C3 maths summary part 1

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  • C3 summary
    • Algebraic fractions
      • Can be simplified by cancelling down
        • Must be fully factorised first
      • to add and subtract find the lowest possible denomanator
      • if the numerator is bigger then the denominator then use the long devision method
    • Functions
      • Two types of function
        • many to one
        • one to many
      • range=y
      • domain= x
      • when combining functions do the inside first
      • to find the inverse function swap the y and x and rearange
        • the previous range is now the domain and vice versa
        • the graph is reflected in the line y=x
    • Exponentials and log
      • exponentials
        • y=a^x
          • always passes through (0,1)
      • log
        • inverse
          • exponentials
            • y=a^x
              • always passes through (0,1)
        • y=ln(x)
          • passes through (1,0)
      • to solve you must use the fact that they are inverse
    • Numerical methods
      • if an interval has a sign change then there is a root
      • iteration formulas can be used to solve




A good visual mind map of Core 3 content

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