PowerPoint to teach A Level Further Maths Decision/Discrete Maths Option: Two-Stage Simplex Algorithm (artificial variables). Primarily written for Edexcel but suitable for OCR specifications. Complete, step-by-step approach with worked examples of A Level standard. Format is such that students can also use as revision at their own pace and includes a handy flowchart for revision. The full set of 16 PowerPoints in this series cover the whole of the Edexcel D1 course: Algorithms Bin-Packing Algorithm Critical Path Analysis (GANTT) Dijjkstra’s Shortest Path Algorithm Floyd’s shortest distance algorithm Graphs & Networks Kruskal’s Minimum Spanning Tree Linear Programming Planarity Algorithm Prim’s Minimum Spanning Tree Route Inspection Algorithm Simplex Algorithm 1 - Edexcel tableau Simplex Algorithm 2 (artificial variables) - Edexcel tableau Simplex Algorithm 3 (Big M method) - Edexcel tableau Sorting Algorithm: Quick-sort, Bubble-sort (& Shuttle-sort for OCR) Travelling Salesperson Problem, including Nearest Neighbour Algorithm (+ tour improvement algorithm for OCR) Updated 2022

This is a PowerPoint presentation which uses animation, simple layouts, graphics and diagrams to clearly explain all topics required for a full understanding of Decision Maths Year 1, The simplex algorithm. This is completely in-line with the Edexcel A-level Further Maths specification. teachingisgood is happy to declare that this presentation also includes loads of practice questions, which build up a key understanding and build exam skills, as well as exam-style questions which push problem solving skills with questions aimed at the highest achieving students. This presentation is part of a series of presentations for A-level Further Maths, some of which also include interactive quizzes, videos and fun ways to test students and develop knowledge. The topics covered in this presentation is as follows. Formulating linear programming problems The simplex method Problems requiring integer solutions Two-stage simplex method The big-M method

PowerPoint to teach A Level Further Maths Decision/Discrete Maths Option: Simplex Algorithm (Edexcel Tableau). Additional PowerPoints are available for problems involving artificial variables and the Big M method. Primarily written for Edexcel but suitable for OCR specifications. Complete, step-by-step approach with worked examples of A Level standard. Format is such that students can also use as revision at their own pace and includes a handy flowchart for revision. The full set of 16 PowerPoints in this series cover the whole of the Edexcel D1 course: Algorithms Bin-Packing Algorithm Critical Path Analysis (GANTT) Dijjkstra’s Shortest Path Algorithm Floyd’s shortest distance algorithm Graphs & Networks Kruskal’s Minimum Spanning Tree Linear Programming Planarity Algorithm Prim’s Minimum Spanning Tree Route Inspection Algorithm Simplex Algorithm 1 - Edexcel tableau Simplex Algorithm 2 (artificial variables) - Edexcel tableau Simplex Algorithm 3 (Big M method) - Edexcel tableau Sorting Algorithm: Quick-sort, Bubble-sort (& Shuttle-sort for OCR) Travelling Salesperson Problem, including Nearest Neighbour Algorithm (+ tour improvement algorithm for OCR) Updated 2022

PowerPoint to teach A Level Further Maths Decision/Discrete Maths Option: the Big M method for the Simplex Algorithm. Primarily written for Edexcel but suitable for OCR specifications. Complete, step-by-step approach with worked examples of A Level standard. Format is such that students can also use as revision at their own pace and includes a handy flowchart for revision. The full set of 16 PowerPoints in this series cover the whole of the Edexcel D1 course: Algorithms Bin-Packing Algorithm Critical Path Analysis (GANTT) Dijjkstra’s Shortest Path Algorithm Floyd’s shortest distance algorithm Graphs & Networks Kruskal’s Minimum Spanning Tree Linear Programming Planarity Algorithm Prim’s Minimum Spanning Tree Route Inspection Algorithm Simplex Algorithm 1 - Edexcel tableau Simplex Algorithm 2 (artificial variables) - Edexcel tableau Simplex Algorithm 3 (Big M method) - Edexcel tableau Sorting Algorithm: Quick-sort, Bubble-sort (& Shuttle-sort for OCR) Travelling Salesperson Problem, including Nearest Neighbour Algorithm (+ tour improvement algorithm for OCR) Updated 2022

