A Level Mathematics C1 Revision Notes

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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