Maths C2

adamchaplin1997
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adamchaplin1997
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Mind Map on Maths C2, created by adamchaplin1997 on 02/26/2015.

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Maths C2
1 Differentiation
1.1 finding gradients or rates of change
1.2 f(x) differentiated is f'(x)
1.3 times by the power then take one from the power
1.4 A tangent has the same gradient as the curve
1.5 A normal has a perpendicular gradient to the curve
1.6 stationary points
1.6.1 grad=0
1.6.2 before+ after- max point
1.6.3 before- after+ min point
1.6.4 point of inflection has the same sign either side
1.6.5 Second derivative
1.6.5.1 <0 Maximum
1.6.5.2 =0 Max, Min or inflection
1.6.5.3 >0 Minimum
1.7 a function is increasing when the gradient is > 0
1.8 a function is decreasing when the gradient is <0
2 Intergration
2.1 add one to the power, divide by the power
2.2 with limits, put in the number top-bottom
2.3 +C
2.4 use it to find the area
2.4.1 areas under the x axis give negative integrals
2.4.1.1 do it in parts
2.4.2 bounded by two lines
2.4.2.1 find the area under one graph, subtract the other
2.5 Trapezium Rule
2.5.1 0.5h[y0+yn+2(y1+y2+]
3 Logarithms
3.1 Indices
3.1.1 a^m*a^n=a^(m+n)
3.1.2 a^m/a^n=a^(m-n)
3.1.3 (a^m)^n=a^mn
3.1.4 a^-n=1/a^n
3.1.5 a^(m/n)=n√a^m
3.1.6 a^1=a
3.1.7 a^0=1
3.2 logn(a)
3.2.1 The power of n that gives a
3.3 Log laws
3.3.1 log(AB)=logA+logB
3.3.2 log(A/B)=logA-logB
3.3.3 logA^N=NlogA
3.3.4 logA(1)=0
3.3.5 logA(A)=1
3.4 Linear form
3.4.1 Y=MX+C
3.4.1.1 C=logK
3.4.1.2 M=logA
3.4.2 logY=logK+XlogA
3.4.2.1 Y=logY
3.4.2.2 X=X
3.4.3 Y=MX+C
3.4.3.1 M=N
3.4.3.2 logK=C
3.4.4 logY=logK+NlogX
3.4.4.1 X=logX
3.4.4.2 Y=logY
4 Sequences & Series
4.1 Arithmetic sequence
4.1.1 progression
4.1.1.1 a+(n-1)d
4.1.2 Sum of
4.1.2.1 0.5n[2a+(n-1)d]
4.2 Geometric sequence
4.2.1 Progression
4.2.1.1 ar^(n-1)
4.2.2 Sum of
4.2.2.1 a(r^n -1)/(r-1)
4.2.3 Sum to infinity
4.2.3.1 a/(1-r)
5 Trigonometry
5.1 SOH, CAH, TOA
5.2 Area = 0.5ab sinC
5.3 Sin rule
5.3.1 a/sinA=b/sinB=c/sinC
5.4 Cosine rule
5.4.1 a^2=b^2+c^2-2bc cosA
5.5 Tanθ=Sinθ/Cosθ
5.6 Radians
5.6.1 Arc Length
5.6.1.1 rθ
5.6.2 Area of Sector
5.6.2.1 0.5(r^2)θ
5.6.3 Area of Triangle
5.6.3.1 0.5(r^2)sinθ
5.6.4 1°=π/180
6 Graph Transformations
6.1 Y=F(X)+Q
6.1.1 Translation of (0,Q)
6.2 Y=F(X-P)
6.2.1 Translation of (P,0)
6.3 Y=-F(X)
6.3.1 Reflection in the X-axis
6.4 Y=F(-X)
6.4.1 Reflection in the Y-axis
6.5 Y=AF(X)
6.5.1 Y direction stretch scale factor A
6.6 Y=F(AX)
6.6.1 X direction stretch scale factor 1/A
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