Notes, summaries, assignments, exams, and problems for Vocational training

Relatively Prime

When the greatest common factor of two numbers is 1

Rational Number

Any number that can be expressed as a ratio of two integers

Reciprocal

One of two numbers whose product is 1, also called multiplicative inverse

Relation

A set of ordered pairs

X Coordinate

The first number in an ordered pair; it tells the distance to move right or left from the origin (0,0)

Y Coordinate

The second number in an ordered pair; it tells the distance to move up or down from the origin (0,0)

X Axis

The horizontal axis on a coordinate plane

Y Axis

The vertical axis on a coordinate plane

Coordinate Plane

A plane formed by the intersection of a horizontal line (the x-axis) and a vertical line (the y-axis)

Vertical Line Test

A method for seeing if a graph represents a... Continue reading "Math Terminology: Definitions and Examples" »

Scene: A Restaurant

David: Sorry, ladies. Your entrees are here; the main course will be served later so it doesn't cool down.

Claudia: Thank you, very kind.

David: A pleasure.

Miriam: How good is the food! The truth is that it's worth spending a bit more money and eating well.

Claudia: The truth is that, at the moment, I love everything.

David: Ladies, may I clear the entrees and serve the main course?

Miriam: Of course.

Claudia: Here you are.

David: Here are your hamburgers. Could you please cut into the meat to see if it is cooked to your liking?

Claudia: It's perfect.

Miriam: Perfect, thank you very much.

Claudia: My goodness! I'm full. I don't know if I'll be able to manage dessert.

Miriam: I am the same; this eating well is not my thing.

Ordering Dessert

David:

Catching Up Over Lunch

Miriam: Hi Claudia, how are you? I haven't seen you in a long time.

Claudia: I know! I’m fine, and you?

Miriam: I am fine, but I have a lot of work and I'm taking care of the children—it's non-stop!

Claudia: Oh yes, I can imagine. How’s little Nerea?

Miriam: She is so big now. Look how time flies. (She shows her a photo.)

Claudia: She is beautiful.

Arrival and Ordering Drinks

David: Welcome to New York Burger. My name is David, and I'll be your waiter. How many people are there?

Claudia: Table for two, please.

David: All right, come with me this way. (They sit at a table.)

Miriam: Thank you very much.

David: (He leaves the menu card on the table.) Do you want something to drink while you decide what you want to eat?

Claudia:

COMMUNITY LANGUAGE LEARNING (CLL)

Who Invented It?

Charles A. Curran

How Is It Carried Out?

A group of learners sits in a circle with the teacher standing outside the circle. A student whispers a message in their native language to the teacher. The teacher translates it into the foreign language. The student repeats the message in the foreign language. Students then compose further messages in the foreign language.

What Are the Five Stages in CLL?

1. Birth Stage: A feeling of security and belonging is established.
2. The learner's abilities improve.
3. The learner speaks independently and may need to assert his or her own identity.
4. The learner is seen as secure enough to take criticism.
5. The learner works upon improving style and knowledge.

When Is CLL Used?

It... Continue reading "Overview of Language Teaching Methods" »

What is FMEA?

FMEA (Failure Mode and Effects Analysis) is a methodology aimed at achieving Quality Assurance. Through systematic analysis, it contributes to the identification and prevention of failure modes for both products and processes/services. It is a tool that systematically investigates the potentially weak points of products, processes, and services, quantifying and evaluating their risk of failure.

Objectives of FMEA

• Customer satisfaction
• Introduce the philosophy of prevention to companies
• Analyze the effects and failures that may affect a product or process
• Stipulate the means and procedures for each failure mode, and assign a method of detection for each failure
• Adopt corrective and preventive actions

Types of FMEA

Design FMEA

The study of... Continue reading "FMEA Essentials: Prevent Failures & Enhance Quality" »

Quantifiers and Question Tags Rules

Quantifiers (Context)

• Some: Used in positive statements.
• Any: Used in negative statements or questions.
• Something / Someone / Somewhere: Used in positive contexts.
• Anything / Anyone / Anywhere: Used in negative contexts.

Question Tag Examples

• He likes [it], doesn’t he? (Positive statement, negative tag)
• [She] ran [fast], didn’t she? (Past simple example)
• [They] have been [working], haven't they? (Correcting polarity for 'Have been...')
• I’m [tired], aren't I? (Special case for 'I am')
• Imperative: [Close the door], will you?

Common English False Friends (Falsos Amigos)

This section highlights common words that sound similar in English and Spanish but have different meanings.

• Actually (De hecho) / Actualmente (Nowadays)

Key Vocabulary and Phrases

Phrasal Verbs

• build up: construir / desarrollar
• carry on: continuar
• get out of: salir de (un lugar) / evitar
• get over: superar
• hook up: enganchar / conectar
• join in: unirse
• let someone down: decepcionar a alguien
• live on: vivir con / subsistir con
• set up: configurar / establecer

General Terms & Concepts

• handle: encargarse de / manejar
• overwhelmed: abrumado
• reassurance: consuelo / tranquilidad
• well-being: bienestar

Idioms Related to Emotions & Conflict

• cool it: tranquilizarse
• blow your top: enojarse mucho / perder los estribos
• defuse a situation: calmar la situación
• fly off the handle: perder los estribos
• see red: enojarse mucho
• give someone a piece of your mind: regañar a alguien / decirle lo que piensas
• keep the peace: mantener

European Day of Languages: Celebrating Diversity

The European Day of Languages, celebrated annually on September 26, was launched in 2001 by the European Commission and the Council of Europe. This initiative represents 800 million citizens across 47 countries. It is celebrated annually as a tribute to Europe's rich linguistic diversity. The continent boasts over 200 native languages, with the EU recognizing 24 official languages and approximately 60 regional or minority languages. Additionally, many languages from other parts of the world are spoken across Europe.

Official Languages of the European Union

• Bulgarian
• Croatian
• Czech
• Danish
• Dutch
• English
• Estonian
• Finnish
• French
• German
• Greek
• Hungarian
• Irish
• Italian
• Latvian
• Lithuanian
• Maltese
• Polish
• Portuguese
• Romanian
• Slovak
• Slovenian
• Spanish
• Swedish

Member

Strategic planning setting long-term goals that may extend 5 to 10 years into the future. Long-term loosely detailed budgets are often created to reflect expectations for these long-term goals. After the goals are set, management designs key strategies for attaining these goals. Companies usually prepare a budget for every month of the fiscal year.

·A rolling budget is a budget that is continuously updated so that the next 12 months of operations are always budgeted.

Who is Involved in the Budgeting Process?

·Participative budgeting involves the participation of many levels of management. It helps create more realistic budgets and it has more acceptance by managers. It also has some disadvantages, such as higher complexity and it involves more... Continue reading "Strategic Planning and Budgeting Process" »

Coleridge centered on the ideal of Romanticism, representing the self.

• Description of the supernatural
• Individuality represented by dreams

These poets embody the movement in literary terms. For Coleridge, poetry is the exponent of Romanticism and is represented as the priority of English literature (a cultural interpretation). The poets consider themselves a kind of leader who helps to understand society. The poet is the one who teaches and guides, leading others to the truth.

Poetry explains to people how the world works. It is a vital way of teaching. Every poet interprets Romanticism in a very different way. The Romantic elements are seen from different points of view as they structure their Romanticism. Wordsworth and Coleridge use very different... Continue reading "Coleridge and Wordsworth: Romanticism, Language, and Imagination" »