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

1) DIJKSTRA (SSSP) — STEP TABLE (PAST-PAPER INSTANCE A)

Given edges: a→b(2), a→c(7), a→e(10), b→d(2), c→d(1), c→g(2), d→f(2), e→g(1), f→g(2). Source = a.
Rule: Pick unsettled vertex with minimum dist; relax outgoing edges.

Vertices:   a   b   c   d   e   f   g

Init:
Dist      = 0   2   7   ∞  10   ∞   ∞
S = ∅

Step 1: Pick a (min=0), S={a}
Relax from a: already set b=2, c=7, e=10
Dist      = 0   2   7   ∞  10   ∞   ∞

Step 2: Pick b (min=2), S={a,b}
Relax b→d: dist(d) = dist(b)+2 = 2+2 = 4
Dist      = 0   2   7   4  10   ∞   ∞

Step 3: Pick d (min=4), S={a,b,d}
Relax d→f: dist(f) = 4+2 = 6
Dist      = 0   2   7   4  10   6   ∞

Step 4: Pick f (min=6), S={a,b,d,f}
Relax f→g: dist(g) = 6+2 = 8
Dist

Irregular Verbs List (1–70)

This comprehensive list presents 70 essential irregular verbs. Study the four principal forms (Base Form, Past Simple, Past Participle, and Present Participle) alongside their Spanish meanings to improve your fluency.

1. sweep – swept – swept – sweeping – barrer
2. drink – drank – drunk – drinking – beber
3. ride – rode – ridden – riding – cabalgar/montar
4. fall – fell – fallen – falling – caer
5. sing – sang – sung – singing – cantar
6. set – set – set – setting – colocar
7. eat – ate – eaten – eating – comer
8. buy – bought – bought – buying – comprar
9. meet – met – met – meeting – conocer (gente)
10. know – knew – known – knowing – conocer (saber)
11. get – got – gotten

Big Cities or Small Villages?

Nerea (excited): Silvia, imagine us living in a big city — lights, cafés, subways, people everywhere! It’s so alive!

Silvia (smiling): Alive, yes… but also loud, crowded, and always rushing. I’d rather live in a small village.

Nerea (laughing): A village? What would you even do there all day?

Silvia: Plenty! Walk in nature, talk to neighbors, breathe clean air. Life feels real there.

Nerea: But I love the city’s energy! So many things to do — theaters, shops, concerts!

Silvia: And in a small village, you have time to think, to listen, to just be.

Nerea (teasing): You and your peace and quiet!

Silvia (laughing): And you and your noise and lights!

Nerea (pausing): Still… cities can be stressful. Always traffic,... Continue reading "The Great Debate: City Energy vs. Countryside Calm" »

Lab 8: Temperature and Microbial Growth

Key Concepts

• Psychrophiles grow best between 0–20°C. Often found in cold environments like glaciers.
• Mesophiles prefer 20–45°C. These include human pathogens like E. coli.
• Thermophiles thrive at 55°C or higher. They are often found in hot springs.

Materials and Their Functions

• Tryptic Soy Broth (TSB): A nutrient-rich medium that supports bacterial growth.
• Incubators set to different temperatures (4°C, 25°C, 37°C, 55°C): Used to simulate environmental conditions.
• Spectrophotometer (OD600): Measures turbidity (cloudiness) of a culture to estimate cell density.
• Classification by growth: “+++” indicates heavy growth; “0” means no growth.

In this lab, students investigated how temperature affects... Continue reading "Microbiology Lab Fundamentals: Growth, Metabolism, Genetics" »

The Human Digestive System: An Introduction

The digestive system transfers organic nutrients, vitamins, minerals, and water from the foods we eat to the internal environment. Upon entering the body, food moves through the gastrointestinal (GI) tract, and the nutrients are absorbed and transported to the circulatory system where they are utilized.

Net Gain to the Body

Food and air are the primary sources of net gain to the body.

Distribution within the Body

Nutrients and substances are distributed throughout the body via the GI tract, lungs, storage deposits, and metabolism.

Net Loss from the Body

Excretion from the body occurs via the lungs, GI tract, kidneys, and skin.

Epithelial Cells

Epithelial cells separate compartments and are crucial in the digestive... Continue reading "Human Digestion and Metabolic Regulation" »

Mastering English Grammar and Vocabulary

Grammar and Sentence Practice

1. Peter was looking forward to escaping from Auschwitz with Mary.
2. In spite of women having a professional life, they still have to do most of the housework.
3. Peter and Mary were given two different books in the afternoon.
4. He isn't attracted by the wages and the working conditions.
5. Mary has pushed the table into the corner.
6. Mary, whose purse has been stolen, was very upset.
7. If Peter tried harder, he could find a job.
8. If he hadn't arrived so late, he would have seen the famous writer.
9. Mary doesn't mind working hard for the organization.
10. The teacher asked the students to stop those attacks.
11. They used to live in peace when they were children.
12. Unless you return my trainers, I will tell the teacher.

General Formal Letter Template

Dear [Title + Surname] (e.g., Dear Sir/Madam or Dear Mr. Smith),

I am writing to you regarding/concerning [briefly state the topic or issue]. I would like to [express your purpose: suggest, complain, request, express concern, etc.].

Firstly, [present your first main point – describe the situation or give background information]. This is important because [give a reason or example].

Secondly, [give another reason, suggestion, or concern]. This could help [explain the benefit or consequence].

Furthermore/In addition/Moreover, I believe that [add a final thought or broader benefit].

I hope you will take my [suggestion/request/concern] into consideration. I would be grateful if you could let me know your thoughts on this... Continue reading "Effective Formal Letter Writing Techniques" »

Mastering English Grammar and Workplace Vocabulary

This document provides a concise collection of examples and exercises focusing on essential English grammar concepts, including relative clauses and pronouns, alongside practical workplace vocabulary. Enhance your understanding of formal and informal language usage and expand your professional lexicon.

Essential Workplace Vocabulary

• The deadline is tomorrow, not a day later.
• The perks include a company car.
• He first started working here as a clerk.
• That’s nonsense. It’s just not true.
• She’s been promoted to a new position.
• I’m not a slave. I don’t work for free.
• This week I’m working the early shift.
• I need help. This task requires teamwork.

Common Relative Pronouns and Prepositions

Here is... Continue reading "Mastering English Grammar: Clauses, Pronouns & Workplace Terms" »

Gross Income and Business Deductions

Gross Income: Includes revenue from sales, services, rents, dividends, interest, etc. Exclusions include life insurance proceeds and municipal bond interest. Expenses associated with the production of tax-exempt income are not deductible.

Deductions Above the Line (for AGI)

Deductions for Adjusted Gross Income (AGI) include business expenses, rental expenses, self-employed health insurance, and IRA contributions.

• Ordinary & Necessary Test: An expense must be customary and appropriate for the business.
• Meals Deduction: Can deduct 50% of meals if the expense is ordinary, necessary, and reasonable, the employee is present, the person eating is a current or potential client, and the meal is purchased separately