# step

## Counting Pennies, Generating Functions and STEP

STEP I 1997, Question 1 Show that you can make up 10 pence in eleven ways using 10p, 5p, 2p and 1p coins. In how many ways can you make up 20 pence using 20p,10p 5p, 2p and 1p coins? There is an interesting way of approaching this question using generating functions. A generating function …

## Carr’s Synopsis and Sixth Term Entrance Papers

Students in search of extension work in maths, particularly as far as Sixth Term Entrance Papers (STEP) are concerned, should peruse Carr’s Synopsis of results in Elementary Pure Mathematics. This book is famous for being the volume used by the autodidact Ramanujan to teach himself mathematics.  The book is merely a list of results and …

## Algebraic Form of the Modulus Function

Sneaky play with algebraic notation and function definition lays traps for scholarship students in school maths.

## Functional Transfromations – Core Maths into STEP

Linking core maths 3 functional transformations to Step algebra and solutions of equations.

I think that mathematically interested sixth formers, wanting to study the subject at University, should have some background knowledge.  Many would have heard about the Riemann Hypothesis and a link to prime numbers; this subject is beyond the scope of this blog but school pupils, with knowledge of prime numbers and geometric progressions, can see …

## 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.

## Theory of Equations

this fact about polynomials might be useful sometime …

Carr’s 626, in his magical book for Edwardian mathematical autodidacts, provides summary of general solutions for trigonometrical equations useful to STEP and A level students.