# Core Mathematics 2

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- Created by: Amber Eliza
- Created on: 19-05-16 11:20

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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

- You can divide a polynomial by (x + or - p)
- 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.

- Use to find an unknown length.
- a/sinA = b/sinB = c/sinC
- Use to find an unknown angle .
- You need two sides and an opposite angle.

- Use to find an unknown angle .

- sinA/a = sinB/b = sinC/c
- 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.

- a^2 = b^2 + c^2 -bcsinC
- Area of a Triangle
- 1/2absinC

- The Sine Rule
- 3)Exponentials and Logarithms
- Laws
- Multiplication
- Same base but added

- Division
- Same base but minused

- Power
- Power number in front of the log

- Multiplication
- log a x = y ? x = ay
- You can solve an equation by letting y=n^x

- Laws
- 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

- 1) Algebra & Functions

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