• A Level Mathematics C1 Revision Notes

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Contents

Algebra and Functions

  • Indices and Surds
  • Quadratic functions, completing the Square, the discriminant and their graphs
  • Simultaneous Equations
  • Solving linear and quadratic inequalities
  • Factorisation of Quadratics
  • Simple Graphing
  • Simple Transformations of f(x)

Coordinate geometry in the (x,y) plane

Sequences and Series

Differentiation

Integration

  • indices
  • surds
  • function notation
  • polynomials
    • general equation
    • algebraic division
    • the remainder theorem
    • the factor theorem
  • quadratics
    • general equation
    • solving quadratic equations
      • factorising
      • completing the square
      • the quadratic formula
      • the discriminate
  • graphs
    • quadratic graphs
    • cubic graphs
    • higher power polynomials
    • reciprocal graphs
  • transforming graphs
    • y = f(x) + a
    • y = f(x – a)
    • y = af(x)
    • y = f(ax)
  • simultaneous equations
    • algebraic solutions
    • graphical solutions
  • inequalities

Coordinate Geometry

  • the gradient of a line
  • straight lines
    • general equation
    • perpendicular lines
    • parallel lines
    • midpoints of straight lines
    • find the equation of any straight line
  • the distance between two points
  • the equation of a circle
  • circle theorems
    • angles in semi-circles
    • bisecting a chord
    • angle between the tangent and radius

Differentiation and Integration

  • gradients of curves
  • differentiation and the derivative (gradient function)
  • the tangent and finding the equation of the tangent to a curve at a point
  • the normal and finding the equation of the normal to a curve at a point
  • sketching curves using derivatives and function values
  • the second derivative
  • turning points an stationary points
  • integration, indefinite integrals and constants of integration
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