Mathematics: Core 3

Mathematics: Core 3

1. Algebra and Functions

   • Function
   • Domain
   • Range
   • One-one
   • Inverse
   • Composition
   • Graphs
   • Transformations
     • Composition of transformations
   • Modulus
     • The modulus of a number is its magnitude or size, irrespective of if it has a plus or minus sign. For example,  mod(-6) = mod (+6) = 6
     • You also get graphs of modulus functions. The graph of f(x) is turned into the graph of mod (f(x)) by reflecting all the bits below the x-axis in the x-axis.
     • Mathematics: Core 3 (Notes 1 of 1)
     • Solving equations and inequalities
   • Exponentials and logarithms
     • Graphs
     • Growth and decay

2. Trigonometry

   • Inverse trig functions
     • Graphical relationship to trig functions
   • Sec, Cosec, Cot
     • Solving equations for any angle
   • Identities

3. Differentiation and Integration

   • Derivatives of exponential and logarithms
   • Chain rule
   • Product rule
   • Quotient rule
   • dy/dx = 1/ (dx/dy)
   • Integrate exponentials and 1/x
   • Integrate with linear substitution
   • Volume of revolution

4. Numerical Methods

   • Roots of equations
     • Graphically
     • Sign change
   • Iterative formulae
   • Simpson's rule