# Maths C4

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- 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

- Involves writing an algebraic fraction as 2 or more simpler fractions
- 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

- Parametric equation
- Binomial Expansion
- formula: 1+ nx +n(n-1)(x)^2 /2! ....
- 'n' is a positive integer - the expansion is finite

- formula: 1+ nx +n(n-1)(x)^2 /2! ....
- 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

- A quantity with both magnitude and direction
- 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

- formulas

- Partial fractions

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