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
• 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
• 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