Maths

• Equations of circles

  $x^2 +$$y^2 =$$r^2$
• Final velocity

  $v^2 =$$u^2 +$$2as$
• Speed/displacement

  $s =$$ut +$$½at^2$
• velocity

  u + at
• Density (g/cm3) or (kg/m3)


  mass ÷ volume
• Pressure (N/cm2) or (N/m2)


  force ÷ area
• Arc length

  ᵃⁿᵍˡᵉ⁄₃₆₀ x π2r
• direct proportion

  y=kx
• inverse proportion

  y= k/x
• directly proportional to the square of x

  $y=$$kx^2$
• inversely proportional to the square root of x

  y=k/√x
• inversely proportional to the cube of x

  $y =$$k/x^3$
• inversely proportional to the cube root of x

  $y=$$k^3√x$
• Congruency proofs

  SSS = side, side, side

  RHS = right angle, hypotenuse side

  SAS = side, angle, side

  ASA = angle, side, angle
• Volume of a pyramid

  1/3 x base x height
• Volume of a cone

  $1/3 *$$πr^2 *$$h$
• Surface area of cones

  $πr^2 +$$πrl$

  l = slant height
• reflection in the x-axis

  y = -f(x)
• reflection in the y-axis

  y = f(-x)
• moving up (translation)

  y = f(x) + a
• moving down (translation)

  y = f(x) - a
• moving right (translation)


  y = f(x-a)
• moving left (translation)

  y = f(x+a)
• area rule

  1/2 x ab x sin(c)
• area of sector

  ˣ⁄₃₆₀ x $πr^2$
• sine rule (side)

  a/sin(A) = b/sin(B) = c/sin(C)
• sine rule (angle)

  sin(A)/a = sin(B)/b = sin(C)/c
• cosine rule

  $a^2 =$$b^2 +$$c^2 - 2bcCos(A)$
• stratified sample

  sample size x stratum size/total population
• LQ

  n+1/4
• Median

  n+1/2
• UQ

  3(n+1/4)
• Frequency density

  frequency/class width
• Mean (frequency table)

  midpoint x frequency
• Given that

  P(AnB)/P(B) = P(A|B)
• AnB


  Middle of the 2 circles
• AuB


  All in A and in B
• A'


  What is not in A (including middle)
• B' 


  What is not in B (including middle)