Core 1

Core 1

1. Algebra Review

   • Linear Equations
     • ax+b=0
   • Simultaneous Eqations
     • Elimination
     • Substitution
   • Inequalities
     • X by -1, Reverse the inequality

2. Surds

   • Irrational numbers
   • ab = a x b
   • Rationalise the denomiator
     • change the sign, times by top and bottom
   • a x a = a

3. Co-Ordinate Geomentry

   • Distance between 2 points
   • Mid-points
   • Gradient
   • Perpendicular Lines
   • Line Equation
   • Line Intersection
   • Parallel Lines

4. Quadratics

   • Parabolas
   • Quadratic functions
   • Factorising
   • Sketching Graphs
   • Completing The Square
   • Translations
   • Quadratic Formula
   • The discriminant

5. Polynomials

   • Adding
   • Subtracting
   • Mutliplying
   • Finding Coefficients

6. Factors, Remainders, Cubic Graphs

   • Algebraic Division
   • Factor Theorem
   • Remainder Theorem
   • Factorisation
   • Graphs of Cubics

7. Simultaneous Equations, Quadratic Inequalities

   • Line and Curve Intersection
   • Quadratics
     • Tangents
     • b^2-4ac
     • Inequalities
   • Completing the Square

8. Circles

   • General Formula
     • Centre
     • Radius
   • Translations
     • Sketching
     • Vectors
   • Circle Properties
     • Chords
   • Normals
   • Equation of Tangent

9. Differentation

   • Gradients of Chords
   • Tangents at a Point
   • Gradient of curve
   • Derivative
   • Notation
   • x power by coefficinent
     • reduce power by 1

10. Aplplications of Differentation

    • rates of change
    • increasing/ decreasing functions
    • tangents
    • normals
    • Curve Equation

11. Max,Min, Optimisation Problems

    • Second Derivative
      • Max < 0
      • Min > 0
    • Least Value of Quadratic
    • Points of Inflection
    • Optimisation
      • 1 Variable

12. Integration

    • Add 1 to Power, then divide by that number
    • + c
    • Equation of Curve
    • Area Under/ Between Curves
    • Definate/Indefinate Integrals