Further Maths

• gradient + coordinate line equation

  y - y1 = m(x - x1)
• nCr


  n = row of pascal

  → power of bracket

  r = entry within row

  → coefficient of term
• proving positive numbers → > 0 & complete the square
• proving multiples → take out factor of that number
• proving even → take out factor of two
• proving square → take out factor of itself
• increasing function


  → if dy/dx > 0
• decreasing function


  → if dy/dx < 0
• stationary points; minimum point of curve 


  → if $d^2y/dx^2 ≥ 0$
• stationary points; maximum point on a curve 


  → if $d^2y/dx^2 ≤ 0$
• → if 2nd derivative > 0, coordinates are minimum
• → if 2nd derivative = 0, coordinates are stationary
• → if 2nd derivative < 0, coordinates are maximum