# further pure

## support for school mathematics exams

I have developed a database driven website which shares past papers, markschemes and my own ‘write outs’ for most Edexcel modules in mathematics and further mathematics: jped Exam Bucket I use this mostly as a resource for my own teaching; using it I can lay my hands of exam questions and solutions of different types …

TOP TIP: Root three in this Further Pure 2 exam betrays presence of 30 or 60 degree angles in this complex numbers question. All maths students should know exact values of 30, 45 and 60 degree angles – they come up so much. See my exam bucket http://jped.co.uk/ExamBucket/exambucket.php, for this FP2 2014 and many others.

## Ellipse, stuck at origin, rotates

Take ellipse: apply rotation to variables: to make new equations: then vary  to get rotating ellipse: note that addition of an  term only to the original equation, under certain limitations of coefficients, means a rotation only.

Successive approximations of the Sine function formed by truncating the Taylor Series.

Summary of parabola facts, worthy of Victorian text book, attempts to exhaust obvious question contexts in Further Pure and STEP. Prove them!

Polynomial rule requires subtle proof by induction to establish it’s truth.  One for students of STEP or Further Pure mathematics.  Not sure this is the most elegant expression of this proof. Inspired by Carr’s Synopsis of Elementary Results in Mathematics.