step maths

t-Formulae and parameterisation of the circle

t-Formulae are used in integration to tackle rational expressions of tigonometric functions.  After a spell in the cold, when they were not included in some A level specifications, they are now back in sixth form lessons. It all starts with the subsitution, from which the following functions can be derived, ,  ,  . These derivations …

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The Natural Logarithm is an integration defined function. The shaded area under the graph is the value of the natural logarithm of the upper limit in the integration.

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.