Further Mathematics Support Programme

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Presentation transcript:

Further Mathematics Support Programme

Diagonals in a Dodecagon Let Maths take you Further…

Diagonals in a dodecagon How many different length diagonals are there in a regular dodecagon?

Diagonals in a dodecagon The side length AB is 2 units. All shapes shown are regular. The diagonal AD is a line of symmetry for the squares and triangles it dissects. How could you calculate the lengths: AC AD AE AF AG?

Surds skills Expanding the expression: 𝑎 + 𝑏 2 =𝑎+𝑏+2 𝑎𝑏 Hence, to find the square root of an expression involving surds, it is sometimes possible to manipulate the expression in order to obtain something in the form of: 𝑎+𝑏+2 𝑎𝑏 This can then be factorised to: 𝑎 + 𝑏 2 Finding the square root of this gives: ( 𝑎 + 𝑏 )

Surds skills Simplify 𝟏𝟏+𝟒 𝟔 This has to be ‘2’ 11+4 6 = 11+2 24 11+4 6 = 11+2 24 = 8+3+2 8 × 3 = ( 8 + 3 ) 2 = 8 + 3 Try the method to simplify the following expressions: a) 15+10 2 b) 18+6 5 c) 24+6 7 This has to be ‘2’