The resource is in two parts. Firstly, a software application which generates trinomials, and their solutions. Secondly a detailed step-by-step method of solution. Applicable from GCSE to A Level and beyond.

The program will draw from 1 to 10 cubes, with variable line-thickness, variable numbers of internal cubes, and variable perspective views. The cubes can then be used in an almost endless number of mathematical applications. It isn’t an application for pupils, it’s an application which can help to produce material for pupils.

The work sheet guides participants to investigate the numbers involved in the SUM of CUBES. While the material could be a useful introduction to the sum of cubes at 6th form level, it is also accessible to pupils in the lower school, and class 6 in primary schools. In the sixth form it could be an introduction to the sum of cubes, which can be followed up with rigorous proof. The intention for pupils below the age of 16 would be to introduce the wonder and excitement in some of the relationships found in mathematics.

The simulation is effectively a working PDP8 computer, allowing students to write and run code either at full speed, or in single-step mode. The accumulator, address, and contents registers are displayed. There is a small coded program which will display multiplication in operation. PDP-8 Simulation The PDP-8 was a family of 12-bit minicomputers that was produced by Digital Equipment Corporation (DEC) and release in March 1965. It was the first commercially successful minicomputer, with over 50,000 units being sold over the model’s lifetime. The PDP-8 combined low cost, simplicity, expandability, and careful engineering for value. The greatest historical significance was that the PDP-8’s low cost and high volume made a computer available to many new customers for many new uses. Its continuing significance is as a historical example of value-engineered computer design Download URL https://secure.internxt.com/d/sh/file/7487812d-5eb8-402b-a254-d3fced86835e/14193d82cde5bef8b2a78b02a88b2bf52fbdc72b72aa98f4509320965522fff4

The software enables users to explore the Simplex Algorithm for small problems. Linear Programming problems can be entered, edited, saved, and loaded. The solution can be followed stage by stage, allowing users to specify pivot points, or providing the pivot points automatically. If required, the whole Simplex solution can be performed automatically. An installation for the software can be downloaded from the link below. https://share.ue.internxt.com/d/sh/file/8fa2b330-6e61-47cf-aa5b-4a245124ad39/ee2a701db0334350e5aff1e233d61037b1d83ea6ba98492ec588f4d40320ec90 The installation program is inside the downloaded zip file.

The resource gives an investigation of numbers involved in the 12 days of Christmas. A formula is developed for variations where any other number is used.

The short article shows two methods of discovering the formula for calculating Triangular Pyramid Numbers.

Factorise is a 64-bit program for Windows which will factorise three types of expression: A number, A quadratic trinomial, or A cubic polynomial (which has factors). Recently enhanced, download link: https://drive.google.com/file/d/1Ef7THvPuEYfjY3iXmn5WuNI1Eb0DzuEB/view?usp=drive_link If you have any comments to make about this item, I would be pleased to receive them at n3.14158r@yahoo.com

The resource shows a simple Linear Optimisation problem together with its solution, obtained by software. The software is available to download. The software can be downloaded using the link below. https://secure.ue.internxt.com/d/sh/file/5635225a-8fea-4bf9-965a-501aeb6f625d/a9f80f7c45ea045b15216bebd84bfc21af44230b29d5da59baee412861af14ec The file provided is a zip file which contains the installation file, Extract the installation file and run it. There will be warnings from the operating system, which need to be ignored to progress the installation. If you have any comments to give me about this resource, I shall be very pleased to receive them.

This short note explains how distance under constant acceleration can be calculated without recourse to calculus.

The resource shows a method of deriving the sum of squares of integers which can be easily understood by secondary pupils (up to year 11).

The resource shows how the formula for the sum of cubes can be teased out using quite simple pattern recognition.

The work involved in evaluating polynomials can be considerably reduced by using the principle of nesting.

The PDP8 was the world’s first widely available computer. It has a very small instruction set and had a maximum of 32768 words of 12-bit memory. Instructions (in binary) can be entered via the 12 switches on the front panel, and programs can be run at full speed, or in single-step mode. During program execution, the accumulator is displayed on the panel. It can load programs off images of paper tape. A copy of the installation can be obtained by emailing pdp@meltonisl.com

A level students will encounter the expressions for the sums of powers of integers, often using mathematical induction to prove their validity, but I don’t remember students ever being asked to investigate and derive those expressions. This note shows how the sum of fourth powers of integers can be derived and understood by A-level, or younger students. It must be understood that this method does not prove the validity of the expression obtained, but it will allow readers to understand how the expression can be derived.

This article describes how to obtain the formula for a hexagon made up of circles.

What is described here is a method of finding expressions for several sums of squares at once. The number can be determined by the user. The only drawback with this method is that it gives the expressions in polynomial form, rather than in factor form.