Advanced Programme Mathematics Notes
General tips
• Round to the correct decimals (when asked).
• Calculator must be in radians.
• Check your answers (it must make sense) - calculator.
• Use a calculator for help.
• Write formula and substitute numbers correctly.
• Use the best reasoning - concise answers.
• Correct notations.
• Put units in.
• The questions are correct - don't try to make your own answer !
• K method
• Check for Restrictions
Algebra
Algebra Tips :
• Use a calculator when you found the derivative, to test if that is actually the derivative.
• Do not divide the value if you're not sure if it's not zero (you may lose half your answers).
Complex numbers
• Know to separate real and imaginary numbers.
• You can equate the real and not real part.
Functions
• A stationary point has no change of sign for 1st
derivative test f'(x).
Mathematical Induction
• Say true for n € |N over other restrictions.
• Say true For n = 1.
• Say "which is a multiple of " to explain how something is divisible in Mathematical
induction.
• Say : "Assume true for e.g. 8p p € N".
• Say : "It is proven by Mathematical Induction statement is true for .... ".
Newton Raphson Method
• The value they give you is X0.
• Use Xi for formula, before substituting and after generic formula (notation).
Riemann Sums
• Know your upper and lower approximation.
• Upper + lower approximation/2 = a more accurate integration. They cancel each other's
errors.
Derivative
• For weird things like complex trig graphs and Lin, use quotient & chain rule.
Volume
• It is always half, as the radius is half of the circle.
Statistics
Statistics Tip :
• Be careful some events are not independent.
• Central limit theorem is used when you've not sure if it is normally distributed.
General tips
• Round to the correct decimals (when asked).
• Calculator must be in radians.
• Check your answers (it must make sense) - calculator.
• Use a calculator for help.
• Write formula and substitute numbers correctly.
• Use the best reasoning - concise answers.
• Correct notations.
• Put units in.
• The questions are correct - don't try to make your own answer !
• K method
• Check for Restrictions
Algebra
Algebra Tips :
• Use a calculator when you found the derivative, to test if that is actually the derivative.
• Do not divide the value if you're not sure if it's not zero (you may lose half your answers).
Complex numbers
• Know to separate real and imaginary numbers.
• You can equate the real and not real part.
Functions
• A stationary point has no change of sign for 1st
derivative test f'(x).
Mathematical Induction
• Say true for n € |N over other restrictions.
• Say true For n = 1.
• Say "which is a multiple of " to explain how something is divisible in Mathematical
induction.
• Say : "Assume true for e.g. 8p p € N".
• Say : "It is proven by Mathematical Induction statement is true for .... ".
Newton Raphson Method
• The value they give you is X0.
• Use Xi for formula, before substituting and after generic formula (notation).
Riemann Sums
• Know your upper and lower approximation.
• Upper + lower approximation/2 = a more accurate integration. They cancel each other's
errors.
Derivative
• For weird things like complex trig graphs and Lin, use quotient & chain rule.
Volume
• It is always half, as the radius is half of the circle.
Statistics
Statistics Tip :
• Be careful some events are not independent.
• Central limit theorem is used when you've not sure if it is normally distributed.