Simplex Algorithm topics covers; Identify when the simplex algorithm should be applied (ie for situations that have three or more basic variables) Introduce and use slack variables to convert inequalities into equalities (only less than or equal to inequalities will be used during assessment) Use the simplex algorithm to maximise an objective function subject to linear constraints Use the simplex algorithm to minimise an objective function P by maximising the objective function Q = –P understand and use the stopping condition for the simplex algorithm (ie the objective row being non-negative) Find the optimal value of the objective function from a simplex tableau Identify any basic or slack variables that have zero values Find the values of any basic or slack variables that have non-zero values Interpret a Simplex tableau at any stage of the algorithm. Convert higher order games to linear programming problems and solve using the Simplex algorithm These PowerPoints form full lessons of work that together cover the full A level Further Maths course for the AQA exam board. Together all the PowerPoints include; • A complete set of notes for students • Model examples • Probing questions to test understanding • Class questions including answers • Individual whiteboard work • Links to exercises in ‘AQA approved textbooks by Hodder ed’ these can easily be edited for your textbook The PowerPoints can be used in the lesson and also given to students that have missed a lesson Videos of the lessons are all on You Tube so you can see the PowerPoint lessons fully first Please leave a review as it will really help me to improve my resources

These two PowerPoint presentations fully explain the ideas behind the Two-Stage Simplex and the Big-M Algorithms. They both provide clear, animated, step-by-step examples explaining how to apply the algorithms. [ I have also separately uploaded a free preview so that you can see the style of the presentation. ] Slack, surplus and artificial variables are explained, as is the creation of the additional objective function (i.e. A = “The total of the artificial variables”), and the modification of the original objective function when using the Big-M method. The slides can be used as the basis for teaching the topic to an A-Level mathematics class, and they also clear enough to be used as a revision/self-study aid. For example, "triggers " are used to show how values within a tableau are calculated using row operations on the previous tableau. Extensive use has been made of PowerPoint’s animation features such as “appear”, “fade” etc… I hope this resource will be useful within your teaching, and I would happy to receive any feedback that you might have. Regards and best wishes Gerard

Discrete 1 - Decision 1 - Simplex Algorithm - - Worksheet with 12 questions to be completed on separate paper - solutions included

A step by step guide to the simplex algorithm that avoids the complicated language of the textbook.

A powerpoint that runs through an example of how to use the simplex algorithm to solve a maximisation problem, followed by an exam question taken from an AQA D2 paper.

This free sample PowerPoint SlideShow is an extract from my 40 slide PowerPoint presentation that fully explains the ideas behind the Two-Stage Simplex Algorithm, and gives clear, animated, step-by-step examples showing how to use it. Extensive use has been made of PowerPoint’s animation features. Slack, surplus and artificial variables are explained, as is the creation of the additional objective function i.e. A = “The total of the artificial variables”. The slides can be used as the basis for teaching the topic to a A-Level mathematics class. They provide enough, clearly explained details to also act as a useful revision/self-study aid. I hope you find this resource useful within your teaching practice. Regards and best wishes, Gerard

