# CORE 2

HideShow resource information

- Created by: MadelineD
- Created on: 24-05-16 10:26

View mindmap

- Core 2
- Algebra & Funtions
- Factor Theorem
- If r=0 (cx+d) is a factor

- Choosing Factors
- Coefficient of highest power and constant.

- If f(x) is polynomial and f(p)=0. x-p is factor of f(x).
- If f(x) is divided by (ax-b) then the remainder is f(b/a)

- Factor Theorem
- Sine & Cosine Rule
- a/sinA = b/sinB = c/sinC (length)
- sinA/a = sinB/b = sinC/c (angle)
- 1/2absinC
- sin(180-x) = sinx
- a^2 = b^2 + c^2 - 2bc cosA
- CosA = (b^2 + c^2 - a^2) / 2bc

- Exponentials & Logarithms
- LOGaN = x a^x = N
- Multiplication law - LOGaXY = LOGaX + LOGaY
- Division law - LOGaX/Y = LOGaX - LOGaY
- Power law - LOGaX^k = kLOGaX
- Changing base - LOGaB = LOGcB / LOGcA
- E.G. LOG 4 29 = LOG 10 29 / LOG 10 4

- Coordinate Geometry
- Midpoint: (x1+x2/2 , y1+y2/2)
- Distance: /(x2-x1)^2 + (y2-y1)^2
- Equation: (x-a)^2 + (y-b)^2 = r^2

- Binomial Expansion
- nC0xa^n + nC1xa^n-1xb + nC2xa^n-2xb^2 ...
- n! / (n-r)!r! = NCR = (n r)
- E.G. 4th term in row 15. 15C4 = (15 4) = 15!/(15-4)!4! =1365

- Coefficient
- E.G. coefficient of x^3 in (3-2x)^5 x^3=5C3x3^2x(-2x)^3 10x9x(-8x^3)=-720x^3 coefficient of x^3 = -720

- Radians
- Radians to degrees x 180/pi
- Degrees to radians x pi/180
- area of sector: 1/2r^2Q
- length of arc: rQ

- Geometric Sequences & Series
- a - first term. r - common ratio.
- Common ratio: u2/u1
- Sn = a (1-r^n)/1-r or a (r^n-1)/r-1
- S(infinity) = a/1-r

- Graphs of Trigonometric Functions
- sin = o/h cos = a/h tan = o/a
- CAST
- sin(-Q)= -sinQ cos(-Q)=cos Q tan(-Q)=-tanQ
- sin(90-Q)= cosQ cos(90-Q)= sinQ

- Differentiation
- y is increasing function if gradient is positive dy/dx > 0
- y is increasing function if gradient is negative dy./dx < 0
- Gradient at max & min = 0
- 1st - differentiate and find x when dy/dx =0
- 2nd - second derivative and sub in x positive=max negative=min
- 3rd - sub in x to find y

- Trigonometric Identities
- tanA = sinA/cosA
- sin^2x + cos^2x = 1
- 1 - sin^2x = cos^2x
- 1 - cos^2x = sin^2x

- Intergration
- area under curve - points curve cross x axis. (put into integration with limits)
- area between line (equation y1) and curve (equation y2)
- [b/a (y1 - y2)

- trapezium rule: [b/a dx = 1/2 h[y0+2(y1+y2...+yn-1)+yn]

- Algebra & Funtions

## Similar Mathematics resources:

Teacher recommended

## Comments

No comments have yet been made