Notes, summaries, assignments, exams, and problems for Baccalaureate

System Types
The systems of equations can be classified by the number of solutions that can arise. According to that case may have the following cases:
· Incompatible system if it has no solution.
· Compatible system if you have any solution in this case can also distinguish between:
or compatible system determined when it has a finite number of solutions.
indeterminate or compatible system when it admits an infinite set of solutions.
Fitting and classification:

Calculating the rank of a matrix for determining

1. We can rule a line if:.
· All the coefficients are zeros.
· There are two equal lines.
• A line is proportional to another.
• A line is a linear combination of others.
Delete the third column because it is a linear... Continue reading "Matrices: multiplication, rank, determinant, inverse and Rouche-Frobenius theorem" »

Operating Systems

Core Concepts: Budget, bundled software, command line, commercially owned, coordinate, developer, development, entire, freely available, Graphical User Interface (GUI), issue, modify, multi-task, open source, programming language code, proprietary, release, stable, storage.

Installing an Operating System

Key Terms: Allocate, BIOS (Basic Input/Output System), bit, component, crash, distro, environment, infrastructure, kernel, partition, patch, pre-installed, prerequisite, requirement, run, screen resolution, segment, step-by-step.

Advanced Operating System Concepts

Technical Terms: Batch processing, bootstrap loader, clustered systems, command interpreter, control program, distributed systems, error detection, file-system manipulation,... Continue reading "Essential IT and Computing Terminology Glossary" »

Core Principles of Enlightenment Thinkers

John Locke believed in natural rights.

The idea that government power comes from the people is called the social contract.

Montesquieu supported the separation of powers to avoid the concentration of power.

A system with elected representatives is called republicanism.

A government ruled by a king with total power is known as an absolute monarchy.

The Enlightenment was a movement that promoted reason, science, and progress.

A revolution represents a major political or social change.

Key Terms and Definitions

• Revolution: A big political or social change.
• Enlightenment: A movement based on reason and science.
• Absolute Monarchy: When a king has total power.
• Social Contract: An agreement between the people and the

Urban Vocabulary and Grammar Exercises

Section 1: Word Associations

• Packed — people
• High-rise — flats
• Slums — poor
• Ran an errand — shop
• Congestion — big city
• Smashed — window
• Litter — floor

Section 2: Collocations and Prepositions

• Reason — for (d) → 2.
• Lack — of (c) → 3.
• Access — to (e) → 1.
• Break — from (b) → 5.
• Along — with (a) → 4.

Section 3: Post-War Housing in Britain

In 1945, Britain had a...

1. Housing
2. Lack of
3. Abandoned
4. Suburbs
5. Neighbourhoods
6. Built-up
7. Room for
8. Solution to

Section 4: Sentence Completion

1. Which city will hold the next Olympic Games?
2. Housing prices have increased five times faster than...
3. We will have them brought...
4. The bins in our neighbourhood should be emptied...
5. Years ago it was believed...
6. A lot of old buildings in

Daily Life and Celebrity Encounters

How many kilometers did Jason walk each day?
After looking at his map, he realized that he had walked four or five kilometers each day.

What did Jason advise Antonio to do regarding celebrities?
Jason advised him not to go crazy and not to ask for their autographs. He told Antonio to notice them but not bother them if he wanted to act like a true New Yorker.

Why do famous people like living in New York?
They like living there because they can maintain a little anonymity.

Cultural Visits: Chinatown and Little Italy

Who was Lin?
Lin was Peter’s uncle. He owned a shop in one of the food markets in Chinatown.

Who did Antonio go to Chinatown with?
Antonio went to Chinatown with Peter, the ballet dancer.

Why did the food

Part 1: Vocabulary and Grammar Practice

Exercise 1

• 1. People / Shoppers
• 2. Floors
• 3. Poorer
• 4. Bank
• 5. Traffic jam
• 6. Window
• 7. Street

Exercise 2

• 1. d
• 2. c
• 3. e
• 4. b
• 5. a

• 1. Access to
• 2. Reason for
• 3. Lack of
• 4. Along with
• 5. Break from

Exercise 3

• 1. Housing
• 2. Lack of
• 3. Abandoned
• 4. Suburbs
• 5. Neighbourhoods
• 6. Built-up
• 7. Room for
• 8. Solution to

Exercise 4

• 1. Will hold
• 2. Have increased
• 3. Will have brought
• 4. Should be emptied
• 5. Was believed
• 6. Will be demolished
• 7. Have been banned
• 8. Haven't been found
• 9. Has turned down

Exercise 5

• 1. Free parking spaces in town should be given to locals.
• 2. Have the city's historic landmarks been shown to the tourists?
• 3. City life is thought to be too stressful by many.

Exercise 6

• 1. Had / got its logo designed by a local artist
• 2. Is believed

Grammar, Vocabulary, and Functional Language Practice

1. Choosing the Correct Past Tense Form

Choose the correct verb form to complete the sentences.

1. We drove / were driving to work when the accident happened.
2. There was a new woman at work today who I didn't meet / hadn't met before.
3. I was trying to repair my bike when a man was stopping / stopped to help me.
4. The parcel had arrived / arrived just after I got home.
5. When I tried to use my phone, I realised it hadn't worked / wasn't working.
6. He ate / had eaten already so he was cooking just for the children.

2. Past Simple or Present Perfect

Complete the sentences with the past simple or present perfect form of the verbs in brackets.

1. She has never studied (never / study) Turkish before. This is her first

Causes of the Decline of the Mughal Empire

The decline of the Mughal Empire was a complex process resulting from a combination of political, economic, administrative, military, and social factors that unfolded primarily after the death of Aurangzeb in 1707. The causes can be broadly categorized as follows (relevant for BA 3rd semester examination answers):

I. Political and Administrative Factors

• Weak Successors: Aurangzeb's death was followed by a series of weak, inefficient, and short-reigning emperors who were unable to maintain control over the vast empire. They often became puppets in the hands of powerful nobles.
• Wars of Succession: The absence of a fixed law of succession (primogeniture) led to frequent and destructive wars among the royal

Cultural Acceptance of White Lies

In my society, telling small lies is often accepted and even expected in daily interactions. People commonly use “white lies” to avoid hurting others’ feelings or to be polite. For example, it’s typical to compliment someone’s cooking even if you didn’t enjoy it, simply to be respectful.

While constant lying is frowned upon, these social lies are seen as necessary to maintain harmony. I believe this is generally a good thing—telling the absolute truth can sometimes cause unnecessary pain. As long as the intention behind the lie is kind, I think it plays a useful role in communication and relationships.

Graffiti: Art Form or Act of Vandalism?

Graffiti has long sparked debate. Some see it as vandalism,... Continue reading "Social Ethics, Urban Art Debate, and Professional Writing Examples" »

The Importance of Embracing Change

Change is one of those things that everyone talks about, but not everyone understands. We can see it in ________, ________, and even in our personal lives. Sometimes it feels exciting, and other times it’s uncomfortable. However, I’ve come to realize that ________ plays an important role in how we grow and adapt. In this post, I want to share my thoughts on why ________ is so relevant today, and how it affects the way we live, learn, and think.

Growth Through Innovation and Progress

First of all, ________ gives us the opportunity to develop and improve. Without it, everything would stay the same, and society would never move forward. Just think about how much progress we’ve made in recent years—from _... Continue reading "Embracing Change for Personal and Social Growth" »