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Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

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DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

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Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

At what angle must the billiard ball be struck for it to return to its start position?

Your answer will depend on the length and breadth of the table, but does it depend on where the ball is to start with?

Billiard Table

Don't be too quick to accept this diagram - what assumptions might it be useful to make about the rebound angles?

Now use that to draw your own diagram.