Linear Programming, Glossary

Knowing the vocabulary of Linear Programming precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Constraint, A constraint is a condition in a linear programming problem, written as a linear inequality such as $x+y\le 10$, that limits the possible values of the variables. Each constraint comes from a real restriction in the situation. Together, the constraints define the region of allowed solutions. →
• Objective Function, The objective function is the quantity to be made as large or as small as possible in a linear programming problem, such as profit or cost, written as a linear expression like $k=3x+2y$. The goal is to find the values of the variables that give its optimum value. →
• Feasible Region, The feasible region is the set of all points that satisfy every constraint in a linear programming problem at once, shown as a shaded area on a graph. Any point inside it is an allowed solution. The optimum value of the objective function is always found at one of its corners. →
• Optimum Value, The optimum value is the largest or smallest value of the objective function that can be reached within the feasible region. It is found by testing the corner points of the region, since the maximum or minimum of a linear function always occurs at a vertex. This gives the best solution. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Linear Programming chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Linear Programming terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Linear Programming questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.