# Maths revision

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Partial fractions
If it is an improper fraction, use the Remainder Thereom to find the number that is divisible, and then use the partial fractions method. If it has x(x^2 -1) partial fractions becomes A/x + Bx+c/x^2 -1
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Trigonometric formulae
sin(A+B) = sinAcosB+cosAsinB, cos(A+B) = cosAcosB-sinAsinB, sin(A+B) = sinAcosB-sinAsinB, cos(A-B) = cosAcosB+sinAsinB
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Double angle formulae
sin(2A) = 2sinAcosA, cos(2A) = cos^2A-sin^2A
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Tangent formulae
tan(A+B) = tanA+tanB/1-tanAtanB, tan(A-B) = tanA-tanB/1+tanAtanB, tan(2A) = 2tanA/1-tan^2A
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Equivalent expressions
asinx+bcosx can be written in the form: rsin(x+[alpha]) where a=rcos[alpha] and b=rsin[alpha] and rcos(x-[alpha]) where a=rsin[alpha] and b=rcos[alpha]
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Equivalent expressions 2
asinx-bcosx can be written in the form: rsin(x-[alpha]) where a=rcos[alpha] and b=rsin[alpha] and rcos(x+[alpha]) where a=rsin[alpha] and b=rcos[alpha]
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Exponential growth and decay
Growth - y=ae^bt, Decay - y=ae^-bt, Limiting Function - y=c+ae^-bt and y=c-ae^-bt
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Parametric equations
Translate - a add a to function for x, b add b to the function for y. Stretch (xd) multiply x function by d, Stretch (yd) multiply y function by d. Reflection (xd) multiply y function by -1, Reflection (yd) multiply x function by -1
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Cartesian equations
Make t the subject and put into an equation, make the cartesian according to y. If substitution doesn't work, for instance x=t^2+1/t and y=t^2-1/t, add them together
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Circles and Ellipses
Circle centre (0,0) radius 1, cartesian - x^2+y^2=r^2. If centre (a,b) x=rcos[angle]+a y=rsin[angle]+b and cartesian - r^2=(x-a)^2+(y-b)^2. Ellipses cartesian - x^2/a^2+y^2/b^2=1
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Binomial thereom
to coverge |ax|
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Parametrically defined functions
dy/dx = dy/dt / dx/dt
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Differentiating implicit functions
d(x^3)/dx = 3x^2, d(2y^3)/dx = 6y^2 x dy/dx, d(4xy)/dx = 4y+4x x dy/dx
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Integrating trigonometric functions
sin2x=2sinxcosx, cos2x=cos^2-sin^2x, cos2x=2cos^2x-1, cos2x=1-2sin^2x
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Vector notation in 3D
|AB| = [squareroot](x^2-x^1)^2+(y^2-y^1)^2+(z^2-z^1)^2 which is the distance between A and B. General form of a vector equation r= [p1p2p3] + h*[d1d2d3]
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Intersecting lines
Parallel lines = multiples, Intersect = value for h* and u* are the same. If does neither = Skew lines
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Dot product
cos[angle] = a1b1+a2b2+a3b3/|a|.|b|, a.b = a1b1+a2b2+a3b3 = |a|.|b| x cos[angle]
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## Other cards in this set

### Card 2

#### Front

If it is an improper fraction, use the Remainder Thereom to find the number that is divisible, and then use the partial fractions method. If it has x(x^2 -1) partial fractions becomes A/x + Bx+c/x^2 -1

#### Back

Partial fractions

### Card 3

#### Front

sin(A+B) = sinAcosB+cosAsinB, cos(A+B) = cosAcosB-sinAsinB, sin(A+B) = sinAcosB-sinAsinB, cos(A-B) = cosAcosB+sinAsinB

### Card 4

#### Front

sin(2A) = 2sinAcosA, cos(2A) = cos^2A-sin^2A

### Card 5

#### Front

tan(A+B) = tanA+tanB/1-tanAtanB, tan(A-B) = tanA-tanB/1+tanAtanB, tan(2A) = 2tanA/1-tan^2A