Maths Formulas

• Volume of a Cylinder

  Volume = π × r² × h
• Volume of a Cuboid

  Volume = length × width × height
• Volume of a Prism

  Volume = area of cross section × length
• Volume of a Sphere

  Volume = (4/3) × π × r³
• Volume of a Pyramid

  Volume = (1/3) × area of base × height
• Volume of a Cone

  Volume = (1/3) × π × r² × h
• Surface Area of a Cylinder 


  Surface Area = 2πr² + 2πrh
• Curved S.A of a Cone

  Curved surface area = πrl, Total surface area = πr(r + l)
• S.A of a Sphere

  Surface area = 4πr²
• Area of a Rectangle

  Area = length × width
• Area of a Parallelogram

  Area = base × perpendicular height
• Triangle


  Area = (1/2) × base × height
• Trapezium


  Area = (1/2) × (sum of parallel sides) × perpendicular height
• Circle


  Area = πr², Circumference = 2πr or πd
• Arc length


  Arc length = (θ/360) × 2πr
• Arc sector


  Area = (θ/360) × πr²
• Pythagoras Theorem


  c² = a² + b²
• Sine Rule


  a/sin(A) = b/sin(B) = c/sin(C)
• Cosine Rule


  c² = a² + b² - 2ab cos(C)
• Angles in a Polygon

  Interior angle + Exterior angle = 180°, Sum of interior angles = (n-2) × 180°
• Compound Measures


  Force = Pressure × Area, Distance = Speed × Time, Mass = Density × Volume
• Circle Theorems


  Angle at the centre = 2 × angle at the circumference, Angle between tangent and chord = angle in alternate segment, Angle in a semicircle = 90°, Perpendicular from centre bisects chord, Opposite angles in a cyclic quadrilateral total 180°
• Straight Lines


  Gradient = (y2-y1)/(x2-x1), Equation of a line = y = mx + c
• Equation of a Circle

  (x-h)² + (y-k)² = r²
• Compound Growth & Decay

  Amount after t years = A(1+r/100)^t
• Quadratics


  Quadratic formula: x = (-b ± √(b²-4ac))/(2a)
• Direct and Inverse Proportion


  y = kx (direct), y = k/x (inverse)
• Kinematics


  s = ut + (1/2)at², v = u + at
• Probability


  P(A or B) = P(A) + P(B), P(A and B) = P(A) × P(B|A)
• Pie Charts


  Angle = (Frequency/Total Frequency) × 360°
• Histogram


  Frequency Density = Frequency/Class width
• Stratified Sample


  Account in sample = (Group number/Total) × Sample size
• Midpoint of 2 points

  (x1+x2)/2, (y1+y2)/2