Maths

• r is the product moment correlation co-efficient used to describe the relationship of values, positive corelation or negative and the magnitude describes the strength whilst the sign decides the direction
• if r = +1 there's perfect positive correlation, if r = -1 there's perfect negative correlation, if r = 0 there's no linear association between two variables
• How to calculate PMCC?

  1. make sure frequency is turned off in calculator
  2. input table of values with the linear equation option
  3. press option and regression calculations
• Formulas needed to calculate PMCC

  
• 1 standard deviantion covers 68 % of the data

  2 standard deviations covers 95% of the data

  3 standard deviations covers 99.7% of the data

  68-95-99.7 rule
• PMCC measure the type and strength of linear correlation between 2 variables
• In context to PMCC and signifcance level, when you are testing for no correlation you half the level of significance
• In context to PMCC, when testing for no correlation,

  r is either less than the negative PMCC or greater than the PMCC for the critical regions
• When is a binomial distribution suitable?

  Fixed number of trials

  Fixed probabilities

  only 2 outcomes

  independent
• When events are mutually exclusive P(aUb) = P(a) + P(b)

  there is no overlap between the sets
• When events are independent P(A and B) = P(A) * P(B)
• P(A or B) = P(A) + P(B) - P(A and B)
• the integral of tan(x)

  ln(Sec|x|)+c
• The integral of cot(x)


  ln|sin(x)| + c
• integral of cosec

  ln|cosecx -cotx| + c
• integral of sinkx

  -1/k coskx
• Integral of cosx


  sinx + c
• differentiate tanx

  (secx)^2
• integrate (secx)^2


  Tanx + c
• Product rule - differentiation

  y=uv

  y' = v'u + vu'
• quotient rule

  y = u/v

  y' = (vu' - v'u)/v^2
• A2 Trig identitiy

  Tan^2 x = 


  Sec^2 x - 1
• Cot =

  Cos/sin or 1/tan
• Cot^2 x =


  Cosec^2 x - 1