Mathematics: Applications and Interpretation HL
Number, finance, and discrete models
Financial mathematics, matrices, recurrence, graph theory, and constrained decision models for IB Mathematics AI HL.
Model amortised loans
Use loan repayment structure, interest rate, and term information to interpret repayment and balance calculations.
Use annuities and sinking funds
Use annuity and sinking-fund structures to calculate future value, deposit size, or accumulated interest.
Use transition matrices in context
Apply transition matrices to two-state models and interpret next-state or long-run behaviour.
Use graph theory and adjacency matrices
Interpret vertices, edges, degree, adjacency matrices, and simple route conditions in applied networks.
Optimise linear programming models
Use constraints, feasible vertices, and objective functions to identify an optimal applied decision.
Use recurrence relations in finance
Model balances using recursive interest and contribution rules.
Solve systems using matrices
Represent and solve two-variable applied systems with matrix methods.
Use inverse matrices in applications
Use inverse-matrix logic to recover inputs from a linear model.
Interpret eigenvalues in long-term models
Use dominant eigenvalue or scaling behaviour to interpret repeated matrix action.
Apply shortest path reasoning
Use network route totals to identify or justify a shortest path.
Apply minimum spanning tree reasoning
Choose edges that connect all vertices with minimum total weight and no cycle.
Use travelling salesperson bounds
Calculate and interpret lower or upper bounds for route-planning networks.
Use critical path analysis
Use activity times and dependencies to determine project duration and float.
Use depreciation models
Calculate depreciated value using a repeated-percentage model.
Interpret linear programming shadow values
Calculate objective improvement from a marginal resource increase.