# EDEXCEL CORE 3

Mindmap of key topics in Edexcel Mathematics Core 3

• Created by: Maham
• Created on: 06-02-13 15:42
• 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
• 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)
• 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)
• 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)
• 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).
• 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).