Core Mathematics 2

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  • Core Mathematics 2
    • 1) Algebra & Functions
      • You can divide a polynomial by (x + or - p)
        • Divide first term by x, then multiply this by the  (x+ or - p). Then subtract this, and just repeat this.
      • The factor Theorem
        • If f(p) of f(x) =0, then x-p is a factor of f(x)
      • The Remainder Theorem
    • 2) The Sine & Cosine Rule
      • The Sine Rule
        • sinA/a = sinB/b = sinC/c
          • Use to find an unknown length.
            • You need two angles and an opposite side.
        • a/sinA = b/sinB = c/sinC
          • Use to find an unknown angle .
            • You need two sides and an opposite angle.
      • Ambiguous Case
        • sinx and sin(180-x)
      • The Cosine Rule
        • a^2 = b^2 + c^2 -bcsinC
          • To find a side given two sides and the angle in between.
        • cosA = (b^2 +c^2 -a^2) / 2bc
          • To find an angle give all sides.
      • Area of a Triangle
        • 1/2absinC
    • 3)Exponentials and Logarithms
      • Laws
        • Multiplication
          • Same base but added
        • Division
          • Same base but minused
        • Power
          • Power number in front of the log
      • log a x = y ? x = ay
      • You can solve an equation by letting y=n^x
    • 4) Coordinate Geometry
      • To find the mid point 1/2(x1+x2) 1/2(y1+y2)
      • d=?[(x2-x1)^2 + (y2-y1)^2]
      • r^2=(x-a)^2+(y-b)^2
        • (a,b) is the centre of a circle
    • 5) Binomial Expansion
      • (a+bx)^n = nC0 a^n + nC1 a^n-1 *b +...+ nCnb^n
    • 6) Radians
      • 1 Radian = 180/?
      • 1 degree = ?/180
      • l=r?
      • area of sector A=1/2(r^2?)
      • Area of segment is  A= 1/2r^2(?-sin?)
    • 7) Geometric Sequence & Series
      • multiply by a common ratio to get to next term.
      • nth term = ar^n-1
      • Sn=      a(1-r^n) / 1-r
      • Sum to infinity =a/1-r if |r| 0
    • 8) Graphs of Trigonometric Functions
    • 9)  Differentiation
      • y is an increasing function if its gradient is negative, dx/dy < 0
    • 10) Trigonometric Identities & Equations
    • 11) Intergration

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