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

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Algebra I: Equations, Inequalities, and Functions

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Algebra I Review

Inequalities

What happens to the inequality sign if you multiply or divide by a negative number?

Flip the inequality symbol

Which part of the inequality sign determines when you have a closed circle on a graph?

The line under the symbol. (Equal to line)

Domain is the _______ value of an ordered pair, which is also known as the _________ value.

x, independent

Range is the ______ value of an ordered pair, which is also known as the _______ value.

y, dependent

Linear Equations

What is the formula to find the slope of a line?

m = (y2 - y1) / (x2 - x1)

Write the equation of the point-slope form of a line.

y - y1 = m(x - x1)

Write the equation of the slope-intercept form of a line.

y = mx + b

Write the equation of the standard form of a line.

Ax +
... Continue reading "Algebra I: Equations, Inequalities, and Functions" »

Year-End Accounting Adjustments and Profit Determination

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B. Changes in Inventories

The company must make an inventory of the stocks it has, doing a physical count of them and checking the result with the information recorded in the book balance. After verifying this data and correcting any differences, it is necessary to stabilize stock accounts; that is, to correct the accounting balance of these accounts to reflect reality.

C. Verification of Accounting Data

Before determining the result of the accounting fiscal year, the company must verify accounting data by checking, on the one hand, that there are no mistakes in arithmetic or transcription and, on the other, contrasting it with the economic reality. To do this, perform the following inventories and balances:

  • Trial Balance: Its purpose is to check
... Continue reading "Year-End Accounting Adjustments and Profit Determination" »

IAS 10: Events After the Balance Sheet Date - Key Accounting Standards

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International Accounting Standard No. 10

Events Occurring After the Balance Sheet Date

Objective

The objective of this Standard is to prescribe:

  1. when an entity shall adjust its financial statements for events after the balance sheet date and
  2. the disclosures that an entity should give about the date on which the financial statements were authorized for issue and about events after the balance sheet date.

The Standard also requires the entity that does not prepare its financial statements under the assumption of going concern, if the events after the balance sheet date indicate that this hypothesis of continuity is not appropriate.

Scope

This Standard is applicable in the accounting and disclosures related to events after the balance sheet date.

The events

... Continue reading "IAS 10: Events After the Balance Sheet Date - Key Accounting Standards" »

Understanding Statistical Concepts and Variables

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Statistical Concepts

Population

A population is the set of all elements that are subjected to a statistical study.

Individual

An individual or statistical unit is each of the elements of the population.

Sample

A sample is a representative subset of the reference population; the number of individuals in a sample is less than that of the population.

Sampling

Sampling is the collection of data to be studied, obtained from a small proportion that is representative of the population.

Value

A value is each of the different results that can be obtained in a statistical study. For example, if you toss a coin 5 times, you get two values: heads and tails.

Data

Data refers to each of the values obtained by performing a statistical study. If you toss a coin 5 times,

... Continue reading "Understanding Statistical Concepts and Variables" »

Municipal Capital Gains and Vehicle Taxes: Key Details

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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... Continue reading "Municipal Capital Gains and Vehicle Taxes: Key Details" »

Understanding Inheritance Tax: Reductions, Rates, and Coefficients

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Inheritance Tax Base Reductions

We highlight three primary types of base reductions:

Kinship-Based Reductions

The amount of reduction varies depending on the heir's kinship group. There are four standard groups:

  • Group I: Descendants under 21 years old.
  • Group II: Descendants aged 21 and older, ascendants, and the spouse.
  • Group III: Second and third-degree collateral relatives by affinity.
  • Group IV: Fourth-degree or more distant collateral relatives, and strangers.

Life Insurance Reductions

If the beneficiary is a spouse, ascendant, or descendant, a 100% reduction applies, up to a maximum limit.

Primary Residence Reductions

If the heir is a spouse, descendant, or ascendant and inherits the primary residence, a 95% reduction applies, up to a specific ceiling.... Continue reading "Understanding Inheritance Tax: Reductions, Rates, and Coefficients" »

Precision Measurement: Instruments and Unit Systems Explained

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Measuring Instruments: Definition and Features

A measuring instrument is a device designed to be used to make measurements, either alone or in conjunction with ancillary equipment.

For proper use, the key features of a measuring instrument to be aware of are:

  1. Graduated System

    This system will have its divisions. If the tenth division is a number, it indicates the metric system, where each division is 1 mm. Otherwise, it is the English system.

    Figure 1.2: Metric Ruler
  2. Range

    The range of a measuring instrument is the field between the minimum and maximum values that can be measured.

    Figure 1.4: Range of a Ruler and a Micrometer
  3. Degree of Accuracy or Reading

    This refers to the value of the minimum, exact subdivision that can be read on the instrument.

    Figure
... Continue reading "Precision Measurement: Instruments and Unit Systems Explained" »

Introduction to Measurement and Observation

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Description: An Explanation of an Observation


Measurement: A Way to Describe the World with Numbers


Estimation: Using Knowledge of Something Familiar to Guess the Size of a New Object


Precision: How Close Measurements Are to Each Other


Accuracy: Comparing the Measurement to the Actual, Accepted, or Real Value


S.I.: International System of Units


Meter: The S.I. Unit of Length


Volume: The Amount of Space an Object Occupies


Mass: The Amount of Matter in an Object (S.I. Uses Kilogram)


Kilogram: S.I. Unit for Mass


Weight: The Measurement for Force (S.I. Uses the Newton)


Kelvin: The SI Measurement of Temperature (Same as C but Starts at -273 C)


Rate: The Amount of Change in a Measurement in a Given Amount of Time


Table: Displays Information in a Row or Columns

... Continue reading "Introduction to Measurement and Observation" »

Statistical Measures: Central Tendency, Position, and Dispersion

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Understanding Key Statistical Measures

Statistical measures help us analyze and interpret data. They can be broadly categorized into measures of central tendency, position, and dispersion.

Measures of Central Tendency

Measures of central tendency describe the central value around which data are distributed. They provide a single value that represents the typical or central point of a dataset.

The Mode

Definition of Mode

The mode (represented by Mo) is the value with the highest absolute frequency in a dataset. It can be found for both qualitative and quantitative variables.

Mode Examples

To find the mode of a distribution:

  • Example 1: 2, 3, 3, 4, 4, 4, 5, 5
    Mo = 4
  • Example 2 (Bimodal/Multimodal): If a dataset has two or more values with the same highest
... Continue reading "Statistical Measures: Central Tendency, Position, and Dispersion" »

Understanding Financial Audit: Role, Regulations, and Objectives

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Understanding Financial Audit: Role and Regulations

The audit function is primarily regulated by Law 19/1988 of July 22 on the Audit of Accounts and its corresponding audit regulation, which is updated almost annually. These rules govern the external, financial, or economic-financial audit, carried out by independent professionals.

An audit involves the verification and review of financial statements (whether economic, financial, or economic-financial). This verification must be performed by individuals who, among other qualifications, are graduates in relevant fields with extensive accounting knowledge.

Auditors are ultimately independent professionals; they are not public officials and have no affiliation with the company being audited. In conducting... Continue reading "Understanding Financial Audit: Role, Regulations, and Objectives" »