AZSCI Math & Computational Thinking 2

Question 1

A student develops a computational model to simulate the spread of a virus in a closed school environment. The model includes variables for transmission rate, recovery rate, and student density. When running the simulation with an extremely low transmission rate (approaching zero), the model unexpectedly shows a small, persistent number of infections instead of a complete die-off. Which of the following best describes this scenario?

Accepted Answer

An edge case where the algorithm for calculating new infections fails to handle near-zero inputs correctly.

Answer

This scenario describes an edge case, which is a problem that occurs at an extreme or minimum operating parameter. An extremely low transmission rate is an extreme parameter for the model. The algorithm likely has a flaw in how it handles this specific boundary condition, leading to unexpected behavior that doesn't reflect the real-world outcome of the virus dying out.

Question 2

A team of students is using a block-based programming environment to create a computational model of a predator-prey relationship between wolves and rabbits. To ensure their model is robust, they must consider edge cases. Which of the following represents the most critical algorithmic edge case to test?

Accepted Answer

The model's behavior when the initial population of either wolves or rabbits is set to zero.

Answer

In programming and algorithm design, an edge case often involves empty or zero inputs. Testing the model with a starting population of zero for either species is a critical edge case. A robust algorithm must handle this scenario without crashing or producing illogical results, such as rabbits spontaneously generating or the wolf population growing without a food source.

Question 3

A scientist is analyzing a large dataset of daily temperatures for a specific city over 50 years to identify climate trends. Which mathematical technique is most appropriate for identifying a long-term pattern of warming while minimizing the effect of seasonal fluctuations and random daily variations?

Accepted Answer

Applying a moving average with a multi-year window to the dataset.

Answer

A moving average is a statistical technique used to analyze data points by creating a series of averages of different subsets of the full data set. It is commonly used with time-series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. A multi-year window would be effective in minimizing seasonal effects and revealing the underlying long-term climate pattern.

Question 4

When decomposing a complex scientific problem for computational modeling, what is the primary risk of creating a model with an excessive number of variables and interactions (i.e., making it overly complex)?

Accepted Answer

The model becomes computationally 'expensive,' requiring excessive processing power and time, and may obscure the fundamental relationships being investigated.

Answer

While detailed models can be powerful, excessive complexity is a significant risk in computational thinking. Overly complex models can be difficult to build, debug, and interpret. They often require significant computational resources (making them 'expensive') and the sheer number of interacting parts can make it difficult to isolate and understand the key causal relationships under investigation.

Question 5

A student is designing an algorithm to control a rover on a distant planet. The rover must navigate from a starting point to a target, avoiding obstacles. The student's algorithm uses a 'left-wall' following strategy. In which of the following scenarios would this specific algorithm most likely fail to find the target, even if a clear path exists?

Accepted Answer

A maze where the target is in the center, surrounded by a circular, detached wall.

Answer

A 'left-wall' following algorithm is a simple method for solving certain types of mazes. However, it fails in mazes that have detached loops or 'islands' because the algorithm will simply trace the perimeter of the island it first encounters and will never be able to reach the center or cross the gap to a different section of the maze. This represents a specific structural edge case for this type of algorithm.

(AZSCI) Arizona Science Test Practice Test

(AZSCI) Arizona Science Test Practice Test

AZSCI Math & Computational Thinking 2