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

Zero Conditional

Verdad absoluta: If it snows, it is cold.
Snows: present simple, is: present simple

First Conditional

Probabilidad (Unless: si no)
If I eat too much, I will get fatter.
Present simple, future

Second Conditional

Improbable (unlikely)
If I won the lottery, I wouldn't travel around.
Past simple, wouldn't + infinitive.

Third Conditional

Imposible
If I had studied, I would have passed.
Would have + past participle, past perfect

1. Integration of Polynomials

Let f(x) = -x² + 2x + 3. The integral is:

• a) ∫(-x² + 2x + 3) dx = -x³/3 + x² + 3x + C
• b) [-x³/3 + x² + 3x] from 1 to 2 = 11/3

2. Finding f(x) from f'(x)

Let f'(x) = 3x² - 3. Given f(2) = 1, find f(x):

f(x) = x³ - 3x + C. Substituting f(2) = 1: 8 - 6 + C = 1, so C = -1. Thus, f(x) = x³ - 3x - 1.

3. Solving for f(x) with Initial Conditions

Let f'(x) = 6x² + 2x - 1. Given f(2) = 5:

f(x) = 2x³ + x² - x + C. Substituting f(2) = 5: 2(8) + 4 - 2 + C = 5, so 18 + C = 5, C = -13. Thus, f(x) = 2x³ + x² - x - 13.

4. Polynomial Integration

Let f(x) = 3x² - 4x:

• a) ∫f(x) dx = x³ - 2x² + C
• b) Evaluation results in 32.

5. Definite Integral Properties

Consider ∫₁⁵ f(x) dx = 6:

• a) ∫₁⁵ 2f(x) dx = 2 ∫₁⁵ f(x) dx = 2(6) = 12
• b) ∫₁³ 3 dx

PASSIVE VOICE

Tense Forms

Present: is/are + past participle

Past: was/were + past participle

Future: will be + past participle

Present Perfect: have/has been + past participle

Modal + BE + past participle

Modals

Expressing Ability and Possibility

can, can't, could, will be able to

Giving Advice

should, shouldn't

Expressing Obligation and Prohibition

must, have to, mustn't

Future Forms

Going to: Plans or clear evidence

Present Continuous: Future plans already made

Will: Predictions, spontaneous decisions, promises

MAKING ARRANGEMENTS

Asking to Meet

Are you available/free on ...?

Can we meet on ...?

How does the 3rd sound to you?

Would Friday suit you?

Is next Tuesday convenient for you?

What about sometime next ....?

Responding to Meeting Requests

Yes, Monday is fine.... Continue reading "English Grammar Essentials: Tenses, Modals, and More" »

Unit 4: Purpose and Action Phrases

• Claro sentido de la finalidad: A clear sense of purpose
• Ser aconsejable: Be to your advantage to
• Ser inútil para: Be useless at
• Resultar útil: Come in useful
• Con una finalidad: For a purpose
• Hacer un buen uso de: Make good use of
• Propósito de vida: Purpose in life
• Ponerte en desventaja: Put you at a disadvantage
• Entender el porqué: See the point of
• No tener mucho sentido: Seem a bit pointless
• Sacar el máximo partido: Take full advantage of
• Llega un momento en la vida: There comes a point in life
• Cubrir las espaldas: Cover your back
• Hincar codos: Get your head down
• Tener estómago para: Have the stomach for
• Vigilar a: Keep an eye on
• Fustigarse: Kick yourself
• Abalanzarse: Leap in
• Echar una mano: Lend a hand
• Antes de correr

The Internet: A Global Network

The Internet is a global network of interconnected computer networks, linking billions of devices worldwide using TCP/IP. It comprises millions of networks, including private, public, academic, business, and government, and provides extensive information resources.

The History of the Internet

The Internet, originating from ARPANet, an experimental network created in the 1960s by the US military, was launched online in 1969 under a contract by ARPA, connecting four US universities. The history of the Internet reflects the continuous growth of this network, connecting millions of people, businesses, governments, schools, and universities.

