Core Worksheets

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

Algebra and functions

  1. Laws of indices
  2. Manipulating surds
  3. Rationalising surds
  4. Factorising quadratics
  5. Completing the square
  6. Solving quadratics
  7. Quadratic graphs
  8. Linear simultaneous equations
  9. Quadratic simultaneous equations
  10. Linear inequalities
  11. Quadratic inequalities
  12. Discriminant
  13. Polynomial basics
  14. Polynomial division
  15. Factor and remainder theorem
  16. Reciprocal graphs
  17. Simplifying rational expressions
  18. Transforming graphs
  19. Combining graph transforms
  20. Modulus function
  21. Solving modulus equations
  22. Modulus transforms
  23. Domain and range
  24. Inverse functions
  25. Composite functions
  26. Partial fractions 

Coordinate geometry

  1. Line lengths and midpoints
  2. Equation of a line
  3. Parallel and perpendicular lines
  4. Equation of a circle
  5. Geometric properties of circles
  6. Parametric equations
  7. Parametric conversion

Differentiation

  1. Differentiation terminology
  2. Differentiate powers of x
  3. Differentiate from first principles
  4. Tangents and normals
  5. Increasing, decreasing and stationary
  6. Max and min points
  7. Inflection and convex-concave
  8. Differentiate exponentials and logarithms
  9. Differentiate trig functions
  10. Chain rule
  11. Chain rule tricks
  12. Product rule
  13. Quotient rule
  14. Mixed differentiation rules
  15. Implicit differentiation
  16. Parametric differentitiation
  17. Forming differential equations
  18. Connected rates of change

Exponentials and logarithms

  1. Exponential basics
  2. Logarithm basics
  3. Laws of logarithms
  4. Power equations
  5. Logarithm equations
  6. Natural exponential and logarithm
  7. Modelling data with exponentials

Integration

  1. Integrate powers of x
  2. Finding a function from the gradient
  3. Definite integration and area
  4. Negative area
  5. Area between two curves
  6. Integrate known derivatives
  7. Integration by substitution
  8. Integration by parts
  9. Integration tricks
  10. Integration using partial fractions
  11. Integration using trig addition formulae
  12. Integration using trig identities
  13. Seperable ODEs

Numerical methods

  1. Locating roots
  2. Fixed iterative methods
  3. Cobweb and staircase diagrams
  4. Newton-Raphson method
  5. Trapezium rule
  6. Rectangle area bounds

Proof

  1. Sets and interval notation
  2. Implies
  3. Disproof by counter-example
  4. Proof by exhaustion
  5. Proof by deduction
  6. Proof by contradicition

Sequences and series

  1. Permutations and combinations
  2. Binomial theorem
  3. Binomial expansion for rational powers
  4. Basic sequence definitions
  5. Series and sigma notation
  6. Arithmetic sequences
  7. Arithmetic series
  8. Geometric sequences
  9. Geometric series

Trigonometry

  1. Basic trig
  2. Sine rule
  3. Cosine rule
  4. Area of any triangle
  5. Intro to radians
  6. Arc length and sector area
  7. Basic identities
  8. Solving simple trig equations
  9. Solving complex trig equations
  10. Addition angle formulae
  11. Double angle formulae
  12. Small angle approximations
  13. Magnitude and phase form (R,alpha)
  14. Inverse trig functions
  15. Reciprocal trig functions
  16. Reciprocal identities

Vectors

  1. Vector basics
  2. Magnitude and direction
  3. Vector add, sub and multiply
  4. Unit and parallel vectors
  5. Vector geometry