A-level Mathematics/AQA/Pure Core 1

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  • 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
      • 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