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" »

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" »

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" »

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" »

Spanish Language Pitfalls and Punctuation Essentials

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Understanding Linguistic Vices

Linguistic vices refer to any defect or impairment that may present in words or sentences, hindering clear and correct communication.

Common Linguistic Vices

Here are some common linguistic errors:

  • Cacophony: This is a very obvious error, consisting of the repetition of syllables or sounds that are contiguous or in close proximity, creating an unpleasant effect.
  • Monotony: A linguistic vice produced by the frequent use of the same words or expressions to refer to different situations, leading to a lack of variety in language.
  • Ambiguity or Amphibology: This vice involves expressing ideas so obscurely that they are not clearly understood, or can be interpreted in two or more ways, leading to confusion.
  • Solecisms: These
... Continue reading "Spanish Language Pitfalls and Punctuation Essentials" »

Understanding Functions: Definitions, Properties, and Types

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Function

A function defines the relationship between an initial set and a final set, so that each element of the initial set (independent variable) corresponds to a single element of the final set (dependent variable).

Domain of the Function

The domain of a function is the set of possible values that the independent variable (e.g., coins) can take.

Range of the Function

The range of a function is the set of possible values that the dependent variable (e.g., drinks) can represent.

A function can be represented by tables, graphs, and algebraic formulas.

Increasing and Decreasing Functions

  • A function is increasing on an interval if for any pair of values a and b in this interval, where a < b, the rate of change is positive.
  • A function is decreasing
... Continue reading "Understanding Functions: Definitions, Properties, and Types" »

Essential Trigonometric Identities and Formulas

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Pythagorean Identities:
sin (a + b) = sin(a) · cos(b) + cos(a) · sin(b)
cos (a + b) = cos(a) · cos(b) - sin(a) · sin(b)
tan (a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
sin(2a) = 2 · sin(a) · cos(a)
cos(2a) = cos2(a) - sin2(a)
tan(2a) = 2tan(a) / (1 - tan2(a))
sin(a / 2) = ±√((1 - cos(a)) / 2)
cos(a / 2) = ±√((1 + cos(a)) / 2)
tan(a / 2) = ±√((1 - cos(a)) / (1 + cos(a)))
sin(a)sin(b) = 2sin((a + b) / 2) · cos((a - b) / 2)
sin(a) - sin(b) = 2cos((a + b) / 2) · sin((a - b) / 2)
cos(a) + cos(b) = 2cos((a + b) / 2) · cos((a - b) / 2)
cos(a) - cos(b) = -2sin((a + b) / 2) · sin((a - b) / 2)
Basic Trigonometric Identities:
sin2(x) + cos2(x) = 1
1 + tan2(x) = sec2(x)
1 + cot2(x) = csc2(x)
tan(x) = sin(x) / cos(
... Continue reading "Essential Trigonometric Identities and Formulas" »