Mathematics: Core 4

Mathematics: Core 4

1. Algebra and Graphs

   • Divide polynomials
     • Quotient
     • Remainder
   • Simplify rational expressions
   • Partial fractions
   • Binomial expansion
     • \((1+x)^n\)
   • Parametric equations
     • Converting between Cartesian and parametric

2. Differentiation and Integration

   • Derivatives of sinx, cosx, tanx
   • Implicit and parametric differentiation
   • Integration of trig functions
   • Using trig relations to allow integration
   • Using partial fractions to allow integration
   • recognise integrals of the form f'(x) / f(x)
   • Integration by parts
     • Link to product rule
   • Integration by substitution

3. First order differential equations

   • Formulate differential equations from a situation
     • Including constant of proportionality
   • Use integration to find a general solution
   • Use an initial condition to find a particular solution
   • Interpret the solution in terms of the initial problem

4. Vectors

   • Use standard notations
   • Addition and subtraction and scalar multiplication
     • Interpret geometrically
   • Unit vectors, position vectors, displacement vectors
   • Magnitude
   • Scalar product
     • Angle between vectors
   • Equation: r=a + tb
   • Parallel, intersect or skew
   • Point of intersection