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Simpsons Rule
• Formula given• Watch out for radians• Part b always linked to
part a
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Trig Equations
Can’t change
• Use tan2x + 1 = sec2x
Or 1 + cot2x = cosec2x• Work through in
sec x etc• Convert to cos etc
at end• Bow ties to finish
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Parametric Differentiation
• x and y both in terms of another letter, in this case t
• Work out dy/dt and dx/dt• dy/dx = dy/dt ÷ dx/dt• To get d2y/dx2 diff dy/dx again with
respect to t, then divide by dx/dt
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Implicit Differentiation
Product!
• Mixture of x and y• Diff everything with respect to
x• Watch out for the product• Place dy/dx next to any y diff• Put dy/dx outside brackets• Remember that 13 diffs to 0
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Log Differentiation and Integration
• Bottom is power of 1
• Get top to be the bottom diffed
• Diff the function• Put the original
function on the bottom
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Exp Differentiation and Integration
• Power never changes• When differentiating, the
power diffed comes down• When integrating, remember
to take account of the above fact
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Trig Differentiation and Integration
• Angle part never changes• When differentiating, the
angle diffed comes to the front• When integrating, remember
to take account of the above fact
• Radians mode
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Products and Quotient Differentiation
• U and V• Quotient must be U on top, V on
bottom
• Product: V dU/dx + U dV/dx
• Quotient: V dU/dx – U dV/dx V2
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Iteration
Radians
• Start with x0
• This creates x1 etc• At the end, use the limits of the
number to 4 dp to show that the function changes sign between these values
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Modulus Function
Get lxl =, then take + and - value
Solve 5x+7 between -4 and 4 as inequality
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Inverse Functions
• Write y=function• Rearrange to get x=• Rewrite inverse function in terms of
x
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Composite Functions
• If ln and e function get them together to cancel out