Further Pure Worksheets

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

Complex numbers

  1. Complex solutions to quadratics
  2. Add, subtract and multiply complex numbers
  3. Complex conjugate pairs
  4. Rationalise complex numbers
  5. Argand diagram
  6. Modulus and argument
  7. Modulus, argument form
  8. Modulus, argument multiplication
  9. Loci of complex numbers
  10. De Moivre's theorem
  11. Summing using de Moivre's theorem
  12. Euler's identity and exponential form
  13. Forms of a complex number
  14. Nth root of a complex number

Differential equations

  1. Integrating factor
  2. Auxilary equation
  3. Second order homogeneous ODEs
  4. Second order imhomogeneous ODEs
  5. Modelling with differential equations
  6. Hooke's law and simple harmonic motion
  7. Simple harmonic motion with damping
  8. Oscillations
  9. Coupled differential equations

Further algebra and functions

  1. Root relationships of quadratics
  2. Root relationships of cubics and quartics
  3. Using common series
  4. Finding Maclaruin's series
  5. Using common Macluarin's series
  6. Limits of rational polynomials
  7. Evaluate limits using Macluarin's series
  8. Evaluate limits using L'hopital's rule
  9. Inequalities of polynomials
  10. Solving rational inequalities algebraically
  11. Modulus equations adn inequalities
  12. Graphs of modulus and reciprocals
  13. Sketching rational graphs
  14. Oblique asymptotes and ranges of rational graphs
  15. Conic graphs

Further calculus

  1. Differentiating inverse trig functions
  2. Integrating using inverse trig functions
  3. Partial fraction integration
  4. Integrating using trig subsitutions
  5. Meal value of a function
  6. Improper integrals
  7. Two limit rules
  8. Reduction formulae
  9. Volume of revolution
  10. Arc length of curves
  11. Surface area of revolution

Further vectors

  1. Scalar/dot product
  2. Equation of a line
  3. Intersection of lines
  4. Angle between lines
  5. Distance between a line and point
  6. Vector/cross product
  7. Using the vector/cross product
  8. Equation of a plane
  9. Intersection of lines and planes
  10. Angles between planes and lines
  11. Angle between two planes
  12. Distance between a plane and point
  13. Distance between two lines

Hyperbolic functions

  1. Hyperbolic trig functions
  2. Inverse hyperbolic trig functions
  3. Reciprocal trig functions
  4. Hyperbolic trig identities
  5. Differentiating hyperbolic trig functions
  6. Integrating hyperbolic trig functions
  7. Integrating using inverse hyperbolic trig functions

Matrices

  1. Basics of matrices
  2. Multiplying matrices
  3. Matrix transforms in 2D
  4. Matrix transforms in 3D
  5. Multiple matrix transforms
  6. Invariant points and lines
  7. Determinant of 2x2 matrices
  8. Determinant of 3x3 matrices
  9. Inverse of 2x2 matrices
  10. Inverse of 3x3 matrices
  11. Singularities
  12. Solving simultaneous equations with a matrix
  13. Determinant factorization
  14. Eigenvalues and Eigenvectors
  15. Matrix diagonalization
  16. Cayley-Hamiltonian theorem

Numerical methods

  1. Mid-ordinate rule
  2. Simpsons rule
  3. Eulers step method
  4. Improved Eulers method
  5. Other improved Eulers methods

Polar coordinates

  1. Polar coordinates basics
  2. Sketching polar coordinates
  3. Area under a polar curve

Proof

  1. Proof by induction for series
  2. Proof by induction for sequences
  3. Proof by induction for divisibility
  4. Proof by induction for matrices
  5. Method of differences