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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Discrete Mathematics & Logic | 25% | - Set theory, relations, functions - Proof techniques and mathematical induction - Propositional and predicate logic - Boolean algebra and digital logic |
| Topic 2: Algorithms & Complexity | 25% | - Algorithm design and analysis - Sorting and searching algorithms - Recursion and iterative structures - Big O notation, time and space complexity |
| Topic 3: Software Engineering & Programming Basics | 15% | - Software development lifecycle - Testing and debugging fundamentals - Basic syntax and control structures - Programming paradigms |
| Topic 4: Data Structures | 20% | - Arrays, linked lists, stacks, queues - Data storage and retrieval principles - Primitive and composite data types - Trees, graphs, hash tables |
| Topic 5: Computer Architecture & Organization | 15% | - Instruction sets and execution cycles - Von Neumann architecture - Memory hierarchy and performance - CPU, memory, I/O systems |
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問題 #32
What code would print a subarray of the first 5 elements in numpy_array?
答案：A
解題說明：
NumPy arrays support slicing using the same start:stop convention as Python sequences. To take the first five elements, you want indices 0 through 4. The slice numpy_array[:5] means "start from the beginning (default start is 0) and stop before index 5." Because the stop index is exclusive, this returns exactly the first five elements. Printing that slice with print(numpy_array[:5]) displays a 1D view (or copy depending on context) containing those elements.
Option A, numpy_array[1:5], starts at index 1, so it returns elements 1 through 4-only four elements-and it excludes the element at index 0, so it is not the first five elements. Options B and D are incorrect because NumPy arrays do not provide a .get() method for slicing in this manner; .get() is a method associated with dictionaries, not arrays.
Textbooks stress slicing because it is efficient and expressive, especially in data analysis. With slicing, you can take prefixes, suffixes, windows, or regularly spaced samples without writing loops. In NumPy, slicing is particularly important because many slices create views into the same underlying data buffer, enabling memory-efficient operations on large datasets. Understanding inclusive start and exclusive stop boundaries is critical to avoid off-by-one mistakes and to work correctly with batches and segments of numerical data.
問題 #33
Which file system is commonly used in Windows and supports file permissions?
答案：B
解題說明：
Windows commonly uses the NTFS (New Technology File System) for internal drives and many external drives because it supports advanced features required for modern operating systems. One of the most important features is support forfile and folder permissionsvia Access Control Lists (ACLs). Permissions enable the OS to enforce security policies by controlling which users and groups can read, write, execute, modify, or delete specific resources. This is fundamental to multi-user security and is a standard topic in operating systems and security textbooks.
FAT32 is an older file system designed for simplicity and broad compatibility. It does not provide the same fine-grained permission model as NTFS, which is why it is often used for removable media where cross- platform compatibility matters more than access control. HFS+ is historically associated with Apple's macOS systems, and EXT4 is widely used on Linux. While these file systems have their own permission and feature models, they are not the common Windows default for permission-managed storage in typical Windows deployments.
NTFS also supports journaling (improving reliability after crashes), large file sizes, quotas, compression, and encryption features (through Windows facilities). In enterprise environments, NTFS permissions integrate with Windows authentication and directory services, enabling centralized user management. Therefore, for Windows systems requiring file permissions, NTFS is the correct answer.
問題 #34
What Python code would return the value 40 from np_2d, where np_2d = np.array([[1, 2, 3, 4], [10, 20, 30,
40]])?
答案：D
解題說明：
In a 2D NumPy array, indexing is written as array[row_index, column_index] using zero-based indices. The array np_2d = np.array([[1, 2, 3, 4], [10, 20, 30, 40]]) has two rows (indices 0 and 1) and four columns (indices 0, 1, 2, 3). The value 40 is located in the second row and the fourth column. Using zero-based indexing, that corresponds to row index 1 and column index 3. Therefore, np_2d[1, 3] returns 40.
Option A attempts to access row 3, which does not exist and would raise an IndexError. Option C attempts to access column 4 in row 0, but valid column indices are only 0 through 3, so it would also error. Option D likewise refers to a non-existent row 4. Only option B uses valid indices and points to the correct location.
Textbooks emphasize multi-dimensional indexing because it underlies matrix operations, dataset manipulation, and feature extraction in data science. Correctly interpreting rows and columns is essential when rows represent observations (like people) and columns represent attributes (like age, weight, height). This question tests precise control over row/column addressing, which prevents subtle bugs in numerical analysis.
問題 #35
Which line of code below contains an error in the use of NumPy?
答案：C
解題說明：
The NumPy library provides arrays and efficient numerical operations, including sorting. However, NumPy doesnotprovide a function named np.quicksort. That is the API misuse in the code, making option A the correct answer. In NumPy, sorting is commonly performed using np.sort(arr) (which returns a sorted copy) or arr.sort() (which sorts in-place). If a specific algorithm is desired, NumPy exposes it through the kind parameter, such as np.sort(arr, kind="quicksort"), kind="mergesort", or kind="heapsort". Textbooks present this as a typical design: a single sorting interface with selectable strategies, rather than separate top-level functions per algorithm name.
Option C is correct and necessary: import numpy as np is standard convention. Option B is also correct:
printing a variable is valid assuming it exists. Option D, written as arr = np.array([3, 2, 0, 1]), is valid NumPy usage for constructing a 1D array from a Python list.
A subtle point taught in scientific computing courses is that library APIs matter as much as syntax: you can write perfectly valid Python that still fails if you call a function that the library does not define. In this case, the fix is to replace np.quicksort(arr) with np.sort(arr) or np.sort(arr, kind="quicksort") depending on whether you need to specify the algorithm.
問題 #36
Which process is designed to establish the identity of the user such as with a username and password?
答案：C
解題說明：
Authenticationis the security process of proving or establishing a user's identity. In textbook terminology, authentication answers the question: "Who are you?" Common authentication factors include something you know (password, PIN), something you have (smart card, hardware token), and something you are (biometrics). Username and password is the classic "something you know" mechanism, where the username identifies the account and the password serves as a secret used to validate that the user is the rightful owner of that account.
Authentication is distinct fromauthorization, which determines what an authenticated user is allowed to do (permissions, roles). It is also distinct from registration, which is the administrative act of creating an account or enrolling a user in a system. "Verification" is a general term that can appear in many contexts, but in security frameworks the precise term for identity establishment is authentication. "Certification" usually refers to issuing or validating credentials such as digital certificates (PKI) or professional certifications, not the act of logging in with a password.
Textbooks emphasize that authentication should be strengthened with practices like hashing and salting passwords, multi-factor authentication (MFA), lockout policies, and secure transport (e.g., TLS) to prevent credential theft. The core concept remains: the process that establishes identity using credentials like a username and password is authentication.
問題 #37
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