Edexcel FP1 Further Pure Maths
- Real and imaginary numbers
- Addition, Subtraction and Multiplying complex numbers and simplifying powers of i
- Complex conjugates
- Division of a complex number by a complex number
- Argand diagram
- Modulus and argument of a complex number
- Mod-Arg form of a complex number
- Solving problems with complex numbers
- Square roots of a complex number
- Solving quadratic equations with complex roots (complex conjugate pairs)
- Solving cubic equations
- Solving quartic equations
Solving equations of the form f(x)=0
Coordinate systems
- Cartesian Form
- Parametric form
- Tangents and Normals
- Exam Questions
Hyperbola (rectangular)
- Cartesian and Parametric Forms
- Tangents and Normals
- Exam Questions
- Introduction and dimension of a matrix
- Addition and subtraction and multiplying a matrix by a scalar
- Matrix multiplication
- Identity and Inverse of a 2x2 matrix
Applications
- Simultaneous Equations
- Linear Transformations
- Rotations about the origin of:
- Reflections in the:
- Enlargement, scale factor k, centre (0,0) where:
- Transformations Test:
- Combinations of Transformations:
- Inverse Matrices:
- Area Scale Factor:
Series
Series
- Proof of the sum of the series ∑r
- Proof of the sum of the series ∑r²
- Proof of the sum of the series ∑r³
- Further examples
Divisibility and Multiple Tests
- Proof that an expression is divisible by a certain integer (power type)
- Proof that an expression is divisible by a certain integer (non-power type)
Recurrence Relations
- Proof of the general term from a recurrence relationship (example 1)
- Proof of the general term from a recurrence relationship (example 2)
Matrices