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

Types of Auditor Opinions

Unqualified Opinion

An unqualified opinion is issued when:

• The audit was performed without limitations in scope and in accordance with the National Technical Standards (NTA).
• The annual accounts have been prepared in accordance with accounting rules and Generally Accepted Accounting Principles (GAAP), consistent with prior years.
• The information, including supporting documentation, is sufficient for adequate comprehension.
• The financial statements, taken as a whole, fairly represent the company's business in accordance with the information available to the auditor.

Qualified Opinion

A qualified opinion is issued when the auditor concludes that there are significant circumstances that prevent the annual accounts from presenting... Continue reading "Auditor's Opinions: Types and Implications" »

• Rating Alphabetical: Documents are classified based on the name of the person or the reason for the company shown in the document.
• Geographical Breakdown: Documents are classified by place of residence of the person or entity, as the province-city-street and finally the name.
• Classification of Materials: Documents are grouped according to the topic at hand, understood as a common feature field.
• Alphabetical Materials as Logical Categories:

a) Number: Each field is assigned a number, and each subdivision a number.
b) Alphanumeric: Each field is assigned a letter or number, and subdivisions another letter or number that is added to the first component.

• Rating Chronological: Ordering progressively, by date of entry or maturity.
• Decimal Classification:

Adverbs

An adverb is a word that acts as the core of an adverbial phrase. It modifies a verb, an adjective, or another adverb.

Classification of Adverbs

• Place: out there, here, up close, in front, within, above, across, away, etc.
• Time: now, before, even yesterday, after, today, then, tomorrow, never, soon, always, yet, etc.
• Quantity: something, pretty, almost, too much, well, nothing, just, so, so much.
• Manner: agile, well, good, bad, fair, bravely, and so on.
• Order: before, after, later, first, respectively, and so on.
• Affirmation: true, certainly, of course, actually, probably, yes, indeed, and so on.
• Negation: never, no, never, no, etc.
• Doubt: perhaps, possibly, probably, maybe, perhaps, etc.
• Question: how, when, where.
• Relative: how, when, where.

Prepositions

A... Continue reading "Adverbs, Prepositions, Verbs, Pronouns & Conjunctions" »

Process Control Elements

Raw Materials Management

Raw materials required for the process must be as specified in the transaction records, with checks on their source, condition, quantity, and production/receipt date. All details should be properly registered.

Labor Force and Training

Every process, regardless of its degree of automation, involves a quantitative and qualitative workforce component, which may be more or less specialized. The workforce employed in a process must be educated and trained in operations. They must be able to distinguish a good product from one that is not, know how to react to non-conformities, and maintain relevant operational records. Personnel can range from trainees requiring strong supervision to highly experienced... Continue reading "Essential Elements of Process Control and Quality Assurance" »

Identification of Financial Statements

The financial statements shall be clearly identified and distinguished from any other information published in the same document.

Characteristics of Financial Statements

• Accuracy: Displaying information in a clear, precise, and true manner.
• Opportunity: Must be submitted on time.
• Relevance: Only present information unique to the company's operations.
• Integrity: The information submitted must be complete and not incomplete or unreliable.
• Frequency: Financial statements should be made with a fixed periodicity.

Notes to Financial Statements

Clarifications or explanations of events or situations, quantifiable or not, are an integral part of every financial statement. They must be read together for correct interpretation.... Continue reading "Financial Statements: Identification, Characteristics, and Inventory Accounting" »

Teaching and Learning Concepts

Concrete Bases (Teaching)

Convert mathematics into something concrete. Create recognizable contexts to which children can assign their own meanings.

Construction (Learning)

Learning is a constructive activity, contrary to the idea that children simply absorb knowledge presented to them.

Models (Teaching)

To achieve progress, students must have tools at their disposal that enable them to establish a link between informal and formal mathematics. Models and materials are important.

Raising the Level (Learning)

The learning process occurs at different levels of formality. Changes can be sudden and create discontinuity in the learning process.

Time for Reflection (Teaching)

The teacher has to find time to include reflection... Continue reading "Principles of Math Teaching and Learning" »

Secondary Data Analysis: Sources and Elaboration

Secondary data analysis considers both qualitative and quantitative perspectives. It uses references like coding sheets in quantitative designs and identifies interviews or focus groups for qualitative data. Official statistics and public sources are used to verify field data.

Desrosieres argues that statistical indicators from official sources reflect social reality in institutions. These indicators are presented without analysis, as tables of results. This means the original data has been elaborated, which is typical of secondary sources. Secondary sources have developed, summarized, and synthesized the data. The degree of elaboration is the key difference between secondary data analysis and... Continue reading "Secondary Data Analysis: Sources, Types, and Elaboration" »

Hurwicz Criterion: Coefficient of Optimism

In this approach, a decision-maker may have an intermediate attitude. Since no probabilities are associated with each state of nature, this author suggests using a coefficient of optimism, simultaneously called C, and a coefficient of pessimism, (1 - C), where 0 ≤ C ≤ 1.

The coefficient C indicates the decision-maker's stance toward risk. When it is closer to 1, the decision-maker will be more optimistic, while closer to 0, the decision-maker is more pessimistic.

This criterion focuses only on the extreme scores of each alternative, weighing the result of maximum optimism with the coefficient C and the result of minimal value with the coefficient of pessimism (1 - C). The sum of these two products... Continue reading "Decision-Making Under Uncertainty: Criteria and Tables" »

Fundamental Concepts in Algebra

Numerical Language

Expressing mathematical information using only numbers.

Algebraic Language

Expressing mathematical information using both numbers and letters.

Algebraic Expression

A set of numbers and letters combined with mathematical operation signs.

Numerical Value of an Algebraic Expression

The number obtained by replacing the letters with their corresponding values and performing the indicated operations.

Monomial

A monomial consists of a number and one or more letters:

• The number (including its sign) is called the coefficient.
• The letter or letters that accompany it are called the literal part.

Degree of a Monomial

The sum of the exponents of the letters that form it.

Similar Monomials

Two or more monomials are similar... Continue reading "Fundamental Concepts of Algebra and Equations" »