Practice Modeling in CS Thinking
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Modeling is the process of building a simplified representation of a real system so you can study, predict, or explain its behavior. A model keeps the details that matter for the question and leaves out details that do not.
A model is a useful simplification. It is not reality itself, but a focused version of reality.
Showing a random 20 of 80 problems.
Example 1
challengeGeorge Box wrote 'all models are wrong, but some are useful.' Give a CS example illustrating each half of the quote.
Example 2
easyA model assumes 'no friction' to predict a sliding box's motion. What part of the model is 'no friction'?
Example 3
mediumA model assumes constant 5% monthly growth: . With , find .
Example 4
challengeA model assumes events are independent, but in reality one event makes another more likely. Qualitatively, how will the model's risk estimate be biased?
Example 5
easyA map of a city leaves out individual trees and house colors but keeps streets and intersections. What modeling principle does this show?
Example 6
mediumLinear regression fits . If a model with gives predictions for but observed values are , compute the residuals.
Example 7
hardA budget model: . Compute average cost per item at and .
Example 8
hardA 2D physics engine models objects as circles with and ignores rotation. Name one real-world phenomenon that this model can't reproduce.
Example 9
hardModeling time: when is a monotonic clock (e.g., `CLOCK_MONOTONIC`) preferred over wall-clock time (`CLOCK_REALTIME`) in code?
Example 10
mediumWhat word names a quantity in a model that you tune to fit data (like the slope of a line)?
Example 11
easyFill in: a model is a __________ representation of a real system.
Example 12
easyA weather app models temperature as a single float in Celsius. Name one real-world detail this model deliberately ignores.
Example 13
mediumA spreadsheet model and the real system disagree after a parameter changed. What is the disciplined first step before trusting either?
Example 14
mediumA spam classifier models messages as bags-of-words. What information about word order is lost?
Example 15
mediumA model uses inputs, parameters, and assumptions to produce an output. Which one would you most likely change if the model is structurally right but numerically off?
Example 16
mediumA queueing model assumes customers arrive once per minute and each is served in 30 seconds. Will the queue grow over time?
Example 17
easyA queue at a coffee shop is modeled as a FIFO list. Which CS data structure is the right code representation?
Example 18
easyA model says next year's class size , with in years from now. Find at .
Example 19
easyTo decide which simplification to keep in a model, what question should guide you?
Example 20
challengeA neural-net language model has a context window of 8K tokens. State two distinct modeling consequences of this finite window.