Introduction

What is Mathematical Modelling?

Mathematical modelling is the process of converting a real-life problem into mathematical language. Instead of studying the physical situation directly, we create a model — a simplified representation using equations, graphs, or computer programs — that captures the essential behaviour of the problem.

In Class XI, you learned that this conversion involves:

• Identifying the key variables and constraints from the real situation.
• Expressing relationships between them using mathematical conditions.
• Solving the resulting mathematical problem.
• Interpreting the solution back in the original context.

Why Study It Separately?

Many earlier problems in calculus, algebra, or geometry already used modelling implicitly. Treating it as a separate topic helps you understand the step-by-step process of abstraction, apply multiple tools (matrices, calculus, linear programming) to a single problem, and build a systematic approach to unfamiliar real-world scenarios.

What This Chapter Covers

In this chapter, you will extend your modelling skills using three techniques:

1. Matrices – to handle systems of linear equations and data in tabular form.
2. Calculus – to model rates of change, optimization (maxima/minima), and growth/decay.
3. Linear Programming – to find the best outcome (maximum profit, minimum cost) under given constraints. …