Linear models and optimisation.
Build linear models, compare choices and optimise feasible decisions with graphs, algebra and justified practical restrictions.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Forming linear equations from situations
Translate a practical situation into a straight-line rule with defined variables, units and a useful domain.
- 02
Solving simultaneous equations graphically/algebraically/with technology
Find where two linear conditions hold together and verify the result by substitution.
- 03
Interpreting intersections and break-even points
Interpret an intersection as equal cost or break-even, then compare choices on either side.
- 04
Linear inequalities
Translate practical limits into inequalities, solve them and decide whether boundaries are included.
- 05
Feasible regions
Build the overlap of all constraints and find its vertices before optimising.
- 06
Objective functions
Write the quantity to optimise separately from the constraints and evaluate it with the correct units.
- 07
Linear programming
Combine decision variables, constraints and a vertex comparison into a complete linear programming argument.
- 08
Integer constraints and interpreting an optimal solution
Handle whole-number decisions by systematic checking rather than blind rounding of a continuous solution.
- 09
Assumptions and limitations
Evaluate a model's assumptions and explain the limits of a mathematically optimal recommendation.
Topic review
Revisit the key ideas, then choose a practice paper.