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

English Grammar Practice: Set 1

1. I’m looking forward to trying the new restaurant.
2. She asked me where I had bought that jacket.
3. When did you move to Spain?
4. We shouldn’t have left the house without a jacket.
5. I have my car revised every February.
6. The match was cancelled due to heavy rain.
7. That is the city where we lived for four years.
8. An event is being organized to raise money for charity.
9. She apologised for breaking my mug.
10. At 10:30, she will be playing football.
11. It is thought that she is one of the best actors in the world.
12. If you went to bed earlier, you wouldn’t always be tired.
13. I wish I had revised English grammar.
14. We have been sent an invitation.
15. She said that they were going to visit their grandparents the next day.

English Grammar Practice: Set

Handshaking Lemma

In any undirected graph, the sum of the degrees of all vertices is twice the number of edges.

Formula: Σdeg(v) = 2|E|

Euler's Formula for Planar Graphs

For planar graphs, the relationship between vertices (V), edges (E), and regions (R) is defined as:

V - E + R = 2

Sum of Degrees and Odd Vertices

The sum of the degrees of all vertices in any graph is always even because each edge contributes 2 to the total sum. Furthermore, the number of vertices with an odd degree must always be even.

Graphs with No Odd Degree Vertices

If all vertices in a graph have an even degree, the graph is Eulerian, meaning it contains an Eulerian circuit.

Complete Graphs

A complete graph with n vertices, denoted as K_n, has an edge between every pair of distinct... Continue reading "Essential Graph Theory Formulas and Concepts" »

Essential Business & Financial Definitions

• Start-up: A new business

• Benefit: An advantage or gain

• Idea: A concept or thought

• Problem: A challenge to solve

• Solution: A way to solve a problem

• Product: A good for sale

• Service: A helpful action or work

• Customer: A buyer or user

• Target Audience: The intended group of people

• Competition: Other businesses in the market

• Business Plan: A roadmap for a business

• Marketing: Promoting products or services

• Funding: Money for a business

• Earn: To receive money for work

• Income: Money received regularly

• Sales: Transactions of goods or services

• Profit: Money earned after costs

• Goods: Physical products

• Savings: Setting money aside

• Budget: A plan for money management

Synonyms for Key Business Terms

• Start-up: New company, new venture

• Benefit:

Essential English Vocabulary

• Library: I went to the library to borrow a history book.
• Bookshop: She bought the novel at the bookshop near school.
• Gang: The gang was arrested for robbing the bank.
• Bargain: These shoes were a real bargain – only 10 euros!
• Camp: My little brother is going to summer camp next week.
• Field: They have a small house in the middle of the field.
• Bigot: The bigot used his power to silence anyone who disagreed.
• Moustache: The man with the big moustache looked like a detective.
• Vase: She put the flowers in a beautiful glass vase.
• Glass: He drank a glass of water after his run.
• Groceries: I went to the supermarket to buy some groceries.
• Rudeness: His rudeness shocked everyone at the meeting.
• Journey: The journey by train through the

William Shakespeare: Biography

Born: 1564 | Died: 1616
Profession: Poet and playwright
Origins: Stratford-upon-Avon

Family Background

• Father: John Shakespeare (glove maker and alderman)
• Mother: Mary Arden (daughter of an affluent farmer)
• Wife: Anne Hathaway
• Children: Susanna, Judith, and Hamnet (Hamnet died at age 11)

Professional Career

• Actor
• Part-owner of The Lord Chamberlain's Men (later The King's Men)

The Company of Boys (1999)

A troupe of boy actors directed by Arby. They rehearsed in Cambridge, USA, before traveling to London to perform Julius Caesar and A Midsummer Night's Dream at the Globe Theatre.

Shakespearean Literary Styles

• Comedy: Happy endings, entanglements, disguises, and love (e.g., A Midsummer Night's Dream).
• Tragedy: Sad endings, death,

Understanding the Unified Process (UP) Model

This document provides a clear representation and explanation of the Unified Process (UP) Model and its key phases.

Unified Process (UP) Model Diagram

Time →
+----------------+----------------+----------------+----------------+
|  Inception     | Elaboration    | Construction   | Transition     |
+----------------+----------------+----------------+----------------+
|   Requirements |  Architecture  |  Development   |  Deployment    |
|    Analysis    |   Design       |  Implementation|  Testing       |
+----------------+----------------+----------------+----------------+
|     Iteration based development across all phases (Iterative & Incremental) |

Unified Process Model Phases

1. Inception Phase:

Key Compliance Requirements Under the Companies Act, 2013

This document summarizes essential provisions under the Companies Act, 2013 (CA, 2013) related to corporate finance, statutory appointments, and governance roles.

Dividend Definition and Types

A dividend is a portion of a company’s net profits distributed to its shareholders as a return on their investment. It is decided by the Board of Directors and typically approved by the shareholders at the Annual General Meeting (AGM).

Key Types of Dividends

• Interim Dividend: Declared by the Board of Directors during the financial year, before the AGM.
• Final Dividend: Declared at the AGM after the financial year ends and accounts are approved; requires shareholder approval.
• Cash Dividend: The most common

This document is an excerpt from a 1950 speech by Senator Joseph McCarthy, a key figure during the early years of the Cold War. In this speech, McCarthy warns of widespread communist infiltration within the U.S. government, claiming that traitors were working to weaken American democracy from the inside.

Historical Context of McCarthy's Speech

In the early Cold War period, tensions between the United States and the Soviet Union were intensifying. The U.S. feared the spread of communism abroad and at home, especially after the Soviet Union tested its first atomic bomb in 1949 and China became a communist nation. These events fueled widespread paranoia and set the stage for what became known as McCarthyism.

Audience and Purpose of the Speech

McCarthy’s... Continue reading "Senator Joseph McCarthy's 1950 Speech: The Internal Communist Threat" »

Common Regular Verbs in English

Regular verbs follow a consistent pattern when forming the past tense and past participle, typically by adding -ed or -d to the base form.

Essential

What is E-commerce?

Definition of E-commerce

E-commerce is the process of conducting commercial transactions, such as buying and selling goods or services, using the internet and electronic communication.

Types of E-commerce

• Business-to-Consumer (B2C): Businesses selling directly to individual consumers (e.g., online retailers).
• Business-to-Business (B2B): Businesses selling to other businesses (e.g., wholesale suppliers).
• Consumer-to-Consumer (C2C): Individuals selling directly to other individuals (e.g., online marketplaces).
• Mobile Commerce (M-commerce): Transactions conducted through mobile devices.

Significance of E-commerce

E-commerce is important because it offers businesses the ability to reach a global audience, operate 24/7, reduce costs,... Continue reading "E-commerce Essentials: Digital Commerce & Online Business Benefits" »