The ARPANet

The ARPAnet, created in 1969, began with four computers connecting.... Continue reading "The Internet: A Comprehensive Overview" »

English Grammar: Verb Tenses

Present Simple

• Used for actions that happen regularly (but are not happening at this moment).
• Examples: schedules, calendars

Present Continuous

• Used for actions happening now.
• Examples: fixed and sure plans, orders

Past Simple

• Used for actions that were completed in the past.
• Regular verbs: Verb + -ed
• Irregular verbs: second column of the irregular verb list
• Negative: didn't + subject + verb
• Interrogative: did + subject + verb

Past Continuous

• Used for actions that lasted for a long time in the past (often with specific times or dates).
• Affirmative: subject + was/were + verb + -ing
• Negative: subject + wasn't/weren't + verb + -ing
• Interrogative: was/were + subject + verb + -ing

Past Perfect Simple

• Used for an action that happened before

C++ Priority Queue Implementation

This document provides a C++ implementation of a priority queue using a heap data structure. The code includes the class definition, member functions, and supporting utilities.

Priority Queue Class Definition

#ifndef priority_queue_h_
#define priority_queue_h_

#include <iostream>
#include <vector>
#include <cassert>

template <class T>
class priority_queue {
private:
    std::vector<T> m_heap;

public:
    priority_queue() {}

    priority_queue(std::vector<T> const& values)
    {
        m_heap = values;
        for (int i = 0; i < m_heap.size(); i++){
            percolate_down(i);
            for (int j = i; j < m_heap.size(); j++){
                percolate_down(

The Causative

• a) I paint my house every year. = Yo pinto mi casa cada año.
• b) I have my house painted every year. = Yo tengo mi casa pintada todos los años.
• c) I get my house painted every year. = Yo tengo pintada mi casa cada año.
• a) I repaired my car. = Yo reparé mi coche.
• b) I had/got my car repaired. = Yo hice reparar mi coche.

Causative Examples

1. I didn't cut my hair myself. I had my hair cut.
   - Yo no me corté el pelo yo mismo. Yo hice cortar mi pelo.
2. Jill didn't make her dress. She had it made in Paris.
   - Jill no fabricó su vestido. Ella hizo fabricarlo en París.
3. I'm not painting the kitchen myself. I am having the kitchen painted.
   - Yo no pinté la cocina yo mismo. Yo hice pintar mi cocina.
4. We didn't frame these pictures. We had them framed.

Influences and Lines of Spanish Poetry

The process of rehumanization converged in several poetic lines, extending influences from the past:

• Romanticism: Drawing back to Bécquer and Garcilaso.
• Surrealism: Exemplified by poets like Aleixandre, Lorca, Cernuda, and Alberti.
• Social and Revolutionary Poetry: Influenced by Neruda, Alberti, and Miguel Hernández.
• Transcendent Poetry: Which sought to emulate the artistic quality of the poets of the Generation of '27.

Spanish Poetry in Exile: Three Main Groups

Poetry written in exile from Spain is generally grouped into three categories:

1. The Generation of '27.
2. The Generation of '14.
3. A third group whose work was constructed entirely while in exile.

The Generation of 1936: Rooted and Uprooted Poetry

Dámaso Alonso... Continue reading "Spanish Poetry Generations: Movements from '27 to Post-Franco Era" »

Fundamental Concepts in Physics

The Atom

An atom is composed of electrons, protons, and neutrons.

Temperature

Temperature is the physical quantity that describes the sensation of cold or hot, directly related to the average kinetic energy of molecules. It represents the average kinetic energy of each molecule.

Heat

Heat is the transfer of energy from one body to another due to a temperature difference. It is a form of energy that can be perceived through temperature variations.

Types of Thermal Expansion

• Linear Expansion
• Surface Expansion
• Volumetric Expansion

Thermodynamics

Thermodynamics is the branch of physics that studies heat transfer and the conversion of energy into its various forms.

Laws of Thermodynamics

• Zeroth Law
• First Law
• Second Law

Zeroth Law