Notes, summaries, assignments, exams, and exercises for Mathematics for Baccalaureate

Municipal Capital Gains Tax (Plusvalía)

Taxpayers for Capital Gains Tax

This tax applies to two types of contributors:

• The person who transmits or constitutes property rights for consideration.
• The person who acquires property rights free of charge (the acquirer).

Tax Base Calculation

To determine the tax base, three key facts are considered:

1. The cadastral value of the land at the time of accrual, excluding the value of any construction.
2. The period elapsed from acquisition to transmission, rounded down to a maximum of 20 years.
3. The annual percentage increase set by the City (in the tax ordinance), within a state-mandated ceiling.

Usufruct and Life Interest

For usufruct, a distinction is made between temporary usufruct and life interest. A percentage...

Essential Language and Literary Concepts

Vocabulary Definitions

• Ratification: To confirm something is true or valid.
• Sullen: Bad-tempered and sulky; gloomy.
• Persuade: To induce someone to do something through reasoning or argument.
• Obey: To comply with a command, instruction, or law.
• Prescribed: To lay down as a rule or course of action to be followed; to determine.
• Literal: Taking words in their most basic sense without metaphor or allegory.
• Prolific: Producing much fruit, foliage, or many offspring; producing many works.
• Clause: A distinct article or provision in a document, such as a contract or law.
• Maize: A cereal grain, especially corn, that is already mature.
• Diligence: Careful and persistent work or effort.
• Ninety: The cardinal number equivalent

Accounting Fundamentals

Accounting is defined as the science that informs traders of the composition of their assets, as well as operations that modify them, using specific books and accounting records. Its purpose is to provide an economic and financial rating of a company.

Objectives of Accounting

• Financial Situation: Inform the economic and financial situation of the company and its patrimony. This data is collected through inventory balances and, more recently, the statement of changes in net equity.
• Performance Reporting: Report the results of losses or gains obtained during the development of the company's financial activities, typically shown through the profit and loss account.
• Contextual Analysis: Report the causes behind these results

Theme 3: Linguistic Foundations

Bilingualism is the routine use of two languages in the same region or by the same person. Diglossia is a specific type of bilingualism where both languages exist in an unequal situation of social prestige.

Semantic Meaning

• Denotation: The set of basic semantic features of a word; its literal meaning.
• Connotation: The set of values that appear in discourse alongside the denotation of a term.

Lexical Structures

• Family Lexica: A set of words related to each other by their signifier, sharing the same lexeme.
• Semantic Field: A set of words related by meaning.

Synonymy and Its Types

Synonymy is the relationship between two words that have different signifiers but the same or similar meaning.

• Absolute Synonymy: Words that have

1. Find the GCD of (143, 227)

The Euclidean Algorithm is used to find the Greatest Common Divisor (GCD) of two integers by repeatedly dividing the larger number by the smaller number until the remainder becomes 0.

• Step 1: 227 = 143 × 1 + 84
• Step 2: 143 = 84 × 1 + 59
• Step 3: 84 = 59 × 1 + 25
• Step 4: 59 = 25 × 2 + 9
• Step 5: 25 = 9 × 2 + 7
• Step 6: 9 = 7 × 1 + 2
• Step 7: 7 = 2 × 3 + 1
• Step 8: 2 = 1 × 2 + 0

Since the remainder becomes 0, the last non-zero remainder is 1.

Answer: GCD(143, 227) = 1

2. Find m and n such that gcd(a, b) = ma + nb for a = 56 and b = 72

Given:

a = 56, b = 72. We need to find integers m and n such that: gcd(56, 72) = 56m + 72n.

Step 1: Find the GCD using the Euclidean Algorithm

72 = 56 × 1 + 16
56 = 16 × 3 + 8
16 = 8 × 2 + 0
Hence,...

Fundamental Geometry Postulates

• 1.1 Ruler Postulate: Points on a line can be matched one-to-one with real numbers. The real number corresponding to a point is its coordinate.
• 1.2 Segment Addition Postulate: If B is between A and C, then AB + BC = AC.
• 1.3 Protractor Postulate: Consider ray OB and a point A on one side of OB. The rays of the form OA can be matched one-to-one with real numbers from 0 to 180.
• 1.4 Angle Addition Postulate: If P is in the interior of ∠RST, then the measure of ∠RSP + the measure of ∠PST = the measure of ∠RST.
• 2.1 Two Point Postulate: Through any two points, there exists exactly one line.
• 2.2 Line-Point Postulate: A line contains at least two points.
• 2.3 Line Intersection Postulate: If two lines intersect, their

Chapter 1: Core Accounting Fundamentals

Key Financial Statements Equations

• Balance Sheet (BS) Equation: Assets = Liabilities + Stockholders' Equity (SHE)
• Income Statement (IS) Equation: Revenues - Expenses = Net Income (NI)
• Retained Earnings (RE) Equation: Beginning RE + Net Income - Dividends = Ending RE

Debit and Credit Rules

• A Debit increases: Expenses, Assets, Dividends (DEAD)
• A Credit increases: Liabilities, Revenues, Equity (CLEAR)

Objective of Financial Reporting

1. Provide information useful to equity investors and creditors.
2. Maintain the Entity Perspective (separating the company from its owners/people).
3. Ensure Decision Usefulness.

Adjusting Entries: Deferrals and Accruals

Deferrals (Cash Paid/Received Before Recognition)

Prepaid Expenses

Meaning: Paid...

Hypothesis Tests for Population Means

Test 1: Sample of 10 — Mean < 550

(a) In a random sample of 10 people who take a test, the average score is 532.4, and the standard deviation is 28.3. Do the data provide significant evidence, at the 5% level, that the population mean score is less than 550?

1. Step 1: Hypotheses.

   H₀: μ = 550 vs. H_a: μ < 550 (1 point) Where μ is the population mean score.

2. Step 2: Significance level.

   α = 0.05 (1 point)

3. Step 3: Test statistic.

   Test Statistic: t_obs = (X̄ − μ₀)/(s/√n) = (X̄ − 550)/(s/√n) (1 point)

4. Step 4: Rejection region.

   The test rejects H₀ at level α in favor of H_a if t_obs < −t_α,df=9, where t is based on 9 degrees of freedom. (1 point)

5. Step 5: Calculation and conclusion.

   Test Statistic:

Genetic Algorithm Implementation Functions

The following Python functions demonstrate key components of Genetic Algorithms, including crossover, selection, and population initialization.

Four-Point Crossover Method

This function performs a four-point crossover using four parents to generate offspring.

def four_point_cross(parent1, parent2, parent3, parent4):
    pos_alea = sorted(list(np.random.choice(range(1, parent1), 4, replace=False)))
    hijo1 = parent1[:pos_alea[0]] + parent2[pos_alea[0]:pos_alea[1]], parent1[:pos_alea[1:2]], parent2[pos_alea[2]:pos_alea[3]], parent1[:pos_alea[3:]]
    hijo2 = parent2[:pos_alea[0]] + parent3[pos_alea[0]:pos_alea[1]], parent2[:pos_alea[1:2]], parent3[pos_alea[2]:pos_alea[3]], parent2[:pos_alea[3:]]
    hijo3

1. Equivalent Units Calculation

2. Cost per Equivalent Unit