This A-Level Decision Maths Simplex Algorithm worksheet leads to mastery and develops deep order thinking into the hows and whys of Simplex. Featuring both closed and open questionning, the worksheet explores the ‘behind the scenes’. Students are expected to consider the alogorithmic steps, graphical representations, integer/non-integer solutions, forming questions from the answer, optimisation, constraints, variation of questionning, the use of ICT and has recommended extensions provided. Answers are provided on the second page but some are suggestions as there are open-ended questions. The format is in the Edexcel style.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has numerous applications in physics, engineering, and technology, making it an important subject for students to understand. In this article, we’ll provide a comprehensive overview of trigonometry and explain some simple examples that demonstrate its key concepts. What is Trigonometry? Trigonometry is the study of triangles and their properties. It deals with the relationships between the angles and sides of triangles and how they can be used to solve problems in real-world scenarios. The subject is divided into several branches, including plane trigonometry, spherical trigonometry, and analytic trigonometry. Key Concepts in Trigonometry There are several key concepts in trigonometry that are essential for understanding the subject. Some of the most important concepts include: Triangles: A triangle is a two-dimensional shape that is formed by three points. Triangles are the basis for all trigonometry, as the relationships between their sides and angles are what the subject is all about. Angles: An angle is a measure of the amount of rotation between two lines or rays. In trigonometry, angles are used to define the relationships between the sides of triangles. Sides: The sides of a triangle are the lines that connect the vertices. The relationships between the sides and angles of a triangle are the key to understanding trigonometry. Trigonometric Functions: Trigonometric functions are mathematical functions that describe the relationships between the sides and angles of triangles. The most common trigonometric functions include sine, cosine, and tangent. Simple Examples of Trigonometry Trigonometry can seem like a complex subject, but it’s actually quite simple once you understand the key concepts. Here are a few examples that demonstrate how trigonometry can be used to solve real-world problems: Example 1: Finding the Height of a Building Suppose you’re standing on the ground and you want to find the height of a tall building. You can use trigonometry to solve this problem. To do this, you’ll need to take a measurement of the angle between the ground and the top of the building, as well as the distance between you and the building. Using the sine function, you can calculate the height of the building by dividing the measurement of the angle by the distance. The formula for this calculation is: height = distance * sin(angle) Example 2: Finding the Distance Between Two Points Trigonometry can also be used to find the distance between two points. For example, suppose you want to find the distance between two points on a map. To do this, you’ll need to know the coordinates of both points and the angle between them. Using the cosine function, you can calculate the distance between two points by using the following formula: distance = square root of (x2 - x1)^2 + (y2 - y1)^2

The powerpoint will work through an example of using the two-stage method for solving simplex algorithm problems. A video of the powerpoint being used can be found at the address below: https://youtu.be/SLwAUYvSfZI

This PowerPoint will guide you through an example of using the Big M Method for solving simplex algorithm problems with “greater than or equals to” constraints. There is a video of the PowerPoint being used available at the link below. https://youtu.be/grGWsUHdWQM

This powerpoint will go through the main points when dealing with an integer solution constrained simplex algorithm problem. A video of the powerpoint in use can be found at the address below: https://youtu.be/tsXlclDkzuA

This PowerPoint will guide you through the application of The Simplex Algorithm, as featured in the Edexcel Further Maths Decision course. The PowerPoint covers both Maximising and Minimising problems. There is a video demonstrating the use of this PowerPoint available at the link below: https://youtu.be/t0NkCDigq88

This is a powerpoint to demonstrate the use of the Simplex Algorithm when integer solutions are called for, and it supplements the other Simplex Algorithm powerpoint that is available on TES too. There is a video demonstrating the use of this powerpoint available at the link below: https://youtu.be/ICBrU_wghSs

The first resource guides your students through the whole process of using the Simplex algorithm to solve a linear programming problem. The first page explains how the initial tableau is formed, how the objective function must be written and how the inequalities that represent constraints must be written as equations with the introduction of slack variables. The first exercise (11 questions) gives them the opportunity to practise writing the initial tableau correctly for different problems. Grids are provided so students focus their time and energy on only the values in the tableau. The next section describes how an iteration of the algorithm is performed and links the iterations to the graphical solution, showing how each iteration moves to a different vertex of the feasible region. There is then another exercise with 10 questions for students to practise performing iterations and finding the optimal solution. Again, grids are provided so students focus their time and energy on only the steps of the algorithm and the values in the tableau. Fully worked solutions are provided to all the questions in the exercises. The second resource is a spreadsheet that automatically solves any simplex tableau in 2/3 variables with 2/3 constraints - a useful resource for doing/checking solutions to other questions from a textbook or examination paper.