## Further Pure Worksheets

To find a worksheet click on the **topic** you want and then choose from the list of **subtopics**

Complex numbers

- Complex solutions to quadratics
- Add, subtract and multiply complex numbers
- Complex conjugate pairs
- Rationalise complex numbers
- Argand diagram
- Modulus and argument
- Modulus, argument form
- Modulus, argument multiplication
- Loci of complex numbers
- De Moivre's theorem
- Summing using de Moivre's theorem
- Euler's identity and exponential form
- Forms of a complex number
- Nth root of a complex number

Differential equations

Further algebra and functions

- Root relationships of quadratics
- Root relationships of cubics and quartics
- Using common series
- Finding Maclaruin's series
- Using common Macluarin's series
- Limits of rational polynomials
- Evaluate limits using Macluarin's series
- Evaluate limits using L'hopital's rule
- Inequalities of polynomials
- Solving rational inequalities algebraically
- Modulus equations adn inequalities
- Graphs of modulus and reciprocals
- Sketching rational graphs
- Oblique asymptotes and ranges of rational graphs
- Conic graphs

Further calculus

Further vectors

- Scalar/dot product
- Equation of a line
- Intersection of lines
- Angle between lines
- Distance between a line and point
- Vector/cross product
- Using the vector/cross product
- Equation of a plane
- Intersection of lines and planes
- Angles between planes and lines
- Angle between two planes
- Distance between a plane and point
- Distance between two lines

Hyperbolic functions

Matrices

- Basics of matrices
- Multiplying matrices
- Matrix transforms in 2D
- Matrix transforms in 3D
- Multiple matrix transforms
- Invariant points and lines
- Determinant of 2x2 matrices
- Determinant of 3x3 matrices
- Inverse of 2x2 matrices
- Inverse of 3x3 matrices
- Singularities
- Solving simultaneous equations with a matrix
- Determinant factorization
- Eigenvalues and Eigenvectors
- Matrix diagonalization
- Cayley-Hamiltonian theorem

Numerical methods