GCSE Maths

• Area of a Parallelogram/Square/Rectangle


  base x height
• Area of a triangle


  base x perpendicular height x 1/2
• Area of a trapezium


  1/2 x (a+b) x h

  • A and B are the lengths on the top and bottom on the trapezium
• Volume of a cuboid


  length x width x height
• Volume of a prism


  area of cross section x length
• Area of a circle

  
• Volume of a cylinder

  
• Volume of a pyramid


  1/3 x perpendicular height x area of base
• Area of a sector

  
• Length of an arc

  
• Gradient of a line

  y2 - y1/x2-x1
• Perpendicular gradients


  -1/m
• Midpoint of two points


  (x1 + x2/2), (x1 + y2/2)
• SOHCAHTOA

  • sin x = opp/hyp

  • cos x = adj/hyp

  • tan x = opp/adj
• Constructing pie charts


  angle = frequency/total x 360
• Trigonometric formulae (finding sides)


  • sine rule - a/sin A = b/sin B = c/sin C

  • cosine rule - a squared = b squared + c squared - 2bcCosA

  • area of a triangle = 1/2 x a x b x sin C
• Stratified sampling


  frequency of group/total frequency x sample size
• Angles in polygons


  • sum of interior angles of a polygon = 180(n-2)

  • interior + exterior angles = 180 degrees

  • exterior angle of polygons = 360/n

  • number of sides of a polygon = 360/exterior angle
• Trigonometric formulae (finding angles)


  • sin-1 (opp/hyp)

  • cos-1 (adj/hyp)

  • tan-1 (opp/adj)
• Compound measures

  • speed = distance/time

  • density = mass/volume

  • pressure = force/area
• Volume of a cone

  
• Area of a segment

  area of sector - area of triangle
• Enlarged perimeter/area/volume

  • original perimeter x S.F

  • original area x S.F squared

  • original volume x S.F cubed
• Volume of a sphere

  4/3 x pi x radius cubed