Certainly! Here's a sample AP Computer Science Exam question on the topic of base cases:

Question: Explain the concept of base cases in recursive functions. Provide an example of a recursive function with a base case and explain how the base case prevents infinite recursion. Additionally, discuss the importance of identifying and handling base cases in recursive functions.

Answer: Base cases are critical components of recursive functions as they define the stopping condition for the recursion. When a recursive function reaches its base case, it stops calling itself and begins to unwind the stack, ultimately reaching the initial function call. This prevents the function from entering an infinite loop and consuming excessive system resources.

Consider the following example of a recursive factorial function in Java:

public class Factorial {
    public static int factorial(int n) {
        if (n == 0) {
            return 1; // Base case
        } else {
            return n * factorial(n - 1); // Recursive case
        }
    }
}

In this example, the base case is when the input n is equal to 0. When this condition is met, the function returns 1, preventing further recursion. If the base case did not exist, the function would continually call itself with decreasing values of n, leading to infinite recursion.

Identifying and handling base cases effectively is crucial in recursive functions to ensure proper termination of the recursion and prevent stack overflow errors. Additionally, base cases contribute to the overall correctness and efficiency of recursive algorithms.

It is important to clearly define base cases for each recursive function and understand how they contribute to the termination of the recursion, as well as the correctness and efficiency of the algorithm. Therefore, when designing recursive functions, developers must carefully consider and address the base cases to ensure the proper functioning of the recursive algorithm.