Maths Core 3

jack3740
Mind Map by jack3740, updated more than 1 year ago
jack3740
Created by jack3740 almost 5 years ago
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A-level Core maths C3 Mind Map on Maths Core 3, created by jack3740 on 03/15/2015.

Resource summary

Maths Core 3
1 Functions
1.1 y = f(x)
1.1.1 Composite function fg(x) can be worked out by f(g(x))
1.2 Transformations of graphs
2 e and ln
2.1 y=e^x is the same as x = ln(y)
2.1.1 ln rules
2.1.1.1 ln(A) + ln(B) = ln(A+B)
2.1.1.2 ln(A) - ln(B) = ln(A/B)
2.1.1.3 nln(A) = ln(A^n)
2.2 f(x) = e^x
2.3 f(x) = ln(x)
3 Triganometary
3.1 Minor trig functions
3.1.1 cosec(x) = 1/sin(x)
3.1.2 sec(x) = 1/cos(x)
3.1.3 cot(x) = 1/tan(x)
3.1.3.1 tan(x) = sin(x)/cos(x)
3.1.3.2 cot(x) = cos(x)/sin(x)
3.2 Identities
3.2.1 Compound angle formulae
3.2.1.1 sin(A±B) = sin(A)cos(B) ± cos(A)sin(B)
3.2.1.2 cos(A±B) = cos(A)cos(B) ∓ sin(A)sin(B)
3.2.1.3 tan(A±B) = [tan(A) ± tan(B)] / [1 ∓ tan(A)tan(B)]
3.2.2 Double angle formulae
3.2.2.1 sin(2A) = 2sin(A)cos(A)
3.2.2.2 cos(2A) = cos^2(A) - sin^2(A)
3.2.2.2.1 cos(2A) = 2cos^2(A) - 1
3.2.2.2.2 cos(2A) = 1- 2sin^2(A)
3.2.2.3 tan(2A) = [2tan(A)] / [1 - tan^2(A)]
3.2.3 Pythagorean identities
3.2.3.1 sin^2(x) + cos^2(x) = 1
3.2.3.1.1 sin^2(x) = 1 - cos^2(x)
3.2.3.1.2 cos^2(x) = 1 - sin^2(x)
4 Differentiation
4.1 Chain rule
4.1.1 y = f(g(x)) => dy/dx = f'(g(x)) . g'(x)
4.1.2 dy/dy = dy/du . du/dx
4.2 Differentials
4.2.1 y => dy/dx
4.2.2 f(x) => f'(x)
4.2.3 x^n => nx^(n-1)
4.2.4 e^x => e^x
4.2.5 ln(x) => 1/x
4.2.6 sin(x) => cos(x)
4.2.7 cos(x) => -sin(x)
4.2.8 tan(x) => sec^2(x)
4.2.9 cosec(x) => -cosec(x)cot(x)
4.2.10 sec(x) => sec(x)tan(x)
4.2.11 cot(x) => -cosec^2(x)
5 Modulus Function
5.1 y = |x|
5.1.1 graph
5.1.1.1 to draw graph just reflect at the point where it crosses the x axis
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