# C4

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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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## Differentiation

• 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

• 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
|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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## Integration

Common Integrals:

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