x) = 1 - 2Sin^2(x)

Cos(2x) = 2Cos^2(x) - 1

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What is the trig identity for Tan(2x)?

2Tan(x) / 1 - Tan^2(x)

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Exponentials

In(1) = 0

In(e) = 1

In(e^x) = x

e^(Inx) = x

For y = Ae^kx, k>0 = Growth, k<0 = Decay.

For f(t) = A x b^t, b>1 = Growth, 0<b<1 = Decay.

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Calculus

y = Ae^kx+b, Differential = (Ak)e^kc+b

y = Ae^kx+b, Integral = Ae^kx+b / k 

y = In(f(x)), Differential = f '(x) / f(x)

y = 1/x, Integral = In|x|

Discriminants - for quadratics;   (Can relate to stationary points)

<0 NO SOLUTIONS

=0 ONE REPEATED SOLUTION

>0 TWO DISTINCT SOLUTIONS

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Differentiation and Integration

Differentiation;

Bracket Rule - Times number outside by power, lower power, multiply by differential

Chain Rule - Let u = .......

Product Rule - u'v + uv'

Quotient Rule - (u'v - uv') / v^2

Integration;

Raise power by one, divide by new power * differential of the bracket

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Volume of Revolution

360' Rotation about x-axis, V = pi * definite integral of y^2

360' Rotation about y-axis, V = pi * definite intergral of x^2 (Rearrange y = ..so x is subject)

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