# Core Maths

## Integration by Substitution

Current UK exam textbooks pass over proofs and mathematical discussions in a hurry to show the ‘how to’ of exam questions. Integration by substitution is a little more than just backwards chain-rule and deserves a fuller treatment. Try this, Let, then, Suppose that there exists a function g, of another variable , such that and …

## The linear combination of a sine and a cosine is itself a sine wave

A linear combination of two functions, and is a sum involving constant multiples of the functions.  That is, where . So, in the case of and , we would have, . It is a slightly surprising fact that the linear combination of two sine waves is itself a sine wave.  The set of sine waves …

## 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 …

This method for finding the centre, and by extension the equation, of a circle given three non-colinear points, brings the ancient textbook master Euclid onto Descartes’ coordinate plane and right  into the 21 century classroom.

Area sandwich proves that finding areas is opposite to differentiation – The Fundamental Theorem of Calculus

Pascal’s Triangle with binomial coefficients expressed modulo prime numbers in an ascending sequence.

Pascal’s triangle with each term expressed as a remainder when divided by 2.  The pink squares show whether a number is odd or not.  This appears to give a fractal pattern.

How to make Pascal’s Triangle.

Added as complement to last post.