A2. Introduction to Mathematical Modelling
- 1. NUMBER SYSTEMS
- 2. A POLYNOMIALS
- 3. COORDINATE GEOMETRY
- 4. LINEAR EQUATIONS IN TWO VARIABLES
- 5. INTRODUCTION TO EUCLID'S GEOMETRY
- 6. LINES AND ANGLES
- 7. TRIANGLES
- 8. QUADRILATERALS
- 9. CIRCLES
- 10. HERON'S FORMULA
- 11. SURFACE AREAS AND VOLUMES
- 12. STATISTICS
- 13. APPENDIX 1: PROOFS IN MATHEMATICS
- 14. APPENDIX 2: INTRODUCTION TO MATHEMATICAL MODELLING
A2.1 Introduction - Learning Objectives
A2.2 Review of Word Problems
Example 1:
Travelling 432 km on 48 litres of petrol. How much petrol for 180 km?
Example 2:
Investment of ₹15,000 at 8% simple interest. Time required to earn ₹4,000?
Example 3:
Motorboat travels upstream and downstream. Speed in still water?
Exercise A2.1
- Find months beyond which buying a computer is cheaper than renting.
- Two cars travel towards each other from different locations. When do they meet?
- Find the moon's orbital speed around the Earth.
- Find average daily usage of water heater based on electricity bills.
A2.3 Some Mathematical Models
Example 4:
Find number of tiles to cover a room of 6 m × 5 m using 30 cm tiles.
Example 5:
Use enrolment data of girls in primary schools to estimate when it reaches 50%.
Exercise A2.2
- Model Olympic 400-metre gold medal timings and predict next event's timing.
A2.4 The Process of Modelling, its Advantages and Limitations
- Step 1: Formulation – stating the problem, identifying relevant factors, and mathematical description
- Step 2: Finding the solution using known methods
- Step 3: Interpretation of solution in real-world terms
- Step 4: Validation – checking model accuracy with reality
Exercise A2.3
- How is mathematical modelling different from textbook word problems?
- Identify relevant factors for reducing vehicle wait time at traffic junctions.