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
    • 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).

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