Worksheet Chapter 8: Mathematical Modeling

1. A small business models monthly profit P (in RM) from selling x items using P(x) = 40x - 500. (a) What is the break-even quantity (where P = 0)? (b) What assumption does this linear model make about unit production costs?

2. True or False: If a model fails validation tests, you must immediately report the faulty results as the final findings.

3. A school hall rental costs RM300 base fee plus RM15 per guest. (a) Formulate a linear mathematical model for total rental cost C in terms of n guests. (b) Calculate the total cost for 80 guests. (c) If the school budget cap for hall rental is RM2,000, find the maximum number of guests that can be invited.

4. True or False: A linear model is suitable for a situation where the rate of change between two variables is variable and fluctuating.

5. A food delivery app charges a delivery fee modeled by F = 3.50 + 1.20d, where d is distance in km. What is the dependent variable?

6. Fill in the blank: The process of evaluating whether a mathematical model's predictions align with real-world observations is called model _________.

7. A printer depreciates in value according to V = 1200 - 150t, where V is value in RM and t is time in years. Find its value after 4 years.

8. The trajectory of a water jet from a fountain nozzle is modeled by h = -0.5d² + 2d + 1.5, where h is height and d is horizontal distance in meters. Calculate the maximum height reached by the water jet.

9. List the 6 sequential steps in the mathematical modeling framework.

10. State TWO reasonable assumptions when modeling the time taken for a drone to fly a delivery route between two locations.