A-level Mathematics/AQA/Pure Core 1

• Co-ordinate Geometry
  • Equation of a line, y = mx + c
  • Finding a line
    • two points
    • gradient, one points
    • etc.
  • When are lines perpendicular or parallel?
• Surds
  • Simplification -
  • Rationalising the Denominator.
• Quadratics
  • Diff b/w expression and equation
  • Factorising
  • Completing the square
    • Vertex of, line of symmetry of
  • Formula
  • Sketching
  • Discriminant of
    • Implications made by discriminant value
• Inequalities
  • Three-part inequalities
  • Quadratics
  • Solution by sketch and completing square
• Circles
  • Circle Theorems
    • Tangents are perpen. to radii
    • Tangents from an external point are equal, etc.
    • MORE
  • Co-ordinate Geometry Form of
  • Circle from three points, finding tangents to a point
• Other algebra
  • Factor Theorem
  • Remainder Theorem
  • Simultanoues Eq.
    • Elimination
    • Substitution
  • Curve Sketching
    • Intersections of curves as sol'n to sim. eq.
    • Translations of curves.
• Diff'n
  • IDEA: finding the gradient of the tangent to a curve
  • As a limit
  • function (f'(x), f(x)) and Liebniz notation (dy/dx)
  • Diff'n polynomials
  • Higher Derivatives
    • Stationary points
    • Maxima and Minima
  • Increasing and decreasing functions
    • Practical Applications
• Int'n
  • Inverse process
  • Net Area b/w curve and x-axis
    • Idea that below x-axis is NEGATIVE
  • Diff b/w definite and indefinite int'n
  • Area b/w curve and x-axis
  • Are b/w two curves b/w two points
• MASHUPS