10 questions · Form 5 Mathematics Bab 8: Mathematical Modeling
A cell phone plan charges a base fee of RM20 per month plus RM0.10 per SMS sent. Which model represents the monthly cost C for sending x SMS?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. A cell phone plan charges a base fee of RM20 per month plus RM0.10 per SMS sent. Which model represents the monthly cost C for sending x SMS?
Answer: A
This is a linear relationship where RM20 is the fixed y-intercept (c) and RM0.10 is the rate per SMS (m).
2. Which factor represents a common limitation when modeling real-world traffic flow mathematically?
Answer: A
Unpredictable external factors like weather and human behavior introduce real-world noise that simplified models cannot fully capture.
3. Which of the following statements about mathematical models is TRUE?
Answer: A
Models simplify reality; therefore, they are approximations bound by assumptions and constraints.
4. If a quadratic model for profit P(x) in thousands of RM yields P(x) = -2(x - 5)² + 50, what is the maximum profit achievable?
Answer: C
The maximum occurs at the vertex x = 5 where P(5) = 50. Since units are in thousands of RM, maximum profit = RM50,000.
5. Which mathematical function best models the height h of a ball thrown vertically upwards as a function of time t?
Answer: A
Projectiles under gravity follow parabolic paths described by quadratic equations of the form h(t) = -gt² + vt + c.
6. A water tank drains such that the volume remaining V (in liters) after t minutes is modeled by V = 500 - 20t. How long will it take to empty completely?
Answer: B
Set V = 0 => 0 = 500 - 20t => 20t = 500 => t = 25 minutes.
7. An investment of RM1,000 grows according to A = 1000(1.05)ᵗ, where t is in years. What type of model is this?
Answer: A
Equations with time t in the exponent of a base greater than 1 represent exponential growth models.
8. Why are assumptions made during the mathematical modeling process?
Answer: A
Real-world situations are complex; assumptions simplify the scenario to focus on the key variables.
9. What should be done if the predictions from a mathematical model do not match real-world data during the validation step?
Answer: C
Validation tests accuracy. If a model fails validation, assumptions must be re-evaluated and the model refined iteratively.
10. Which of the following is a dependent variable when modeling the fuel consumed by a car on a road trip?
Answer: A
Fuel consumed depends on factors such as distance traveled and speed, making it the dependent variable (y).