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Quiz Chapter 8: Mathematical Modeling

10 questions · Form 5 Mathematics Bab 8: Mathematical Modeling

Question 1 of 10Score: 0

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?

Full Question List & Answer Key

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?

  1. A. C = 0.10x + 20
  2. B. C = 20x + 0.10
  3. C. C = 0.10x² + 20
  4. D. C = 20(0.10)ˣ
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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?

  1. A. Unpredictable weather conditions and driver behavior
  2. B. The existence of speed limits
  3. C. Distance between traffic lights
  4. D. Number of lanes on a road
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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?

  1. A. A mathematical model is an approximation and may have limitations
  2. B. All mathematical models are 100% accurate for any situation
  3. C. Once built, a model can never be modified
  4. D. Assumptions have no effect on the accuracy of a model
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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?

  1. C. RM50,000
  2. A. RM5,000
  3. B. RM2,000
  4. D. RM50
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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?

  1. A. Quadratic function
  2. B. Linear function
  3. C. Exponential function
  4. D. Reciprocal function
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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?

  1. B. 25 minutes
  2. A. 20 minutes
  3. C. 50 minutes
  4. D. 500 minutes
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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?

  1. A. Exponential growth model
  2. B. Linear model
  3. C. Quadratic model
  4. D. Cubic model
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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?

  1. A. To simplify real-world complexities so a mathematical model can be constructed
  2. B. To eliminate the need to collect real-world data
  3. C. To guarantee 100% accuracy in predictions
  4. D. To avoid using algebra or calculus
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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?

  1. C. Revisit assumptions and refine the model
  2. A. Ignore the real-world data and publish the model
  3. B. Discard mathematics entirely
  4. D. Change the real-world data to match the model
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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?

  1. A. Volume of fuel consumed
  2. B. Distance traveled
  3. C. Average driving speed
  4. D. Inflation rate
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Answer: A

Fuel consumed depends on factors such as distance traveled and speed, making it the dependent variable (y).

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