Maths C4

Created by: mel-12345-issa
Created on: 11-03-15 19:46

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CORE 4
- Partial fractions
  - Involves writing an algebraic fraction as 2 or more simpler fractions
    - Substitution
    - Equating coefficients
- Coordinate geometry
  - Parametric equation
    - Example: X=1+T Y=T-2
    - Example: X= Sin t + 9 Y= Cos 2t +4
    - find dy/dx by doing: dy/dt divided by dx/dt
    - Area under the curve: {y dx/dt
  - Cartesian equation
    - Y= Mx + C
    - P --> C Use: trig identity Sin(2)t + Cos(2)t =1
- Binomial Expansion
  - formula: 1+ nx +n(n-1)(x)^2 /2! ....
    - 'n' is a positive integer - the expansion is finite
- Vectors
  - A quantity with both magnitude and direction
    - Equal vectors have the same magnitude and direction
    - Magnitude = Modulus [A]
      - The vector a has the same magnitude as -a but is in the opposite direction
  - PQ + QP = 0
    - AB= B- A or AB= AO + OB
  - A vector parallel to a is written by Xa where X is a non zero scalar
    - Vector parallel to the x, y and z axis =i+ j + k
    - A.B = 0 (parallel vectors)
  - Position vector = from the origin e.g. OA, OB, OC
    - Cos AOB = a.b/[A][B]
  - Vector equation: r=a +tb
- Differentiation
  - Chain rule
  - Product rule
  - Implicit: Y becomes dy/dx
  - Connected rates of change: da/db = da/dc x dc/db
    - decrease: -k (k>0)
    - Increase: k
- Integration
  - formulas
    - {1/x = ln[x]
    - {e(x) = e(x)
    - {a(x) = 1/ln[a] * a(x)
    - {Six = -Cos
    - {ln x= x ln[x] - x
    - {(ax+b)^n = 1/a * (ax+b) ^(n+1) / n+1
    - {1/ax+b = 1/a * ln[ax+b]
    - {sec(ax+b) = 1/a * ln[sec(ax+b) +tan(ax+b) ]
  - {f'(x)/f(x) = ln[f (x)] +C
  - Integration by parts: uv - {v du/dx

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Maths C4

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