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A Circle Journey

The initial task involves using factors of 12 and -12 to set up two points. Compasses are used to draw a circle that has the two points as its diameter. An interesting feature of the resulting...

Annulus Volume of Revolution

A segment of a circle is created using a chord parallel to the x-axis. The resulting segment of the circle is then revolved 360° about the x-axis. The problem is to calculate the volume of the resulting annulus.

To find a general solution to the problem involves using an elemental disc ring and integrating...

Brackets Out, Brackets In

The problem starts with choosing three distinct, non-zero integers between -5 and 5 that do not sum to zero. These are then used in a six factorisations that make use of...

A Geometric Progression Problem

There is an initial investigation of geometric progressions where the interval between the first and second, and the third and fourth terms are given, with the challenge of discovering two possible values for the first term and associated common ratio. There are ten examples to work on to enable collaboration...

Integration Stretch

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...

Cubic, Tangent, Circle

The graph of a cubic function with three real roots is drawn. A circle is then drawn so that the circumference of the circle passes through two adjacent roots. A tangent to...

Hyper-parabola

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...

Rebuilding design and technology

This Working Paper has been written to inform all those who are concerned about the status and nature of Design & Technology in the secondary school curriculum. It has been developed in response to the serious and continuing decline in the uptake of GCSE Design & Technology since the subject was introduced...

Raspberry Pi Networking

This resource details an activity where students set up their own network of Raspberry Pis in a classroom, using another machine as their server. As with all of these sorts of activities, it is highly recommended to work through the whoole activity first, downloading the required software ahead of a lesson and...

The Shortest Race

The introduction to this problem involves modelling a race from one tree to another, and the requirement to touch a fence on the way. The challenge is to determine the...

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