# EDEXCEL CORE 3

Mindmap of key topics in Edexcel Mathematics Core 3

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- Created by: Maham
- Created on: 06-02-13 15:42

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- CORE 3
- Differentiation
- Chain Rule: dy/du x du/dx - use this for compound functions
- Quotient Rule: [v(du/dx) -u(dv/dx)]/v2 - use this for f(x) = u/v
- Product Rule: v(du/dx) + u(dv/dx) - use this for f(x) = uv
- Standard Differentiations
- f(x) = e^x
- dy/dx = e^x

- f(x) = lnx
- dy/dx = 1/x

- f(x) = sinx
- dy/dx = cosx

- f(x) = cosx
- dy/dx = -sinx

- f(x) = e^x

- Trigonometry
- sec(x) = 1/cos(x)
- 1 + tan^2(x) = sec^2(x)

- cot(x) = 1/tan(x)
- 1+cot^2(x) = cosec^2(x)
- cosec(x) = 1/sin(x)
- Trigonometry
- sec(x) = 1/cos(x)
- 1 + tan^2(x) = sec^2(x)

- cot(x) = 1/tan(x)
- 1+cot^2(x) = cosec^2(x)
- cosec(x) = 1/sin(x)

- cosec(x) = 1/sin(x)

- 1+cot^2(x) = cosec^2(x)
- Double Angle Formulae
- sin(2A) = 2sinAcosA
- cos(2A) = cos^2A - sin^2A
- 2cos^A -1
- 1 - 2sin^2A

- tan(2A) = (2tanA)/(1-tan^2A)

- Compound Angle Formulae
- sin(A + B) = sinAcosB + sinBcosA
- cos(A + B) = cosAcosB - sinAsinB
- tan(A + B) = (tanA +tanB)/(1 - tanAtanB)

- sec(x) = 1/cos(x)

- Trigonometry

- cosec(x) = 1/sin(x)

- 1+cot^2(x) = cosec^2(x)
- Double Angle Formulae
- sin(2A) = 2sinAcosA
- cos(2A) = cos^2A - sin^2A
- 2cos^A -1
- 1 - 2sin^2A

- tan(2A) = (2tanA)/(1-tan^2A)

- Compound Angle Formulae
- sin(A + B) = sinAcosB + sinBcosA
- cos(A + B) = cosAcosB - sinAsinB
- tan(A + B) = (tanA +tanB)/(1 - tanAtanB)

- sec(x) = 1/cos(x)
- The modulus of a number is its magnitude - how far away it is from 0.
- Algebraic Fractions
- Find common denominator to simplify

- Functions
- One-to-many = not a function
- Composite function: fg(x) means ‘apply g first, then f ’
- Inverse function: Domain and range swap - and the x and y coordinates where it meets the axis swap as well

- Numerical Methods
- To find the root of a function - use graph, iteration or change of sign
- In general, if you find an interval in which changes sign, then the interval must contain a root of the equation
- Iteration involves using the iterative formula to find the approximate rooot

- Exponentials
- The inverse of the exponential function ex is the logarithmic function base e, ln(x).

- Differentiation
- Composite function: fg(x) means ‘apply g first, then f ’
- Inverse function: Domain and range swap - and the x and y coordinates where it meets the axis swap as well
- In general, if you find an interval in which changes sign, then the interval must contain a root of the equation
- Exponentials
- The inverse of the exponential function ex is the logarithmic function base e, ln(x).

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