← Further Maths syllabus

EnglandFurther Maths

Discrete mathematics

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you schedule a project, find its shortest completion time and identify the activities that cannot be delayed?

Activity networks, forward and backward passes to find earliest and latest times, the critical path, float, and resource scheduling with Gantt charts.
A focused answer to the AQA A-Level Further Mathematics critical path analysis content, covering activity networks, forward and backward passes to find earliest and latest times, the critical path, float, and resource scheduling with Gantt charts.
11 min answer →

How do you analyse a two-player zero-sum game, find a stable solution, and handle games with no saddle point?

Two-player zero-sum games, the pay-off matrix, play-safe strategies, saddle points and stable solutions, dominance to reduce a game, and mixed strategies including conversion to linear programming.
A focused answer to the AQA A-Level Further Mathematics game theory content, covering two-player zero-sum games, the pay-off matrix, play-safe strategies, saddle points and stable solutions, dominance to reduce a game, and mixed strategies including conversion to a linear programming problem.
11 min answer →

What is a graph, what vocabulary describes it, and how are graphs represented and classified?

Graph terminology including vertices, edges, degree, paths and cycles, special graphs such as trees and complete graphs, the adjacency matrix representation, and Eulerian and Hamiltonian graphs.
A focused answer to the AQA A-Level Further Mathematics graphs and networks content, covering graph terminology such as vertices, edges, degree, paths and cycles, special graphs such as trees and complete graphs, the adjacency matrix representation, and Eulerian and Hamiltonian graphs.
10 min answer →

How do you formulate a linear programming problem and solve it graphically or with the simplex method?

Formulating linear programming problems, the feasible region and graphical solution, the vertex (objective line) method, slack variables, and the simplex algorithm for maximisation.
A focused answer to the AQA A-Level Further Mathematics linear programming content, covering formulating problems, the feasible region and graphical solution, the vertex and objective line methods, slack variables, and the simplex algorithm for maximisation.
11 min answer →

How do standard algorithms find minimum spanning trees, shortest paths and good routes through a network?

Kruskal's and Prim's algorithms for minimum spanning trees, Dijkstra's algorithm for the shortest path, and the route inspection and travelling salesperson problems.
A focused answer to the AQA A-Level Further Mathematics network algorithms content, covering Kruskal's and Prim's algorithms for minimum spanning trees, Dijkstra's algorithm for the shortest path, and the route inspection and travelling salesperson problems.
11 min answer →