- 1. What Is an Inequality? Rules and Solving in One Variable
Recognise and interpret the four inequality symbols, apply the three rules for solving linear inequalities in one variable — including reversing the sign when multiplying or dividing by a negative — and write the solution set correctly.
- 2. Showing Inequalities on the Number Line
Represent the solution set of a one-variable inequality on a number line using correct circle and arrow conventions, write the inequality that matches a given diagram, and show combined (double) inequalities as bounded segments.
- 3. Combined (Double) Inequalities
Solve a double inequality by applying the same operation to all three parts at once, reverse both signs when dividing by a negative, and represent the solution as a bounded segment on the number line.
- 4. Range of Values — Satisfying Two Inequalities at Once
Solve two separate linear inequalities, find the intersection of their solution sets on a number line, state the combined range satisfying both, and recognise when there is no solution.
- 5. Two-Variable Inequalities — Solutions as Ordered Pairs
Define what it means for an ordered pair to satisfy a two-variable inequality, test any pair by substitution, and recognise that the solutions form a half-plane region with infinitely many points.
- 6. Drawing the Boundary Line — Intercepts and the Dashed/Solid Rule
Convert a linear inequality to its boundary line equation, find the x- and y-intercepts to draw the line accurately, and distinguish a dashed boundary (strict) from a solid boundary (non-strict).
- 7. Shading the Correct Half-Plane — The Test Point Method
Use the test-point method to decide which half-plane satisfies a linear inequality, shade the correct region, and produce a complete graph of a two-variable inequality.
- 8. Reading Inequalities from Graphs
Find the boundary equation from intercepts on a graph, read the inequality symbol from the line style and shading, and write the complete two-variable inequality a shaded graph represents.
- 9. Graphing Simultaneous Linear Inequalities — The Feasible Region
Draw several linear inequalities on the same axes, identify the feasible region as the intersection of all shaded half-planes, and test whether a point lies inside the region.
- 10. Finding the Corner Points of the Feasible Region
Identify all corner points (vertices) of a feasible region: read axis vertices from intercepts, find interior vertices by solving pairs of boundary equations simultaneously, and verify every candidate against all constraints.
- 11. The Corner Point Theorem — Finding Maximum and Minimum Values
State and apply the Corner Point Theorem: evaluate a linear objective function at every vertex of a feasible region and identify where the maximum and minimum occur, including the degenerate case.
- 12. LP Formulation — Writing Constraints and the Objective Function
Translate a word problem into a linear programme: define decision variables precisely, convert each restriction into a linear inequality using signal words, and write the objective function to be maximised or minimised.
- 13. Complete LP Solution — The Full Process
Apply the complete six-step linear-programming algorithm from formulation to final contextual answer: define variables, write constraints, graph the feasible region, find vertices, evaluate the objective, and interpret the optimum with units.
- 14. Complete LP Solution — Real-Life Applications
Apply the complete LP algorithm to multi-constraint, WAEC-format real-life problems: read coefficients from context, graph and find vertices, evaluate the objective, avoid common errors, and write a full contextual answer with units.
- 15. Unit 8 Consolidation — Inequalities and Linear Programming
A mixed review of the whole unit: solving and representing one-variable inequalities, number lines and combined ranges, graphing and reading two-variable inequalities, optimisation at feasible-region vertices, and the complete LP algorithm.
