Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the...

Drinks cans are made by stamping out circular discs from a sheet of tin. Given the dimensions of the sheet of tin and the diameter of the circle stamped out, students are required to calculate the wastage and to investigate whether there is a more efficient method. The problem requires students to be able to...

This series of activities from NASA take a mathematical approach to looking at the Earth and its atmosphere. They are intended as supplementary problems for students looking for additional challenges in mathematics and physical science from age 11 to 19 years.

The problems were created to be authentic...

This series of activities from NASA take a mathematical approach to looking at electromagnetic radiation. They are intended as supplementary problems for students looking for additional challenges in mathematics and physical science from age 11 to 19 years. The problems were created to be authentic glimpses of...

This excel program is about finding the equation of straight lines in the form ax+by+c=0. The first two sheets deals with the equation of the line through two given points and the equation of the line through a point perpendicular to a given line. The resource is an...

This activity, from Shirley Fall, contains ten linked problems which are intended to lead to students developing a rule for integrating functions of the form y=ax n where n not equal to -1. Problem 1 begins by exploring the area enclosed under a straight line y=2x+3 from x=0 to x=a for varying values of a, leading...

In this resource from Shirley Fall, students are presented with a general straight line y=mx+c and are shown that the gradient of the line between any two points that lie on the line is always equal to m. Students should be encouraged to explain the proof to check...

This activity, from Shirley Fall, requires students to use and interpret function notation, sketch graphs using key points, explore the common transformations of translate parallel to the y axis, translate parallel to the x axis, stretch parallel to the y axis from the...

This resource contains two interactive excel programs which enable students to investigate cubic functions and the relationship between the factorised form and the graph.

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This question asks us to consider a person opening a burger bar, doing all of the cooking themselves, and then estimate how much space should they rent?

The main topics required are rates (number of burgers per hour that one person could cook, number of customers per hour), and areas. 

The network flow problem involves finding the optimum route through a flow network; a directed graph where each arc has a capacity and each arc receives a flow. Typical examples include: evacuation plans and delivery services. The problem involves students analysing the plan of a school canteen and deciding whether...

This excel file contains a series of sheets which give practice in rearranging formulae and substituting values. Clicking on the subject of the formula reveals the rearranged form. The answers to the calculations are also available.

Mathcentre provide these resources which cover aspects of functions and graphs. They include explanations of linear functions, the exponential constant, the graph of a function and linear relationships.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant...

Mathcentre provide these resources which cover aspects of functions and graphs often used in the field of engineering. They include descriptions of the hyperbolic function and identities, the logarithm function and its graph as well as the graphs of the trigonometric functions.

Comprehensive notes, with...

Mathcentre provide this resource which covers the slope intercept form, an aspect of geometry that involves the gradient and vertical intercept of a graph, which can be established from the terms of a linear equation.

Comprehensive notes, with clear descriptions are provided, together with relevant diagrams...