AS Decision Maths Tips for each Topic

Kruskal and Prim What examiner’s are looking for A table of values in the order that they are added and the total Kruskal will be in ascending order Prim, by adding the next lowest edge to any existing vertex Label vertices on any spanning tree you have to draw Your spanning tree shouldn’t contain any loops A minimum spanning tree will have n – 1 edges (n being the vertices) Know how to use Prim’s matrix, particular with lower bound questions Spanning trees can be in travelling salesman questions

Djikstra’s What examiner’s are looking for Limitations of Djikstra is that you can’t use negative numbers

Chinese Postman Problems What examiner’s are looking for To identify the ODD vertices (there will normally be four) Find the shortest distance between the combinations of odd vertices. STATE which edge is to be repeated and its length. Add the repeated edges to the total of all edges (I generally draw the repeated edges on the diagram) Remember when stating how many times a vertex will be visited this includes the REPEATED edges and is number of edges at the vertex divided by 2 (expect the start and end vertex, which will be edges ÷ 2 + 1)

Travelling Salesman What examiner’s are looking for To be able to use the nearest neighbour algorithm to trace a journey To understand that the best Upper bound is the LOWEST value Know that a tour for an upper bound may be improved upon To be able to find the best lower bound by deleting a vertex, either from a spanning tree or Prim’s matrix, and adding the lowest two connectors Be able to use and solve inequalities in nearest neighbour questions To be able to state if the upper and lower bound create an optimal journey (it can be done)

Graph Theory (1) What examiner’s are expecting you to know

Graph Theory (2) What examiner’s are expecting you to know

Matchings What examiner’s are looking for To be able to draw a bipartite graph from an adjacency table or worded matchings To be able to draw a adjacency matrix from a bipartite graph and use 1 and 0 only in the table for matchings From an initial match, how to solve and annotate a solution to a final match eg A – 1 – C – 5 – B – 3 etc. / / You must state the final match eg A5, B4, C6, D2, E1, F3.

Algorithms What examiner’s are looking for Most questions ask you trace one or two algorithms Ensure you are familiar with the correct format for setting out the problem You may be asked to comment on what the algorithm shows or what happens if a line is removed (this type of question will normally generate a continuous loop) You must follow instructions set out in the question

Sorting Algorithms What examiner’s are looking for Your ability to understand the different processes involved in Bubble sort Quick sort Shell sort and Shuttle sort It is vital you know how they differ and learn the processes involved in applying each algorithm You must know how comparisons and swaps are generated for each pass or after each pass

Linear Programming What examiner’s are looking for Your ability to formulate a linear programming problem and write each inequality as simply as possible To manipulate data that has three variables to two (this often means recognising that one of the variables equals another) or the value of one variable is given Graph the information which should establish a feasible region. This must be stated. You may need to draw an objective line on your graph, if requested. Ensure you have a sharp pencil and lines are drawn very accurately (to within half a small square) It is likely you will need to find a maximum / minimum value for loss or profit, by using the co-ordinates of intersecting lines that create the feasible region, for a given equation. To solve problems using the data formed in the first paragraph