The coordinates of two points on a line are given. The task is to find the shortest distance from the line of a third given point. The task involves finding the equation of...

A hyperbola is given with a parabola ax²  touching each branch of the hyperbola at single points. The task is to determine the value of a.

A formal proof of the general situation involves substituting the equation of the parabola into the equation of the hyperbola. The...

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation introduces Euclid's axioms and theorems and provides historic information on the development of geometric principles, as well as discussing hyperbolic geometry. A link to Non-Euclid software, from Joel...

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation starts with the inequalities associated with triangles and challenges students to develop proofs of the inequalities found in other situations, using the arithmetic, geometric and harmonic means.

The...

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation highlights the concept of infinity and its implications, as well as introducing the mathematician Georg Cantor and the arguments relating to infinity that he came up with.

The resource is designed to...

From the Integrating Mathematical Problem Solving project by Mathematics in Education and Industry (MEI), this activity for post-16 students shows how regular sampling of a variety of prices is used to get a measure of inflation. There is more than one possible way to do this. A measure of inflation is used to...

This toolkit looks at how inflation is measured and what the data is used for. Students can use the Shopping prices comparison tool and data from the Consumer Prices Index including owner occupiers’ housing costs (CPIH) dataset. They can use them to explore the implications of inflation for consumers, businesses...

The initial problem looks at an area given between two curves. The first curve is a parabola with the x and y axis intercepts given. The second curve is a stretch parallel...

This task involves investigating various aspects of interest and depreciation, including compound interest and the effects of calculating  compound interest over different periods of time (e.g. monthly vs. weekly). The task requires...

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation begins with a reminder of some transformations of the plane before introducing the less well known transformation of Inversion. Students are able to experiment with an Autograph file to explore this concept...

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this presentation students explore non-periodic tiling patterns using templates of kites and darts, as well as discovering the many remarkable facts to be found in these tilings.

The resource is designed to explore...

An ‘L’ shape is shown and the task is to find the centre of mass using only a straight edge and pencil. The solution makes use of the fact that the centre of mass of two objects will lie on a...

Linear Programming involves creating a function that represents a real life problem. The aim is to optimise this function given certain constraints. Simple examples of linear programming will have few variables and constraints, however, real life situations will have many more variables and constraints that will...

Carom Maths provides this resource for teachers and students of A Level mathematics.

In this presentation students are given a function and explore the mapping of natural numbers, as well as being challenged to find the inverse function. A link to the online encyclopaedia of integer sequences is provided for...

A matching is a set of edges on a bipartite graph in which no two edges share a common vertex. A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y. A matching in a bipartite graph is the pairing of some or all of the vertices in X with some or all of the...