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

Understanding Invoices

An invoice is a document derived from a legally established commercial operation. To create invoices, information from the order note and delivery note will be taken into account.

Invoice Issuance Essentials

Key considerations for issuing invoices include:

• Issuance Requirement: Issue invoices for all operations undertaken in your business activity. It's crucial to keep a copy of each invoice, even in cases of self-consumption, with certain exceptions.
• Mandatory Issuance Cases: Invoices must be issued in all circumstances for the following operations:
  • When the recipient requests it.
  • For goods delivered to another Member State of the European Union.
  • When recipients are Public Administrations.
  • For work executions.
  • For deliveries of

Static Methods of Investment Selection

These methods do not take into account the timing of various cash flows and operate as if all cash flows were received at the same time. The methods are time-based. Key considerations include the Payback Period, total net cash flow, committed currency, and net cash flow per average annual committed unit.

Payback Period

The Payback Period is the time it takes to recover the initial outlay of an investment.

Drawbacks:

• They generally add cash flows regardless of when they are received at different points in time.
• They do not provide the real return on investment.

Advantages:

• It is a simple and intuitive method to calculate.
• It aligns with the company's expectation to recoup the investment minimum quickly.

Dynamic Methods

Geometry Fundamentals

Understanding Angles

An angle is the portion of a plane formed by two rays (semi-straight lines) sharing a common endpoint. The rays are called the sides of the angle, and the common endpoint is called the vertex.

Angle Designation

• By three letters, with the vertex letter always in the middle (e.g., ∠ABC).
• By the letter of the vertex (e.g., ∠B).
• By a number or a Greek letter, often placed near the vertex (e.g., ∠α).

Types of Angles

• Adjacent angles: Angles that share a common vertex and a common side.
• Linear Pair: Two adjacent angles whose non-common sides form a straight line (sum is 180°).
• Right angle: An angle that measures exactly 90°.
• Straight angle: An angle that measures exactly 180°.
• Complementary angles: Two angles

Linear Equations

First-degree algebraic expressions with several unknowns.

Linear equations with 2 unknowns correspond to the general equation: ax + by = c

Solution of a Linear Equation

A solution is any pair of values for the unknowns that verifies the equation.

If x1, y1 are real numbers, the pair (x1, y1) is a solution of the linear equation in two unknowns if: ax1 + by1 = c.

Linear equations with 2 unknowns have infinite solutions.

Graphical Representation

The equation ax + by = c is a straight line. Each point on this line is a solution of the equation.

Systems of Linear Equations

A linear system of two linear equations with two unknowns is an algebraic expression of the form:

ax + by = c
a'x + b'y = c'

Solution of a System

A solution is any pair of... Continue reading "Solving Linear Equations and Systems" »

Practice 4: Salaries, Overtime, SSO, PHL

Basic Salary

• = (Additional Table at $[$D$24] * Time Worked)

Total Overtime

• Fx = IF(logical test = E10 [Overtime] > 40)
• True-Value: E10 - 40
• False-value: 0

Triple Overtime

• Fx = IF Function
• Logic Test: Total Overtime [G10 > 8]
• True-Value: G10 - 8
• False-value: 0

Payment of Extra Time Triple

• Triple Overtime (H10) * Pay Per Hour (D24) * 3

Double Overtime

• = G10 (Total Overtime) - H10 (Triple Overtime)

Payment of Extra Time Double

• = J10 (Double Extra Time) * D24 (Pay per hour) * 2

Compulsory Social Security (SSO)

• = (F10 [Basic Salary] + I10 [Payment of Triple Overtime] + K10 [Payment of Double Overtime]) * 5%

Housing Policy Act (HPL)

• = (F10 [Basic Salary] + I10 [Payment of Triple Overtime] + K10 [Payment of Double Overtime]

Data Visualization: Types and Applications

Graphics are a visual representation of data, prioritizing simplicity, easy interpretation, and adherence to standards.

Classification of Graphics

• Structural graphics: Representing a single set of data.
• Relational graphics: Connecting two sets of data.
• Special graphics.

Types of Graphics

• Organizational Charts: Represent the structure of an organization.
• Classification Plans: Represent elements of a total set, subdivided into smaller subsets. These can be square or pyramidal.
• Schedules: Use current statistics, ordering data over time to identify peaks and trends.
• Histograms: Represent class intervals or monthly values, highlighting extreme values.
• Function Tables: Establish mutual relationships between two sets

The definition of a weighted average:

What is a Weighted Average?

A weighted average is the result of multiplying each number in a set by a value assigned to it (its weight), and then calculating the arithmetic mean of the resulting products. It's used when the components contributing to the average are not equally important.

For example, if a teacher states that an examination is worth 40% of the final mark, another is worth 35%, and a third is worth 25%, the weighted average would be calculated as follows:

mediaPond = (ex1 * 40 + ex2 * 35 + ex3 * 25) / 100

Basically, it's an average of a dataset that allows you to define the degree of importance for each data point's contribution to the average.

If the data are 2, 3, 5, 7, 9, 6, 8, the average... Continue reading "Understanding Weighted Averages: Definition and Applications" »