🔍 Unit 3: Modular Programming & Recursion — Pre-Unit Diagnostic

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Purpose: Confirms readiness for functions, scope, and recursion. Tests prior fluency with calling pre-built functions, basic decomposition, and self-referential reasoning.

Question 1 — Function call comfort

Predict the output:

print(len("apple")) print(min(8, 3, 5)) print(round(3.7))

Question 2 — Define a simple function (Unit 1 review)

Write a Python function area_of_rectangle(length, width) that returns the area.

Question 3 — Decomposition: a real task

Imagine you are writing a program that sends each student in a class an email with their final mark. Break the overall task into 3-5 smaller subtasks that could each become a separate function.

Question 4 — Logic: self-reference (math)

Define the factorial of a positive integer n in your own words, using the idea of "smaller version of the same problem". Write your definition for both n = 1 and n > 1.

Question 5 — Mental trace

Work out each step. F(n) is defined as: F(1) = 1, F(n) = n + F(n-1). What is F(5)?

Question 6 — Naming & abstraction

A friend writes a function called do_it() that does many things at once. List two better names if the function (a) calculates a tax, (b) reads a file and writes a summary.

Question 7 — Reading a function signature

If you see def f(x, y=10, z=0):, answer:

How many arguments are required when calling f?
What is f(2)'s effective (x, y, z)?
What is f(2, 5)'s effective (x, y, z)?

Question 8 — Reflection

Have you ever written a function that calls itself? If yes, what was it for? If no, what about recursion intrigues or worries you?

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