Simpsons Rule
• Formula given
• Watch out for radians
• Part b always linked to part
a
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
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
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
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
Exp Differentiation and Integration
• Power never changes
• When differentiating, the power
diffed comes down
• When integrating, remember to
take account of the above fact
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
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
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
Modulus Function
Get lxl =, then take + and - value
Solve 5x+7 between -4 and 4 as
inequality
Inverse Functions
• Write y=function
• Rearrange to get x=
• Rewrite inverse function in terms of x
Composite Functions
• If ln and e function get them
together to cancel out