formulas

• Pythagoras Theorem applies when looking at right-angled triangles
• Area of a rectangle


  Length x Width
• Area of a triangle


  1/2 x Base x Height
• Area of a trapezium


  1/2 x (a + b) x Height
• Area of a parallelogram


  Base x Height
• Area of a circle


  π x r^2
• Circumference of a circle


  π x Diameter
• Volume of a prism


  Area of cross-section x Length
• Volume of a cylinder


  π x r^2 x Height
• Radius


  The distance from the centre of a circle to the edge
• Height


  The distance from the base to the top of an object
• Calculating volume of a cylinder


  1. Calculate pi x radius^2

  2. Multiply by height
• Do not round working out when calculating volume
• Pythagoras Theorem


  a^2 + b^2 = c^2, where a and b are the shorter sides of a right-angled triangle and c is the hypotenuse (longest side)
• Density


  Mass / Volume
• Speed


  Distance / Time
• Pressure


  Force / Area
• sin 0


  0
• sin 30


  1/2
• sin 45


  1/√2
• sin 60


  √3/2
• sin 90


  1
• cos 0


  1
• cos 30


  √3/2
• cos 45


  1/√2
• cos 60


  1/2
• cos 90


  0
• tan 0


  0
• tan 30


  1/√3
• tan 45


  1
• tan 60


  √3
• Volume of a pyramid


  1/3 x Area of base x Height
• Area of a triangle using sine


  1/2 x a x b x sin(C)
• Cosine rule


  Used to find the length of a side in a triangle when the lengths of the other two sides and the angle between them are known
• Using the cosine rule

  1. Substitute values into the formula

  2. Solve for the unknown side length
• Rearranged cosine rule


  cos a = (b^2 + c^2 - a^2) / (2bc)
• Using rearranged cosine rule

  1. Substitute values into the formula

  2. Solve for the unknown angle
• Area of a triangle using sine


  1/2 * a * b * sin c
• Calculating area of a triangle using sine


  1. Identify the lengths a, b and angle c

  2. Substitute into the formula

  3. Calculate the area
• Area of a sector


  π * r^2 * (θ/360)