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Co-ordinate Geometry

  • To find the Cartesian equation of a curve give parametrically you eliminate the parameter t between the parametic equations.
  • The are under a graph is given by y dx. By the chain rule y dx = y dx/dt dt.
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The Binomial Expansion


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  • You can find the gradient of a curve given in parametric coordinates
    dy/dx = dy/dt ÷ dx/dt
  • Implicit differentiation
    When f(y) is differentiated with respect to x it becomes f'(y)dy/dx. 
    A product term such as f(x) . g(y) is differentiated by the product rule and becomes
    f(x) . g'(y)dy/dx + g(y) . f'(x)
  • y = a^x         dy/dx = a^x lna 
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  • Vectors that are equal have the same magnitude and the same direction.
  • The modulus is another name for its magnitide
    Vector is written as |a|
  • The modulus or magnitude of xi + yj is x² + y²  
  • The distance between the points  (x, y₁, z₁) and  (x, y, zis
    √(x₁-x₂)² + (y₁-y₂)² + (z₁-z₂)²
  • The scalar product of two vectors a and b is written as a.b and defined by a.b |a||b| cosθ where θ is the angle between a and b.
  • cosAOB =  a.b  
  • If two vectors are perpindicular the angle between them is 90
    because cos90° = 0       then        a.b = |a||b| cos 90° = 0
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Common Integrals:

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Trigonometric Identities and Standard Patterns

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Substitution and Integration by Parts

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Trapezium Rule and Volume of Revolution

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Separating the Variables

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